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Impacts of environmental change on tree productivity in temperate-maritime forest ecosystems Hember, Robbie Andrew 2011

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IMPACTS OF ENVIRONMENTAL CHANGE ON TREE PRODUCTIVITY IN TEMPERATE-MARITIME FOREST ECOSYSTEMS by Robbie Andrew Hember M.Sc., Trent University, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Forestry) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2011  © Robbie Andrew Hember, 2011  Abstract This thesis investigated observed responses of forest productivity to environmental change and their predictability using semi-empirical carbon (C) cycle models in temperate-maritime conifer forests in coastal British Columbia, Canada. Effects of environmental stress and historical responses to environmental trends were constrained using observations of gross primary production (Pg) from eddy-covariance flux towers and stemwood growth (Gsw) and mortality (Msw) from permanent forest inventory plots. Observations suggested a long-term increasing trend in Gsw extending back to the Little Ice Age, with decadal fluctuations in association with several 20th century drought episodes. Statistical models driven with climate variability, alone, could not reproduce the observed trend in Gsw, while climate variability and sensitivity to carbon dioxide (CO2), combined, expressed a moderately strong capacity to reproduce past trends and variability. Observations also indicated substantial wave-like fluctuations in Msw that could not be explained by stand density-dependent processes, alone, while additional functions of drought sensitivity via linear-threshold functions of evapotranspiration (ET) and precipitation (P) improved model predictions. The capacity to predict tree productivity was explored within a more mechanistic modelling framework, focusing on evaluation of physical principles used to simulate Pg in production efficiency models (PEMs) and subsequent application within the established forest productivity model, 3-PG, to simulate Pg, Gsw, and Msw. Comparison with observations highlighted several deficiencies in the representation of environmental stress in PEMs that restrict the capacity to accurately simulate transient responses to environmental change, some ii  of which arise from the model reduction and scaling techniques employed by PEMs, while others reflect unsettled physiological understanding. Consistent with regression model simulations, absence of CO2 fertilization in 3-PG led to inability to reproduce observed trends in Gsw. This research demonstrated that representation of environmental sensitivity in models of Gsw and Msw does not lead to appreciable increases in model precision, yet is absolutely necessary to achieve temporally-unbiased simulations at the regional scale. Findings also demonstrate the critical role of observation networks, including permanent forest inventories and longterm continuous meteorological and hydrological measurements as a necessary means of advancing and implementing model representation of environmental controls on forest productivity.  iii  Preface All thesis questions, analyses, and conclusions, including two scientific papers, were authored by me. Co-authors, Werner Kurz and Juha Metsaranta offered guidance and general direction of research and questions to pursue, as well as technical advice on how to process BC forest inventory data. Co-authors Werner Kurz and Rob Guy helped with the direction and interpretation of results in Chapter 4. Co-author Andy Black provided helpful comments on the results in Chapter 5. Committee members Andy Black and Rob Guy provided helful comments on Chapter 6. A version of Chapter 3 has been submitted to a peer-reviewed journal: [Hember, R.A.], Kurz, W.A., Metsaranta, J., Black, T.A., Guy, R., Coops, N.C., submitted. Accelerated regrowth of temperate-maritime forests due to carbon dioxide fertilization and climate change. A version of Chapter 5 has been published: [Hember, R.A.], Coops, N.C., Black, T.A., Guy, R.D., 2010. Simulating gross primary production across a chronosequence of coastal Douglas-fir stands with a production efficiency model. Agricultural and Forest Meteorology, 150, 238-253. I conducted all research pertaining to this publication, while co-authors helped with the editorial process.  iv  Table of Contents Abstract .................................................................................................................................... ii  Preface ..................................................................................................................................... iv  Table of Contents .................................................................................................................... v  List of Tables ........................................................................................................................ viii  List of Figures ......................................................................................................................... xi  List of Abbreviations, Acronyms, and Symbols ................................................................ xxi  Acknowledgements ............................................................................................................ xxiv  Dedication ............................................................................................................................ xxv  Chapter 1.1  1.2  1.3  1.4   1: Introduction ........................................................................................................ 1  Background ............................................................................................................... 1  Forest C-cycle models............................................................................................... 4  Research goals .......................................................................................................... 6  Dissertation structure ................................................................................................ 8   Chapter 2: Derivation of tree stem growth, mortality, and net production from permanent forest inventory plots .......................................................................................... 9  2.1  Synopsis .................................................................................................................... 9  2.2  Introduction ............................................................................................................... 9  2.3  Tree C balance ........................................................................................................ 10  2.4  Data and methods .................................................................................................... 12  2.4.1  Study area and inventory data ............................................................................. 12  2.4.2  Environmental data ............................................................................................. 17  Chapter 3: Accelerated regrowth of temperate-maritime forests due to environmental change..................................................................................................................................... 20  3.1  Synopsis .................................................................................................................. 20  3.2  Introduction ............................................................................................................. 21  3.3  Materials and methods ............................................................................................ 26  3.3.1  Study area and data ............................................................................................. 26  3.3.2  Detection of long-term trend in Psw .................................................................... 27  3.3.3  Detection of measurement-period trends in Psw and Gsw .................................... 28  3.3.4  Relationships with environmental variables ....................................................... 29  3.4  Results ..................................................................................................................... 32  3.4.1  Age-response functions ....................................................................................... 32  3.4.2  Long-term trends in Psw ...................................................................................... 34  3.4.3  Measurement-period trends ................................................................................ 35  3.4.4  Relationships with environmental variables ....................................................... 38  v  3.4.5  Summary of historical reconstruction ................................................................. 43  3.5  Discussion ............................................................................................................... 45  3.5.1  Measurement and sampling errors ...................................................................... 46  3.5.2  Comparison with other tests for growth enhancement ....................................... 47  3.5.3  CO2 fertilization, climate change, and interactions ............................................ 51  3.5.4  Implications for the sink in northern forests ....................................................... 58  3.5.5  Implications for age-class yield tables ................................................................ 59  Chapter 4: Drought-induced mortality waves in temperate-maritime forests .............. 62  4.1  Synopsis .................................................................................................................. 62  4.2  Introduction ............................................................................................................. 63  4.3  Methods................................................................................................................... 71  4.3.1  Inventory data ..................................................................................................... 71  4.3.2  Climate data ........................................................................................................ 72  4.3.3  Correlation analysis ............................................................................................ 74  4.3.4  Multivariate statistical models ............................................................................ 76  4.4  Results ..................................................................................................................... 78  4.4.1  Observed tree mortality....................................................................................... 78  4.4.2  Correlation analysis ............................................................................................ 80  4.4.3  Multivariate statistical models ............................................................................ 90  4.4.4  Climate sensitivity .............................................................................................. 95  4.5  Discussion ............................................................................................................... 99  4.5.1  Drought-induced mortality waves....................................................................... 99  4.5.2  Driving mechanisms and climate sensitivity .................................................... 100  4.5.3  Modelling drought-induced mortality in 3-PG ................................................. 103  4.5.4  How does drought-induced tree mortality affect the C balance ....................... 106  Chapter 5: Simulating gross primary production of Douglas-fir stands with a production efficiency model ............................................................................................... 109  5.1  Synopsis ................................................................................................................ 109  5.2  Introduction ........................................................................................................... 110  5.3  Model description ................................................................................................. 112  5.4  Materials and methods .......................................................................................... 117  5.4.1  Study sites and field measurements .................................................................. 117  5.4.2  Experimental design.......................................................................................... 121  5.5  Results ................................................................................................................... 124  5.5.1  Radiation absorption ......................................................................................... 124  5.5.2  Variability of g ................................................................................................. 127  5.5.3  Model calibration .............................................................................................. 133  5.6  Discussion ............................................................................................................. 139  vi  5.6.1  5.6.2  5.6.3  5.6.4   Predictions of g and Pg ..................................................................................... 139  Model processes ................................................................................................ 143  Environmental drivers ....................................................................................... 145  Concluding remarks .......................................................................................... 150   Chapter 6: Modelling environmental controls on productivity in temperate-maritime forests ................................................................................................................................... 152  6.1  Synopsis ................................................................................................................ 152  6.2  Introduction ........................................................................................................... 152  6.3  Data ....................................................................................................................... 154  6.3.1  Eddy covariance ................................................................................................ 154  6.3.2  Inventory measurements ................................................................................... 154  6.4  Representation of environmental stress in 3-PG................................................... 155  6.4.1  Net primary production ..................................................................................... 155  6.4.2  Canopy LUE and Qa ......................................................................................... 157  6.4.3  Water stress ....................................................................................................... 163  6.4.4  Thermal stress ................................................................................................... 176  6.5  Evaluation of 3-PG simulations ............................................................................ 183  6.5.1  Stand development and tree C dynamics .......................................................... 183  6.5.2  Gross primary production ................................................................................. 186  6.5.3  Stemwood growth ............................................................................................. 187  6.6  Discussion ............................................................................................................. 187  Chapter 7.1  7.2  7.3  7.4   7: Conclusion ....................................................................................................... 191  Summary of findings............................................................................................. 191  Observations of tree productivity.......................................................................... 193  Modelling tree productivity .................................................................................. 196  Future directions ................................................................................................... 198   References ............................................................................................................................ 200  Appendix A: Estimation of historical vapour pressure deficit ....................................... 222   vii  List of Tables Table 2.1 Species composition at permanent sample plots leading with Douglas-fir and western hemlock. Values expressed as percent of the total population. ................................. 13  Table 2.2 Statistical description of stand structure, carbon state variables, and fluxes derived from measurements at permanent sample plots leading with Douglas-fir and western hemlock (utilization level = 4.0 cm). Stand age (A); tree density (N); diameter at breast height (DBH); site index (SI); stemwood carbon (Csw); net stemwood production (Psw); stemwood growth (Gsw); stemwood mortality (Msw); proportional mass of expiring trees (PMET). .................. 19  Table 3.1 Trends in age-detrended net stemwood production (Psw) and stemwood growth (Gsw) for plots of Douglas-fir and western hemlock in southwest British Columbia, Canada, integrated over 1959-1998. Values express the mean ( 95% C.I.) of the slope coefficient multiplied over the 40-year analysis period in absolute units and as percentages of the mean measurement-period flux. Bold values mark field significance at the 95% confidence level. 38  Table 3.2 Partial correlation analysis of all interval measurements for Douglas-fir and western hemlock (n=5258). Values indicate the partial correlation coefficient, r. Bold values indicate significance at the 99% confidence level. ................................................................. 39  Table 3.3 Coefficients (95% C.I.) derived from forward stepwise regression models of stemwood growth (Gsw). All explanatory variables were standardized (mean=0.0, S.D.=1.0) prior to fitting. All models explained a significant proportion of variance at the 99% confidence level. ..................................................................................................................... 43  Table 4.1 Generalized extreme value (GEV) fits to annual demographic (dN) and gravimetric (Msw) mortality in coastal Douglas-fir. n is sample size, -logL is negative log likelihood, shape, scale, and location are fitted parameters for the GEV probability distribution. .......... 80  Table 4.2 Partial correlation analysis of tree mortality in permanent sample plots of coastal Douglas-fir (n = 621 plots, 2623 interval measurements). Correlations are shown for relationships between dependent variables: demographic mortality (dN); gravimetric mortality (Msw); and the proportional mass of expiring trees (PMET); and independent viii  variables: Stand age, A (years); the difference between potential and actual stemwood carbon, Csw; summer (June-July-August, JJA) air temperature deviation, T (˚C), summer vapour pressure deficit deviation, Δe (hPa); summer precipitation, P (mm month-1), 3-PG model predictions of evapotranspiration, ET (mm month-1), climate moisture index using 3-PG model predictions of ET, CMI (mm month-1), maximum soil water deficit from 3-PG model predictions (MSWD). Significant correlation coefficients at the 99% confidence level are shown in bold. ......................................................................................................................... 82  Table 4.3 Partial correlation analysis for the relationship between demographic (dN) and gravimetric tree mortality (Msw) and environmental variables in permanent sample plots of coastal Douglas-fir. Each partial correlation coefficient indicates the relationship when intrinsic factors (A, N, Csw, Csw) are simultaneously considered, but no other environmental variables are considered. Significant coefficients are shown in bold. .................................... 83  Table 4.4 Linear-threshold model parameters derived from fits to permanent inventory measurements of demographic and gravimetric tree mortality in coastal Douglas-fir. .......... 83  Table 4.5 Description of predictive skill for tested multivariate statistical models of relative demographic tree mortality (dN) in stands of Douglas-fir (n = 17190 intervals): residual sum of squares (RSS); Akaike’s information criterion (AIC); correlation between model residuals and stand age, r(A), competition index, r(Csw), stand density, r(N), summer temperature, r(T), summer vapour pressure deficit, r(Δe), summer precipitation, r(P), and the correlation between observed and predicted sample-average dN, spanning 1959-1998, r(dN). Bold correlation coefficients mark significance at the 99% confidence level. Header subscripts indicate polynomial order or threshold. .................................................................................. 93  Table 5.1 Study site properties.............................................................................................. 118  Table 5.2 List of model variable ........................................................................................... 122  Table 5.3 Seasonal range of leaf area index (L) and fraction of absorbed photosynthetically active radiation (FPAR) during measurement years. ............................................................ 124  Table 5.4 Daily and monthly estimates of gross photosynthetic efficiency (g C MJ-1)........ 130  ix  Table 5.5 Parameters for daily (a) site-specific models with climate (b) site-specific models with climate and nonlinear light response (c) ecosystem-specific models with climate and nonlinear light response. ....................................................................................................... 133  Table 5.6 Prediction skill according to coefficient of determination r2, root mean squared error, RMSE, and least-squares slope coefficient, b1, for different models: (1) SS site-specific with no climate and no nonlinear light response; (2) SS-NLR site-specifc with nonlinear light response and no climate; (3) SS-C site-specific with climate; (4) SS-C-NLR site-specific with climate and nonlinear light response; (5) ES-C-NLR ecosystem-specific with climate and nonlinear light response. ....................................................................................................... 134  Table 6.1 Temperature sensitivity (T) (i.e., slope coefficients) derived from regression relationships between gross primary production (Pg) and air temperature (T) at six different classes of vapour pressure deficit (Δe) (4-hPa class width) at the DF49 flux tower. N indicates number of half hour measurements in each regression. Bold coefficients are statistically different from zero at the 99% confidence level. .............................................. 182  Table 6.2 Species-specific parameters describing environmental stress in the LW97 version of 3-PG model (adjusted to include temperature sensitivity according to Sands and Landsberg 2002). .................................................................................................................................... 183  Table A.1 Trend statistics for observed summer (June-July-August) average minimum air temperature (Tmin), dew-point temperature (Td) and the difference. N is the sample size (i.e., number of years in annual time series), trends are expressed as the slope coefficient b integrated over 50 years (˚C/50yr), P is the correlation probability, and S.E. is the standard error. Bold values mark statistical significance. ................................................................... 225  Table A.2 Trend statistics in summer (June-July-August) mean near-surface atmospheric vapour pressure deficit (Δe). N is the sample size (i.e., number of years in annual time series), trends are expressed as the slope coefficient b integrated over 50 years (hPa/50yr), P is the correlation probability, and S.E. is the standard error. Bold values mark statistical significance. .......................................................................................................................... 226   x  List of Figures Figure 2.1 Location of permanent inventory plots, long-term climate stations, and seven subregions in southwest British Columbia, Canada. Cascades region (112 plots); Sunshine Coast region (133 plots); southeast Vancouver Island (327 plots); southwest Vancouver Island (162 plots); northern Vancouver Island (375 plots); Haida Gwaii (149 plots); Mid Coast (18 plots). ...................................................................................................................... 15  Figure 2.2 Properties of the inventory plotted against time (a) total sample size (b) mean stand age (c) mean site index. The measurement period was set as 1959-1998 to include years with at least 200 plots. ............................................................................................................ 16  Figure 2.3 Comparison of between allometric stemwood biomass equations for (a) Douglasfir and (b) western hemlock. ................................................................................................... 16  Figure 2.4. Comparison between estimates of (a-b) stemwood carbon and (c-d) net stemwood production (ΔCsw) derived from the H-DBH allometric regression equations from Ung et al. (2008) and other available equations and calibrations. ........................................................... 17  Figure 3.1 Illustrative example of stationary and nonstationary extrinsic forcing on age responses of stemwood carbon (Csw) and net stemwood production (Psw) in a hypothetical 250-year chronosequence of forest stands. Solid dark curves represent the stationary scenario, while lightly shaded dashed curves represent the nonstationary scenario. (a) relative extrinsic forcing for stationary (constant 1.0) and nonstationary (increasing from 0.5 to 1.0) scenarios (b) comparison between age responses, Psw(A), for 25-year age classes (c) projection of age-class Psw on time (d) comparison between age responses of standing stemwood carbon, Csw(A). The lightly shaded solid curve in panel (d) compares the integration of Psw(A) and the sigmoidal function of measurement-period Csw (formed from different age-classes) for the nonstationary scenario. ............................................................. 25  Figure 3.2 Expected levels of growth enhancement due to CO2 fertilization during the analysis period derived from calibration of biotic growth functions against xi  enrichment/ambient (EC/AC) enhancement factors of 1.20 (β=0.53), 1.30 (β=0.79), and 1.40 (β=1.05)................................................................................................................................... 32  Figure 3.3 Age-response functions of periodic mean annual stemwood growth (Gsw, light shaded circles, dashed curves) and net stemwood production (Psw, dark squares, solid curve) for stands of (a) Douglas-fir and (b) western hemlock observed during the 1959-1998 measurement period. Curves were fitted to all measurement intervals including 33 interval measurements in stands with ages exceeding 200. Symbols mark the mean ( 2 S.E.) for 5year intervals between age class 15 and 100 and 10-year intervals for age class 110 to 190. 33  Figure 3.4 Comparison between age-response functions of (a-b) stemwood carbon (Csw) and (c-d) net stemwood production (Psw) for stands dominated by Douglas-fir and western hemlock. Thick solid curves with dark shading show (a-b) sigmoidal functions fitted to all available measurements of Csw and (c-d) corresponding derivatives. Thin light shaded curves show (c-d) Weibull distribution functions fitted to all available measurements of Psw (as in Figure 3.5) and (a-b) corresponding integrations. Shading expresses the  2 S.E. confidence region. Dashed curves indicate 10%-intervals in each variable. ............................................ 34  Figure 3.5 Time series of mean periodic annual net stemwood production (Psw) for Douglasfir and western hemlock plots. Panels (a) and (b) show observations and predictions derived from age-response functions. Panels (c) and (d) show the age-detrended time series for each species (i.e., Psw(t) - Psw(A)). Shading indicates the 1 standard error region. ...................... 36  Figure 3.6 Time series of mean periodic annual stemwood growth (Gsw) for Douglas-fir and western hemlock plots. Panels (a) and (b) show observations and predictions derived from age-response functions. Panels (c) and (d) show the age-detrended time series for each species (i.e., Gsw(t) - Gsw(A)). .................................................................................................. 37  Figure 3.7 Comparison between deviations from the 1971-2000 base-period mean climate at eight long-term monitoring stations and the periodic mean values for the 1959-1998 plot sample. (a) summer (June-July-August, JJA) temperature, T; (b) summer vapour pressure, ea; (c) summer daytime vapour pressure deficit, Δe; (d) summer precipitation, P; (e) annual days with frost, F and; (f) annual atmospheric carbon dioxide concentration (Ca). ....................... 40  xii  Figure 3.8 Modulation of the relationship between age-detrended periodic stemwood growth (Gsw) and deviations in June-July-August (JJA) air temperature (T) by (a) hydrological conditions (wet, normal, and dry) with atmospheric CO2 restricted to 331  15 ppmv and by (b) atmospheric CO2 with hydrological conditions held constant (normal JJA precipitation  5 mm and normal JJA vapour pressure deficit  0.2 hPa). Symbols express sample quantiles (see Wilks 1995) ordered by JJA T with nine elements.......................................................... 42  Figure 3.9 Contributions of each environmental variable to the measurement-period trend in stemwood growth (Gsw) of 0.84 Mg C ha-1 over 1959-1998 according to regression analysis of Eq. (3.8). “Ca Indirect” represents the combined effect of interactions between Ca and T, Δe, and P. Error bars indicate 95% C.I. based on coefficient errors. ..................................... 42  Figure 3.10 Historical reconstruction of stemwood growth (Gsw) and net stemwood production (Psw) for Douglas-fir and western hemlock plots. The lightly shaded time series expresses the mean ( S.D.) prediction of annual and 10-year moving average Gsw from the regression model, run with eight long-term climate stations with records between 1901 and 2009 (see Figure 2.1 for station locations). The dashed line segment links estimates of mean Psw during the measurement period and the pre-industrial period (defined as a 40-year window marking the period of establishment of stands that were 150 years old during the measurement period). The pre-industrial period mean Psw estimate is 45% of the mean measurement-period Psw (derived from Figure 3.6). .............................................................. 44  Figure 4.1 Types of tree mortality defined by scale and cause. .............................................. 64  Figure 4.2 Individual and sample mean trajectories of the relationship between stand tree density and stemwood carbon for coastal Douglas-fir plots in southwest British Columbia, Canada..................................................................................................................................... 79  Figure 4.3 Relationships between residual absolute demographic mortality (dN) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f)  xiii  maximum soil water deficit (MSWD). Each symbol indicates one of nine sample quantiles (i.e., 1/9th of the dataset, ordered by the independent variable; see Wilks 1995). .................. 84  Figure 4.4 Relationships between residual relative demographic mortality (dN) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD). .................................................................................... 85  Figure 4.5 Relationships between residual absolute gravimetric stem mortality (Msw) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD). .................................................................................... 86  Figure 4.6 Relationships between residual relative gravimetric stem mortality (Msw) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD). .................................................................................... 87  Figure 4.7 Annual time series of sample-average tree mortality in stands of coastal Douglasfir expressed as (a-b) absolute and relative demographic mortality (dN), respectively and (cd) absolute and relative gravimetric mortality (Msw). Thick upper curves express total mortality derived from observations. Thin, solid curves express estimates of densityindependent component of mortality. Thin, broken curves express density-dependent component (calculated as the residual). .................................................................................. 89  Figure 4.8 General patterns of behaviour from Model 1 driven with average stemwood growth (Gsw) for a stand with site class 30 and five different initial stand densities (stems ha1  ) (a) age responses of gravimetric mortality (Msw) and net stemwood production (“Net”) (b)  relationship between tree density (N) and stemwood carbon (Csw) (c) relationship between competitive mass index (Csw) and stand age (d) relationship between N and stand age. ...... 92  xiv  Figure 4.9 Comparison between observed and predicted sample-average periodic annual demographic tree mortality (dN) at inventory plots of coastal Douglas-fir. Model 2 is driven with intrinsic factors only. Model 3 is driven with a combination of intrinsic factors and linear-threshold functions of summer evapotranspiration (ET) and precipitation (P). For demonstrative purposes, Model 3 simulations were run, first, with actual transient time series of ET and P and, second, with fixed levels of ET and P set to pre-industrial levels (defined as the averages for the first 30-year base period (1901-1930) in the available record. .............. 94  Figure 4.10 Temporal patterns of tree mortality in coastal Douglas-fir: (top left, triangles) density-independent demographic tree mortality (dN); (top right axis, diamonds) deviation from long-term normal summer (June-July-August; JJA) precipitation (P); (bottom left axis, circles) density-independent gravimetric tree mortality (Msw); (bottom right axis, squares) deviation from long-term normal summer evapotranspiration (ET). ...................................... 96  Figure 4.11 Modulation of the relationship between demographic tree mortality (dN) and maximum soil water deficit (MSWD; dimensionless) by deviations from (a) normal summer evapotranspiration (ET) and (b) temperature (T). ................................................................... 97  Figure 4.12 Relationship between sample-average (n = 621) annual relative gravimetric mortality (Msw) and deviations from long-term normal summer evapotranspiration (ET) at three levels of maximum soil water deficit (MSWD) including (blue squares) wet soil (green diamonds) moderate soil moisture and (red circles) dry soil predicted with the 3-PG model.98  Figure 4.13 Comparison between trajectories of stand tree density (N) and stem carbon (Csw) at seven sample quantiles of stand age in coastal Douglas-fir. Differences between simulated trajectories reflect two extremes in evapotranspiration and precipitation representative of preindustrial and 1990’s climate. ............................................................................................... 106  Figure 5.1 Dependence of canopy radiation extinction k on (a) diffuse radiation fraction Qd 33m/Qt 33m  (during July) and (b) solar zenith angle z (during all seasons) at DF49. Data shown  in panel b correspond to clear-sky conditions (Qd 33m/Qt 33m < 0.4) to remove a higher degree of noise during overcast-sky conditions. The curve displayed in panel b was fitted only to July data (52.0 < z < 55.5) and extrapolated across the full range of z. ................ 125  xv  Figure 5.2 Dependence of daily gross photosynthetic efficiency (g) on relative absorbed photosynthetically active radiation (Qa′)............................................................................... 128  Figure 5.3 Saturation of daily gross primary production (Pg) and gross photosynthetic efficiency (εg) with total incident photosynthetically active radiation (Qt) during July, 2003 at DF49 (a) observed daily data (open circles, solid curve) and simulation using a multi-layer radiative transfer model (shaded circles, shaded curve) (b) observed dependence of diffuse radiation fraction (Qd/Qt) on Qt (c) sensitivity of modelled εg with increasing daily Qt ranging from 4 to 14 MJ m-2 d-1 run with the upper (solid curve) and lower (broken curve) boundaries of Qd/Qt (d) sensitivity of Pg to increasing Qt for total canopy (circles) sunlitfraction (triangles) and shaded-fraction (squares) run with the upper (solid symbols) and lower (open symbols) boundaries of Qd/Qt........................................................................ 129  Figure 5.4 Relationship between monthly gross photosynthetic efficiency (εg) and standardized absorbed PAR (Qa′). Open symbols indicate monthly observations. Smaller shaded symbols indicate synthetic monthly datasets derived from bootstrap resampling of the daily observations. ................................................................................................................ 132  Figure 5.5 Constraint functions for (a-d) SS-C models (e-h) SS-C-NLR models and (i-l) ESC-NLR. Effects include effects of (a,e,i) increasing standardized absorbed photosynthetically active radiation, Qa′; (b,f,j) sub-optimal temperature, T; (c,g,k) high vapour pressure deficit, Δe; (d,h,l) declining relative soil water content, θr. .............................................................. 135  Figure 5.6 Observed versus predicted monthly mean daily gross photosynthesis (Pg) based on (a-f) site-specific and (g-h) ecosystem-specific parameterization. Dashed line marks 1:1 relationship. ........................................................................................................................... 137  Figure 5.7 Observed and predicted annual total Pg using an ecosystem-specific model at HDF00 (squares), HDF88 (triangles) and DF49 (circles) for all compete years of measurement between 1998-2006. Dashed line marks 1:1 relationship. .............................. 138  Figure 5.8 Daily and 30-day moving average residuals (observed minus SS-C-NLR) Pg. .. 139   xvi  Figure 5.9 Daily and 10-day moving average (black curves) observed and (grey curves) SSC-NLR simulated Pg at DF49. .............................................................................................. 141  Figure 5.10 Relationship between daily gross photosynthetic efficiency (g) and abovecanopy air temperature (T). Curves show Eq. 5 fitted separately to November-March (light shade) and April-September (dark shade) by applying σ = 6.0, Ea = 65 KJ mol-1, and Topt equivalent to long-term mean T during each respective season (indicated by triangles). .... 142  Figure 6.1 Comparison between analytical solutions for scaling leaf-level photosynthesis to a dense forest canopy (L = 8.7, and clumping index 0.7) using multi-layer models (Norman 1980) and light-use efficiency models (Sellers et al. 1992; Sands 1995; Landsberg and Sands 2011) (a) vertical leaf area profile (L of 1-m thick canopy layers) (bars) and associated transmittance of irradiance for a hypothetical forest canopy with spherical leaf angle distribution (k = 0.5), (b) relationships between canopy gross primary production (Pg) calculated with a nonrectangular hyperbolic light-response function assuming incident photosynthetically active radiation of 600 mol quanta m-2 s-1, a maximum photosynthetic capacity at the top of the canopy of Pg max = 10 mol CO2 m-2 s-1, constant convexity ( = 0.85) and constant apparent quantum yield (α = 0.125 mol CO2 mol-1 quanta) and extinction coefficient, k. The solid circle marks the analytical solution from Sands 1995 (discussed in Landsberg and Sands 2011 and used in 3-PG). Square symbols mark solutions using a multilayer radiative transfer scheme from Norman (1980) under varying rates of extinction of Pg max  between k = 0.2 and 0.8. The rectangle denotes the region of extinction implied by results  from Lewis et al. (2000)........................................................................................................ 161  Figure 6.2 Controls on canopy conductance of H2O (gc) in stands of Douglas-fir; (a) relationship between estimates of maximum canopy conductance of H2O (gc max) and leaf area index (L) across stands of Douglas-fir located on Vancouver Island; (b) relative gc versus absorbed solar irradiance, Sa = Sg [1-exp(-k L)], (observed gc divided by modelled gc while holding Sa at 45.0 MJ m-2 d-1) (c) relative gc versus vapour pressure deficit (Δe) (observed gc divided by modelled gc while holding Δe at 1.0 hPa); (d) relative gc versus relative soil water content (θr) (observed gc divided by modelled gc while holding θr at 1.0). Symbols in panels b-d indicate sample quantiles  2×S.E.. Solid curves in panels b-d indicate xvii  constraint functions of the Jarvis-Stewart model derived from the global fit. Dashed curves in panel c indicate exponential equations used in LW97 with kg = 0.19 and kg = 0.05. ........... 167  Figure 6.3 Comparison between observations and model predictions of water stress at Douglas-fir flux towers including relationships between (a) relative gross primary production (Pg) and relative soil water content (θr) at DF49 (solid circles) and HDF88 (open diamonds) (b) relative Pg and relative gs in response to perturbation in θr (c) relative Pg and vapour pressure deficit (Δe) at DF49 (d) relative Pg and relative gc in response to a perturbation in Δe at DF49. Symbols indicate observations stratified across sample quantile classes of the independent variable (Wilks 1995). All sampling constrained to the friction velocity > 0.35 m s-1. Curves labeled “LW97” indicate the values used in the 3-PG model............................. 170  Figure 6.4 Divergent optima in the model efficiency coefficients (MECs) of monthly (circles) gross primary production and (triangles) evapotranspiration across a gradient in the coefficient, kg, that controls reduction of stomatal conductance and photosynthesis. Solid circles indicate the MEC for gross primary production when the model is run normally, while open circles indicate the MEC for gross primary production when simulated soil water stress is turned off. Observations are from the DF49 flux tower. MECs of 1.00 imply perfect agreement between models and observations, MECs of 0.00 imply model skill equivalent to use of the mean observation. ................................................................................................. 176  Figure 6.5 Light-response analysis of gross primary production (Pg) derived from partitioned eddy-covariance CO2 flux measurements above a mature Douglas-fir canopy and with the response to vapour pressure deficit empirically removed and stratified by 5 ˚C classes of air temperature: (a) incident total photosynthetically-active radiation (Qt) and (b) incident diffuse photosynthetically-active radiation (Qd). All sampling constrained to u* > 0.35 m s-1. ............................................................................................................................................... 179  Figure 6.6 Temperature-response functions at the DF49 flux tower: the coefficient representing (a) apparent quantum yield (α) and an Arrhenius fit and (b) maximum gross primary production (Pg max) and a parabolic fit. Values on the right axes of each panel reflect scaling to per unit leaf area assuming L = 8.7. ..................................................................... 180   xviii  Figure 6.7 Temperature (T)-response functions of gross primary production (Pg) derived from hourly eddy-covariance measurements at the DF49 flux tower. Curves are stratified by 4-hPa classes of vapour pressure deficit (Δe) with Qt = 1200  200 mol quanta m-2 s-1 and u* > 0.35 m s-1 (a) observations, (b) observations adjusted to remove vapour pressure deficit effects on Pg (i.e., multiplied by 2-exp(-0.07Δe)), (c) observations with effects of both Δe and relative soil water content, f(θr), removed and (d) comparison between the observed temperature response function, and those expected in the absence of f(Δe) and f(θr), and the theoretical maximum (“marginal f(T)”) at Qd = 200 mol quanta m-2 s-1. Symbols indicate nine temperature quantiles within each Δe class for visual inspection only; raw data indicate significant positive correlation between hourly Pg and T within each class (P < 0.01). ...... 181  Figure 6.8 Demonstration of 3-PG model simulations of stand-level tree development and carbon dynamics for a chronosequence of Douglas-fir plantations near Campbell River, British Columbia. Simulations were conducted with site information and disturbance history for the DF49 flux tower (Morgenstern et al. 2004; Trofymow et al. 2008) and run with the 1998-2006 mean monthly climate to demonstrate model behaviour in the absence of interannual variability. Relevant measurements are shown for comparison: (a) annual total gross primary production (Pg); observations derived from eddy-covariance flux measurements at HDF00, HDF88 and DF49 superimposed on time according to the stand age of each measurement record; (b) net primary production (NPP); circle symbol: DF49 estimate from Jassal et al. (2007); square symbol: DF49 estimate from Schwalm et al. (2007); (c) stand density; initial estimate: Humphreys et al. (2006); 2002 estimate: mean  S.D. from twelve 0.04-hPa National Forest Inventory groundplot measurements (Trofymow 2008); (d) annual 3-PG allocation fractions for branch and bark, roots, foliage, and stem carbohydrate allocation fractions; (e) total leaf area index (L): downward triangles: HDF00 measurements; upward triangles: HDF88 measurements; 2002 DF49 estimates: triangle: Black (2008); square: Chen et al. (2006); 2009 DF49 estimate: mean  S.D. from ten 200-m transects distributed over the DF49 footprint; (f) basal area: circle symbols: age-class means derived from permanent sample plots with site class 35 m (SC35) leading with Douglas-fir in coastal British Columbia; (g) SC35 basal area increment: open symbols: gross basal area increment; closed symbols: net basal area increment; (h) stemwood carbon; square symbol: 2002 xix  estimate derived from groundplot mean  S.D.; circle symbols: age-class means from SC35 permanent sample plots; (i) solid curve and open circles: stemwood growth; dashed curve and closed circles: net stemwood production; (j) aboveground and belowground tree carbon; observed aboveground tree carbon: groundplot mean  S.D.; (k) standing dead wood carbon; observations: groundplot mean  S.D.; (l) foliage and root turnover; observed foliage turnover: mean annual estimate from periodic measurements conducted at 27 traps at DF49 between 2002 and 2005 (Trofymow 2007). .......................................................................... 184  Figure 6.9 Comparison between observed (closed circles) and 3-PG (open circles) predicted annual gross primary production (Pg) at the DF49 flux tower.............................................. 186  Figure 6.10 Comparison of observed (solid) and 3-PG predicted (open symbols) periodic annual stemwood growth (Gsw) at inventory plots of coastal Douglas-fir. Both observations and predictions were detrended to remove variance explained by stand age (see Chapter 3 for details).Solid and dashed lines indicate best-fit trend lines using ordinary least-squares regression. ............................................................................................................................. 187   xx  List of Abbreviations, Acronyms, and Symbols Symbol  Units  Description  AIC A AYM β C Ca Cc Ci Csw Csw 1000 Csw CBM-CFS CCP CMI CO2 CUE DOY DBH DM DP dN dfrost EC/AC ENSO EVI Ea Ei Es Et ET F FPAR fgap FR G Gsw GEV gi gc gs ga  Dimensionless y-1 N/A Dimensionless Mg C ha-1 ppmv; mol mol-1 ppmv; mol mol-1 ppmv; mol mol-1 Mg C ha-1 kg DM stem-1 Kg DM stem-1 N/A N/A Dimensionless N/A g C g-1 C N/A cm Kg Mg C ha-1 yr-1 stems ha-1 y-1; % y-1 Dimensionless N/A N/A N/A kJ mol-1 mm d-1 mm d-1 mm d-1 mm d-1 d month-1; d y-1 N/A Dimensionless Dimensionless Mg C ha-1 yr-1 Mg C ha-1 yr-1 N/A m s-1 m s-1 m s-1 m s-1  Akaike’s information criterion Stand age Age-class yield model Biotic growth factor Carbon Atmospheric carbon dioxide concentration Chloroplast CO2 concentration Intercellular CO2 concentration Stemwood carbon Average stemwood carbon at N = 1000 stems ha-1 Difference between Csw 1000 and Csw Carbon Budget Model of the Canadian Forest Sector (model name) Canadian Carbon Program Climate moisture index (P/ET) Carbon dioxide Carbon use efficiency (NPP/Pg) Day-of-year Diameter at breast height Dry mass Detritus production Demographic mortality Fractional reduction of Pg per frost day Enrichment/ambient CO2 level El Niño Southern Oscillation Enhanced vegetation index Activation energy Wet-canopy evaporation Soil evaporation Transpiration Evapotranspiration Number of days with frost Fraction of absorbed photosynthetically active radiation Canopy gap fraction Fertility rating Growth Stemwood growth Generalized extreme value distribution Internal conductance of CO2 Canopy-level stomatal conductance of H2O Leaf-level stomatal conductance of H2O Aerodynamic conductance of H2O and heat  xxi  GDD  Growing degree days  H HM IBP JJA k kg kgL  m N/A N/A N/A Dimensionless Dimensionless Dimensionless  Kp LUE L l M Msw MDBL MSWD N N1 and N0 NEP NPP O2 P Pg Pg max Psw PBM PEM PMET Qa Qd Qt Q10 R Ra Re Rn Rubisco RuBP Sg So T Topt Td u*  m s-1 N/A m2 m-2 ground m2 Mg C ha-1 yr-1 Mg C ha-1 yr-1 N/A stems ha-1 stems ha-1 g C m-2 yr-1 g C m-2 yr-1 mm d-1 g C m-2 yr-1 mol CO2 m-2 s-1 Mg C ha-1 yr-1  mol quanta m-2 s-1 mol quanta m-2 s-1 mol quanta m-2 s-1 J K-1 mol-1 g C m-2 yr-1 g C m-2 yr-1 W m-2  MJ m-2 d-1 MJ m-2 d-1 ˚C ˚C ˚C m s-1  Tree height Hybrid model (modelling strategy) International Biological Program Summer (June-July-August) Rate constant describing decline in Qt and Pg with canopy depth Rate constant describing decline in gc with increasing Δe Rate constant describing the effect of shading on the relationship between gc and L Whole-plant hydraulic conductance Light use efficiency (modelling strategy) Total canopy leaf area index Leaf area Gravimetric mortality Gravimetric stemwood mortality Maximum mass-density boundary line Maximum soil water deficit Stand density Stand density at the current and previous census Net ecosystem production (Pg – Re) Net primary production (Pg – Ra) Oxygen concentration in air Precipitation Gross primary productivity Leaf-level maximum photosynthesis Net stemwood production Process based model (modelling strategy) Productive efficiency model (modelling strategy) Proportional mass of expiring trees Absorbed photosynthetically active irradiance Diffuse photosynthetically active irradiance Total photosynthetically active irradiance Increase of respiration per 10 ˚C increase in temperature Universal gas constant Autotrophic respiration Ecosystem respiration Net radiation Ribulose 1-5, bisphosphate carboxylase/oxygenase Ribulose 1-5, bisphosphate Shortwave irradiance Extraterrestrial global shortwave irradiance Air temperature Optimum air temperature for photosynthesis Dew-point temperature Friction velocity  xxii  WUE z α  β εg εg max  g C kg-1 H2O Degrees mol C mol-1 quanta; mol CO2 mol-1 quanta  g C MJ-1 quanta g C MJ-1 quanta; mol C mol-1 quanta; mol CO2 mol-1 quanta γ Dimensionless γn Dimensionless  Dimenionless ρs Dimensionless σ Dimensionless T mol CO2 ˚C-1 ψp MPa θfc m3 m-3 m3 m-3 θwp θ m3 m-3 θr Dimensionless  Dimensionless Ω Dimensionless Δe hPa S N/A 3-PG N/A Not applicable (N/A)  Water use efficiency (Pg/Et) Solar zenith angle Apparent quantum yield; quantum yield  Biotic growth factor Gross photosynthetic light use efficiency (Pg/Qt) Maximum gross photosynthetic light use efficiency  Modification of Pg based on Qa Nominal level of Ci /Ca Power in self-thinning function Surface reflectance Shape constant in Arrhenius equation Temperature sensitivity of Pg Plant water potential Soil water content at field capacity Soil water content at wilting point Volumetric soil water content; solar zenith angle Relative soil water content Convexity in leaf-level photosynthetic light-response curve Leaf clumping index Vapour pressure deficit Change in system storage Physiological Principles Predicting Growth (model name)  xxiii  Acknowledgements The author extends special appreciation to supervisor, Nicholas Coops (University of British Columbia), and committee members, Werner Kurz (Canadian Forest Service), Andy Black (UBC), and Rob Guy (UBC) for sharing their wisdom and enthusiasm. This research was supported by a doctoral postgraduate scholarship provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Government of British Columbia’s Forest Investment Account – Forest Science Program (FIA-FSP) graduate student award, Natural Resources Canada’s Pacific Forestry Centre graduate student award, and UBC’s tuition award. I also thank the former Forest Research Branch of the Ministry of Forests, Lands and Natural Resource Operations for production and release of forest inventory data, UBC’s Biometeorology and Soil Physics Group for their dedication towards collection of high-quality meteorological and hydrological measurements, Tony Trofymow (CFS) for access to ecological datasets and several valuable discussions, and Juha Metsaranta (CFS) for providing forest inventory data, editorial comments and guidance on analyses in Chapter 3. I thank all past members of the Annex. Lastly, I thank the Department of Forest Resources Management and the Faculty of Forestry, UBC, for providing an outstanding academic environment.  xxiv  Dedication  I dedicate this thesis to my family for their endless love and support and to the great teachers and professors I had.  xxv  Chapter 1: Introduction 1.1 Background Interest in the terrestrial carbon (C) cycle has increased for reasons ranging from international efforts to understand its role in the global climate system, to local efforts to understand the resilience of specific ecosystems facing increased environmental and human pressures. Although the state of an ecosystem cannot be fully appreciated from focus on any single indicator, the C cycle can provide a strong foundation from which many closelyrelated socioeconomic and ecological traits can be inferred. A central question in all current discourse of C cycle science is how ecosystems respond to environmental change factors and conversely how these responses feedback on climate. Only in the five decades since the International Biological Programme (1964-74) have these questions begun to be addressed quantitatively. Application of the continuity equation is a fundamental concept for studying any dynamic system, stating that the change in the storage of mass (or energy) within a predefined system (ΔS) is equal to the difference between the inputs and outputs over a predetermined timeframe: ∆S  	Inputs  	Outputs																																																																																																																 1.1  This seemingly simple mass-balance (or ‘budget’) approach is effective, yet extremely challenging to apply under real world constraints, such that predictive models play a pivotal role in methods of estimation. For the terrestrial C cycle, the ‘input’ is net primary production (NPP), defined as the net flux of mass into the biosphere through the balance between photosynthesis and respiration by autotrophs (Barbour et al. 1999). Sound 1  understanding of NPP is therefore a necessary part of addressing sensitivity to environmental change. The magnitude of variation observed in NPP makes this question both interesting and challenging to address. Of the major terrestrial biomes, NPP can be as low as 5 g C m-2 yr-1 in tundra and desert ecosystems, while the highest documented estimate of NPP is approximately 3000 g C m-2 yr-1 in freshwater marshes and cultivated land (Whittaker and Likens 1972). The wide range in NPP, at least partially, reflects observations that show photosynthesis operates, on average, around fifty percent of its capacity (Schulze 2006).Yet, for the overwhelming majority of terrestrial ecosystems, observations of NPP are conserved between 400 and 1200 g C m-2 yr-1. The concept that terrestrial ecosystems have a potential productivity more than twice that of average observed NPP is a remarkable feature of the Earth’s biosphere, with wide-reaching implications. An intuitive approach to quantify environmental sensitivity of NPP is to vary experimental treatments over the full natural range of variability. However, in reality this is impractical over most spatial and temporal scales, as the capacity to observe the system is most often restricted to a narrow subspace of natural variation. Nowhere is this more apparent than in forest ecosystems, where many key processes occur on spatial and temporal scales that are extremely difficult if not impossible to sample. Forest ecosystems account for a large component of global NPP and store an estimated 861 Pg (1 Pg = 1015 grams) of C primarily in the form of woody biomass and dead organic matter (Pan et al. 2011) and are thought to have sequestered a proportion of atmospheric CO2, offsetting a significant component of 20th century anthropogenic emissions (Prentice et al. 2  2001; Denman et al. 2007). In British Columbia, Canada, forests are central to the cultural identity, economy, and freshwater supply of the Province. Along coastal areas, approximately 11 Mha of BC’s forests consist of dense evergreen coniferous forests that are among the most unique ecosystems in the world (Waring and Franklin 1979). Over the last 110 years, regional temperature has increased by approximately a 1˚C and is expected to continue over the next 100 years by 2-5 ˚C (BC-MFR 2006). There is a growing demand for comprehensive assessment of environmental impacts on forest ecosystems and how resource management can adapt with changing forest values. Considerable research has been conducted on “main dynamics” of this problem, including the effects of disturbance and ageclass structure on forest biomass (BC-MFML 2010). Although tree productivity and its potential sensitivity to environmental change deserves considerable consideration, it is conspicuously absent from the Province’s review of main dynamics, perhaps reflecting challenges in monitoring environmental responses of tree productivity as one aspect of the more general statement that “climate change significantly complicates the pursuit, monitoring, and assessment of sustainable forest management” (BC-MFML 2010). Despite these challenges, it is worth noting the BC may be one of the most ideal locations in the world to study environmental sensitivity of tree productivity. Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco var. menziesii), for example, is one of the most widely-studied tree species, with an extensive focus on its physiology and ecology. In addition, efforts to monitor tree productivity were initiated as early as 1931 with the first permanent sample plot, which the Province of BC expanded into the 1000’s during 1960-2000. Lastly, with the advent of new techniques to directly measure surface-atmosphere CO2 exchange, the Biometeorology and Soil Physics Group at the University of British Columbia began continuous 3  measurements, which later expanded to include three different-aged stands of Douglas-fir (Morgenstern et al. 2004; Humphreys et al. 2006) as part of the Fluxnet-Canada Research Network (FCRN) and the Canadian Carbon Program (CCP) (Coursolle et al. 2006). Together, these observation networks have strong potential for constraining estimates of forest productivity.  1.2 Forest C-cycle models It is not possible to directly measure all components of the terrestrial C cycle over all domains of interest. Simulation models are therefore employed as an alternative strategy to fill the gaps within and between observation networks. More broadly, models serve two main purposes. First, models act as research tools that organize mathematical relationships that govern individual processes into a framework that can be used to test hypotheses and synthesize experimental findings and their broader implications (e.g., Grant et al. 2007; Kurz et al. 2008b). Second, they are used as predictive tools to extrapolate current conditions and forecast changes in the system (e.g., Friedlingstein et al. 2006). There is a wide spectrum of existing C cycle models that vary in specialization to achieve different research objectives. Complexity and applicability are two important features that define a model, such that the spectrum of existing models spanning a narrow band that extends between models that are simple, easily applied, but not necessarily physically and biologically realistic at one end, and models that tolerate more complexity in order to achieve a higher level of realism, but are not necessarily easy to apply at the other end. Models form a continuous spectrum, however, and the above distinctions can be subjective and relative to the qualifications of the operator. 4  Three different modelling approaches that are actively applied to predict stand-level tree productivity are:   Age-class yield models (AYMs) that infer net stem production – the difference between stem growth and mortality, expressed in either volumetric or gravimetric units – indirectly based on empirical relationships between stand age and yield that are sampled in forest inventories (e.g., Böttcher et al. 2008; Kurz et al. 2009). The methodology of specifically fitting to yield is the defining feature of AYMs. Conventional ‘growth and yield’ models strictly do not fall into this class if they fit to productivity, although they will share similarities;    Process-based models (PBMs) that directly predict net stem production from algorithms describing individual physiological processes, including plant photosynthesis, respiration, carbohydrate allocation, growth, and water and nitrogen cycling (e.g., McGuire et al. 2001; Grant et al. 2007). Although PBMs ultimately exhibit some level of empiricism, they are more suitably defined by the philosophy of operation, achieving site-specificity strictly through boundary conditions and inherent model processes rather than calibration;    Hybrid models (HMs) that adopt a combination of empirical and process-based algorithms to predict net stem production This is by far the most diverse class of models, containing a wide range of strategies that range from the ad hoc adjustment of site index (e.g., Monserud et al. 2006; Nigh 2006), inclusion of extrinsic factors as explanatory variables within growth and yield models (Woollons et al. 1997; Wensel and Turnblom 1998; Ung et al. 2009), and development of simplified process-based models through model reduction and scaling techniques (e.g., Aber et al. 1996; 5  Landsberg and Waring 1997), or formation of hierarchical frameworks (e.g., Bernier et al. 1999; Chen et al. 2003). The Carbon Budget Model of the Canadian Forest Sector (CBM-CFS) is broadly applied in Canada to meet national greenhouse gas emission accounting and reporting obligations and operational-scale C management (Kurz and Apps 1993; Kurz et al. 1999; Kurz et al. 2009; Stinson et al. 2011). Tree productivity is represented with ecozone-specific AYMs for hardwoods and softwoods that are developed from Canada’s national forest inventory (Power and Gillis 2001; Boudewyn et al. 2007). The advantage of the inventory-based approach over PBMs and HMs, is that the prediction uncertainty can be formally quantified from the measurement and sampling errors of the inventory. However, since they are developed to represent average historical conditions and rely on infrequently-updated sampling, they are not equipped to study potential impacts of environmental change on tree productivity. Incorporating explicit representation of tree productivity into the CBM-CFS model requires consideration of both tree growth and mortality as separate processes with potentially distinct links with the environment. While studies of the former are scarce, there are virtually no previous models that presently incorporate process-based representation of environmental impacts on mortality, despite growing appreciation of links between climate and regular tree mortality (van Mantgem et al. 2009) and forest dieback (Auclair et al. 2005; Breshears et al. 2005; Hogg et al. 2005).  1.3 Research goals In 2007, the Canadian Carbon Program (CCP) undertook several activities to address bottomup process modelling to support forest C accounting and management and specifically 6  strategies for incorporating process-based information on the impacts of environmental change on annual predictions of forest productivity within CBM-CFS (CCP-NRA 2007). As a component of this network project, the focus of this dissertation was to gain improved understanding of the scope of the problem, and the capacity to estimate impacts of environmental change on forest productivity with confidence, by developing and analyzing a combination of new and pre-existing models. To make use of BC’s large permanent forest inventory, a major step towards this objective consisted of deriving estimates of “observed” stand-level productivity from tree-level measurements and allometric equations at sample plots and then developing ancillary datasets to represent historical climate variability and site properties needed to operate PBMs. Despite increasing demand to account for environmental change factors in modelling, environmental impacts on forest productivity remain subject to considerable scientific debate. As a means of justifying added representation of environmental sensitivity in CBMCFS, the permanent forest inventory sample was analyzed to determine what types of information can be inferred from the dataset regarding the magnitude and direction of recent trends in forest productivity. Specifically, I sought to develop and apply methods that would test whether systematic changes in productivity occurred over the measurement period. To achieve this, tree growth and mortality were analyzed individually, with specific emphasis on novel insights arising from sample-average time series. The resulting observations were viewed as a valuable benchmark for validating models.  7  1.4 Dissertation structure The body of the dissertation consists of five chapters as outlined below: Chapter 2: This chapter presents a brief description of the permanent forest inventory; Chapter 3: This chapter describes methods designed to estimate temporal trends in observed tree productivity and growth and uses multivariate regression models to quantify the relative contributions of CO2 fertilization and climate change; Chapter 4: This chapter documents historical patterns of demographic and gravimetric tree mortality, strategies to partition total tree mortality into density-dependent and density-independent components, and the parameterization of multivariate statistical models that incorporate representation of drought stress as an explanatory variable; Chapter 5: This chapter outlines evaluation of a generic PEM and the ability to model seasonal and inter-annual variability in gross primary production (Pg) in Douglas-fir; Chapter 6: This chapter evaluates the process-level representation of environmental stress in the forest productivity model, 3-PG, through comparison with a broad range of different observations derived from meteorological towers and forest inventory plots.  8  Chapter 2: Derivation of tree stem growth, mortality, and net production from permanent forest inventory plots 2.1 Synopsis This chapter describes derivation of gravimetric stand-level tree stem growth (G), mortality (M), and net production (P) from tree-level measurements collected at permanent forest inventory plots and available allometric equations. General patterns of variation are described.  2.2 Introduction Net primary production (NPP) is a critical component of the carbon (C) cycle in forest stands. Although there is a large body of observations aimed at understanding the factors that cause spatial and temporal variability of NPP, observations of stand-level dynamics are rare and often limited by inadequate sampling, such that considerable uncertainty remains in how key intrinsic and extrinsic factors limit forest NPP. Forest inventories provide information on the structure and development of stands. Historically, inventories have typically been conducted to assess merchantable timber volume. More recently, monitoring forest biomass has become increasingly important to understand how forests influence the C balance. Using allometric equations, it is possible to estimate the C stored in various tree components. Plot measurements provide estimates of net stemwood production (i.e., change in stemwood carbon over time), as well as the growth of live trees and mortality. The focus of this study is twofold. First, we document the methods used to estimate tree stemwood carbon (Csw) dynamics and associated uncertainties from an inventory in temperate-maritime conifer forest ecosystems in southwest British Columbia, Canada. 9  Second, we analyze general features of variability that govern Csw. This included analysis of how Csw and associated fluxes vary with more commonly-reported structural attributes, including basal area (BA) and height (H).  2.3 Tree C balance The C balance, or change in C storage (ΔC) over a unit period of time (Δt), of a generic system over time is driven by the difference between net	primary	production	(NPP), detritus production (DP), and consumption and herbivory (H): Δ Δ  NPP  DP  H																																																																																																																									 2.1  NPP is defined as the difference between gross primary production (Pg) and autotrophic respiration (Ra). In forest stands, the C balance of live trees (Ctree) is defined by the sum of fluxes into and out of the j=1…n individual tree components: Δ Δ  Δ Δ  Δ Δ  Δ Δ  Δ Δ  Δ 																																																																															 2.2 Δ  where Csw is stemwood, Cbk is bark, Cbr is branch, Cf is foliage, and Cr is roots. The carbon balance for individual components, losing the denominator, is: Δ  NPP  DP  H 																																																																																																								 2.3  10  where NPP(j) = η(j) Pg - Ra(j) and η(j) is the fraction of Pg (and stored carbohydrates) allocated to the jth tree component. It is much easier to measure ΔC(j) than NPP(j), such that NPP(j) is often estimated as the residual of Eq. 2.3: NPP  Δ  DP  H 																																																																																																								 2.4  Tree-level measurements from forest inventory can be combined with allometric regression equations to quantify ΔC(j) for each tree component. Estimation of NPP(j) for most tree components (i.e., Cf, Cbr, Cbk, Cr) then requires additional measurements of DP(j) and H(j) that are not typically performed in forest inventories. However, estimation of NPPsw is more straightforward because, in the absence of stemwood rot, DPsw is entirely manifested through the mortality of trees, which is provided by indication of the vital (i.e., live or dead) status of individual trees in each census. In actuality, stemwood rot is factored into the calibration of allometric equations that produce Csw. In the absence of management, Hsw can also be ignored. Under these circumstances, NPPsw can be quantified by summing measurements of net change in stemwood carbon and tree mortality as (Gower et al. 1999; Clark et al. 2001): NPP  Δ  																																																																																																																						 2.5  It is important to recognize that ΔCsw expresses the net change in stemwood carbon of all trees that were alive at t0, and thus includes both trees that survived and trees that died during Δt. Proliferation of the term, “biomass increment,” to describe NPPsw (e.g., Clark et al. 2001) has led to substantial confusion, given that it might equally be used to describe ΔCsw. Both Gower et al. (1999) and Chave et al. (2003) refer to ΔC(i) as “biomass increment.” Harcombe et al. (1983) and Acker et al. (2000) both describe ΔC(i) as “the difference in standing live  11  bole biomass between one measurement period and the next.” Throughout the current study, a different symbolism and arrangement of terms to describe Eq. 2.5 is altered as: 																																																																																																																															 2.6 where Psw is net stemwood production, Gsw is growth of live tree stemwood and is interchangeable with NPPsw, and Msw is interchangeable with DPsw and describes the loss of live-tree stemwood due to mortality (Chave et al. 2003).  2.4 Data and methods 2.4.1 Study area and inventory data The study is based on data from permanent sample plots that were installed throughout southwest British Columbia, Canada, between 1920’s and 2002 by the British Columbia Ministry of Forests, Lands and Natural Resource Operations (RISC 2003). We focused on plots that were located in stands leading with either Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii) or western hemlock (Tsuga heterophylla (Raf.) Sarg.). The majority of plots were located in lower elevation valleys towards the southern half of the study area (Figure 2.1). According to the Köppen-Geiger classification system, the regional climate is classified as temperate maritime, with the exception of rainshadows found throughout southeast Vancouver Island that exhibit summer drying more like that of drysummer subtropical climates. Winters are mild, wet and overcast. The growing season is cool and wet with mixed cloud cover, with common droughts during mid- to late-summer. Mean annual temperature of the plot sample was 7.6˚C and ranged between -1.1 and 10.4˚C. Mean  12  monthly precipitation during summer (June-July-August) was 73 mm and ranged between 16 and 160 mm. The study plots (n=1276) included a census of approximately 90 stems at the first measurement date over plot areas ranging between 0.01 and 0.25 ha. Each plot consisted of between 1 and 11 census intervals with a median of 5 census intervals per plot. Almost all intervals were 5 or 10 years in length. Stands leading with Douglas-fir tended to contain substantial proportions of western hemlock and western red cedar (Thuja plicata Donn ex D.Don), while stands leading with western hemlock were more homogeneous with low numbers of western red cedar, Douglas-fir, and sparse numbers of Pacific silver fir (Abies amabilis Douglas ex Lunds) and grand fir (Abies grandis (Douglas ex D. Don) Lindley). Less than 3% of the population consisted of deciduous species (Table 2.1).  Table 2.1 Species composition at permanent sample plots leading with Douglas-fir and western hemlock. Values expressed as percent of the total population. Species Pseudotsuga menziesii Tsuga heterophylla Thuja plicata Angiosperm spp. Abies spp. Pinus spp. Picea sitchensis T. mertensiana  Douglas-fir (%) Mean S.D. 64.7 26.3 18.9 21.1 10.1 13.7 2.8 6.9 0.9 4.4 0.8 4.4 0.1 0.5 0.0 0.0  Western hemlock (%) Mean S.D. 3.1 6.7 82.0 16.4 5.9 10.8 1.1 6.1 3.2 9.5 0.6 0.5 3.4 7.9 0.0 1.0  From the database, we extracted the measurement date, stand age, plot area, and individualtree measurements. Stand age was estimated from tree cores. Individual tree measurements included the taxonomy, vital status (i.e., live or dead), outside-bark diameter at 1.3 m, and 13  height. Only trees with diameters exceeding 4.0 cm were included in the census. Stem height was derived from a subsample of measurements in each plot. Tree counts were standardized by plot area expansion factors to calculate the number of trees per hectare. Stemwood was defined as bole, stump, and top components and excluded branches and bark. Tree-level Csw was estimated from measurements of diameter and height using allometric equations of stemwood biomass reported in the national database (Ung et al. 2008), which covered 99% of the tree population (Figure 2.3; Figure 2.4). Equations for western hemlock and red alder, respectively, were substituted for remaining softwood and hardwood species that were absent from the national database. Stand-level Csw was calculated by summing treelevel measurements and multiplying by the plot area expansion factor. Units were converted from dry mass assuming a carbon content of 50% (Lamlom and Savidge 2003). For each census interval, periodic annual stemwood fluxes were calculated from the difference between Csw at consecutive census dates and tree mortality divided by the number of years during each census interval. Estimates of Gsw included the measurement of both surviving and expiring trees (Clark et al. 2001). Trees that surpassed the diameter = 4.0 cm measurement threshold during subsequent censuses (i.e., ingrowth) had a minor influence on Csw and stemwood fluxes and were excluded from all analyses. The plot sample had non-uniform spatial and temporal coverage. Sample size ramped up gradually from a small number of plots initiated in the early part of the 20th century, to a plateau just below 1200 plots during 1968-1990, followed by gradual decline (Figure 2.2a). Mean stand age increased almost monotonically between 1967 and 1996 (Figure 2.2b). Mean site index, defined here as stand-tree height (meters) at breast-height age 50 years, was  14  relatively constant for Douglas-fir and declined slightly for western hemlock resulting in an  120°  overall decline between 32 and 29 m (Figure 2.2c).  Prince Rupert 54°  Haida Gwaii  Bella Coola 52°  British Columbia  Mid Coast  North Island Quatsino  Sunshine Coast Oyster River  50°  Cascades Agassiz  Douglas−fir plot(s) Western hemlock plot(s) Long−term climate station 170  Victoria Southeast  Island  122°  48° 124°  112  126°  58  128°  0  130°  132°  58 km  Southwest Island  Figure 2.1 Location of permanent inventory plots, long-term climate stations, and seven subregions in southwest British Columbia, Canada. Cascades region (112 plots); Sunshine Coast region (133 plots); southeast Vancouver Island (327 plots); southwest Vancouver Island (162 plots); northern Vancouver Island (375 plots); Haida Gwaii (149 plots); Mid Coast (18 plots). 15  # of plots  1200  (a)  800 400  Measurement period 0  Age (years)  90  Site index (m)  100  35  (b)  80 70 60  (c)  30 25 20 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000  Time, years  Figure 2.2 Properties of the inventory plotted against time (a) total sample size (b) mean stand age (c) mean site index. The measurement period was set as 1959-1998 to include years with at least 200 plots.  Douglas−fir  Western hemlock  14000  14000  (a)  (b) 12000 Ung et al 2008 (DBH only)  10000  Gholz et al 1979 Grier and Logan 1977  8000  Feller et al 1992 Harcombe et al 1990 Robertson 2011  6000  4000  2000  0  Ung et al 2008 (DBH + H)  −1  Stemwood biomass (kg tree )  Ung et al 2008 (DBH + H)  −1  Stemwood biomass (kg tree )  12000  Ung et al 2008 (DBH only)  10000  Grier and Logan 1977 Krumlik 1974 8000  Green et al 1992 Harcombe et al 1990  6000  4000  2000  0  20  40  60  80  100  0  0  20  DBH (cm)  40  60  80  100  DBH (cm)  Figure 2.3 Comparison of between allometric stemwood biomass equations for (a) Douglasfir and (b) western hemlock.  16  Douglas−fir  80  (%)  60  sw  40 20 0 −20 −40  Penner et al. 1997 Feller et al. 1992 Gholz et al. 1979  −60  Difference, C  Difference, Csw (%)  60  Western hemlock  80  (a)  (b)  40 20 0 −20 −40 −60  −80  −80 10 30 50 70 90 110 130 150 170  10 30 50 70 90 110 130 150 170  Age class, years  Age class, years  80  80  (c) (%)  60  sw  40 20  Difference, ΔC  Difference, ΔCsw (%)  60  Penner et al. 1997 Gholz et al. 1979 Ung et al. 2008  0 −20 −40 −60  (d)  40 20 0 −20 −40 −60  −80  −80 10 30 50 70 90 110 130 150 170  10 30 50 70 90 110 130 150 170  Age class, years  Age class, years  Figure 2.4. Comparison between estimates of (a-b) stemwood carbon and (c-d) net stemwood production (ΔCsw) derived from the H-DBH allometric regression equations from Ung et al. (2008) and other available equations and calibrations.  2.4.2 Environmental data Monthly environmental data were assembled from separate construction of averages for the 1971-2000 base period and monthly deviations (i.e., anomalies) from the base-period average. Monthly averages of daily minimum temperature, daily maximum temperature, and total precipitation, were derived from a 250-m resolution version of the ClimateBC dataset (Wang et al. 2006). Deviations in monthly temperature and precipitation were constructed from interpolation of Environment Canada climate station records (EC-MSC 2011) and global NCEP reanalysis (Kalnay et al. 1996), provided by the NOAA/OAR/ESRL PSD, 17  Boulder, Colorado, USA, for 1948-2002. The resulting dataset overwhelmingly reflects Environment Canada station records, as the reanalysis was only used in adjacent regions (over the Pacific Ocean and Coast Mountains) that are sparsely populated with stations. This was done to avoid edge-effects apparent in the spatial interpolation when those adjacent regions were left empty. Four climate variables were considered, including annual days with frost (F), summer (June-July-August, JJA) mean air temperature (T), summer mean daytime vapour pressure deficit (Δe), and summer mean monthly precipitation (P). Time series of F were constructed from nonlinear regression functions of air temperature. A temperaturebased model was used to estimate Δe, assuming daily minimum temperature was approximately equal to dew-point temperature (Thornton et al. 1997; Kimball et al. 1997; Landsberg and Sands 2011). Testing this method against actual long-term measurements of dew-point temperature at a subsample of stations, we found that positive historical trends in minimum temperature exceeded those of dew-point temperature, which caused the model to predict unrealistic increases in vapour pressure and consequent reduction of a positive trend in Δe. To avoid unrealistic increase in vapour pressure, a constant (1971-2000 normal) minimum temperature was applied in the model. Temporal variability in resulting predictions of Δe, therefore, entirely reflected changes in saturation vapour pressure, while spatial variability (between plots) reflected changes in both saturation vapour pressure and vapour pressure. Pre-industrial atmospheric carbon dioxide concentration (Ca) was set as 280 ppmv (Flückiger et al. 2002). The interval between 1958 and 2002 was filled using measurements at Mauna Loa, U.S.A. (http://www.ipcc-data.org/ancilliary/ipcc_ddc_co2_mauna_loa.txt). A third-order polynomial was used to interpolate between the assumed pre-industrial state in 1850 and the beginning of measurements in 1958.  18  Table 2.2 Statistical description of stand structure, carbon state variables, and fluxes derived from measurements at permanent sample plots leading with Douglas-fir and western hemlock (utilization level = 4.0 cm). Stand age (A); tree density (N); diameter at breast height (DBH); site index (SI); stemwood carbon (Csw); net stemwood production (Psw); stemwood growth (Gsw); stemwood mortality (Msw); proportional mass of expiring trees (PMET).  A N DBH H SI Csw Csw (ingrowth) Psw Gsw Msw PMET  Units yr-1 stems ha-1 cm m m Mg C ha-1 Mg C ha-1 Mg C ha-1 yr-1 Mg C ha-1 yr-1 Mg C ha-1 yr-1 -  Douglas-fir Mean S.D. 66 33 2037 1608 21 9 19 7 30 6 107 71 1 3 2.6 1.7 3.2 1.4 0.64 1.0 0.41 0.41  Western hemlock Mean S.D. 68 6841 2789 1483 24 11 23 10 30 6 154 89 1 4 2.9 2.2 3.8 1.4 1.0 1.5 0.36 0.41     19  Chapter 3: Accelerated regrowth of temperate-maritime forests due to environmental change 3.1 Synopsis To assess impacts of environmental change on forest productivity, live-tree stemwood carbon (Csw) dynamics were analyzed at nearly 1300 permanent inventory plots in southwest British Columbia, Canada. Net stemwood production (Psw) was calculated from periodic remeasurements of Csw during the measurement period, 1959-1998, for a chronosequence of stands ranging from 20 to 150 years old. Differences between the integrated age response of net stemwood production, Psw(A), and the age response of standing stemwood carbon, Csw(A), suggested that Psw increased by between 45 to 60% over the last 150 years. Consistent with this long-term enhancement, stemwood growth (Gsw) increased over the more recent measurement period by 0.84 ± 0.60 (95% C.I.) Mg C ha-1 yr-1 (or 0.60% yr-1), while Psw increased by just 0.44 ± 0.78 Mg C ha-1 yr-1 (or 0.43% yr-1). A multivariate regression model of Gsw was developed to report statistical relationships with environmental variables. Lacking historical records of nitrogen deposition (Nd), driving variables were restricted to include atmospheric carbon dioxide (CO2) concentration (Ca), temperature (T), vapour pressure deficit (Δe), and precipitation (P). The regression model suggested that all tested variables exhibited significant control over Gsw, attributing a 10  5% increase in Gsw due to net effects of direct climate and a 14  5% increase in Gsw to CO2 fertilization in the form of direct stimulation and strong positive interaction with T. Positive and negative interactions between Ca and P and Δe, respectively, suggested that CO2 fertilization was overridden by severe water stress. Total CO2 fertilization corresponded with a biotic growth factor (β) of 0.85 ± 0.34. These findings reinforce previous evidence to suggest that a 20  combination of climate change and other factors (likely involving a combination of CO2 fertilization and increasing nutrient availability) have accelerated regrowth of northern temperate forests through enhancement of net primary production (NPP). Lower trend in measurement-period Psw, however, suggested that 48% of recent growth enhancement was offset by increasing tree mortality, emphasising the need to further understand the environmental effects on tree mortality.  3.2 Introduction Many studies suggest that the ‘residual land sink’ may be caused by enhancement of net primary production (NPP) due to the combined effects of climate change, carbon dioxide (CO2) fertilization, and nitrogen deposition (Prentice et al. 2001; Denman et al. 2007; Ciais et al. 2010; Keeling et al. 2011). Confirmation of historical enhancement is difficult, however, because it requires long-term observations over the period in which trends have occurred. With this question in mind, repeated forest inventory measurements present a unique opportunity to identify past trends in forest productivity and correlation with environmental change factors (e.g., Phillips et al. 1998; Caspersen et al. 2000; Clark et al. 2003; Lewis et al. 2004a; McMahon et al. 2010). Inventory measurements have been used extensively to assess whether intact tropical rainforests currently act as a tree carbon sink, sequestering more atmospheric carbon than they turn over to detritus (Phillips et al. 1998; Chave et al. 2003; Clark et al. 2003; Lewis et al. 2004a; Rolim et al. 2005; Lewis et al. 2009; Gloor et al. 2009; Clark et al. 2010; Pan et al. 2011). In contrast, the majority of inventory programs located in northern temperate forests represent younger stands, where carbon sequestration by trees exceeds detritus production as 21  a natural condition of early regrowth following disturbance. Under these circumstances, the question shifts to whether environmental changes have altered the rate of regrowth relative to some reference, such as that under pre-industrial conditions (Caspersen et al. 2000; Joos et al. 2002). A defining feature of permanent inventory plots over that of temporary ones is the added capacity to estimate the fluxes that govern live-tree carbon storage from repeated measurements. Although estimation of NPP requires additional estimation of continuous detritus production from foliage, roots, and branches, the change in live-tree stemwood carbon (Csw) can be readily estimated from inventory data and allometric equations alone. The amount of stemwood carbon observed at time, t, is governed by the integration of net stemwood production (Psw) since the previous stand-replacing disturbance:  	 																																																																																																																										 3.1  Periodic mean annual values of Psw are calculated over the time interval ∆t between census dates, Δt, as: ∆ ∆  																																																																																																										 3.2  By including measurements of both live and dead trees, two important flux components can also be derived as: 																																																																																																																															 3.3  22  where Gsw is stemwood growth (i.e., the proportion of NPP that is allocated to stemwood) and Msw is the loss of live-tree stemwood carbon due to tree mortality. While periodic variability of Psw is governed by conditions specifically experienced over the census interval, Csw is governed by the net effect of all past conditions imposed on Psw over the life of the stand. As a result, Caspersen et al. (2000) recognized that the direction and magnitude of changes in productivity can be determined for the recent past by comparing actual measurements of Csw with expected values inferred from integration of Psw. Assume that historical growth enhancement has occurred – how would it be manifested in a chronosequence of inventory remeasurements? First consider that the temporal response, Psw(t), in intact stands is controlled by a combination of intrinsic and extrinsic factors. The combined effect of intrinsic factors, consisting mostly of increasing tree mortality and senescence, cause Psw to peak between five to sixty years after establishment, then decline with stand age (A) before reaching a dynamic steady-state (Ryan et al. 1997; Acker et al. 2002; Ryan et al. 2004; Hudiburg et al. 2009). In the absence of extrinsic forcing, the temporal response will approximate the age response, Psw(t)  Psw(A). Alternatively, systematic change imposed by extrinsic factors will cause the temporal response to diverge from the age response, Psw(t) ≠ Psw(A). To illustrate, Figure 3.1 compares the behaviour of Psw and Csw for a hypothetical chronosequence of forest stands subject to stationary and nonstationary extrinsic forcing. In this example, inventory remeasurements are conducted over a contemporary 50-year measurement period, centered at t=0, while stand ages in the chronosequence extend back 225 years. Intrinsic factors are represented by a general curve for Psw(A) exhibiting a sharp  23  increase between 10 and 30 years, followed by asymptotic decline to 35% below culmination. In the stationary scenario, Psw(A) is multiplied by a constant factor of 1.0 such that extrinsic forcing remains unchanged over the time period of the chronosequence. In the nonstationary scenario, extrinsic forcing imposes a relative increase in productivity from 0.5 to 1.0 over 100 years preceding the measurement period (Figure 3.1a), representing a gradual growth enhancement of 50%. In the stationary scenario, values of Psw for all stand age classes converge along a single ageresponse function, whereas in the nonstationary scenario, each stand age class exhibits a unique trajectory of Psw(A) due to interaction with time (Figure 3.1b). Projecting Psw(A) on time further illustrates the temporal behaviour of individual stand age classes in the chronosequence (Figure 3.1c). In the stationary scenario, Csw(A) is derived from integration of a single age-response function of measurement-period Psw. For the nonstationary scenario, Csw(A) was defined by fitting a sigmoidal function to integrations of Psw(A) for each age class. As expected, the magnitude of Csw(A) differs markedly between scenarios especially for older age classes (Figure 3.1d). While the stationary scenario implies less curvature and sustained accumulation into older age classes, the growth enhancement scenario causes significant exaggeration of asymptotic leveling off of Csw(A), indistinguishable from that expected to occur as stands approach carrying capacity. The latter behaviour is counterintuitive prima facie, as one might expect growth enhancement to increase – not decrease – accumulation. Under the growth enhancement scenario, Csw asymptotes because, the older the stands are, the longer they lived under the pre-enhancement regime. In this way, the ability to estimate the age response for a contemporary measurement period (e.g.,  24  Psw(A, t=0)) and compare it with Csw(A) provides a valuable method to infer the direction and magnitude of extrinsic forcing over the chronosequence period.  Stationary scenario  (a)  t−50  t−25  t−75  t−100  Nonstationary scenario  Psw(A)  Extrinsic forcing  1.0  (b)  0.5  t−125 t−150 t−175 t−200  Pre−industrial period  Measurement period Chronosequence period  0 t−200  t−100  t=0  0  50  Time, years  100  150  200  150  200  Stand age (d)  sw  P (t)  Csw(A)  (c)  t−200  t−100  Time, years  t=0  0  50  100  Stand age  Figure 3.1 Illustrative example of stationary and nonstationary extrinsic forcing on age responses of stemwood carbon (Csw) and net stemwood production (Psw) in a hypothetical 250-year chronosequence of forest stands. Solid dark curves represent the stationary scenario, while lightly shaded dashed curves represent the nonstationary scenario. (a) relative extrinsic forcing for stationary (constant 1.0) and nonstationary (increasing from 0.5 to 1.0) scenarios (b) comparison between age responses, Psw(A), for 25-year age classes (c) projection of age-class Psw on time (d) comparison between age responses of standing stemwood carbon, Csw(A). The lightly shaded solid curve in panel (d) compares the integration of Psw(A) and the sigmoidal function of measurement-period Csw (formed from different age-classes) for the nonstationary scenario.  25  This analysis approach was applied to inventory remeasurements of Csw in southwest British Columbia, Canada, to understand how environmental changes have affected historical forest regrowth. Two analyses were conducted to test for the presence of historical trends. As described above, I first tested whether changes in Psw occurred over the last 150 years through comparison of the age-response functions, Csw(A) and Psw(A) as in Caspersen et al. (2000). As many plot measurements spanned 40 years, I was also able to perform a second set of tests for the presence of temporal trends in Psw(t) during the measurement period. To gain additional insight into whether NPP was the main driver of variability in Psw, tests were also conducted to assess trend in Gsw(t). Lastly, correlation and regression analysis were used to determine whether Gsw was related to climate variables and atmospheric carbon dioxide concentration (Ca). I hypothesized that, in the absence of historical growth enhancement: (1) integration of Psw(A) would equal Csw(A) over the range of stand ages in the chronosequence; (2) Psw(t) would converge with Psw(A) over the measurement period and decline with time as a result of monotonic increase in sample stand age; and (3) Gsw would be uncorrelated with individual environmental factors, or alternatively in the presence of correlation, that the net effect of all environmental factors would be negated by opposing directions of individual effects.  3.3 Materials and methods 3.3.1 Study area and data The study area and data are described in Chapter 2.  26  3.3.2 Detection of long-term trend in Psw To make the comparison between Csw and Psw at specific stand ages, I fitted age-response functions to all available interval measurements for each variable. The age response of Csw was modelled with a sigmoidal function:  1  exp    																																																																																														 3.4  where b0…b2 are fitted parameters. The age response of Psw was modelled using a Weibulldistribution function (Chen et al. 2003):  1  1 exp  																																																																																															 3.5  where b3…b6 are fitted parameters. Separate models were fit for Douglas-fir and western hemlock to account for differences in magnitude and shape of each response. The presence of long-term historical changes was assessed by plotting the integration of Eq. 3.5 against Csw(A) from Eq. 3.4. A formal estimate of the long-term change in Psw was calculated according to the difference between the integration of Psw(A) and Csw(A) at stand age 150. Both Eqs. 3.4 and 3.5 are intentionally simplistic, excluding indicators of site quality, such as site index (SI), for the specific reason that variables like SI should be partial functions of environmental change. Use of Eq. 3.4 deviates from the methods in Caspersen et al. (2000) in that they simply calculated average Csw at 80 years (mean or median not specified) rather than a response function. Tests were conducted to ensure that Csw(A) at the benchmark value  27  of A was essentially equivalent to using the mean (the difference being an order of magnitude lower than the comparison used to infer long-term change).  3.3.3 Detection of measurement-period trends in Psw and Gsw In the second analysis, I tested whether temporal trends existed in Psw and Gsw by regressing each dependent variable against t. The linear regression curve was fitted between 1959 and 1998, which restricted the time series so as only to include years where there were at least 200 plots (Figure 2.2a). As productivity was expected to decline with A in response to intrinsic factors (Ryan et al. 1997; Acker et al. 2002; Ryan et al. 2004), and because average stand age of the sample varied with time, the tests were applied to age-detrended time series after subtracting age-response functions for each variable. This is an important processing step because declines in productivity resulting from intrinsic factors could effectively mask trends resulting from extrinsic factors. For Psw, I used the same age-response function (Eq. 3.5) developed for the previous analysis. Unlike the clear decline in Psw, the age response of Gsw is often found to remain high (e.g., Caspersen et al. 2000; Hudiburg et al. 2009). I again used Eq. 3.5 to model the age response of Gsw as it appeared to have the flexibility to represent either sustained growth or decline. Application of the periodic mean annual flux to each year in the census interval and repetition of interval measurements within plots reduces the degrees of freedom of the sample. Lacking a method to quantify the effective sample size (i.e., one that properly represents the degrees of freedom of the sample), I instead constructed a sampling distribution for the regression slope from a large set of artificial time series, within which each yearly element consisted of a single measurement randomly drawn from the sample of 28  available plots. Using this sampling criterion, there was a low probability of selecting interval measurements from the same plot multiple times and an extremely low probability of selecting the same interval measurement multiple times within a single test. Cross-correlation of the resulting artificial time series indicated that autocorrelation was consistently removed over all time lags. Residual variation of Gsw was also consistently independent of time and normally distributed, while residual variation of Psw was consistently independent of time, but normally distributed for only 75% of the tests. Best estimates and of the trends were defined by the mean slope (± 95% confidence interval derived from 2×S.E.) of the artificial distribution. To further understand spatial variability in trends within the study area, the tests were also conducted for individual subregions (as labelled in Figure 2.1).  3.3.4 Relationships with environmental variables Partial correlation analysis was first used to assess multicollinearity between explanatory variables and relationships between periodic annual stemwood fluxes and explanatory variables. Although the primary objective is to understand environmental controls on Psw, the extreme distribution of Msw and expected differences in underlying processes require that Gsw and Msw be modelled separately. Here, focus was placed on a model of Gsw in order to address the hypothesis that variability in Psw was driven by NPP and restrict discussion of Msw to what can be inferred from the residual between patterns of Psw and Gsw. Combined environmental influence was assessed by building four candidate models of age-detrended Gsw using forward stepwise multiple linear regression analysis. Given widely varying evidence on the relative contribution of CO2 fertilization, I specifically sought to test whether models representing both climate change and CO2 fertilization out-performed models representing only climate variables. All models consisted of additive linear effects: 29  ∆  																																																																																						 3.6  ∆  																																																																								 3.7  ∆ ∆  where  ∆   ∆  																		 3.8 																																							 3.9  is the model prediction of Gsw, β0… β8 are fitted coefficients, and ε is a random error  (see list of symbols). Eq. 3.6 tests whether climate variables, alone, influenced fluxes, whereas Eq. 3.7 tests whether climate and Ca, together, influenced fluxes. Eq. 3.8 includes interactive terms to assess the importance of dependencies between climate variables and Ca. Lastly, Eq. 3.9 represents climate only and includes quadratic terms to assess whether adding nonlinearities in the representation of climate out-performs linear models that include Ca. Models were evaluated relative to each other according to Akaike’s information criterion (AIC) for least-squares estimation, AIC = n log(MSE/n)+2K, where n is the sample size, MSE is the mean squared error, and K is the number of model parameters (Burnham and Anderson 2004). Models were fitted using all plots from both species. Explanatory variables were first standardized (z-scored) to facilitate interpretation. While the significance and relative importance of environmental variables are indicated by regression coefficients, their forcing was calculated as the difference between trends in Gsw resulting from applying the model with and without the effect of each respective variable. Summation of forcings from all variables retained in the model equals the observed trend in Gsw. A significant positive forcing indicates that a specific explanatory variable caused an increase in Gsw over the measurement period. 30  Regression coefficients representing the direct link between Gsw and Ca and coefficients representing interaction between Ca and climate variables were classified as ‘direct’ and ‘indirect’ CO2 fertilization, respectively. To facilitate comparison with other studies, the regression-based estimate of total CO2 fertilization was summarized according to the “biotic growth factor” (β) described by Bacastow and Keeling (1973):  1  	ln  																																																																																											 3.10  where t0 was set to 1850, Ca(t0) was set to 280 ppmv, and β was determined to match relative enhancement of Gsw over 1959-1998. The majority of enrichment CO2/ambient CO2 (EC/AC) enhancement ratios for temperate trees (found by increasing Ca from 375 to 550 ppmv) range between 1.20 and 1.40 (Norby et al. 2005; Moore et al. 2006; Ainsworth and Rogers 2007; McCarthy et al. 2010), corresponding to β factors between 0.53 and 1.04. Mauna Loa measurements of Ca increased from 316 to 367 ppmv over the measurement period. Extrapolation of β factors, derived from experimental EC/AC factors of 1.2 and 1.4, correspond with growth enhancement between 8 and 16% due to CO2 fertilization over the measurement period and between 14 and 28% over the chronosequence period (Figure 3.2). Use of the β factor in this way to judge the range of expected levels of CO2 fertilization implies that the effect is only slightly curvilinear during the study period, suggesting that assumed linearity in the regression models (Eqs. 3.7 and 3.8) are reasonable first approximations. Although there is vast evidence that CO2 fertilization is an important factor in many observations of forest growth and therefore worth incorporating into the regression models, it 31  is critical to recognize that the statistical approach, alone, is incapable of distinguishing CO2 fertilization from other environmental factors, such as nitrogen deposition (Nd), that may also have changed over the study period. Lacking knowledge of historical Nd, I resort only to discussing possible alternative explanations for the component attributed here to CO2 fertilization (including Nd).  1.30  Relative enhancement  1.25  16% (β=1.05)  1.20  12% (β=0.79) 1.15  8% (β=0.53)  1.10  1.05 Analysis period 1.00 1850  1870  1890  1910  1930  1950  1970  1990  Time, years  Figure 3.2 Expected levels of growth enhancement due to CO2 fertilization during the analysis period derived from calibration of biotic growth functions against enrichment/ambient (EC/AC) enhancement factors of 1.20 (β=0.53), 1.30 (β=0.79), and 1.40 (β=1.05).  3.4 Results 3.4.1 Age-response functions Weibull distribution functions provided unbiased fits to Psw(A) and Gsw(A) for both Douglasfir and western hemlock (Figure 3.3). During early stand establishment, Psw nearly equaled Gsw and both fluxes increased rapidly to a culmination between 10 and 40 years. After culmination, Psw diverged from Gsw as mortality due to self-thinning began and both fluxes 32  declined in parallel of each other. By stand age 150, both Gsw and Psw declined by approximately 35% in both Douglas-fir and western hemlock, beyond which there was considerable uncertainty due to reduction in sample size.  4  Fluxes (Mg C ha−1 yr−1)  (a)  Douglas−fir  Gsw  3  Psw  2  1  0 0  20  40  60  80  100  120  140  160  180  200  Stand age, years 5  Fluxes (Mg C ha−1 yr−1)  (b)  Western hemlock  4  3  2  1  0 0  20  40  60  80  100  120  140  160  180  200  Stand age, years  Figure 3.3 Age-response functions of periodic mean annual stemwood growth (Gsw, light shaded circles, dashed curves) and net stemwood production (Psw, dark squares, solid curve) for stands of (a) Douglas-fir and (b) western hemlock observed during the 1959-1998 measurement period. Curves were fitted to all measurement intervals including 33 interval measurements in stands with ages exceeding 200. Symbols mark the mean ( 2 S.E.) for 5year intervals between age class 15 and 100 and 10-year intervals for age class 110 to 190.  33  Douglas−fir 400  Western hemlock 400  (a)  (Mg C ha−1)  sw  +53%  Csw(A)  250 200  sw  +40%  300  −1  Integration of P (A)  300  C  (b)  350  Csw (Mg C ha )  350  150  250 200 150  100  100  50  50  0  0 0  25  50  75  100  125  150  175  200  0  25  50  Stand age, years  (c)  3.5  75  100  125  150  175  200  150  175  200  Stand age, years  (d)  4.5  P (A) sw  4.0  3.0  sw  1.5  P  P  3.5  (Mg C ha  2.0  sw  (Mg C ha  −1  2.5  −1  sw  −1  yr )  Derivative of C (A)  −1  yr )  3.0  1.0  2.5 2.0 1.5 1.0  0.5  0.5  0  0 0  25  50  75  100  125  150  Stand age, years  175  200  0  25  50  75  100  125  Stand age, years  Figure 3.4 Comparison between age-response functions of (a-b) stemwood carbon (Csw) and (c-d) net stemwood production (Psw) for stands dominated by Douglas-fir and western hemlock. Thick solid curves with dark shading show (a-b) sigmoidal functions fitted to all available measurements of Csw and (c-d) corresponding derivatives. Thin light shaded curves show (c-d) Weibull distribution functions fitted to all available measurements of Psw (as in Figure 3.5) and (a-b) corresponding integrations. Shading expresses the  2 S.E. confidence region. Dashed curves indicate 10%-intervals in each variable.  3.4.2 Long-term trends in Psw As stand age increased, integration of the age responses for Psw taken from Figure 3.3 increasingly exceeded the age-response function of Csw measurements (Figure 3.4a-b). Similar to the hypothetical scenarios shown in Figure 3.1, the discrepancy between response 34  functions of Csw was negligible prior to stand ages 50 to 75 years. At stand age 150 years, integrations of Psw(A) exceeded Csw by 53% and 40% for stands of Douglas-fir and western hemlock, respectively. The overall difference for all stands was 47%. The difference between estimates of Csw(A) inferred from integrations of Psw(A) and actual Csw(A) at 150 years implied average Psw was 32% higher during the measurement period (1959-1998) than it was during the chronosequence period (c. 1809-1998).  3.4.3 Measurement-period trends Periodic annual measurements of Psw for each species exhibited large decadal variability with positive long-term trends between 1959 and 1998 (Figure 3.5a-b). The time series of Psw(A) exhibited fluctuations and slight negative trend, suggesting a substantial degree of variability was caused by addition and removal of plots with anomalous A and gradual increase in average A of the sample. Subtracting Psw(A) from the actual time series of Psw exhibited smoother variability and slightly amplified the long-term linear trends for each species sample (Figure 3.5c-d). Nonparametric sampling of the rate of change with time for both species indicated a region-wide increase in Psw of 0.44 ± 0.78 Mg C ha-1 over 40 years relative to the decline expected with stand age (Table 3.1). This corresponded to a 17% (0.43% yr-1) increase relative to the measurement-period mean Psw (2.55 Mg C ha-1 yr-1). This is only statistically significant at the 1×S.E. confidence level. Subregional trends widely varied between -2.23 and 1.06 Mg C ha-1 40 yr-1. Significant positive trends occurred across the Haida Gwaii archipelago, southeast Vancouver Island, the Sunshine Coast, and the Cascades. North and southwest Vancouver Island exhibited insignificant increases, while just 18 plots located in the Mid Coast subregion exhibiting significant decrease in Psw.  35  Douglas−fir 3.4  Western hemlock  (a)  (b)  (Mg C ha−1 yr−1)  3.2 3.0 2.8 2.6  P  sw  2.4 2.2  Observation Age response  2.0  sw  Age−detrended P (Mg C ha  −1  −1  yr )  1.8  0.8  (c)  (d)  0.6 0.4 0.2 0 −0.2 −0.4 −0.6 1965  1975  1985  Time, years  1995  1965  1975  1985  1995  Time, years  Figure 3.5 Time series of mean periodic annual net stemwood production (Psw) for Douglasfir and western hemlock plots. Panels (a) and (b) show observations and predictions derived from age-response functions. Panels (c) and (d) show the age-detrended time series for each species (i.e., Psw(t) - Psw(A)). Shading indicates the 1 standard error region.  Time series of Gsw exhibited weak positive long-term trends prior to age-detrending, whereas predictions from the age-response function exhibited no trends. Age-detrending of Gsw, once again, led to less variability with significant positive trend for both species (Figure 3.6c-d). For the whole study area, age-detrended Gsw increased by 0.84 ± 0.60 Mg C ha-1 over 40 years (Table 3.1). In relative terms, this constituted an increase of 24% (0.60% yr-1) relative to the mean for the measurement period (3.50 Mg C ha-1 yr-1). All subregions exhibited 36  significant increases in age-detrended Gsw except for the north Vancouver Island and the Mid Coast subregions.  Douglas−fir 4.4  (a)  (b)  (Mg C ha−1 yr−1)  4.2 4.0  Observation  3.8  Age response  3.6 3.4  sw  G  Western hemlock  3.2 3.0 2.8  sw  Age−detrended G (Mg C ha  −1  −1  yr )  2.6 0.8  (c)  (d)  0.6 0.4 0.2 0 −0.2 −0.4 −0.6 1965  1975  1985  1995  1965  Time, years  1975  1985  1995  Time, years  Figure 3.6 Time series of mean periodic annual stemwood growth (Gsw) for Douglas-fir and western hemlock plots. Panels (a) and (b) show observations and predictions derived from age-response functions. Panels (c) and (d) show the age-detrended time series for each species (i.e., Gsw(t) - Gsw(A)).  37  Table 3.1 Trends in age-detrended net stemwood production (Psw) and stemwood growth (Gsw) for plots of Douglas-fir and western hemlock in southwest British Columbia, Canada, integrated over 1959-1998. Values express the mean ( 95% C.I.) of the slope coefficient multiplied over the 40-year analysis period in absolute units and as percentages of the mean measurement-period flux. Bold values mark field significance at the 95% confidence level. Region Haida Gwaii Mid Coast North Vancouver Is. Southwest Vancouver Is. Southeast Vancouver Is. Sunshine Coast Cascades Entire study area  N 149 18 375 162 327 133 112 1276  Psw Mg C ha-1 40 yr-1 1.06  0.72 -2.23  0.42 0.39  0.98 0.43  0.86 0.87  0.76 0.87  0.70 0.75  0.70 0.44  0.78  % 47  32 -163  30 13  34 16  32 33  28 33  26 30  28 17  30  Gsw Mg C ha-1 40 yr-1 1.33  0.48 -0.06  0.38 0.35  0.80 0.89  0.56 1.19  0.64 1.10  0.60 1.37  0.56 0.84  0.60  % 39  14 -2  14 9  22 25  16 36  20 32  18 42  18 24  18  3.4.4 Relationships with environmental variables Partial correlation analysis of all plot intervals combined together indicated significant interdependence between all variables involved, however, coefficients were extremely low (Table 3.2). Both Gsw and Psw were significantly correlated with A, Ca, and all tested climate variables. T and Δe exhibited strong correlation, while Δe and P exhibited weak inverse correlation. Ca was weakly correlated with all climate variables. Aggregation of environmental variables through space and time to correspond with the sample of periodic census measurements substantially reduced their variability, as illustrated by comparison with 10-year moving averages for a subset of eight climate station records spanning 19012009 (Figure 3.7). The plot sample indicates a change in summer T ranging from -0.4 ˚C during the 1970`s to 0.2 ˚C during the 1990`s, whereas long-term stations indicate an increase of 1.0 ˚C (Figure 3.7a). During the measurement period, ea was 0.30 to 0.45 hPa  38  higher than during earlier decades (Figure 3.7b), whereas Δe was not substantially different from the long-term average (Figure 3.7c). Summer P for the plot sample exhibited two droughts that followed the 1964-1965 and 1983-1984 El Niño events. Both long-term station and plot-sample time series suggest that P was increasing slightly over the long term and was higher during the 1990’s than during any other period (Figure 3.7d).  Table 3.2 Partial correlation analysis of all interval measurements for Douglas-fir and western hemlock (n=5258). Values indicate the partial correlation coefficient, r. Bold values indicate significance at the 99% confidence level. A F T Δe P Ca Gsw Psw  A 1.00  F -0.04 1.00  T -0.03 -0.52 1.00  Δe -0.01 0.29 0.73 1.00  P 0.00 -0.17 -0.12 -0.15 1.00  Ca 0.18 -0.30 0.10 -0.06 0.06 1.00  Gsw -0.16 0.07 0.05 -0.06 0.04 0.09 1.00  Psw -0.22 0.05 0.03 -0.05 0.05 0.04 0.72 1.00  Environmental variables were consistently retained in forward stepwise multiple linear regression models of age-detrended Gsw with the exception of F, which was excluded in all models and P2, which was excluded from Eq. 9 (Table 3.3). As expected from partial correlation analysis, models only explained a low fraction of variance in observations, with adjusted R2 values ranging between 0.13 and 0.14. Although all models were equally poor predictors, Eq. 3.8 exhibited the lowest AIC, indicating that a model with climate variables, Ca, and associated interactions formed the most parsimonious model of age-detrended Gsw.  39  (a)  0.5 Long−term station records (10−year moving average) Plot sample  0.5  JJA ea (hPa)  JJA T (°C)  1.0  0.0 −0.5 Measurement period  −1.0  (b)  0.0 −0.5 −1.0 −1.5  (c)  10  (d)  1.0  JJA P (mm)  JJA Δe (hPa)  1.5  0.5 0.0 −0.5  50  (e)  2  Ann C (ppmv)  1  (f)  25 0  a  Ann F (days)  −10 −20  −1.0 3  0  0 −1  −25 −50 −75  −2 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010  1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010  Time, years  Time, years  Figure 3.7 Comparison between deviations from the 1971-2000 base-period mean climate at eight long-term monitoring stations and the periodic mean values for the 1959-1998 plot sample. (a) summer (June-July-August, JJA) temperature, T; (b) summer vapour pressure, ea; (c) summer daytime vapour pressure deficit, Δe; (d) summer precipitation, P; (e) annual days with frost, F and; (f) annual atmospheric carbon dioxide concentration (Ca).  Comparison between standardized regression coefficients in Eq. 3.8 suggested that Gsw was most sensitive to deviations in T and Δe, followed by P and Ca. Converting coefficients back to absolute units, the regression model indicated a marginal temperature sensitivity of 0.77 Mg C ha-1 yr-1 per 1.0 ˚C increase above normal summer T. Under most field conditions, however, the temperature sensitivity is likely to be much lower due to modulation by hydrological conditions and Ca (Figure 3.8). Separate estimation of the temperature sensitivity under high P and low Δe (i.e., “wet” conditions) and normal Ca (i.e., 1971-2000 40  average of 331  15 ppmv) suggested that the marginal temperature sensitivity was likely closer to 1.01 Mg C ha-1 yr-1 per 1.0 ˚C, while transition to “dry” conditions reversed the direction of the response (Figure 3.8a). When hydrological conditions were restricted (near normal P and normal Δe), observations showed a sharp contrast between strong negative response to positive T deviations (-0.1 to 0.4 ˚C) at low Ca, whereas Gsw could increase and remain high when Ca was at moderate and high levels, respectively (Figure 3.8b). This illustrates the strong positive interaction between Ca and summer T in the regression model (Table 3.3). Positive and negative interactions between Ca and P and Δe, respectively, indicated that positive effects of increasing Ca were fully overridden by water stress during periods of low summer P, or high summer Δe. That is, change in Ca had no effect on Gsw under the most severe drought conditions for this study area (i.e., summer P below 26 mm per month or summer Δe increasing above 12.5 hPa). Comparison of the environmental forcings suggested that direct effects of Ca and indirect interaction between Ca and T were the main drivers of increasing Gsw over the measurement period (Figure 3.9). Without CO2 fertilization, temperature would have led to an increase of just 0.16 Mg C ha-1 yr-1 over 40 years. Although Gsw was strongly sensitive to Δe, a lack of long-term trend in Δe led to insignificant forcing. Despite an overall increasing trend and unusually high P during the 1990’s, an extreme drought during the mid-1980’s severely reduced Gsw especially in stands of western hemlock (Figure 3.6d), leading to an overall forcing that was only weakly positive. Direct and indirect CO2 fertilization accounted for a combined 0.49  0.18 Mg C ha-1 yr-1 increase over 40 years (or 0.35  0.13 % yr-1). Calibration of the biotic growth function against this estimate over 1959-1998 indicated a biotic growth factor of β = 0.85  0.34. 41  0.6  0.6  (b) 351 ppmv  −1  yr )  Wet  0.4  −1  0.4  Age−detrended Gsw (Mg C ha  Age−detrended Gsw (Mg C ha−1 yr−1)  (a)  0.2 Normal 0  −0.2  Dry  −0.4  −0.6  0.2  0  331 ppmv 314 ppmv  −0.2  −0.4  −0.6 −0.8  −0.4  0  0.4  0.8  −0.8  JJA T deviation (°C)  −0.4  0  0.4  0.8  JJA T deviation (°C)  Figure 3.8 Modulation of the relationship between age-detrended periodic stemwood growth (Gsw) and deviations in June-July-August (JJA) air temperature (T) by (a) hydrological conditions (wet, normal, and dry) with atmospheric CO2 restricted to 331  15 ppmv and by (b) atmospheric CO2 with hydrological conditions held constant (normal JJA precipitation  5 mm and normal JJA vapour pressure deficit  0.2 hPa). Symbols express sample quantiles (see Wilks 1995) ordered by JJA T with nine elements. 0.5  Gsw forcing (Mg C ha−1 yr−1)  0.4  0.3  0.2  0.1  0  −0.1  −0.2  T  Δ  e  P  C a Direct  Ca Indirect  Figure 3.9 Contributions of each environmental variable to the measurement-period trend in stemwood growth (Gsw) of 0.84 Mg C ha-1 over 1959-1998 according to regression analysis of Eq. (3.8). “Ca Indirect” represents the combined effect of interactions between Ca and T, Δe, and P. Error bars indicate 95% C.I. based on coefficient errors.  42  Table 3.3 Coefficients (95% C.I.) derived from forward stepwise regression models of stemwood growth (Gsw). All explanatory variables were standardized (mean=0.0, S.D.=1.0) prior to fitting. All models explained a significant proportion of variance at the 99% confidence level.  Intercept F T Δe P Ca T×Ca Δe×Ca P×Ca T2 Δe2 P2 Adj. R2 AIC  Eq. 3.6 Value -0.023 -0.009 0.113 -0.083 0.105 n/a n/a n/a n/a n/a n/a n/a 0.13 -8523  C.I. 0.009 0.013 0.018 0.016 0.010 n/a n/a n/a n/a n/a n/a n/a  Eq. 3.7 Value -0.022 -0.013 0.080 -0.058 0.099 0.065 n/a n/a n/a n/a n/a n/a 0.13 -8714  C.I. 0.010 0.013 0.018 0.015 0.010 0.010 n/a n/a n/a n/a n/a n/a  Eq. 3.8 Value -0.042 -0.007 0.133 -0.090 0.085 0.057 0.152 -0.021 0.014 n/a n/a n/a 0.14 -8928  C.I. 0.011 0.017 0.021 0.020 0.015 0.015 0.024 0.013 0.011 n/a n/a n/a  Eq. 3.9 Value 0.004 -0.012 0.101 -0.065 0.142 n/a n/a n/a n/a -0.014 -0.009 -0.006 0.13 -8502  C.I. 0.012 0.013 0.019 0.016 0.011 n/a n/a n/a n/a 0.008 0.006 0.006  3.4.5 Summary of historical reconstruction Combining the three analyses to give an overview of historical fluxes indicated a reasonable degree of coherence between estimates of long-term enhancement of Psw, measurementperiod trends in Psw and Gsw, and model predictions of Gsw (Figure 3.10). Whereas trends in Gsw outpaced Psw during the study period, comparison between model predictions of Gsw back to 1901 and long-term rate of increase in Psw suggests that this is a subtle distinction and that both fluxes likely increased parallel over most of the chronosequence period. Without knowing the shape of the extrinsic forcing prior to the measurement period, it is not possible to exactly calculate mean Psw for the pre-industrial period at the beginning of the chronosequence (i.e., 1829  20 years). 43  5.0  Stemwood fluxes (Mg C ha−1 yr−1)  4.5 4.0  G model mean ± S.D. sw G observations sw Psw observations Psw long−term enhancement  3.5 3.0 2.5 2.0 Pre−measurement period average  1.5 1.0  Pre−industrial period average  0.5 0.0 1800 1825 1850 1875 1900 1925 1950 1975 2000  Time, years  Figure 3.10 Historical reconstruction of stemwood growth (Gsw) and net stemwood production (Psw) for Douglas-fir and western hemlock plots. The lightly shaded time series expresses the mean ( S.D.) prediction of annual and 10-year moving average Gsw from the regression model, run with eight long-term climate stations with records between 1901 and 2009 (see Figure 2.1 for station locations). The dashed line segment links estimates of mean Psw during the measurement period and the pre-industrial period (defined as a 40-year window marking the period of establishment of stands that were 150 years old during the measurement period). The pre-industrial period mean Psw estimate is 45% of the mean measurement-period Psw (derived from Figure 3.6).  However, estimates are partially constrained by knowledge that the historical trajectory of Psw and Csw for 150 year-old stands must intersect the age responses during the measurement period and that Psw increased by 17% over the measurement period. This means that mean Psw for the chronosequence period prior to the measurement period was 24% lower. Assuming initiation of extrinsic forcing in 1900 would imply a pre-industrial mean that was 45% lower than the measurement-period mean (shown in Figure 3.10), whereas assuming initiation of extrinsic forcing in 1850 would imply a pre-industrial mean that was 60% lower, 44  which likely represent upper and lower bounds of uncertainty. Lastly, it is worthwhile noting that, although the relationship between observed and predicted time series of sample-average Gsw does not appear strong in Figure 3.10, this largely reflected poor agreement in the western hemlock sample, while that of the Douglas-fir sample was exceptionally strong (not shown).  3.5 Discussion Permanent inventory plots (n = 1276), sampling a combined area of 88 ha distributed over 26 Mha of temperate-maritime coniferous forest during a 40-year period, were analyzed to assess historical growth enhancement. I hypothesized that, in the absence of growth enhancement: (1) integrated values of Psw(A) would equal Csw(A) across all age classes; (2) temporal variability of Psw would converge with Psw(A) and decline over the measurement period; and (3) Gsw would be uncorrelated with individual environmental factors. The first hypothesis was rejected on the basis that integration of Psw(A) increasingly exceeded Csw(A) as stand age increased, implying a long-term 45 to 60% enhancement of Psw. The second hypothesis was rejected on the basis of significant increase in age-detrended Gsw over the measurement period, although positive trend in age-detrended Psw was only significant at the  1 S.E. confidence level. Lastly, the third hypothesis was rejected on the basis that multiple linear regression models identified correlation between Gsw and all tested environmental variables and that the observed trend in Gsw was caused by positive responses to substantial increases in Ca and T that exceeded negative responses to small increases in ∆e. Rejection of all three hypotheses presents strong evidence to suggest that environmental change has led to significant acceleration of forest regrowth over the last 150 years in southwest British Columbia. 45  3.5.1 Measurement and sampling errors Detection of changes in Psw from remeasurements depends strongly on the accuracy of allometric equations (Clark et al. 2001; Keller et al. 2001; Chave et al. 2003). In unpublished work, I found that different allometric parameterizations available for each species (Grier and Logan 1977; Gholz et al. 1979; Harcombe et al. 1990) had substantial influence over the magnitude of Csw, but a lesser effect on the relative magnitude of trends in Psw(t) and Gsw(t). Stemwood allometric equations taken from the national database (Ung et al. 2008) produced predictions that were slightly below the average from other available parameterizations for Douglas-fir and slightly above other available parameterizations for western hemlock (Grier and Logan 1977; Harcombe et al. 1990). Additional destructive sampling, focusing on measurements of large-diameter trees is needed to reduce uncertainty in age responses for our study area. Industry-based inventory sampling exceeded area requirements for studying tree carbon dynamics proposed by Keller et al. (2001) and Chave et al. (2003). However, even with 1276 (and more than 5200 interval measurements), spatial bias and climatic redundancy in the placement of plots likely introduced errors in regression analysis, possibly affecting relationships with environmental variables (Ung et al. 2009; Crookston et al. 2010). I was unable to address these errors due to the vast distribution of plots and a lack of site description for individual plots. Spatial and temporal heterogeneity of the plot sample is another drawback to use of industry-based inventories. As measurement campaigns gradually ramp up and decline (Figure 2.2a), plots are respectively added and subtracted from the sample, introducing unnatural variability. As a consequence, variability could be driven by addition or removal of plots with extraneous site quality. In plots of Douglas-fir, average site 46  index did not significantly change during the measurement period (P < 0.001). In western hemlock, mean site index declined from 30 m in 1975 to 27 m in 1998. Hence, there is no reason to believe that changes in average intrinsic site qualities of the sample contributed to temporal trends (Table 3.1). Furthermore, heterogeneous sample properties should be, at least partially, alleviated by analyzing age-detrended time series. As another consequence, sample size declined towards the limits of the measurement period, as reflected in higher error bounds (Figures 3.5 and 3.6). However, confidence that declining sample size at the edges of the measurement period did not strongly affect trend estimates was gained through individual tests for seven subregions, which suggested that growth enhancement was wide spread (Table 3.1). Correlation and regression analysis indicated that fluxes derived from the inventory were strongly influenced by environmental variables despite exhibiting extremely low correlation. This likely arose from a combination of errors in inventory measurements, errors in environmental variables (especially hydrological variables for remote plots), and a high degree of unmodelled variability in the biological response to individual environmental factors. Successful isolation of the marginal response of Gsw to summer temperature (Figure 3.8a) implied that industry-based inventories can provide valuable information about key biosphysical processes at sub-continental scale, despite extremely high levels of noise, if sample size is large enough.  3.5.2 Comparison with other tests for growth enhancement Five degrees south of our study area, Graumlich et al. (1989) reported 60% increases in stand-level productivity of four high-elevation temperate-maritime coniferous stands over the 47  20th century, which is consistent with the upper bound of our estimate for southwest British Columbia. Our study therefore presented independent observation-based evidence of standlevel growth enhancement, suggesting that results of Graumlich et al. (1989) are regionally representative. Estimates here are also generally consistent with predictions of increasing forest NPP from model predictions (Kicklighter et al. 1999; Chen et al. 2000; McGuire et al. 2001; Cramer et al. 2001; Nemani et al. 2003; Piao et al. 2009) and many tree-level measurements (LaMarche et al. 1984; Spiecker, 1999; Soulé and Knapp 2006; Lopatin et al. 2008; Salzer et al. 2009; Cole et al. 2010). In a similar type of analysis to the one conducted here, McMahon et al. (2010a) showed that recent biomass production exceeded values inferred from standing biomass in mid-Atlantic U.S. temperate forests. In contrast, a pioneering study by Caspersen et al. (2000) reported negligible differences between recent standing biomass and integrated productivity using a large sample of forest inventory remeasurements throughout the eastern U.S., while Foster et al. (2010) also stated reservations over the conclusions of McMahon et al. (2010a). One consideration is that the magnitude of enhancement, inferred from remeasurements taken over a short time period and over a local area (e.g., McMahon et al. 2010a), may partially reflect natural climatic fluctuations rather than long-term trends. Another important consideration is that, because regional-scale Msw is governed by rare and clustered episodes, comparisons need to carefully address the distributional properties of Psw (Fisher et al. 2008; Lewis et al. 2009). For example, extreme mortality events were detected here in more exposed areas (Mid-coast subregion), which despite representing a small proportion of the sampled forest area, had a non-trivial effect on overall sample average fluxes. In addition to affecting attempts to extrapolate from the sample to study area (Fisher et al. 2008), this also 48  has important implications for the detection of enhancement, as large non-stand-replacing disturbances will strongly influence mean Msw as well as integration of Psw(A). To detect growth enhancement, ideally we would know the probability distribution of Msw for the average stand on the landscape, but in reality we resort to construct the distribution from a chronosequence. Whereas permanent inventory samples (e.g., Lewis et al. 2009; McMahon et al. 2010a; this study) may possibly underestimate regional-scale mortality, Caspersen et al. (2000) likely overestimated mortality for the average stand, reported as 2.1% yr-1, which is substantially higher than the median rate of mortality for eastern U.S. states (0.9% yr-1; my unpublished calculations), or the area-weighted average of <1.0% yr-1 reported by Brown and Schroeder (1999). The latter study did not specify whether this was the mean or median. Hence, there is an important distinction between the conclusion made by Caspersen et al. (2000) – that average stands across the landscape did not experience growth enhancement – and one arguing that growth enhancement in intact stands was offset by catastrophic mortality events. Hurricanes, convective storms, and ice storms are likely important factors in the eastern U.S. database, while additional inclusion of removals (i.e., harvesting) in the sample is also partially confounding. These issues warrant a more formal definition of “intact” stands, which requires careful consideration of the distinction between regular and catastrophic tree mortality; the latter acting effectively like land-use changes within permanent sample inventories. McMahon et al. (2010a, 2010b) calculated historical growth enhancement by comparing Psw(A) with the derivative of Csw(A). One possible drawback to this approach is that the derivative of Csw(A) at a given stand age bears no physical meaning regardless of the extent to which the asymptote in Csw(A) is governed by the traditional view that stands enter into an 49  aggrading style of dynamic equilibrium, or whether extrinsic factors have gradually amplified the trajectory of actual Csw(A), or conversely decreased the trajectory of Csw(A) derived from fits to chronoseuqnces over time. Although discrepancies between estimates of Csw(A) for younger age classes are relatively small (within the uncertainty of fitted age responses (Figure 3.4a and 3.4b)), these discrepancies translate into much larger relative discrepancies in estimates of Psw (Figure 3.4c and 3.4d). As an example, actual measurements of Psw in stands of western hemlock exceeded estimates inferred from the derivative of Csw(A) by a factor of three at stand age 100 (Figure 3.4d), implying that it is not a realistic indicator of Psw. Adhering to the original methodology used by Caspersen et al. (2000) would yield results suggesting that the long-term enhancement would be negligible at the A = 80 year benchmark, or at least extremely difficult to discern (Joos et al. 2002). Hypothetical scenarios in addition to the real-world examples imply that the agreement is largely because environmental changes have had a substantial influence on the yield of 80 year-old stands. Whereas the U.S. inventory emphasizes spatial sampling at the expense of remeasurements, the British Columbia inventory emphasized remeasurements at the expense of spatial sampling. Each strategy has unique benefits. Here, extensive temporal sampling allowed for unprecedented ability to estimate trends during the measurement period, supporting the hypothesis that positive trend in Gsw (i.e., increasing NPP) was the primary driver behind long-term enhancement of Psw. The other main advantage of extended temporal sampling is that the record within each plot extended over a greater proportion of the lifespan of the stand, increasing the likelihood of accurately sampling the probability distribution of Msw for the average stand. 50  By using a much larger sample size that experienced no change in species composition, some of the other main concerns raised by Foster et al. (2010) were avoided. While I agree with Foster et al. (2010) that discrepancies (as shown in Figure 3.4) may arise from higher previous mortality, I have no reason to believe that older stands in our sample experienced substantially higher rates of mortality at previous age classes compared with what is observed at those age classes during the measurement period. Conversely, I do have an a priori expectation of previously lower Gsw (Prentice et al. 2001; Denman et al. 2007). Whereas age-response functions confirmed that productivity does indeed decline with stand age (Ryan et al. 2004), temporal-response functions showed that fluxes simultaneously increased with time. Alternative explanations attributing positive temporal trends to intrinsic factors, such as increasing allocation of NPP to stemwood, expanding access to belowground resources, or recovery from repression have not been fully dismissed; however, I can think of no reason why such factors would cause fluxes to decline with stand age, but increase with time.  3.5.3 CO2 fertilization, climate change, and interactions Comparison between different candidate models indicated that a model driven with summer climate variables, Ca, and interactions edged out models based solely on climate and was, therefore, the most parsimonious way to account for extrinsic controls on Gsw using regression. The selected model attributed a large proportion of historical growth enhancement to CO2 fertilization. Although correlation between explanatory variables makes it difficult to fully judge parameter uncertainty (Table 3.2), large sample size and temporal coverage over a wide range of climatic anomalies, including a 1˚C increase in T between the 1970’s and 1990’s, helped to identify the direct climatic responses to continuously increasing 51  Ca. The tight relationship between T and Δe, in particular, makes the magnitude of their individual effects difficult to identify such that they are likely less reliable than their combined effect. We suspect that another round of remeasurements, and possibly integration with the U.S. inventories, would further help to reduce uncertainty in the relative impact of CO2 fertilization. The contribution of CO2 fertilization to growth enhancement reported here is within the range of estimates reported by CO2-enrichment experiments (Norby et al. 1999; Norby et al. 2005; Ainsworth and Rogers 2007) and biosphere model predictions (McMurtrie et al. 1992; Lloyd and Farquhar, 1996; Chen et al. 2000; Alexandrov et al. 2003). By adding “Ca Direct” and “Ca Indirect” from Figure 3.9 together, total CO2 fertilization accounted for a growth enhancement of 14  5 % between 1959 and 1998, which translates into a growth factor of β = 0.85  0.34. Taking uncertainty into account, the estimate is indistinguishable from various syntheses for tree species (Norby et al. 2005; Ainsworth and Rogers 2007) and experimental analysis of net photosynthesis for Douglas-fir seedlings (Lewis et al. 2004b). A significant positive interaction between Ca and T in the effect on Gsw contrasts with findings by Lewis et al. (2001) and Lewis et al. (2004b) for Douglas-fir, yet it is consistent with other experiments as well as the general physiological understanding of photosynthesis (Berry and Bjorkman 1980; Long, 1991; Lloyd and Farquhar 1996; Lloyd and Farquhar 2008). At low Ca, positive sensitivity of ribulose-1,5-carboxylase/oxygenase (Rubisco) activity and regeneration of ribulose-1,5-bisphosphate (RuBP) to increasing temperature is counteracted by competitive inhibition of carboxylation and consequent photorespiration, while this is attenuated by increasing Ca. As proposed by Long (1991), the interaction here was strong enough to change the direction between negative responses at lower Ca and positive responses at higher Ca. 52  Positive interaction between Ca and P suggested that CO2 fertilization was entirely overridden by soil water deficits. Negative interaction between Ca and Δe, similarly, suggested that CO2 fertilization was also entirely overridden by high atmospheric vapour deficits. This appears consistent with observations that indicate stomatal closure with increasing Δe continues to limit photosynthesis at elevated Ca (Dai et al. 1992), that stomata become more responsive to Δe at higher Ca (Bunce 1998; Katul et al. 2009), and increasing evidence that Δe and P influence photosynthesis through ‘non-stomatal’ controls (Grassi and Magnani 2005; Warren et al. 2003). It is frequently proposed that CO2 fertilization may be increasingly pronounced with increasing aridity, where declining stomatal conductance and declining desiccation could alleviate water stress (e.g., Gedalof and Berg 2010; Holtum and Winter 2010), yet this may be offset or more than compensated for if high Δe and low P override direct CO2 stimulation. These empirically-derived interactions may provide a valuable constraint for biosphere models that predict contrasting geographic patterns of CO2 fertilization (e.g., Alexandrov et al. 2003; Hickler et al. 2008). Observation-based studies are divided on whether CO2 fertilization contributes to historical growth enhancement. Gedalof and Berg (2010) analyzed a large sample of tree-ring chronologies and found that positive tree-ring growth trends (after removing variation explained by the Palmer Drought Severity Index) were restricted to a small proportion of tests. Girardin et al. (2011) presented a more detailed approach, using a process-based biosphere model to remove climatic effects on tree-ring growth, and also found limited evidence of CO2 fertilization in boreal coniferous evergreen forest stands. Tree-ring chronologies present an invaluable source of information to study past trends in productivity, yet it is unclear from studies like Gedalof and Berg (2010) whether detrending tree-size 53  signals inadvertently removes a proportion of the extrinsic forcing, increasing the probability of Type II errors in detection studies. Because the age-effect is negative, detrending it from chronologies is never going to lead to false-positive detection of positive trends, but should be expected to lead to some finite proportion of false-negative detection of positive trends. This problem, arising primarily from the effect of suppression and release in closed stands, would be partially circumvented by reconstructing entire stands, as exemplified by Graumlich et al. (1989) and Metsaranta and Lieffers (2009). Future studies should seek coherence by combining permanent forest inventories, dendrochronologies, and application of process-based models (e.g., Girardin et al. 2011). This would require further exploration of whether given extrinsic forcing on NPP imposes equivalent relative effects on the key dependent variables, such as ring width, basal area, height, and Gsw. If growth enhancement equally affects basal area and height, then perhaps we only ought to expect a fraction of total growth enhancement to be detected in diameter- or height-based metrics, individually. Despite the aforementioned arguments that CO2 fertilization likely contributed to growth enhancement, results only conclusively show that its inclusion in the model led to superior performance relative to models forced only with climate variability. That is, direct (immediate) effects of climate variables, alone, did not appear to fully explain the growth trends. This is consistent with application of a process-based model, 3-PG, which did not represent CO2 fertilization, and was equally unable to account for observed trends in Gsw (Chapter 6). I cannot argue conclusively from statistical modelling results that CO2 fertilization is a cause of the observed trends. Although direct stimulation of photosynthesis due to increasing Ca is  54  a compelling explanation (i.e., simple and supported by a wide range of observations), several alternative hypotheses need to be dismissed, including:    Trends in nutrient availability due to increasing Nd: Long-term changes in Nd could directly contribute to enhancement; however, estimates of historical variability in the study area are scarce and conflicting. Chen et al. (2003) assumed a linear increase in Canadian national average Nd (for forested regions) between pre-industrial (0.5 kg ha-1 yr-1) and mid-1990 levels (2.5 kg ha-1 yr-1). The pre-industrial estimate is obviously much less certain (others report 1.0 kg ha-1 yr-1 (Galloway et al. 2004)), while current estimates are less uncertain, but vary across the study area between approximately 2.5 and 4.3 kg ha-1 yr-1 depending on position relative to industrial centres (Raymond et al. 2010). The national trend used by Chen et al. (2003) is at least somewhat contradicted by annual measurements 40 km east of Vancouver (i.e., in the Lower Fraser River subregion), which show no discernable trend in NO3 and a weak negative trend in NH4, spanning 1971-2007 (Feller 2010). In fertilization experiments conducted on coastal Douglas-fir planted on Vancouver Island, Miller (1983) reported 51, 88, and 111% increases in 15-year stand growth in response to initial applications of 157, 314, and 471 kg N ha-1, respectively. Extrapolation between these values and zero (which forms a slightly curvilinear relationship) and dividing each treatment by the number of years in the experiment (15 years) implies a growth-sensitivity (at low levels of N fertilization) of 4.9 % per kg N-1 ha-1. This estimate is roughly consistent with the sensitivity of 5.5% increase in aboveground biomass increment per kg N-1 ha-1 recently recorded across stands over eastern U.S. regions (Thomas et al. 2010), but much higher than the sensitivity of 1.5% per kg N-1 55  ha-1 reported for forest regions in Europe (Solberg et al. 2009). Combining the sensitivity using results from Feller (1983) with the national trend assumed by Chen et al. (2003) implies that increasing Nd would have led to a growth enhancement of 9.8% since 1890. Several of the assumptions in this calculation require further investigation, perhaps starting with improved confidence in the estimate of preindustrial Nd for the study area.    Indirect effects of temperature: Regression models, explored here, only account for direct physiological effects of T, Δe, and P on photosynthesis. These effects express immediate thermal stress imposed on enzyme-facilitated reactions (and additional immediate temperature-related effects on biochemical processes) and immediate water stress on gas diffusion (and possibly other non-stomatal controls on biochemistry). They would therefore not entirely account for antecedent mechanisms, such as positive feedback through leaf area expansion, or enhanced nutrient availability via accelerated nutrient mineralization. Such phenomena could be explored by including autoregressive functions, or lagged responses to climatic variables; however, such analyses might be more appropriately tested with annually resolved dendrochronologies (e.g., Girardin et al. 2011), or possibly stable carbon isotope ratios (e.g., Bert et al. 1997; Arneth et al. 2002).    Indirect effects of water stress: Some studies argue that productivity could be indirectly enhanced by CO2 when Ca-induced stomatal closure drives declines in transpiration and subsequent alleviation in the frequency and intensity of soil water deficits (Holtum and Winter 2010; Gedolof and Berg 2010; Arneth et al. 2002) as an 56  alternative to direct CO2-stimulation, which Holtum and Winter (2010) described as being supported by “underwhelming” evidence in natural situations. It is interesting to note that regional-scale simulations of the soil water balance in our study area did indeed exhibit major decreases in the severity of soil water deficits towards the latter part of the study period (see Chapter 4); yet, this clearly expressed responses to increased P rather than Ca because the latter forcing is not represented by the model. This phenomenon should also be accounted for through P in the statistical model of Gsw. The hypothesis has received wide interest, including studies based on water-use efficiency (WUE) derived from stable carbon isotope ratios (e.g., Arneth et al. 2002; Knapp and Soule 2011). Here, the regression model contradicted this hypothesis showing P-interaction that implied direct CO2-fertilization was overridden by drought. Statistical analysis of productivity (as performed here) cannot, alone, resolve these questions (Arneth et al. 2002); however, it remains unclear how additional knowledge of WUE from stable carbon isotope ratios would be any different (see Conclusion of Birt et al. 1997). This is worth further consideration, granted that collection of such data is feasible.    Trends in the ratio of aboveground to belowground carbohydrate allocation: Very little is known about the magnitude of long-term changes due to difficulties in measuring belowground carbon.    Trends in site quality due to natural disturbances, or enhanced management practices: These factors were dismissed on the basis of the assumption that the  57  inventory sample represents intact stands that are largely free of macro-scale disturbances and human management following establishment.  3.5.4 Implications for the sink in northern forests Historical trends in Gsw in our study area may reflect a general response of northern forests to increasing CO2 and warming when nutrients and water are in adequate supply. Assuming similar conditions exist in at least some other temperate regions, including those more affected by Nd surrounding industrial centres, implies a significant contribution to the northern land carbon sink, consistent with atmospheric observations and inversion models (Keeling et al. 1996; Tans et al. 1998; Gurney et al. 2002; Stephens et al. 2007; Ciais et al. 2010; Keeling et al. 2011). Although NPP in temperate-maritime forests appears able to respond strongly to recent environmental change, growth enhancement in other regions may be limited by genetic constraints (Crookston et al. 2010; McLane et al. 2011), nutrient limitations (Lewis et al. 2004b; Chen et al. 2011), or declining forest health associated with droughts (Hogg et al. 2008) or biological agents (Hogg et al. 2005; Kurz et al. 2008a). For these reasons, we suspect growth enhancement is highly situational, requiring investigation at a sub-continental scale. Thus care should be taken in generalizing our results for northern temperate forests. In addition, the effect of growth enhancement on tree carbon storage can be counteracted by tree mortality. Here, positive trends in Gsw exceeded those of Psw by 48% (increases of 0.84 versus 0.44 Mg C ha-1 over 40 years), implying that enhancement of NPP outpaced concomitant increases in tree mortality in much the same way as has been reported for intact tropical forests (Phillips et al. 1998; Gloor et al. 2009). Increases in tree mortality in our 58  study area have been substantiated by van Mantgem et al. (2009) and are also observed in the present dataset (see Chapter 4). Unlike the sample in van Mantgem et al. (2009), a large component of tree mortality in our sample can be attributed to self-thinning as a natural condition during regrowth. Enhancement of NPP attributed to a combination of CO2 fertilization and climate change in biosphere models may overestimate the effect on treecarbon storage when the density-independent component of Msw is not represented, which may explain discrepancies between predictions and observations of Psw reported by Albani et al. (2006). While we report a moderately large immediate reduction in enhancement of treecarbon storage due to tree mortality, it is critical to expand the analysis period to cover the residence time of dead carbon pools to appreciate how much growth enhancement will remain stored in the ecosystem over the long term (Harrison et al. 2004; Kurz et al. 2008b). It is also important to expand the spatial domain to properly represent effects of forest degradation, non-stand-replacing disturbances, and density-independent tree morality (Fisher et al. 2008; Lewis et al. 2009).  3.5.5 Implications for age-class yield tables Discrepancies are frequently reported between field estimates of site index and estimates derived from normal yield tables (i.e., those developed from old-growth stands), while estimates of site index are also often dependent on stand age (Stearns-Smith 2001). Forestry operations and research in the northern part of our study area indicate that historical age-class yield tables underestimate yields in second-growth stands of western hemlock by as much as 85% (Nigh and Love 1997). This led to Province-wide efforts to produce adjustments for site index of old-growth stands across British Columbia (Nigh 1998; Nussbaum 1998), which found discrepancies were widespread. Several factors may contribute to decline in site index 59  with stand age. Nussbaum (1998) and Nigh (1998) both proposed that old-growth site index estimates tend to be underestimated due to several measurement biases. Age-class yield tables rely on lengthy chronosequences and the assumption that extrinsic factors remain stationary over the period of construction and application (Goodale et al. 2002). Results here demonstrate how nonstationarity during yield-table construction invalidates the ‘space-time substitution’ and drastically alters the shape of the age response (Figure 3.1), while nonstationarity during application will cause trajectories to diverge from expectations. Based on these findings, I suggest that “bias in the age versus height model used to estimate oldgrowth site index” (paraphrased from Nussbaum 1998 and Nigh 1998), is the principal source of error in site index tables and that it is directly related to environmental change. It is unclear whether these biases exist in inventory-based forest carbon cycle models. If Psw is explicitly calculated from the difference between two consecutive inventories, then enhancement should be fully represented. Where estimates are derived from the “one inventory plus change” methodology, estimates may not fully account for growth enhancement. Northern Hemisphere (Goodale et al. 2002) and global (Pan et al. 2011) inventory studies have used a combination of these two approaches. In Canada, inventorybased predictions using the Carbon Budget Model of the Canadian Forest Sector (CBMCFS3) are based on the “one inventory plus change” approach due to limited availability of remeasurements (Kurz et al. 2009). Finding an alternative to age-class yield tables for operational use in forest management remains a challenge. Here, I developed a highly simplified regression-based model, or ‘age-class productivity’ curves, that explicitly account for environmental change factors. This approach presents clear benefits over adjustment of age-class yield tables with dated corrections (e.g., Nussbaum 1998; Nigh 1998) and exhibits 60  considerable potential for improvement. Alternatively, age-class yield tables may be replaced with process-based model predictions. Regardless of the approach, time series of forest growth and mortality obtained from permanent inventory plots provide critical (observationbased) evidence and foundation for model predictions of future forest productivity.  61  Chapter 4: Drought-induced mortality waves in temperate-maritime forests 4.1 Synopsis This chapter analyzed relationships between tree mortality and climate using a large sample of permanent inventory plots in temperate-maritime Douglas-fir forests. To help detect climate signals, statistical methods were devised to partition total mortality into densitydependent and density-independent components. Over a 40 year analysis period, the dominant cause of mortality transitioned from self-thinning to density-independent processes. The density-independent component drove wave-like fluctuations that closely corresponded with below-normal summer precipitation (P) following major El Niño-Southern Oscillation (ENSO) events and a background warming trend. Models of demographic tree mortality (dN) were developed to account for drought stress in addition to self-thinning according to linearthreshold functions of P and evapotranspiration (ET) derived from the Physiological Principles Predicting Growth (3-PG) model. An estimate of the density-independent component of gravimetric mortality (Msw) increased from approximately 0.0 % yr-1 during the early 1970’s to 0.20 % yr-1 during the mid-1990’s (a 33% increase relative to mean total Msw) in response to increasing ET. Because the two components of mortality are represented as additive rather than complementary processes, simulations conducted at the plot sample suggest that self-thinning alone (i.e., in the absence of recent increases in drought stress) would have led to significantly higher stemwood carbon (Csw). It is unclear how this basic assumption could be further validated. Overall, these findings reinforce previous evidence that drought-induced tree mortality was responsible for recent increases in regular tree  62  mortality throughout Pacific Northwest forests and provide insights into the mechanisms that may be responsible for recent dieback events.  4.2 Introduction Tree mortality contributes an important influence on succession and biodiversity of forest ecosystems (Franklin et al. 1987; Peet and Christensen 1987; Lichstein et al. 2009). The legacy of tree mortality also affects the carbon (C) balance by redistributing tree biomass to less-stable dead organic matter pools and forming canopy gaps that can reduce potential stand-level productivity (Lichstein et al. 2009). Evaluation of yields using forest ecosystem models, widely applied to forecast timber supply and C stocks, suggests that tree mortality is the biggest factor influencing the performance of models (Ung et al. 2009; Härkönen et al. 2010). Yet despite its clear relevance to forest resource management, models often have only basic or incomplete representation of the phenomenon, in part, due to poor understanding of the driving processes and scarcity of observations (Allen et al. 2010). Much of the understanding of tree mortality comes from the study of plant population dynamics, which suggests that the carrying capacity of an ecosystem is driven by a combination of stand density and plant size (Barbour et al. 1999), that competitive stresses lead to predictable rates of tree mortality (Yoda et al. 1963), and that stand yields are largely independent of stand density over a wide range of natural conditions (Kira et al. 1953). In forestry, stand density management emerged as an important tool that allows foresters to maximize yield quality through manipulation of average tree size (Drew and Flewelling 1979). The majority of past research on modelling these effects has, therefore, focused on intrinsic factors (Franklin et al. 1987), mostly in the form of competition-based processes 63  derived from the above studies of plant population dynamics (Pacala et al. 1996; Landsberg and Waring 1997; Keane et al. 2001; Makela 2003). Part of the challenge in representing total tree mortality is conceptually separating individual components that are not well defined by the modelling community and not individually quantified from existing forest inventory programs (King et al. 2007). Piecing together much of the terminology commonly used in the literature, it is helpful to classify tree mortality according to its various types, causes, and scales (Figure 4.1).  Figure 4.1 Types of tree mortality defined by scale and cause.  From a C-balance modelling perspective, it is advantageous to view tree mortality as a type of non-stand-replacing disturbance that redistributes C within the ecosystem. Total tree  64  mortality can be partitioned into two broad classes, characterized by scale, into micro-scale (or regular) tree mortality and macro-scale (or catastrophic) tree mortality. The two broad classes are distinguished by their scale and distribution. Although there is no hard distinction between the two types, it is conceptually valuable to recognize that some processes (i.e., micro-scale tree mortality) occur on a more-or-less regular basis and therefore have a more uniform distribution through both space and time, whereas macro-scale tree mortality is perceived as a die-off event, or episode characterized by low return periods and extreme effects on stand yield. Auclair et al. (1990) provides examples of how mortality rates, in reality, span a continuum involving “sporadic, transient dieback” at the landscape level. The classification system is highly interrelated, as for example, predation, and mechanical types of tree mortality can occur on both micro- and macro-scales. Interaction between types of mortality adds to the challenge in their conceptualization and modelling. Feedbacks must occur where two or more types of mortality are active. Regular tree mortality is also often referred to as “background” mortality (e.g., Rathbun et al. 2010; Allen et al. 2010) and is distinguished here by density-dependent and densityindependent components (Figure 4.1). In some models, a component of regular tree mortality is often referred to as “growth-dependent” (Battles et al. 2008). Clark (1992) showed how the complementary nature of density-dependent and -independent mortality control the timing of overall mortality during stand development. The two are complementary because, an impact on total tree mortality due to a perturbation in one component should be partially offset by alleviation in the other component. For example, if a drought episode kills off a significant proportion of vulnerable individuals, this should lead to subsequent alleviation in competitive stress by freeing up the resources previously demanded by the deceased. 65  Historically, tree mortality has been documented through pathology surveys, focusing on detection and qualitative description of possible causes. More recently, studies have begun to produce quantitative evidence of density-independent mortality. Numerical indices developed from qualitative surveys have shown regional trends in tree mortality of northern hardwoods throughout the northeast U.S. (Auclair et al. 2005). Although it is difficult to fully separate direct physiological effects of environmental stress from a consequent increase in vulnerability to disease and insect attack, drought and heat-related stress are increasingly identified as an important driver of tree mortality (Phillips and Gentry 1994; Condit et al. 1995; Auclair et al. 2005; Hogg et al. 2008; Allen et al. 2010), and are widely implicated at both regular (Auclair et al. 1990; Auclair et al. 1995; Hogg et al. 2005; Hogg et al. 2008; van Mantgem et al. 2009; Clark et al. 2010; Phillips et al. 2010) and catastrophic scales (Brashears et al. 2005; Woods et al. 2005; Kurz et al. 2008a; Lines et al. 2010; Woods et al. 2011). Estimates of mortality in long-term monitoring plots of mature forests indicate a recent doubling (van Mantgem et al. 2009) in response to regional warming. Phillips et al. (2010) compiled ecological plots from Amazonia, Africa, and southeast Asia, for which both drought (2005) and non-drought conditions (mid-1990’s to mid-2000’s) were documented, and found that demographic tree mortality (dN), defined as the decrease of stand density (N) due to mortality, increased significantly during droughts and that drought resulted in greater relative impacts on gravimetric mortality (M) than on dN because larger trees were disproportionately at risk from drought. They also reported that relationships between tree mortality and drought were nonlinear, with increasingly extreme rates of mortality during severe drought. Clark et al. (2010) reported a weakly significant positive correlation between 66  stand-level M and nighttime temperature over a 26-year inventory record in an old-growth tropical wet forest, which contributed to overall high climate sensitivity of net productivity. Climate-induced tree mortality has important implications for the C balance of intact forest ecosystems. In Chapter 3, I showed that although stand-level tree growth in regenerating temperate-maritime forest stands does indeed decline after a certain stand age, consistent with previous studies of NPP (Gower 1996; Ryan et al. 1997; Ryan et al. 2004; Wirth 2009), the trajectory may be much less asymptotic than what is frequently inferred from yield curves, suggesting that tree mortality, as opposed to senescence, plays a leading role in controlling biomass as stands transition from the self-thinning phase into dynamic equilibrium. This also implies that tree mortality, rather than growth, dictates the limit on forest biomass that can be attained by old-growth stands (Stegen et al. 2010; Phillips et al. 2010), and is responsible for the wide range of successional patterns (Fisher et al. 2008; Lichstein et al. 2009) and variation observed across landscapes (Brown and Schroeder 1999; Hudiburg et al. 2009). Temperate-maritime forest ecosystems are defined, in part, by the low frequency of standreplacing wildfires and insect predation such that changes in stand composition and structure depend strongly on the legacy of regular tree mortality and consequent gap dynamics (Daniels and Gray 2006). Large industry-based forest inventories exist for these ecosystems; however, they are largely restricted to young regenerating stands within the stem-exclusion phase, during which stands exhibit self-thinning (Rathbun et al. 2010). Although the sample size of large inventories is a major strength, providing an order-of-magnitude more samples and covering a broader distribution of climate at the regional-scale, the ability to analyze climate-induced tree mortality depends on the ability to account for and understand all the 67  other (intrinsic and extrinsic) factors also operating. Ecological plot networks have been set up specifically to avoid transient dynamics associated with systematic changes in stand development and succession within samples (van Mantgem et al. 2009), which they warned can obscure driving causes. Despite increasing evidence that drought stress affects tree mortality, previous studies do not provide the information necessary to incorporate drought sensitivity into forest ecosystem models. To achieve this in the simpler case of a stand-level empirical model, these requirements include description of which environmental variables explain the most variation in tree mortality, the direction and magnitude of their effect on either dN or M, and ultimately whether they provide additional advantages over that of simpler models based on intrinsic factors, alone. Strategies to model M vary depending on whether the model is based on explicit representation of stand demographics (prognostic approach), or based on statistical functions of gravimetric M (empirical approach). Examples of the latter approach are rare – empirical yield models (Monserud 2003) or age-class productivity models (e.g., Chen et al. 2003) typically fit directly to net stem production, thus avoiding two separate submodels for G and M. One partial exception is Caspersen et al. (2000), who partitioned variability of net stem production into empirical age-response functions of G and M, although M was simply set as a constant proportion of biomass. The most simplistic prognostic model example consists of the routine applied in the 3-PG model (Landsberg and Waring 1997; Landsberg and Sands 2011), whereby demographic M is simulated by tracking stand density from prescribed initial levels and empirical parameters describing the rate of self-thinning. Self-thinning takes place to ensure stand density remains below the maximum mass-density boundary line (MDBL). 68  Narrowing the focus of gravimetric variables to the stemwood component, herein denoted by subscripts “sw”, constraining N below the MDBL is achieved with a nonlinear function parameterized according to the species-specific maximum average tree stemwood carbon (Csw) that can be attained at a tree density of 1000 stems ha-1 (Csw 1000) and the power () that characterizes the rate of self-thinning (Yoda et al. 1963; Westoby 1981):    1000  																																																																																																										 4.1  where f(N) is the maximum value of average stemwood mass that can be attained at tree density N and the carrying capacity of the stand is then N×f(N). This is the converse of the more commonly used, maximum stand density index (SDImax), describing the maximum value of N that can be achieved for a given average tree mass (or size) (Weiskittel et al. 2010). The difference between Csw and f(N) at a given value of N (herein denoted Csw), is a gravimetric version of various stand competition indices (see Drew and Flewelling 1979 for brief overview of various indices). The index should strongly indicate the magnitude of density-dependent tree mortality, as competition for resources intensifies as Csw approaches f(N) (i.e., Cswincreases). In the resulting model, growth rate only affects gravimetric stemwood mortality (Msw) to the extent that it controls the rate at which stands approach the MDBL. Hence, it is unlikely to account for a large proportion of variation in Msw across landscapes. Tree-level “gap models” represent a step up in complexity, frequently representing the probability of tree mortality as functions of each tree’s DBH as well as stand basal area (e.g., Hamilton 1986; Lines et al. 2009). Hence, it is possible that such models can account for 69  extrinsic influences on Gsw to the extent that they translate into changes in DBH and stand basal area. Such models also add internal functions to represent “growth-dependent” causes of tree mortality as opposed to simply density-dependent mortality. Although dynamic global vegetation models appear to have incorporated these mechanisms to varying degrees (Sitch et al. 2008), the exact details in each model are challenging to track down. One way to adjust 3-PG to represent growth-dependent mortality without including explicit representation of extrinsic factors (e.g., drought) at the stand level is to set the Cs 1000 parameter (or some equivalent) as a function of Gsw (e.g. Csw 1000 = b1 Gsw + b0, where b0 and b1 are fitted parameters), in which case stands with low Gsw self-thin faster because they have less distance to cover before they reach the MDBL. The logic here is that low Gsw is indicative of low site quality (i.e., low resource availability), which exacerbates competitive stresses. It remains an open ecological question, whether low growth causes tree mortality, or whether they simply covary (McDowell et al. 2010; Sala et al. 2010). There is increasing evidence, however, that the MDBL is correlated with indicators of site quality, such as site index, but not environment (Weiskittel et al. 2010). Application of the prognostic approaches requires a loop through annual (or sub-annual) time series of stand development and is strongly dependent on the accuracy of Gsw and Csw. A major practical advantage, however, is that the loop is not needed for calibration against permanent sample plots, which can be achieved using basic linear algebra in exploratory multivariate statistical models. As in the 3-PG model, the resulting predictions of demographic mortality can be converted to gravimetric mortality by, Msw = dN × PMET × Csw, where and PMET is the proportional mass of expiring trees (i.e., the ratio of the average mass of expiring trees to average mass of all trees in the stand). Landsberg and Waring 70  (1997) indicated that PMET values range from 0.1 to 0.4 and can be set constant for a given species. To further understand drought-induced tree mortality and consequent impacts on the C balance, historical observations were analyzed at 621 permanent sample plots dominated by Douglas-fir in coastal British Columbia, Canada. Demographic and gravimetric forms of tree mortality were partitioned into density-dependent and -independent components. The density-independent component was then analyzed to assess partial correlations with a variety of drought indicators commonly used in previous studies. Two types of multivariate statistical models were developed in order to assess whether representation of extrinsic factors (i.e., climate) in addition to intrinsic factors influence mortality. The models were evaluated based on standard indicators of model performance when applied collectively to all available plots as well as the capacity to reproduce temporal variability in the sample-average periodic annual time series.  4.3 Methods 4.3.1 Inventory data Estimates of tree mortality were derived from permanent forest inventory plots leading with coastal Douglas-fir in southwest British Columbia, Canada. Based on the vital status (live/dead) of all trees in the plot for each census interval, the instantaneous annual rate of demographic tree mortality was quantified from the derivative of the trajectory of stand density (Sheil et al. 1995; Lutz and Halpern 2006):  71  d  1  100																																																																																																															 4.2  where N1 is the number of live trees in the current census, N0 is the number of live trees in the in previous census, dN is in %, and dt is the census interval in years with monthly precision. Cross checking Eq. 4.2 with the other commonly used algorithm, dN = [ln(N0)ln(N1)]dt × 100 (Condit et al. 1995; Lewis et al. 2004), suggested that differences between methods were negligible for the observed range of dN. Sheil and May (1996) suggested that mortality rates derived from periodic sampling schemes are not independent of time. They gave experimental and theoretical evidence in tropical stands that dN ought to decline with increasing census interval length. Others have found this difficult to show conclusively in the field (Phillips et al. 2010). The overwhelming majority of plot census interval lengths in the BC forest inventory are split between approximately 5 years and 10 years. Tests were therefore conducted to evaluate whether tree mortality rates varied with census interval length. Conventional “t-tests” were not appropriate given skewness of the data. Instead, generalized extreme value (GEV) probability density functions were fit separately to dN and Msw for each subset (i.e., data with either 5 or 10-year census intervals). Differences were gauged according to the ‘location’ parameter of the GEV distribution.  4.3.2 Climate data Both drought and heat are widely implicated in the previous studies of tree mortality, yet it is not well understood what environmental variables have specific influence or why (McDowell et al. 2008; Sala et al. 2008; Adams et al. 2009). In addition, variables that most accurately 72  express the true driving mechanisms do not necessarily make the best predictors especially if they are ‘derived’ variables. For example, evapotranspiration (ET) is a key variable controlling drought (Granier et al. 1999; Angert et al. 2005; McDowell et al. 2008), yet it is not directly measured at many locations and therefore requires extensive modelling. Given a lack of prior knowledge as to which variables would be most effective, several different explanatory variables were considered. Three basic indices of environmental conditions that are readily available from meteorological stations were considered, including air temperature (T), vapour pressure deficit (Δe), and precipitation (P). Monthly datasets of these variables were compiled from a combination of meteorological stations, the ClimateBC product, and global reanalysis datasets (see Section 2.4.2). As potentially improved indicators of drought, monthly ET was estimated using the model 3-PG. Simulation of ET is used by the model in order to track the monthly water balance for a single soil compartment representing the rooting zone. To do so the model simulates ET using the Penman-Monteith equation (Rosenberg 1983), which calculates the rate of surface evapotranspiration as a function of the availability of energy, the availability of water, and regulation of canopy transpiration. The input variables to the Penman-Monteith equation include mean monthly daytime net radiation, T, and Δe. Net radiation is set as a function of solar irradiance (Sg), derived empirically using observations from flux towers. The latter variable was derived from 1000m maps of monthly normals (Schroeder et al. 2009), omitting transient variability. In this version of the model, canopy conductance (gc) was represented according to empirical relationships with leaf area index (L), Sg, Δe, and relative soil water content, θr = (θ – θwp)/(θfc – θwp) (see Chapter 6 for further explanation of the model). Simulations are therefore indirectly sensitive to P through effects of θr on gc. Although gc is coupled to vegetation  73  through L, the influence is negligible in closed stands of Douglas-fir. For these 3-PG simulations, all plots were assumed to have ‘sandy’ soil texture class, a root depth of 1000 mm, and  = 0.22 m3 m-3 at field capacity and  = 0.05 m3 m-3 at wilting point. Other derived indicators of drought were considered, including the climate moisture index (CMI), defined as the difference between P and ET normally averaged over the calendar or water-balance year (Hogg et al. 1997; Hogg et al. 2005; Latta et al. 2009), as well as the maximum soil water deficit (MSWD), defined as the lowest monthly value of θr derived from the 3-PG model. Variability in MSWD should be nearly identical to that of the “maximum climatological water deficit” used by Malhi et al. (2004), with the important distinction that the MSWD was derived from ‘actual’ ET, as opposed to a fixed level (e.g., 3.33 mm d-1 used in the tropics (Malhi et al. 2004; Phillips et al. 2010)). The periodic time step of the census intervals makes it difficult to quantify environmental conditions for specific time periods (e.g., water year). Instead, I limited focus here to analyzing relationships with mean environmental variables for summer (June-July-August; JJA) during the census interval period.  4.3.3 Correlation analysis As a general means of exploring the dataset, dN and Msw were related to a variety of independent variables using partial correlation analysis. In the first set of analyses, dN or Msw were separately correlated against a collection of intrinsic variables, including A, Csw, N, Gsw, and extrinsic variables, including summer T, Δe, and P. The partial correlation coefficients were then analyzed to determine which intrinsic factors exhibited significant control over mortality under combined influence from both intrinsic and extrinsic factors.  74  In a second test, the partial correlation analysis was carried out for a broader array of extrinsic variables, this time considering each extrinsic variable in isolation from the other extrinsic variables, but with all intrinsic factors included in order to judge which environmental variables contributed to mortality in the absence of expected correlation between environmental variables. In a third test, estimates of density-independent dN and Msw were derived from the inventory and regressed against environmental variables. The density-independent component of variation was calculated by fitting thinning models to each plot trajectory of N based on input of Csw using Eq. 4.1. In this approach, N is the dependent variable and Csw is the explanatory variable. Both Csw 1000 and  were free to vary during calibration, such that the models had a strong capacity to match observations. The approach makes the general assumption that the thinning model will account for density-dependent variation at each plot. The unexplained variation was then assumed to be an indicator of density-independent variation. In the case of plots with only two census interval measurements, the model will invariably explain 100% of the variation and is, therefore, incapable of conveying density-independent variation as defined. Three different thresholds for excluding plots with too few census intervals, including samples containing plots with more than three, four, and five census intervals, were tested in order to evaluate impacts of the decision on results. Estimates of densityindependent Msw were then calculated from initial estimates of dN assuming a constant PMET of 0.40, equivalent to the mean for the inventory sample. Absolute and relative versions of mortality were then regressed against summer climate variables and plotted graphically according to the sample quantiles for each independent variable (Wilks 1995).  75  4.3.4 Multivariate statistical models Multivariate statistical models were developed to test whether inclusion of extrinsic factors improved simulations of tree mortality. This was achieved by comparing separate models that only represented intrinsic factors and models that included both intrinsic and extrinsic factors as independent variables. Tree mortality is characterized by rare events, such that observations exhibit an extreme probability distribution, with a substantial number of zeros, a long right tail, and variation that is dependent on either N or Csw for demographic and gravimetric mortality, respectively. In addition to these inherent traits, multiple periodic measurements at clustered plots introduced random effects with poorly known serial dependence. As a result, standard inferential statistics, as well as nonlinear mixed-effects models may not necessarily be reliable. As an alternative strategy, multivariate statistical models were fitted to census interval measurements using unconstrained nonlinear optimization to minimize an aggregate objective function, comprised of the sum-of-squared error of nine sample quantiles describing the relationship between model residuals and each of A, N and Csw. The method targets a solution in which model predictions are unbiased with each independent variable. Intrinsic factors that were considered consisted of A, N and Csw. To test whether additional representation of climate variability contributed to the performance of predictions, two broad categories of models were developed, including those with just representation of intrinsic factors and those including both intrinsic factors and climate. Models were of the form:  76  d  …  																																																																																																	 4.3  where fi(Xi) is the objective function for the ith independent variable, and b0... bm are fitted parameters. To account for highly nonlinear relationships between dN and intrinsic factors, each objective function was defined by a cubic equation unless otherwise stated: 																																																																																																						 4.4 Models tested with only intrinsic factors included: 																																																																																								 4.5  d  Additional representation of environmental variables was explored individually by adding objective functions, f(X): d  																																																																									 4.6  As there is increasing evidence that the drought effects are defined by thresholds above which mortality is unaffected (Phillips et al. 2010), environmental variables were represented according to linear-threshold functions: min  																																																																																																								 4.7  where X reflects T, Δe, P, ET, CMI, or MSWD. Models were analyzed according to their fit to observations of dN from all available measurement intervals. Models were evaluated relative to each other according to Akaike’s information criterion (AIC) for least-squares estimation, AIC = n log(MSE/n)+2K, where n is the sample size, MSE is the mean squared error, and K is the number of model parameters (Burnham and Anderson 2004). 77  4.4 Results 4.4.1 Observed tree mortality The relationship between N and Csw clearly indicated the MDBL for coastal Douglas-fir (Figure 4.2). Some plot trajectories exceed the ‘fit-by-eye’ MDBL and it is unclear whether these reflect real trajectories or whether they are subject to error (perhaps in estimation of plot area). It is clear from Figure 4.2 that self-thinning along the MDBL, which for example is how dN is simulated in the 3-PG model, is the exception to the rule. Masked within the scatter are many plots with low (i.e., <1500 stems ha-1) initial N, which remain stable without dN for long periods of time before losses occur. However, these also are exceptions and the majority of plots are subject to large and sporadic mortality events that force stands off their present self-thinning trajectory even outside the zone of imminent competition mortality (Drew and Flewelling 1979). The effect of census interval length on mortality can be judged according to the difference between GEV location parameters listed in Table 4.1. Census interval length had no effect on the location of dN and had a positive effect on the location of Msw (P < 0.01; confidence intervals not shown). Thus there was not strong support to indicate that changing census length strongly influenced dN as proposed by Shea and May (1996). In contrast, Msw increased with census interval length in a manner opposite to what would be expected from Shea and May’s findings. Conducting a t-test for each sample indicated that the difference for Msw likely arose from significant increase in Csw between census interval lengths of 5 (Csw = 121 Mg C ha-1) versus 10 years (Csw = 141 Mg C ha-1) (P < 0.01), which can be  78  explained by apparent transition towards longer census intervals towards the end of the study period.  Tree density (trees ha−1)  8000  Maximum mass−density boundary line  4000  Density inhibition boundary line 2000  1000 500 250 125 0 0  100  200  300  400  500  600  −1  Stemwood carbon (Mg C ha )  Figure 4.2 Individual and sample mean trajectories of the relationship between stand tree density and stemwood carbon for coastal Douglas-fir plots in southwest British Columbia, Canada.  79  Table 4.1 Generalized extreme value (GEV) fits to annual demographic (dN) and gravimetric (Msw) mortality in coastal Douglas-fir. n is sample size, -logL is negative log likelihood, shape, scale, and location are fitted parameters for the GEV probability distribution.  n -logL Shape Scale Location  dN (% yr-1) All data 2565 4059 0.29 0.85 0.85  dt = 5 713 1147 0.23 0.91 0.90  dt = 10 581 735 0.11 0.69 0.91  Msw (% yr-1) All data 2565 1541 0.67 0.26 0.21  dt = 5 713 366 0.78 0.23 0.17  dt = 10 581 286 0.43 0.27 0.27  4.4.2 Correlation analysis Partial correlation analysis indicated that all tested independent variables exhibited significant control on stand-level mortality of Douglas-fir, despite overall low magnitude of the correlation coefficients (Tables 4.2 and 4.3). As expected, N had the strongest influence on dN. Other tested intrinsic variables (with the exception of A) also influenced dN, implying considerable overall complexity in intrinsic controls. When a combination of extrinsic factors were simultaneously considered, their partial correlations were not significant with the exception of MSWD. dN was consistently correlated with each tested environmental variable (Table 4.3). The strongest correlations were with the derived variables, MSWD, ET, and CMI. Correlation with Gsw differed between demographic and gravimetric mortality, being positively correlated with dN and negatively correlated with Msw. Somewhat surprisingly, Msw was correlated with A and Csw, but not Csw, suggesting that setting gravimetric mortality as a constant proportion of Csw would overestimate Msw as stands transition out of the stemexclusion phase. Msw was also not correlated with extrinsic variables when they were simultaneously considered with the exception of MSWD. Tested in isolation, only T and Δe 80  exhibited significant correlation with Msw and both coefficients were extremely weak (Table 4.3). The PMET parameter was inversely correlated with Gsw (Table 4.2). PMET was also negatively and positively correlated with ET and CMI, respectively (Table 4.3). As a conservative approach to partitioning extrinsic controls from self-thinning, Eq. 4.1 was fitted to each individual plot record, excluding plots with fewer than four census intervals. The models were assumed to account for all intrinsic factors controlling dN and by (potentially over-) fitting to each plot, the method avoided the error in model predictions that would be expected from poor knowledge of initial N, and a MDBL that is representative of resource availability for each plot. The fitted models were used also to translate dN into Msw using a fixed PMET of 0.40, equivalent to the average estimate of PMET for all plots. The residuals for dN and Msw were then compared with deviations from long-term normal summer climate variables to further understand the behaviour of the relationships suggested in Table 4.3. When Eq. 4.1 was fitted to each plot, residual variance was largely positive, indicating increases in dN that were unaccounted for by the self-thinning trajectory. Negative values did occur, but in much less abundance, suggesting that fitting the self-thinning curves to the trajectory at individual plots has a natural tendency to assume the upper boundary of the trajectory. As a consequence, relationships with most environmental variables exhibited a strong degree of nonlinearity (Figure 4.3 to 4.6). As the signals are expressed by sample quantiles, the level of explained variance cannot be inferred from the figures. Values express the sample when plots with fewer than four census interval measurements were excluded. 81  Table 4.2 Partial correlation analysis of tree mortality in permanent sample plots of coastal Douglas-fir (n = 621 plots, 2623 interval measurements). Correlations are shown for relationships between dependent variables: demographic mortality (dN); gravimetric mortality (Msw); and the proportional mass of expiring trees (PMET); and independent variables: Stand age, A (years); the difference between potential and actual stemwood carbon, Csw; summer (June-July-August, JJA) air temperature deviation, T (˚C), summer vapour pressure deficit deviation, Δe (hPa); summer precipitation, P (mm month-1), 3-PG model predictions of evapotranspiration, ET (mm month-1), climate moisture index using 3-PG model predictions of ET, CMI (mm month-1), maximum soil water deficit from 3-PG model predictions (MSWD). Significant correlation coefficients at the 99% confidence level are shown in bold.  A N Csw Csw Gsw T Δe P ET CMI MSWD  dN (stems yr-1) r P -0.02 0.328 0.38 <0.001 -0.13 <0.001 0.18 <0.001 0.05 0.008 0.04 0.015 0.02 0.384 0.00 0.954 0.05 0.042 -0.05 0.055 -0.09 <0.001  Msw (Mg C ha-1 yr-1) r P -0.12 <0.001 -0.06 0.004 0.03 0.188 0.14 <0.001 -0.09 <0.001 0.04 0.103 0.02 0.063 0.02 0.330 0.05 0.042 -0.05 0.055 -0.06 0.008  PMET r -0.03 0.04 0.05 -0.06 -0.13 0.00 -0.01 -0.00 0.00 0.00 -0.056  P 0.099 0.035 0.030 0.003 <0.001 0.697 0.495 0.965 0.933 0.972 0.016  Based on visual comparison excluding plots with fewer than three or five census intervals had only a minor, random effect on the magnitude of relationships, suggesting that the presented relationships were robust with respect to this processing step. After inspecting the relationships, linear-threshold functions were fitted to the samples, as opposed to linear or quadratic functions, in order to evaluate the relationships. Curves were fitted according to the ordinary least-squares criterion for nonlinear regression (Table 4.4). Parameter estimates were only meant for exploratory purposes and development of suitable priors for use in more 82  sound methods of optimization, given several violations of the least-squares method. Parameter uncertainty was therefore intentionally omitted.  Table 4.3 Partial correlation analysis for the relationship between demographic (dN) and gravimetric tree mortality (Msw) and environmental variables in permanent sample plots of coastal Douglas-fir. Each partial correlation coefficient indicates the relationship when intrinsic factors (A, N, Csw, Csw) are simultaneously considered, but no other environmental variables are considered. Significant coefficients are shown in bold.  T Δe P ET CMI MSWD  dN (stems yr-1) r P 0.14 <0.001 0.16 <0.001 -0.11 <0.001 0.22 <0.001 -0.20 <0.001 -0.23 <0.001  Msw (Mg C ha-1 yr-1) r P 0.07 <0.001 0.07 0.001 0.01 0.710 0.04 0.058 -0.01 0.587 -0.05 0.011  PMET r -0.00 -0.01 0.01 -0.12 0.06 0.04  P 0.840 0.540 0.807 <0.001 <0.001 0.087  Table 4.4 Linear-threshold model parameters derived from fits to permanent inventory measurements of demographic and gravimetric tree mortality in coastal Douglas-fir. T Δe (˚C) (hPa) -1 -1 Absolute dN (stems ha yr ) b1 13.65 11.63 b2 -0.59 -0.62 Relative dN (% yr-1) 0.90 b1 0.93 b2 -0.46 -0.38 -1 -1 Absolute M (Mg C ha yr ) 0.27 b1 0.41 b2 -0.31 -0.41 Relative M (% yr-1) 0.33 b1 0.39 b2 -0.33 -0.32  P (mm month-1)  ET (mm month-1)  CMI (mm month-1)  MSWD  -1.64 0.08  8.09 -0.72  -1.07 5.30  -146.43 0.04  -0.07 1.65  0.28 -1.37  -0.06 5.49  -6.99 0.48  -0.03 1.27  0.09 -1.43  -0.02 3.19  -2.25 0.05  -0.03 1.33  0.12 -1.03  -0.02 2.70  -2.51 0.04  83  15 10 5  (b)  20 15 10 5  20  10 5 0  −5  −5  −5  0.25  0.5  −0.4  0  −16 −12  15 10 5  (e)  30  25 20  25  15  20  10 5  0  −5  −5  1 −1  2  3  4  −16 −12  −8  −4  0  8  4 −1  CMI (mm month )  8  (f)  5  −5 0  4  10  0  ET (mm month )  0  15  0  −6 −5 −4 −3 −2 −1  −4  −1  −1  30  −8  P (mm month )  yr )  −1  20  0.8  dN (stems ha  −1  25  (d) dN (stems ha−1 yr−1)  30  0.4  Δe (hPa)  −1  0  (c)  15  0  T (°C)  yr )  25  0  −0.5 −0.25  dN (stems ha  −1  yr )  30  25  −1  30  dN (stems ha  (a) dN (stems ha−1 yr−1)  −1  20  dN (stems ha  25  −1  yr )  30  −0.15 −0.1 −0.05  0  0.05  0.1  MSWD  Figure 4.3 Relationships between residual absolute demographic mortality (dN) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD). Each symbol indicates one of nine sample quantiles (i.e., 1/9th of the dataset, ordered by the independent variable; see Wilks 1995).  The residual variance was herein described as density-independent tree mortality. Visual inspection of the sample quantiles indicated that relationships were consistently the strongest with the derived variables, ET, CMI, and MSWD, rather than T, Δe, and P. Only in rare instances were sample quantiles negative. Relationships were generally stronger for dN than for Msw. For both tested dependent variables, there was a consistent response to ET, increasing linearly above a sharp threshold of approximately -1.0 mm month-1 relative to the 1971-2000 normal ET. Density-independent mortality increased linearly with below-normal 84  levels of summer P. In all cases, the threshold was not as clear because of low levels of mortality that persisted at high P, providing a strong indication that other factors cause mortality even when P is above normal. Relationships with CMI and MSWD were also strong, only with reciprocal sign and slightly lower relative magnitude than ET, alone.  1.6  1.6  (a)  0.4 0  −1  yr )  0.8  −1  0.8  1.2  dN (% ha  −1  −1  (c)  1.2  dN (% yr )  1.2  dN (% yr )  1.6  (b)  0.4  0  −0.4 −0.5 −0.25  0  0.25  −0.4  0.5  −0.4  0  0.4  0.8  −16 −12  Δe (hPa)  T (°C) 1.6  0  −1  0.8 0.4  0.4 0  −0.4 0  1  ET (mm month−1)  2  3  4  8  0.8  0  −0.4 −6 −5 −4 −3 −2 −1  4  1.2  dN (% yr )  −1  dN (% yr )  0.4  0  (f)  1.2  0.8  −4  1.6  (e)  1.2  −8  P (mm month−1)  1.6  (d)  −1  0.4  0  −0.4  dN (% yr )  0.8  −0.4 −16 −12  −8  −4  0  4  8  CMI (mm month−1)  −0.15 −0.1 −0.05  0  0.05  0.1  MSWD  Figure 4.4 Relationships between residual relative demographic mortality (dN) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD).  85  0  −0.2  −1  M (Mg C ha  M (Mg C ha  0.2  0.2  0  −0.2 −0.5 −0.25  0  0.25  −0.4  0  0  0.8  −16 −12  −0.2  0.6 −1  yr )  (e)  0.4  (Mg C ha  0.2  0  −0.2 1 −1  ET (mm month )  2  3  4  0  4  8  −1  (f)  0.4  0.2  0  sw  0  −4  M  0.2  −8  P (mm month )  −1  −1  yr ) M (Mg C ha  M (Mg C ha  0.4  −1  0.4  −1  −1  yr )  0.6  0  0.2  Δe (hPa)  (d)  −6 −5 −4 −3 −2 −1  0.4  −0.2  0.5  T (°C) 0.6  (c)  −1  −1  yr )  0.4  −1  0.4  0.6  (b) yr )  0.6  (a)  M  sw  (Mg C ha−1 yr−1)  0.6  −0.2 −16 −12  −8  −4  0  4  8  −1  CMI (mm month )  −0.15 −0.1 −0.05  0  0.05  0.1  MSWD  Figure 4.5 Relationships between residual absolute gravimetric stem mortality (Msw) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD).  86  0.2 0  0.6 −1  0.4 0.2 0  −0.2  −0.2 −0.5 −0.25  0  0.25  −0.4  0  0.4  0  0.8  −16 −12  0.6  −1  0.2  (e)  0.6  0.4 0.2  0  −0.2  −0.2  −0.2  0  1 −1  2  3  4  −16 −12  −8  −4  0  4  8  4  (f)  0.2  0  ET (mm month )  0  0.4  0  −6 −5 −4 −3 −2 −1  −4  −1  −1  0.4  −8  P (mm month )  M (% yr )  (d)  M (% yr )  (% yr−1)  0.2  Δe (hPa)  M  sw  0.4  −0.2  0.5  T (°C)  0.6  (c)  −1  −1  M (% yr )  0.4  (b) yr )  0.6  M (% ha  (a)  M  sw  (% yr−1)  0.6  8  −1  CMI (mm month )  −0.15 −0.1 −0.05  0  0.05  0.1  MSWD  Figure 4.6 Relationships between residual relative gravimetric stem mortality (Msw) and deviations from long-term normal summer (June-July-August) environmental conditions in inventory plots of coastal Douglas-fir: (a) temperature (T) (b) vapour pressure deficit (Δe); (c) precipitation (P); (d) evapotranspiration (ET); (e) climate moisture index (CMI); (f) maximum soil water deficit (MSWD).  Inspection of the sample-average time series indicated an absence of long-term trends in total dN over the 1959-1998 study period and decadal variability with a coefficient of variation of 45% (Figure 4.7a-b). Analysis of the density-dependent and -independent components of tree mortality suggested that the sample underwent changes in the case of demographic tree mortality, expressing a long-term negative trend in density-dependent dN and larger decadal variability in density-independent variability. In absolute units, the sample-average dN clearly transitioned from being dominated by density-dependent mortality to densityindependent variability during the early 1980’s, corresponding with a mean stand age of 87  approximately 70 years (Figure 4.7a). Temporal patterns (and the relative contributions of each component) differed when analyzing them in relative units (Figure 4.7b). In relative units, density-dependent mortality was also in a state of decline, but with lesser relative magnitude. The partitioning method indicated that sample-average density-independent dN was negative for a brief period during the early 1970’s, which must be viewed as an artifact of the way it was defined and quantified rather than a physically-meaningful phenomenon. One possible explanation for the artifact is that the thinning curves all tend to underestimate the normal trajectory at a specific stage of the stem-exclusion phase, in this case corresponding to a stand age of 62 years. An alternative explanation is that negative estimates reflect the complementary relationship between components (Clark 1992; Güneralp and Gertner 2007). In this case, the negative estimates were preceded by a distinct spike in mortality that affected both absolute and relative dN and was attributed to densityindependent factors, which could feedback on following density-independent mortality rates by alleviating competition for resources. The magnitude of the partition was not sensitive to the processing step of excluding plots with too few census interval measurements, however, it is interesting to note that estimates from the fitting models are unrealistically low due to outliers in dN (i.e., extreme mortality events), this would systematically affect the zeroboundary of the time series. Unlike dN, estimates of the density-dependent component of Msw remained relatively stable (increasing insignificantly) over the analysis period, while the density-independent component increased by a total of 0.45 Mg C ha-1 yr-1 between the early 1970’s and late 1990’s. This reflects a major distinction between patterns of demographic and gravimetric tree mortality as they relate to stand development: As stands move through the stem88  exclusion phase, the demographic substrate decreases, while the gravimetric substrate increases and potential rates of dN and Msw should decrease and increase accordingly. This makes it very difficult to interpret estimates of the contemporary transient sensitivity to extrinsic forcing from the sample (discussed further below).  (a)  2.0  (b)  30 1.6  25  dN (% yr−1)  dN (stems ha−1 yr−1)  35  20 15 10  1.2 0.8 0.4  5 0  0  −5 1960 1965 1970 1975 1980 1985 1990 1995  1960 1965 1970 1975 1980 1985 1990 1995  Time, years  Time, years  1.2  1.0  (d) Msw (% yr−1)  0.8  0.8 0.6 0.4  0.6  0.4  M  sw  (Mg C ha−1 yr−1)  (c) 1.0  0.2  0.2 0  0 1960 1965 1970 1975 1980 1985 1990 1995  Time, years  1960 1965 1970 1975 1980 1985 1990 1995  Time, years  Figure 4.7 Annual time series of sample-average tree mortality in stands of coastal Douglasfir expressed as (a-b) absolute and relative demographic mortality (dN), respectively and (cd) absolute and relative gravimetric mortality (Msw). Thick upper curves express total mortality derived from observations. Thin, solid curves express estimates of densityindependent component of mortality. Thin, broken curves express density-dependent component (calculated as the residual).  89  4.4.3 Multivariate statistical models Starting with a model based on cubic functions of A, Csw, and N (Eq. 4.4 and 4.5), various different combinations of polynomial orders were tested. The model with cubic expression of all three variables (Model 1) explained just 0.04 % of the variation observed in dN (Table 4.5) and predictions of the sample-average annual time series were not significantly correlated with observations (r = 0.2). It is interesting to note that even with cubic expression of each variable, multivariate statistical model predictions were always correlated with the explanatory variables. It is uncertain to what extent this reflects a failure of the simplex search method to find a global minimum, or a failure to account for unmodelled variability, for example, relating to interactions between driving factors. As expected, model residuals were significantly correlated with individual environmental variables (Table 4.5). Correlations for T and Δe were only slightly greater than from partial correlation analysis, as would be expected by accounting for variation due to intrinsic factors. Through trial and error, a slightly improved performer with fewer parameters could be developed by dropping cubic expressions of A and N in place of linear and quadratic functions (Model 2 in Table 4.5). However, this did not eliminate dependence between model residuals and independent variables. Parameters from Model 2 were adopted as the initial parameter estimates for intrinsic functions, while the equations calibrated in Table 4.4 were used as initial parameters for the extrinsic functions in subsequent models with added representation of environmental controls. Again through trial and error, the best model with representation of environmental variables consisted of one driven with linear-threshold functions of P and ET (Model 3 in  90  Table 4.4). The AIC value for models with environmental representation were always higher than that of Model 2, reflecting negligible improvement in the capacity to predict collective variability at plots and the cost associated with added parameters. General behaviour of Model 2 during prognostic simulations is illustrated in Figure 4.8 for five different initial values of N and a fixed PMET of 0.40. The age response of Msw closely resembles that of observations, increasing gradually from stand age 20, reaching a broad peak at approximately 100 years and declining gradually towards zero by 250 years (Figure 4.8a), which leads to a smooth reduction in Psw from that of Gsw. The half-oval shape of the age response closely resembles the theoretical response of density-dependent mortality in more sophisticated theoretical models (Clark 1992). In contrast to typical observations in plots with young stand ages, the model did not express the initial phase of low dN prior to the onset of thinning (Franklin 1987). Additional testing suggested that this might be represented by including quadratic interaction between N and either A, Csw, or Csw. At high initial N, Csw approaches Csw at a slower rate and therefore at older stand ages (Figure 4.8c). At an initial N of just 1000 stems ha-1, stands do not intersect the MDBL until approximately 100 years, while at 5000 stems ha-1, stands reach the MDBL at 50 years. In the absence of density-independent mortality, N reaches asymptotes between 150 and 250 years after initiation (Figure 4.8d).  91  5000  (a)  (b)  3  GGsw  2.5  N (stems ha−1)  Fluxes (Mg C ha−1 yr−1)  3.5  Net Psw  2 1.5 1  Msw M  4000  5000  3000  4000 3000  2000 2000 1000  1000  0.5 0  0 0  50  100  150  200  250  0  100  Stand age, years  200  300  400 −1  500  200  250  Stemwood carbon (Mg C ha ) 4500  (c)  (d)  4000 3500  0.6  N (stems ha−1)  0.8  5000 4000  0.4  3000  s  C ′ (Mg C ha−1)  1  2000 0.2  3000 2500 2000 1500 1000  1000  500  0  0 0  20  40  60  80  Stand age, years  100  0  50  100  150  Stand age, years  Figure 4.8 General patterns of behaviour from Model 1 driven with average stemwood growth (Gsw) for a stand with site class 30 and five different initial stand densities (stems ha1  ) (a) age responses of gravimetric mortality (Msw) and net stemwood production (“Net”) (b) relationship between tree density (N) and stemwood carbon (Csw) (c) relationship between competitive mass index (Csw) and stand age (d) relationship between N and stand age.  The optimization of Model 3 did not substantially alter the initial parameter estimates describing linear-threshold functions of ET and P. For ET, the slope parameter declined from 0.28 to 0.25 % mm-1 and the threshold ET level decreased from -1.37 to -3.27. This was compensated by a change in the slope of the P-effect, decreasing from -0.07 to -0.10 % mm-1. The threshold P declined from 1.65 to -3.26. Together, the changes imply a slight increase in the effect of P relative to that of ET compared with earlier estimates from the single-variable models. The AIC for Model 3 was only slightly higher than for models driven with only CMI 92  and MSWD, yet Model 3 was selected because it exhibited the highest correlation with the sample-average observed time series of dN (r = 0.95, P < 0.01), which expressed marked improvement over Model 1 and Model 2 and slight improvement over other candidate models based on CMI or MSWD (Figure 4.9).  Table 4.5 Description of predictive skill for tested multivariate statistical models of relative demographic tree mortality (dN) in stands of Douglas-fir (n = 17190 intervals): residual sum of squares (RSS); Akaike’s information criterion (AIC); correlation between model residuals and stand age, r(A), competition index, r(Csw), stand density, r(N), summer temperature, r(T), summer vapour pressure deficit, r(Δe), summer precipitation, r(P), and the correlation between observed and predicted sample-average dN, spanning 1959-1998, r(dN). Bold correlation coefficients mark significance at the 99% confidence level. Header subscripts indicate polynomial order or threshold.  P R2 RSS AIC r(A) r(Csw) r(N) r(T) r(Δe) r(P) r(dN)  Model 1 f(A3) f(N3) f(Csw3)  Model 2 f(A1) f(N2) f(Csw3)  < 0.001 0.042 40087 15671 -0.06 -0.04 -0.07 0.17 0.19 -0.04 -0.20  < 0.001 0.049 39129 14143 -0.09 -0.05 -0.06 0.15 0.17 -0.06 -0.06  Model 3 f(A1) f(N2) f(Csw3) f(ETth) f(Pth) < 0.001 0.050 3908 14289 -0.07 0.12 0.12 -0.01 -0.00 0.07 0.95  93  2.0  dN (% yr−1)  1.5  1.0  0.5 Observations Model 2 (without climate) Model 3 (with transient climate) Model 3 (with fixed pre−industrial climate) 0 1960  1965  1970  1975  1980  1985  1990  1995  Time, years  Figure 4.9 Comparison between observed and predicted sample-average periodic annual demographic tree mortality (dN) at inventory plots of coastal Douglas-fir. Model 2 is driven with intrinsic factors only. Model 3 is driven with a combination of intrinsic factors and linear-threshold functions of summer evapotranspiration (ET) and precipitation (P). For demonstrative purposes, Model 3 simulations were run, first, with actual transient time series of ET and P and, second, with fixed levels of ET and P set to pre-industrial levels (defined as the averages for the first 30-year base period (1901-1930) in the available record.  Running Model 3 with ET and P set fixed to pre-industrial conditions indicated that densityindependent tree mortality accounted for a small proportion of total dN during the 1970’s minima, which was slightly higher than previously discussed estimates using a different method (Figure 4.7). It is also apparent from Figure 4.9 that intrinsic factors, alone, in Model 2 failed to represent decadal variability in the observations. By not accounting for extrinsic factors, the model compensates by systematically increasing density-dependent mortality. Resulting predictions exhibited less long-term negative trend in comparison with Model 3 or the earlier partitioned estimate perhaps also in compensation. 94  4.4.4 Climate sensitivity Analysis of the relationships between sample-average annual time series of tree mortality and environmental variables suggested a strong coherence between multi-annual and decadalscale variations (Figure 4.10). The density-independent component of absolute dN varied with drought events, characterized by consecutive years with below-normal summer P. The onset of the episodes corresponded with the intense warm events of the El Niño Southern Oscillation (ENSO) pattern of atmosphere-ocean circulation during the winters of 1964-65 and 1982-83. These two events are noted for their unusual, albeit discontinuous, duration (Trenberth 1997). In coastal British Columbia, the events triggered declines in summer P that enhanced dN by approximately 9 stems ha-1 yr-1 above background levels for the duration of the droughts. The relationship between dN and P was less apparent when P was above the 1971-2000 normal level, consistent with use of linear-threshold functions. These results are consistent with previous links between dN and anomalous weather patterns during ENSO warm events in the tropics (Condit et al. 1995; Williamson et al. 2000), characterized by abrupt spikes above normal rates. In contrast, density-independent Msw along with background rates of dN appeared to vary more with summer ET rather than P. The two variables were tightly correlated with the exception of 1959 and 1960, which could be due to reduced number of plots in the sample. The relationship also diverged during the 1960’s drought perhaps reflecting the added impact of low P. Although there was no apparent divergence during the mid-1980’s drought, comparison between Msw and summer T (which very closely corresponded with ET) exhibited a divergence similar to that between Msw and ET during the 1960’s. It is worth  95  noting that the relationship between sample-average Msw and summer T was slightly stronger than that of ET despite diminished signals between mortality and T in earlier analyses.  35  1964−65 El nino  10  20 15  5  10  0  5 −5 −10  0.8  2.5  0.7  2.0  0.6  1.5  0.4  M (Mg ha  −1  −5  −1  yr )  0  0.5  JJA P (mm month−1)  15  25  1.0 0.5 0  0.3  −0.5  0.2  −1.0  0.1  −1.5  0  −2.0  −0.1  JJA ET (mm month−1)  dN (trees ha  −1  −1  yr )  30  20  1982−83 El nino  −2.5 1960  1965  1970  1975 1980 1985 Time, years  1990  1995  Figure 4.10 Temporal patterns of tree mortality in coastal Douglas-fir: (top left, triangles) density-independent demographic tree mortality (dN); (top right axis, diamonds) deviation from long-term normal summer (June-July-August; JJA) precipitation (P); (bottom left axis, circles) density-independent gravimetric tree mortality (Msw); (bottom right axis, squares) deviation from long-term normal summer evapotranspiration (ET).  Additional analysis was conducted to gain further understanding of which variable was most responsible for controlling dN. Separating the drought responses of absolute dN to MSWD at high and low levels of ET indicated that dN was more sensitive to MSWD at high ET than at low ET (Figure 4.11a). Conversely, the responses to MSWD at high and low T were  96  approximately equivalent (Figure 4.11b). Extreme soil water deficits affected dN equivalently during periods of low T as during periods of high T. Although uncertainty arises due to reduced sample size during periods of low MSWD when ET and T are also low, the different behaviours suggest that ET, rather than T, was the driving variable.  40  dN (stems ha−1 yr−1)  35  (a)  30 High ET 25 20 15 10 5 Low ET 0 −5  dN (stems ha−1 yr−1)  35  (b)  30 25 20 15  High T  10 Low T 5 0 −5 −0.15 −0.10 −0.05  0  0.05  0.10  0.15  MSWD deviation  Figure 4.11 Modulation of the relationship between demographic tree mortality (dN) and maximum soil water deficit (MSWD; dimensionless) by deviations from (a) normal summer evapotranspiration (ET) and (b) temperature (T).  Regressing sample-average annual relative Msw against ET suggested a linear relationship that was modulated by MSWD (Figure 4.12). The responses converged at low ET, suggesting that trees were more resilient to low MSWD when ET was also low, as exemplified by the  97  drought years 1972 and 1977. It is interesting to note that summer P was not exceptionally low during those years, however, I believe these types of discrepancies may occur due to a combination on nonlinearities in the relationship, aggregation to periodic census intervals, and intra-regional variability. It is clear from Figure 4.12 that the frequency of severe soil water deficits declined over the study period and they were entirely absent from the 1990’s, making it difficult to fully constrain the interaction between MSWD and ET at high ET.  0.6  1966 1965 0.5  1967 1968 0.4  1969 1970  M (% yr−1)  1963  1964  0.3  1998 1999 1987 1988 1996 1995 1985 1986 1997 1989 1994 1984 1990 1992 1991 1983 1982 1981  0.2  1971  1979  1980  1978  0.1  1972 1973 0  1976 1974 1975  −0.1 −0.08  −0.06  1977  −0.04  −0.02  0  0.02  0.04  0.06  −1  ET (mm d )  Figure 4.12 Relationship between sample-average (n = 621) annual relative gravimetric mortality (Msw) and deviations from long-term normal summer evapotranspiration (ET) at three levels of maximum soil water deficit (MSWD) including (blue squares) wet soil (green diamonds) moderate soil moisture and (red circles) dry soil predicted with the 3-PG model.  98  4.5 Discussion 4.5.1 Drought-induced mortality waves Early summaries on forest succession exclusively attributed mortality during the stemexclusion and transition to steady-state phases of stand development in evergreen coniferous forests to competition and extrinsic factors, including wind, lightning, ice damage, and disease without any mention of drought impacts (Peet and Christensen 1987; Franklin 1987). To further understand the extent of drought-induced tree mortality, measurements of tree mortality at 621 plots dominated by coastal Douglas-fir were used to derive components of tree mortality and relationships with both intrinsic and extrinsic factors. The majority of stands in the sample were transiting through the stem-exclusion (or self-thinning) phase of stand development (Peet and Christensen 1987). Methods were therefore devised to partition total mortality into density-dependent and density-independent components. Consistent with conventional understanding of forest succession, self-thinning was a major component of tree mortality, but led to approximately constant rates of Msw through time, while density-independent processes linked with drought stress led to additional wave-like fluctuations, constituting the primary source of variation in Msw at the regional scale. Results are consistent with earlier findings, suggesting that demographic mortality rates in oldgrowth stands doubled within the study area over a similar time period (van Mantgem et al. 2009) and provide additional insight to suggest that this phenomenon extends to younger successional stages and also translates into approximately equal relative effects on gravimetric mortality. Van Mantgem et al. (2009) wisely analyzed a sample specifically designed to avoid directional succession so as to minimise its influence over trends. This is a  99  legitimate concern that applies to the current study. Nevertheless, efforts to isolate drought sensitivity and its effects on the C balance, demonstrated here, showed considerable promise to overcome these challenges. In contrast to the doubling in old-growth stands, absolute dN remained stable over the study period in these younger stands, but only because of compensating trends in density-dependent and -independent components. In absolute terms, Msw more than doubled between the 1970’s and mid-1990’s. Findings from van Mantgem et al. (2009) and this study, together, present strong evidence of increasing regular tree mortality in coastal forests of western North America in response to drought. These results underscore the possibility that seemingly stochastic behaviour of tree mortality in stand-density management diagrams – and treatment as such in models – may be practically represented by a density-dependent component and an independent component affected by drought variables.  4.5.2 Driving mechanisms and climate sensitivity The two main hypotheses to explain drought-induced plant mortality include carbon starvation and hydraulic failure (McDowell et al. 2008; Adams et al. 2010). Relationships with ET and MSWD suggest that drought-induced tree mortality arises directly from water stress originating in the atmosphere and the soil root interface. Background rates of Msw appeared to be a strong linear function of summer ET above a specific threshold (McDowell et al. 2008; Phillips et al. 2010), while the response was strongly modulated by MSWD (Figure 4.12). Based on experimental manipulation of T under equivalent water regimes, Adams et al. (2009) found that high T imposed increased mortality risk, attributed to carbon starvation through a combined enhancement of autotrophic respiration and stomatal closure. 100  For field observations such as those used here, it is difficult to directly assess the specific role of autotrophic respiration in exacerbating carbon starvation. Separating the relative contributions of carbon starvation and hydraulic failure is also challenging, as observations of increasing sensitivity to ET with decreasing MSWD applies equally to both theories. This can lead to overall declines in plant water potential, apparently capable of exerting significant ‘non-stomatal’ effects on photosynthetic metabolism (see Chapter 6) as a cause of carbon starvation, or potentially result in xylem cavitation (McDowell et al. 2008; Adams et al. 2009). However, these mechanisms may be so tightly related that they need not necessarily be distinguished in the next generations of inventory-based and dynamic global vegetation models. This research marks novel quantitative analysis linking mortality rates with direct environmental stresses on plant physiology. Doing so requires use of complex variables that are ‘derived’ from process-based models. Although it would be ideal to report the contemporary sensitivity of mortality to ET or MSWD for quantitative comparison with similar studies conducted in other regions, further efforts are required to ensure the accuracy of the derived variables in addition to estimates of mortality. The historical positive trend in summer ET estimated by the 3-PG model (0.13 % yr-1) was approximately half of that reported for EALCO land surface model simulations at meteorological stations in the Pacific coastal region (0.30 % yr-1) for the period between 1960 and 2000 (Fernandes et al. 2007). The difference may reflect an absence of forcing by transient variability of solar irradiance (excluded from the 3-PG model simulations here), which apparently increased over the test period (Fernandes et al. 2007). In the event that recent trend in ET was indeed  101  underestimated by 50% by the 3-PG model, this will greatly exaggerate estimates of contemporary sensitivity. The strength and clarity of the relationship between mortality and ET (as well as CMI and MSWD – which both depend on ET) makes a strong case that there are advantages to explicitly considering environmental and biological controls on the water balance in forest ecosystems with physically-based algorithms. Undocumented analyses suggest that relationships with potential evapotranspiration calculated with the Thornthwaite-Mather equation (Rosenberg 1983) did not perform as well as any of the variables tested here, including only T. Future simulations should presumably continue to consider mortality models forced with ET, P, and MSWD to see how each method influences sensitivity to climate change scenarios. Studies seek to identify the thresholds that lead to extensive dieback and regional die-off events (McDowell et al. 2008). Here, evidence of a threshold was found, describing the sensitivity of regular tree mortality in coastal Douglas-fir very close to its recent (1971-2000) normal summer levels of ET and P. The extent to which the thresholds reflect universal levels for the species is confounded by the general properties of the sample, including directional succession and increases in Gsw (Chapter 3). Future analysis with the model, in practice, allows estimation of conditions that exceed the threshold for regional-scale dieback of the species, although as discussed earlier the exact amount of drought-induced tree mortality that constitutes catastrophic rates (or dieback) in our study area is not well defined. Coastal Douglas-fir was likely an ideal candidate for elucidating such relationships and may explain the strong model fit (Figure 4.9), as the species is noted for its longevity and were 102  located primarily in the low-lying rainshadows of the Strait of Georgia, more protected from wind storms than the windward coasts, which could conceivably mask relationships with drought. An alternative explanation could be that wind storms are active in the sample, but that drought is the mechanism that kills the trees, or diminishes health making them susceptible to wind storms.  4.5.3 Modelling drought-induced mortality in 3-PG The main disadvantage of empirical forest yield models is that they are not responsive to the underlying causes of productivity and cannot, therefore, be used as reliable forecast tools (Schwalm and Ek 2001; Monserud 2003). Results here reinforce that claim by showing quantitatively that regional-scale tree mortality is highly sensitive to environmental change, typically not accounted for in empirical models. Typical of permanent forest inventory measurements, relationships with environmental variables conveyed a high degree of statistical confidence, yet with extremely poor predictive skill, such that additional representation of environmental sensitivity in forest C cycle models cannot be expected to greatly improve model precision across landscapes, yet can be critical in achieving temporally unbiased regional-scale predictions. A major strength of permanent forest inventory plot networks is their sample size, which is important in overcoming otherwise prohibitive noise levels. An important feature of the widely-applied 3-PG model is that tree mortality is restricted to self-thinning and also that the self-thinning submodel is related to Gsw only to the extent that Gsw accelerates the rate at which the stand approaches the MDBL. The MDBL is fixed at a biological maximum for a given species. The Csw 1000 parameter for Douglas-fir is quite high 103  (at least 350 Mg DM ha-1), yet needs to be set much lower to simulate unbiased rates (Waring and McDowell 2002). In reality, part of the discrepancy reflects site-specificity in the MDBL associated with landscape variation in resource competition and asymmetry in the distribution of trees within stands (Weiskittel et al. 2010). Yet, the MDBL was likely set constant in 3-PG by design due to a general lack of such studies and consequent subjectivity in setting Csw 1000 (Weiskittel et al. 2010). As a practical means of trying to separate densitydependent and -independent mortality, this study perceived drought as a factor causing the latter component. Yet, evidence of the perturbation in mortality, starting and ending abruptly with periods of below-normal P, would be equally consistent with the interpretation that drought modulates the MDBL in accordance with change in resource (i.e., soil water) availability. Yet, the current study proposes that added complexity in the representation of intrinsic factors (which effectively make the MDBL dynamic) will not necessarily improve the precision of model predictions at the level of individual stands. Moreover, it is unclear how inverse dependence of tree mortality on Gsw, or positive dependency on basal area, in treelevel models (e.g., Hamilton 1987) would be able to predict increases in tree mortality in the Douglas-fir sample when evidence presented in Chapter 3 suggests that regional-scale Gsw also increased. Analysis of this dataset supports the strong inverse relationship between Gsw and Msw (or Gsw and MDBL) (not shown). Hence, would inverse dependency on Gsw not force a decline in Msw? The only way such models could predict increasing in Msw is if growth enhancement led to increased basal area (or some equivalent indicator of competitive stress) and increased basal area translated into increased Msw. Yet, most models only represent growth enhancement to the extent that they are continuously re-calibrated. The 104  latter connection was not explored here, but represents a potentially important negative feedback on net stemwood production worth further consideration. Chapter 3 outlined statistical models of Gsw based on adjustment of age-response functions, or age-class productivity curves. This study also developed a model of Msw based on direct empirical relationships rather than one indirectly driven indirectly with prognostic simulation of dN, leaving both as options for future development and coupling with the above age-class productivity curves developed in Chapter 3. The direct empirical model of Msw is straightforward and easy to apply, yet lacks the sophistication of explicitly linking biomass losses with population dynamics, as done in 3-PG. The latter approach is favourable in longterm future simulations, as recruitment requires additional consideration. Modelling efforts were restricted to the use of climate anomalies (i.e., deviations from normals) as predictor variables largely because the forest inventories in southwest BC did not span a sufficient range of climatic conditions to identify relationships as they exist over space with statistical confidence. Merging the dataset with permanent forest inventories from the western U.S. Forest Service could alleviate this restriction. While drought-sensitive multivariate statistical models of dN showed a strong capacity to match the observed time series (Figure 4.9), no formal attempt to validate the model was attempted, focusing instead on calibrating the models and gaining a basic understanding of their behaviour. Future validation efforts might consider attempting to reproduce, using two submodels of Gsw and Msw, across-plot variation in long-term enhancement of net stemwood production (as in Chapter 3) using a subsample of plots with stands that were established after the onset of long-term meteorological station records. 105  4.5.4 How does drought-induced tree mortality affect the C balance Simply running the drought-sensitive model (i.e., Model 3) in prognostic simulations for the sample suggests that it has limited capacity to reproduce specific features of the relationship between N and Csw (Figure 4.13). In particular it appears difficult to reproduce the exact curvature observed as stands develop during the stem-exclusion phase. This is partially due to error in setting initial N to the first measurement of N at each plot and adding 200 stems ha-1 as a simple approximation. In the observations, dN declines as loss of N feeds back on the system, while this is not well represented by the model.  2500 Observations Model (1990s climate) Model (pre−industrial climate)  34 2000  N (stems ha−1)  49 1500 59 69 1000  80 92  500  124  Density inhibition boundary line  0 0  50  100  150  C  sw  200  250  300  350  400  (Mg C ha−1)  Figure 4.13 Comparison between trajectories of stand tree density (N) and stem carbon (Csw) at seven sample quantiles of stand age in coastal Douglas-fir. Differences between simulated trajectories reflect two extremes in evapotranspiration and precipitation representative of preindustrial and 1990’s climate.  106  A paradigm in stand density management is that yield (e.g., Csw) is independent of N over a broad range of N, which implies that self-thinning should have a negligible effect on Csw. Evidence that density-independent factors account for approximately 50% of total mortality, however, raises the question of whether the density-independence of yields is true during the stem-exclusion phase. If environmental conditions had remained favourable over the study period, would sample-average Csw be higher for a given stand age than it actually is under transient climate? This question is central to C management, but difficult to determine from the sample. By virtue of its simple design, Model 3 indicates that drought can theoretically regulate Csw. This is exemplified by running the model under current and pre-industrial drought regimes (Figure 4.13), which led to a difference of approximately 40 Mg C ha-1 yr-1 at stand age class 69 and 150 Mg C ha-1 yr-1 by stand age class 124. Intuitively, temperate-maritime Douglas-fir would be a strong candidate for C management due the longevity of the species, sustained growth, and low return periods of stand-replacing disturbance, yet results here suggest that further investigation of drought sensitivity of regular tree mortality in combination with local drought forecasts, as well as the fate of dead wood, may be critical to assess the effectiveness of moderating harvesting rates as a form of C management and the permanence of global C storage in old-growth forests (Luyssaert et al. 2008). In addition to directly altering the trajectory of the N-Csw relationship, droughtinduced tree mortality may also exert its legacy on future net C balance simply by diminishing N. As N falls below 600 stems ha-1, Gsw rapidly declines as the survivors become unable to fill the gaps, which will have a persistent negative impact on potential biomass in older stands until substantial recruitment sets in. This is complicated by a lack of information on recruitment rates and how they may alleviate N-dependent declines in Gsw under such 107  scenarios. Further application of the model to hypothetical landscapes (e.g., Fisher et al. 2007; Kurz et al. 2008b) is required to address how simulations of drought-induced mortality influences net C balance in more detail.  108  Chapter 5: Simulating gross primary production of Douglas-fir stands with a production efficiency model 5.1 Synopsis Eddy-covariance measurements in three different-aged Douglas-fir stands were used to calibrate a production efficiency model (PEM) and explore the sources of error in simulated annual gross primary production (Pg). Parameters were derived on a daily time scale, assessing absorbed photosynthetically active radiation (Qa), maximum gross photosynthetic efficiency (g max), and functions of environmental stress. Despite similar climates, g max varied between sites in correspondence with inventory-based estimates of site index, suggesting that landscape variation of daily g max ranges between 1.00 and 5.54 g C MJ-1 in response to non-climatic factors. Decreasing g with increasing Qa was the strongest driver of daily Pg. We therefore devised a method of incorporating the nonlinear light response (NLR) that is apparent within stands into the model, while maintaining the linearity in the relationship between annual Pg and Qa across stands. The ability to match observed seasonal and inter-annual variability of Pg required that thermal stress be expressed by the combined impact of frost damage, immediate deviations from optimum temperature, and antecedent effects of accumulative heat on plant development. Water stress was expressed using highly simplified empirical functions of vapour pressure deficit and soil water availability. An ecosystem-specific model (i.e., fitted collectively to all stands) explained 80, 93, and 97 % of the monthly variation of Pg in regenerating, juvenile, and mature stands, respectively. The model was able to collectively explain 96 % of variability of annual total Pg with a mean absolute error of 130 g C m-2 yr-1, constituting 6 % of the mean and 113 % of the standard deviation at the mature site. Annual predictive skill was strongly limited by inability to match 109  variations on a synoptic time scale. This may involve, to unknown degrees, potential errors in the derivation of Pg from eddy-covariance measurements, discrepancy between measurement and footprint-weighted environmental conditions, poor representation of acclimation to environmental stress, and unmodelled variability in nutrient status.  5.2 Introduction Gross primary production (Pg) must be known with a high degree of precision to detect trends in the net carbon balance of forest ecosystems using physically-based models. Simulation of Pg over large spatial and temporal domains is impeded, however, by the high cost of resources needed to operate state-of-the-art biochemical models. Production efficiency models (PEMs) provide an alternative approach that can be applied more practically at the regional scale. Rigorous testing through comparison with observations is critical, however, to understand their advantages and disadvantages and how effective they are in monitoring the terrestrial carbon cycle. PEMs make the fundamental assumption that Pg is the product of absorbed photosynthetically active radiation (Qa) and the conversion efficiency of gross photosynthesis (g). Many studies have applied this basic principle, also commonly referred to as the lightuse efficiency (LUE) approach, to simulate forest productivity (e.g., Prince and Goward 1995; Landsberg and Waring 1997; Potter et al. 2003; Xiao et al. 2005; Heinsch et al. 2006; Turner et al. 2006; Coops et al. 2007; Yuan et al. 2007). g is generally treated as a constant fraction based on evidence that, under otherwise unstressed conditions, annual biomass production and irradiance are linearly correlated as they increase from zero in agricultural crops (Monteith 1972, 1977) and forest stands (McMurtrie et al. 1994; Geotz and Prince 110  1998). This assumption may be valid for forest stands with closed canopies, where the majority of foliage experiences low irradiance and because nonlinearity in photosynthetic light response tends to dampen with increasing spatial and temporal scale (Landsberg and Gower 1997; Landsberg et al. 1997). Under the assumption of proportionality, Pg forms a linear function of Qa, which contradicts widely-observed nonlinearity in the light response of forest ecosystems (Wofsy et al. 1993; Grace et al. 1995; Baldocchi and Harley 1995). Herein referred to as the nonlinear light response (NLR), the gradual saturation of Pg with increasing irradiance is assumed to result from canopy heterogeneity of the microclimate and leaf physiology (Norman 1980; Leuning et al. 1995; de Pury and Farquhar 1997). Although there is considerable uncertainty in the contribution of these processes, there is a consensus that g is closely linked to the absolute magnitude of irradiance and to the diffuse radiation fraction (Qd/Qt) (Sinclair and Muchow 1999; Cai et al. 2009). In many forest stands, NLR is well described by a hyperbolic decline in g with increasing Qa and constitutes the largest source of variation in daily total Pg (Ibrom et al. 2008; Mäkelä et al. 2008). In the absence of direct dependence between g and Qa in PEMs, onus is placed on other environmental variables to reflect NLR, such as vapour pressure deficit (Δe) (Xiao et al. 2005). In this study, a PEM was calibrated using estimates of Pg calculated from eddy-covariance (EC) measurements at three sites located on the east coast of Vancouver Island, Canada. The sites represented a range of developmental stages in second-growth Douglas-fir forests, including a regenerating (0 to 6 years-old) stand, a juvenile (14 to 20 years-old) stand, and a 111  mature (50 to 56 years-old) stand. The main objectives of this study were to: 1) test the ability of the model to match seasonal and inter-annual variability of observed Pg and 2) evaluate the impact of individual processes describing environmental stress on the skill and practicality of the model. Uncertainty associated with the driving variables was minimized by using available field measurements. We explored the advantages and disadvantages of accounting for NLR by constraining g based on a hyperbolic function of Qa and comparing predictions with a model that excluded NLR. Variation in model parameters was first assessed by developing site-specific (SS) models, fitted individually to each site. However, as the goal was to develop a model for application over large spatial domains, the degree of parameter convergence for this forest type was assessed by developing an ecosystem-specific (ES) model, in which physiological parameters remained constant across sites. Possible causes of unmodelled variability and their consequences for predicting climate-induced variability of Pg are discussed.  5.3 Model description The model was based closely on 3-PG, originally developed by Landsberg and Waring (1997), and assumed a uniform stand structure within specified spatial units and generalizes the forest canopy as a single foliage layer. Daily total Pg (g C m-2 d-1) was computed according to the LUE approach (Monteith 1972):   																																																																																																																																												 5.1  Daily total Qa (MJ m-2 d-1) was computed using a form of the Beer-Lambert model (Chen 1996):  112  ↓  1  	 1  e    																																																																																																	 5.2  where Qt is daily total incident photosynthetically active radiation (PAR) above the canopy (MJ m-2 d-1), s is the above-canopy reflectance, k describes extinction of radiation with canopy depth, Ω is the foliage clumping index, Le is the effective leaf area index (m2 m-2), and θ is the solar zenith angle (degrees). The biochemistry of photosynthesis was simplified by defining maximum gross photosynthetic efficiency (g max) as the efficiency expected under optimal environmental conditions. Actual gross photosynthetic efficiency was then derived according to functions, ranging between zero and one, that reduce g max multiplicatively in response to environmental stress (Jarvis 1976): Δ    																																																																													 5.3  where T is mean daily daytime air temperature, H is a daily index of cumulative heat, F is daily freezing occurrence (T ≤ 0.0 C), Δe is daily daytime vapour pressure deficit, and θr is relative soil water content of the root zone. Effects of NLR on g were assumed to take the form g =g max f(Qa), where f(Qa) was described by a hyperbolic function of absorbed photosynthetically active radiation (Mäkelä et al. 2008): 1   1  																																																																																																																														 5.4  and γ describes the shape of the decline in g with increasing Qa. Influence of seasonality in the distribution of Qa on  is a potential hazard of using Eq. 5.4. For example, the lowest 113  observed values of daily total Qa during summer are substantially higher than they are during winter. As a result, use of Eq. 5.4 is different from conventional PEMs in that a fixed value of γ leads to curvature in the landscape relationship between biomass production and Qa. To avoid these limitations, Qa was standardized on a monthly basis by scaling daily measurements according to the distribution of Qa during each month to range between zero and unity (denoted Qa′). Hence, absolute values of Qa were substituted with a standardized index, indicating the flux relative to long-term normal seasonal conditions. Thermal effects on g were modelled according to an Arrhenius function, adjusted to account for effects of T on enzyme activity (Alexandrov and Yamagata 2007): 	exp 1  273 exp  273 273  																																																																		 5.5 273  where R is the universal gas constant (8.314 J K-1 mol-1), Ea is the activation energy (kJ mol1  ), Topt is the optimum mean daily daytime air temperature (C), and  describes the width of  the curve bounding Topt. Based on correlation between Pg and growing degree days (GDD) at these sites (not shown), antecedent effects of heat availability were considered based on a function of cumulative GDD with a 5C base temperature:  1    GDD ,  1  1 DOY exp	 10 365  																																								 5.6 ,  114  	1  1    ,  DOY DOY  DOY DOY  DOY DOY  DOY DOY  														 5.7  where c1, GDD is the maximum theoretical reduction of g, K is the seasonal time series of c1, GDD,  DOY is day-of-year, c2, GDD is the optimum cumulative annual (i.e., end-of-year) GDD,  c3, GDD describes the optimum rate of heat accumulation, and DOYst, DOYmd, and DOYed dictate the starting, middle and ending dates in which f(H) actively takes place. Constraint of K using DOYst and DOYed was intended to account for lack of correlation between Pg and cumulative GDD outside the growing season. Effects of frost damage were considered as in the 3-PG model (Landsberg and Waring 1997) according to the binary state of frost occurrence and the coefficient, dfrost, marking the daily fractional reduction in the event of frost. Effects of stomatal closure on CO2 supply were represented using empirical functions of vapour pressure deficit f(Δe) and soil water availability f(θr). Reduction of g due to increased Δe was modelled as: 1 	Δ  Δ  1  																																																																																																																											 5.8  Soil water stress was modelled using a logistic function of relative soil water content: 1   exp	 Φ  1 exp  0.1Φ  0.075  																																																			 5.9   																																																																																																																															 5.10  where θ is volumetric soil water content integrated over the rooting depth (m3 m-3), θr is relative soil water content, θwp and θfc are texture-specific values of soil water content at 115  wilting point and field capacity, respectively (m3 m-3), θth indicates the relative soil water content at which stomatal closure initiates, and  describes the rate of decline in f(θr) with decreasing θr below θth. In most models, g max is perceived as a fixed evolutionary trait, parameterized according to species (Landsberg and Waring 1997) or biome (Heinsch et al. 2006), while external constraint functions are generally introduced to reduce local g from the landscape g max to reflect suboptimal site conditions (Landsberg and Waring 1997). Some of these processes may also be implicitly considered through variation of L in diagnostic simulations (Running et al. 2004). Non-climatic processes, such as stand age, nutrient availability, and disturbance legacy, likely contribute to variation of Pg in many forests. Absence of these effects in simulations may make it difficult to compare estimates of g max fitted at different sites. Waring et al. (2006) considered effects of genetic constraint and site conditions through modification of g max:   FR  																																																																																																																								 5.11  where FR is the fertility rating (ranging between zero and one), and b0 and b1 are coefficients that control the upper and lower limits of g that are observed across the landscape. In this study, the FR for each stand was determined according to the ratio of its site index measurement to the maximum site index of representative stands found across the landscape. Site index is a stand-level indicator of productivity that is widely used in the region to forecast timber yield and is defined as the height (m) of the largest undamaged tree (at breastheight age 50) of the dominant or co-dominant species within a stand. An approximate maximum site index found across the landscape for Douglas-fir is 50 m, so the DF49 site, 116  with an estimated site index of 36 m, would exhibit FR = 0.72. A method similar to that developed by Waring et al. (2006) was used by replacing Eq. 5.11 with:    max    FR  	 FR  …    	 1    FR  FR  																																																																																			 5.12  																																																																																													 5.13  where g max (i) is the maximum gross photosynthetic efficiency of the ith stand, max[g max (i=1...n)]  denotes the highest possible value of g max that can be achieved by the species across  stands i = 1...n in its range (corresponding here with site index = 50 m, FR = 1.00) and  represents the relative partitioning of climatic forcing on g max. The presence of  in Eq. 5.13 is designed to remove the effects of climate on the scaling between landscape maximum and site maximum g, as it is assumed that all climatic forcings on g are expressed separately through the constraints in Eq. 5.3. Hence, the control imposed by climate increases as  increases.  5.4 Materials and methods 5.4.1 Study sites and field measurements The analysis was conducted using a chronosequence of forest stands dominated by Douglasfir. Information pertaining to each study site is reported in Table 5.1. Ground-based measurements of stand structure, site index, and age were obtained from Humphreys et al. (2006) and vector-based forest inventory maps developed by Trofymow et al. (2008). Halfhourly meteorological data were measured continuously at three flux towers, herein referred to as HDF00, HDF88, and DF49 (Humphreys et al. 2006). Volumetric soil water content was 117  measured within the upper 0.6 m of the soil profile at all sites. Daily mean θr was calculated from profile-average estimates of θwp and θfc (Table 5.1). Detailed descriptions of the EC systems, measurement of net ecosystem production (NEP), and derivation of Pg have been previously reported by Morgenstern et al. (2004). Briefly, night-time measurements of net ecosystem production (NEP) were rejected to avoid underestimation during periods of low turbulent mixing (Morgenstern et al. 2004). Measurements of NEP were not corrected for lack of energy balance closure. Estimates of Pg were derived by calculating ecosystem respiration (Re) as an exponential (i.e., Q10) function of soil temperature measured 5 cm below the surface using night-time NEP and subsequent extrapolation of the model to daytime periods. Gross primary production was then calculated as Pg = NEP + Re during daylight periods. During infrequent periods in which daytime NEP measurements were missing or rejected, Pg was modelled using light-response functions. Missing daylight measurement intervals comprised 18.7, 16.8, and 7.9 % of the time series at HDF00, HDF88, and DF49, respectively.  Table 5.1 Study site properties. DF49 49° 52N 125° 20W Spring 1949 50 8.4 36 Gravelly loamy sand Soil coarse fraction (m3 m-3)## 0.43 0.29 0.33 1.75 2.00 1.20 Bedrock depth (m)*** θfc (m3 m-3)+! 0.19 0.35 0.26 3 -3 +! 0.05 0.07 0.06 θwp (m m ) * Trofymow et al. (2008); ** Trofymow pers. comm.***; Jungen (1984); # Humphreys et al. (2006); ## Grant et al. (2007); + assessed from measurements; ! Rowell (1994)  Latitude Longitude Date of last disturbance* Initial stand age (years)* Maximum L (m2 m-2)# Site index** Soil texture***  HDF00 49° 52N 125° 17W Winter 1999 0 2.5 28 Gravelly loamy sand  HDF88 49° 31N 124° 54W Winter 1987 14 6.7 24 Gravelly loam  118  Daily g was calculated as the ratio of daily total gross primary production to daily total absorbed photosynthetically active radiation g = Pg/Qa (g C MJ-1). Accuracy in the estimates of g, therefore, depended on both the meteorological measurements and derivation of Qa. Measurements of total leaf area index (L) were made frequently at HDF00 and HDF88 using the point-quadrant method (Humphreys et al. 2006) and optical methods (Chen et al. 2006). Many studies have used satellite reflectance measurements to estimate L or the fraction of absorbed PAR (FPAR) for application of Eq. 5.2 (Potter et al. 1993; Xiao et al. 2005; Heinsch et al. 2006; Coops et al. 2007; Yuan et al. 2007). Use of satellite reflectance measurements is a valuable input to diagnostic predictions of Qa, however, discrepancies in stand age, species composition, and stem density between the flux footprint and its surrounding pixel may exist (Coops et al. 1998; Turner et al. 2005). To produce continuous daily time series of L, discontinuous field-based measurements at HDF00 and HDF88 were augmented by 16-day composite values of enhanced vegetation index (EVI) derived from the MOD13Q1.005 product of the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite. Time series of EVI for the 250 m MODIS pixels encompassing HDF00 and HDF88, however, did not correspond strongly with field measurements of L. The discrepancy between the flux footprint and MODIS pixel at HDF00 was particularly large, owing to relatively low height of the instrument plane. We therefore extracted the average seasonal time series of EVI, corresponding with age-span of measurements at HDF00, from cut blocks in the surrounding region. This was achieved by overlaying the MODIS time series onto a 25 m forest age map derived from multi-temporal analysis of Landsat images and isolating MODIS pixels that were entirely harvested between 2000 and 2007 resulting in a subset of 119  MODIS pixels with approximately homogeneous stand age. As HDF88 was planted well before the MODIS era, there was more uncertainty in deriving the regional average EVI for this age sequence. Continuous estimates of L at HDF88 were, therefore, derived from the EVI time series from its respective 250 m pixel, adjusted to remove bias with the field measurements. Field measurements of L were made during mid-summer at DF49. These estimates ranged between 7.3 m2 m-2 (Chen et al. 2006) and 8.4 m2 m-2 (Humphreys et al. 2006) and were assumed to represent the seasonal maximum value of L. Incident photosynthetically active radiation above (Qt 33m) and below (Qt 4m) the canopy, as well as reflected photosynthetically active radiation above the canopy (Qt 33m), were measured continuously for five years at DF49. Upward flux below the canopy (Qt 4m) was assumed to be negligible. To produce continuous daily time series of L, the Beer-Lambert equation was rearranged as (Duursma et al. 2003; Cook et al. 2008): ln  ↓  /  ↓  ↑    																																																																																							 5.14  The extinction coefficient k is dependent on the leaf angle distribution and z (Norman 1980; Black et al. 1991; Duursma et al. 2003) and must be known in order to derive L from inversion of Eq. 5.2. When the leaf angle distribution is spherical, the extinction coefficient for a given value of L is determined by path length k = 1/(2 cos z). A spherical leaf angle distribution is commonly assumed for evergreen needle-leaf forests. However, Black et al. (1991) found substantial deviation from a spherical leaf angle distribution and non-uniform influence of element clumping in a juvenile stand of Douglas-fir. Hence, solving for k  120  requires explicit knowledge of seasonal changes in Le, , and the leaf angle distribution of the canopy, which are not readily available. Dependence of k on both the directionality of Qt 33m  and z was, instead, derived empirically by rearranging Eq. 5.14 and solving for k during  July (assuming L = 8.4 m2 m-2). Relationships found during July were then used to extrapolate k during all seasons. Daily average daytime z was derived from hourly values calculated according to methods outlined by Oke (1987). The five-year composite seasonal pattern of L was applied during years in which radiation measurement were not available to produce indirect estimates.  5.4.2 Experimental design Models were categorized as either site-specific (SS) or ecosystem-specific (ES). Analysis of the SS-type models was intended to provide insights into process representation and parameter uncertainty, while analysis of the ES-type model was intended to address the ability to simulate Pg for Douglas-fir at the regional scale using ecosystem-specific parameters. Of the SS-type models, the first set included only a linear function of Qa (denoted SS). A second set included the influence of climatic variables while excluding NLR (denoted SS-C). A third set included only the nonlinear light response (SS-NLR), while a fourth set included climate and nonlinear light response (SS-C-NLR). Comparison between SS-C and SS-C-NLR model predictions was designed to indicate the degree of improvement associated with the inclusion of NLR, while comparison between SS-NLR and SS-C-NLR model predictions was designed to indicate the degree of improvement associated with the consideration of climatic processes.  121  Table 5.2 List of model variable Symbol Value Pg Q↓t Qa Q′ P T GDD Δe W Wr z L Le  Description Gross primary production Incident total photosynthetically active radiation Absorbed photosynthetically active radiation Standardized Q↓t Monthly total precipitation depth Monthly mean above-canopy air temperature Cumulative end-of-month growing degree days (5.0 ºC base) Monthly mean above-canopy daytime vapour pressure deficit Soil water content Standardized soil water conent Solar zenith angle Canopy leaf area index Effective canopy leaf area index  ρa FR  Units g C m-2 d-1 MJ-1 photon MJ-1 photon mm month-1 ºC hPa m3 m-3 degrees m2 m-2 m2 m-2 g C MJ-1 photon -  K  -  Potential f(H) constraint  DOY  Day-of-year  σ Tmin Topt Tmax  Day g C MJ-1 photon K K K  dfrost  -  εg  εg max Ω    c1, GDD DOYmd    θth R Ea k η c2, GDD c3, GDD DOYst DOYed  Day m3 m-3 8.314 J K-1 mol-1 65000 J mol-1 2000 0.56 31 Day 335 Day  Gross photosynthetic efficiency Canopy reflectance Fertility rating  Maximum gross photosynthetic efficiency Canopy clumping index Sensitivity of εg to Q′ Temperature-response function coefficient Minimum growing temperature Optimum growing temperature Maximum growing temperature Fraction of Pg that is lost due to damage associated with frost occurrence (Tmin < 0) Maximum reduction due to GDD Day-of-year in which f(H) constraint peaks Sensitivity of εg to D Soil water constrain coefficient Threshold Wr at which soil water stress initiates Universal gas constant Activation energy Radiation extinction coefficient Fertility scaling coefficient Optimum end-of-year cumulative GDD f(H) coefficient Day-of-year in which f(H) constraint starts Day-of-year in which f(H) constraint ends  122  The models were fitted by constrained nonlinear optimization of the global time series of observed Pg. Constraints were used to restrict parameters within a physically-realistic range. We tested the behaviour of solutions based on several different solvers before choosing the mean absolute error (g C m-2 d-1), which produced fast, stable solutions and high predictive skill. To limit the analysis to key model parameters, several less influential parameters were set constant (Table 5.2). Ea was fixed at 65.0 kJ mol-1 in Eq. 5.5 (Alexandrov and Yamagata 2007; de Pury and Farquahar 1997). c2, GDD and c3, GDD were fixed at 2000 and 0.56, respectively, in Eq. 5.6. The period in which f(H) impacts growth was also set constant, assuming DOYst = 31 and DOYed = 335 in Eq. 5.7. To explore possible causes of NLR, we applied a multi-layer sunlit-/shade-leaf canopy model (Norman 1980) to a short sample period at DF49, during which measurements of diffuse radiation fraction (Qd/Qt) were available. The simulation was intended to show how moredetailed canopy photosynthesis models perceive variation in daily εg. To avoid potential seasonality, the simulation was conducted only during July, 2003. We applied the model using an hourly time step. The canopy was defined by a normally-distributed vertical profile of L starting at 60 m above the ground. The canopy profile was discretized by 1.0 m height intervals, resulting in a maximum of 60 computations of the sunlit and shaded fractions of L, radiative loading, and photosynthesis per time step. Rectangular light-response functions were developed from two sets of parameters, representing sunlit foliage at the top of the canopy and shaded foliage at the bottom of the canopy. Canopy profiles of each parameter were derived for each height interval according to linear interpolation between the sunlit and shaded parameter sets. Photosynthesis was predicted using the Michaelis-Menten model, with parameters chosen that resulted in general agreement with integrated canopy-scale 123  curves reported by Humphreys et al. (2006). Apparent quantum yield (α) was set constant at 0.065 mol CO2 mol-1 quanta for both sunlit and shade foliage. Maximum photosynthetic capacity (Pmax) of sunlit and shaded leaves were set to 6.0 μmol CO2 m-2 s-1 and 60 % of the sunlit estimate to correspond with profiles developed by Lewis et al. (2000). Values of L and  were set constant at 8.4 m2 m-2 and 0.81, respectively. A spherical leaf angle distribution was assumed in each canopy layer, solving sunlit fractions for five leaf angle classes. The model was run with measured hourly values of Qt and Qd. Model predictions of g were then compared with the observed patterns.  Table 5.3 Seasonal range of leaf area index (L) and fraction of absorbed photosynthetically active radiation (FPAR) during measurement years. HDF00 L  FPAR 1998 1999 2000 0.25-0.76 0.00-0.37 2001 0.25-1.05 0.02-0.49 2002 0.25-1.44 0.11-0.60 2003 0.25-2.11 0.14-0.71 2004 0.35-2.95 0.08-0.82 2005 0.35-3.39 0.15-0.87 2006 0.48-3.61 0.19-0.88 # missing, filled with 2002-2006 means  HDF88 L  FPAR  3.17-6.54 2.92-6.21 3.17-5.69 3.17-6.23 3.70-5.88  0.64-0.91 0.67-0.89 0.64-0.89 0.61-0.90 0.68-0.90  DF49 L 5.01-8.20# 5.01-8.20# 5.01-8.20# 5.01-8.20# 5.08-8.14 5.71-8.26 4.80-8.00 5.23-8.05 4.31-8.50  FPAR 0.83-0.94 0.86-0.94 0.79-0.94 0.82-0.94 0.83-0.94 0.82-0.95 0.79-0.94 0.81-0.94 0.82-0.95  5.5 Results 5.5.1 Radiation absorption The albedo in snow-free coniferous forest stands ranges between 0.04 and 0.15 (Jarvis et al. 1976; Oke 1987). Daily mean values of s at HDF00, HDF88, and DF49 were 0.040, 0.051, and 0.038, respectively. In this study, we used the actual daily measurements of s, whereas 124  using fixed long-term averages would have led to biases of 3.3, 5.3, and 3.4 % in modelled Qa as a result of seasonal variation of s and Qt at the three sites, respectively. Maximum and minimum monthly mean estimates of L and FPAR for each measurement year are listed in Table 5.3. At HDF00, direct measurements were, on average, an order of magnitude higher than sixteen-day composite values of EVI. Relative to direct measurements, EVI exhibited a more gradual increase with time since planting. At HDF88, maximum values of EVI were substantially lower than an order-of-magnitude difference in maximum direct measurement of 6.7 m2 m-2, which may be due to spatial discrepancy between measurement domains, or possibly decoupling between EVI and L upon canopy closure.  Z (˚)  Figure 5.1 Dependence of canopy radiation extinction k on (a) diffuse radiation fraction Qd 33m/Qt 33m  (during July) and (b) solar zenith angle z (during all seasons) at DF49. Data shown  in panel b correspond to clear-sky conditions (Qd 33m/Qt 33m < 0.4) to remove a higher degree of noise during overcast-sky conditions. The curve displayed in panel b was fitted only to July data (52.0 < z < 55.5) and extrapolated across the full range of z.  125  Mean daily extinction coefficient at DF49, k, was dependent on both the directionality of incident radiation (i.e., Qd/Qt) and z (Figure 5.1). During July, daily mean Qd/Qt ranged between 0.15-1.00 (Figure 5.1a). Hourly measurements of Qd/Qt occasionally reached above 1.0 due to amplification of the ratio at dusk and dawn and were conditioned to satisfy  1.0 prior to calculation of mean daily values. Using ordinary least-squares linear regression, k declined significantly at a rate of 0.07 per unit increase in Qd/Qt (p < 0.01). Residual variation was high (s.d. = 0.024) and uniformly distributed for Qd/Qt below approximately 0.85. Mean daily z ranged between 52.4 and 78.8 seasonally, and between 52.0 and 55.5 during July (Figure 5.1b). For the narrow range of z during July, k increased significantly at a rate of 0.05 per 10increase in z (p < 0.01). Extrapolation of the curve also adequately described k at high values of z, but failed to account for pronounced reduction of k between 55 and 57 and gradual increase between 57 and 65. This is consistent with patterns observed in Douglas-fir at the hourly time scale (Black et al. 1991) and implies a relatively high mean inclination of foliage (i.e., 60 to 80) according to idealized relationships (Warren Wilson 1959; Warren Wilson 1960), suggesting that canopy architecture produces a distinct diurnal and seasonal interaction between foliage orientation, k and Qa in these ecosystems. While the relationship between k and z was similar over the full range of Qd/Qt, isolation of clear-sky conditions (Qd/Qt < 0.4), as expressed in Figure 1b, removed scatter that corresponded with overcast-sky conditions. The relationship with z suggests that path length through the canopy influences transmittance, however, the effect was not as strong as expected using the conventional assumption, k = 1/(2 cos z), for a spherical leaf angle 126  distribution. Although observations matched the general pattern of idealized curves developed by Warren Wilson (1960), there was a difference in phase and range of the pattern as it relates to z. The discrepancy did not appear to be explained by scaling differences between instantaneous (i.e., hourly) and daily mean daytime z. For simplicity, k was set as a linear function of z as shown in Figure 5.1b and further research is needed to fully understand how this variation can be incorporated into the model. The seasonal variation of L was consistent across sites, increasing between late April and early May and declining between October and December. The average seasonal range of L was 28 % at DF49 and 40 % at HDF88. Seasonal changes in L at DF49 had a negligible effect on model simulations of Qa, which was driven almost entirely by Qt and a. Phenology had a greater impact at HDF88 and HDF00, where FPAR was more responsive to changes in L and estimates of Qa deviated below Qt.  5.5.2 Variability of g The relationship between g and Qa′ was well described by a hyperbolic function during all seasons. Figure 2 shows the observed pattern of NLR at DF49 for six selected months. The relationship was strongest during summer, whereas winter was characterized by more negative anomalies associated with freezing temperatures. The behaviour of NLR within seasons was generally similar between years with the exception during 2004 and 2005 in which g was substantially higher than in other years at moderately low radiation levels 0.2 < Qa′ < 0.5 (Figure 5.2e). Patterns similar to those expressed in Figure 2 were apparent at HDF00 and HDF88, although they exhibited more scatter in g towards low Qa′.  127  Figure 5.2 Dependence of daily gross photosynthetic efficiency (g) on relative absorbed photosynthetically active radiation (Qa′).  Several indicators of εg are reported for each site in Table 5.4. All estimates were derived from snow-free periods. Daily εg max was calculated in different ways, including the 98th percentile, estimates produced by the SS-C-NLR models through constrained nonlinear regression, and from a scaling approach proposed by Prince and Goward (1995), which is based on instantaneous (i.e., hourly) measurements of apparent quantum yield reported by Humphreys et al. (2006). There was considerable variation among methods of calculation. However, estimates derived from the apparent quantum yield were similar to those fitted in the SS-C-NLR models. Daily εg was highly skewed at HDF00, strongly influencing mean εg and εg max derived from ordinary least squares regression of Eq. 5.4.  128  Figure 5.3 Saturation of daily gross primary production (Pg) and gross photosynthetic efficiency (εg) with total incident photosynthetically active radiation (Qt) during July, 2003 at DF49 (a) observed daily data (open circles, solid curve) and simulation using a multi-layer radiative transfer model (shaded circles, shaded curve) (b) observed dependence of diffuse radiation fraction (Qd/Qt) on Qt (c) sensitivity of modelled εg with increasing daily Qt ranging from 4 to 14 MJ m-2 d-1 run with the upper (solid curve) and lower (broken curve) boundaries of Qd/Qt (d) sensitivity of Pg to increasing Qt for total canopy (circles) sunlitfraction (triangles) and shaded-fraction (squares) run with the upper (solid symbols) and lower (open symbols) boundaries of Qd/Qt.  Both mean and maximum εg corresponded with differences in site index (listed in Table 5.1), although the sample size did not permit a statistical analysis. With the exception of a slightly different energy balance at HDF00, climate was largely invariable between sites, such that any correspondence with site index may be attributed to internal (i.e., non-climatic) properties. Monthly g was calculated according to the mean of daily g estimates, which yielded substantially higher values relative to if it were calculated from dividing monthly 129  mean Pg by monthly mean Qa. Estimates of monthly g max were 15, 13, and 20 % lower than those calculated using the scaling approach reported by Waring et al. (2006) at HDF00, HDF88, and DF49, respectively. Figure 3a compares the relationship between Qt and g derived from observations and the multi-layer radiative transfer model during July, 2003 at DF49. Scaled to the canopy based on methods outlined by Norman (1980), the observed decrease of g with increasing Qt was well replicated by the model. Adjustment of the vertical gradient of leaf-level photosynthetic parameters through the canopy shifted the f(Qa) vertically, but the rate of decline in daily εg with increasing Qt was largely insensitive to a wide range of parameters. Imposing absence of light saturation (Pmax → ∞) at all canopy layers resulted in similar decline as shown in Figure 5.3a (not shown).  Table 5.4 Daily and monthly estimates of gross photosynthetic efficiency (g C MJ-1). HDF00  HDF88  DF49  0.79  1.14  1.59  2.72  2.37  3.32  3.61  3.07  4.84  4.42  3.86  4.42  0.86  1.13  1. 62  2.09  2.07  2.45  2.60  2.39  2.87  (a) Daily  g (Mean) g max (98th percentile) g max (SS-C-NLR model) g max (55.2α) 1 (b) Monthly  g (Mean) g max (98th percentile) g max2 1  Estimate based on conversion of apparent quantum yield α (Prince and Goward 1995); Values of α are from hourly light-response curves during June, 2002 (Humphreys et al. 2006) 2 Estimate from 3-PG (Waring et al. 2006)  130  There was strong dependence between mean daily Qd/Qt and total Qt at DF49 (Figure 5.3b). During days with low Qt, Qd/Qt ranged between 0.9 and 1.0. As daily Qt increased, Qd/Qt declined and variation in Qd/Qt increased. To assess the sensitivity of NLR to Qd/Qt, two sets of experimental simulations were conducted using synthetic hourly time series – each set forming incremental increases of Qt ranging between 4.0 and 14.0 MJ m-2 d-1 (Figure 5.3c). The experiments were bounded by a realistic range of Qd/Qt at a given level of Qt during July. One set of simulations was conducted using the upper boundary, while the other set was conducted using the lower boundary (approximated by solid and broken curves in Figure 5.3b, respectively). Using these constraints, simulations indicated that Qd/Qt only had a significant effect on g during days when Qt was high (Figure 5.3c). Increased Qd during days with high Qt significantly increased g. For example, at Qt =13.0 MJ m-2, the model predicted a 0.3 g C MJ -1 increase in εg across the full range of observed Qd/Qt. Figure 5.3d shows the light-response curves of the total, sunlit-, shaded-canopy Pg for the two sets of simulations. The canopy experiences saturation under both extremes in the light regime. Under conditions of low Qd, optimum productivity occurs at a substantially reduced level of Qt. The model attributes this to saturation in both the sunlit- and shaded-canopy fractions. With high L, the model indicates that shaded foliage accounts for a greater proportion of productivity under low-light conditions.  131  Figure 5.4 Relationship between monthly gross photosynthetic efficiency (εg) and standardized absorbed PAR (Qa′). Open symbols indicate monthly observations. Smaller shaded symbols indicate synthetic monthly datasets derived from bootstrap resampling of the daily observations.  As PEMs are often operated beyond daily time scales (e.g., Landsberg and Waring 1997; Heinsch et al. 2006), we assessed the relationship between g and Qa at DF49 on a monthly basis (Figure 5.4). NLR was apparent during most months, however, the relationship was poor, particularly during March, November and December, and difficult to assess from the small sample size. Mean monthly estimates were also calculated from bootstrap resampling of the distribution of daily g and Qa. The synthetic dataset formed strong relationships during all months and the trend lines agreed well with those derived directly from the monthly measurements. Moving to the monthly time scale dampened the degree of nonlinearity that was apparent at the daily time scale, however, the reduction of g remained significant, ranging between -0.86 and -0.41 g C MJ-1 per unit increase in Qa (Figure 5.4). 132  Although there was no relationship apparent in the direct measurements at the monthly time scale during March, resampled estimates from the underlying daily distribution indicated dependence that was consistent with other months. As in the daily data, estimates of g max were higher during late summer and autumn, but also declined more steeply with increasing Qa.  Table 5.5 Parameters for daily (a) site-specific models with climate (b) site-specific models with climate and nonlinear light response (c) ecosystem-specific models with climate and nonlinear light response. g max  f(FR)  γ    Topt  c1,GDD  DOYmd  dfrost  kg    θth  HDF00  2.84  -  -  2.5  19.4  0.73  110  0.20  0.220  16.6  0.41  HDF88  2.57  -  -  1.8  18.8  0.70  114  0.18  0.270  39.0  0.26  DF49  3.23  -  -  1.6  19.5  0.56  125  0.21  0.230  12.9  0.35  HDF00  3.61  -  1.81  1.95  21.6  0.65  110  0.13  0.110  20.0  0.34  HDF88  3.07  -  2.35  1.31  17.8  0.67  109  0.12  0.034  30.8  0.27  DF49  4.84  -  2.62  1.34  20.1  0.72  129  0.11  0.047  8.3  0.42  Universal  4.42  -  1.50  1.50  15.0  0.65  115  0.50  0.045  12.0  0.40  HDF00  -  0.69  HDF88  -  0.64  DF49  -  0.80  SS-C  SS-C-NLR  ES-C-NLR    5.5.3 Model calibration Parameters for each model are listed in Table 5.5. Effects of T and Δe were similar across sites in the SS-C model (Figure 5.5b-c). Effects of Qa′, T, and Δe showed slightly more variation between sites in the SS-C-NLR model (Figure 5.5e-g). Negative effects of Δe were compensated for by effects of Qa′ and were systematically reduced in the SS-C-NLR model 133  relative to the SS-C model at HDF88 and DF49. The shape of the temperature-response function was narrower at HDF00 (Figure 5.5b, 5.5f), which may be the result of greater surface exposure associated with the open canopy air space. Statistical optimisation of the SS-C-NLR models at HDF88 and DF49 resulted in very similar impacts of Qa′ and Δe, whereas immediate effects of T differed substantially. Impacts of antecedent heat availability were variable in the models, with values of c1, GDD ranging between 0.65 and 0.74 in the SSC-NLR models (Table 5.5). Impacts of frost damage were consistently lower than values used in the 3-PG model (Landsberg and Waring 1997; Coops et al. 2007).  Table 5.6 Prediction skill according to coefficient of determination r2, root mean squared error, RMSE, and least-squares slope coefficient, b1, for different models: (1) SS site-specific with no climate and no nonlinear light response; (2) SS-NLR site-specifc with nonlinear light response and no climate; (3) SS-C site-specific with climate; (4) SS-C-NLR site-specific with climate and nonlinear light response; (5) ES-C-NLR ecosystem-specific with climate and nonlinear light response. HDF00 HDF88 2 r RMSE b1 b0 r2 RMSE b1 b0 (1) 0.80 2.63 1.75 0.63 0.86 2.52 1.60 -0.32* (2) 0.70 1.07 0.62 0.36 0.86 1.33 0.71 -0.13* (3) 0.85 1.18 1.12 0.57 0.94 0.76 1.05* 0.14* (4) 0.85 0.80 0.71 0.36 0.96 0.53 0.99* 0.08* * 0.95 0.63 1.03* 0.07* (5) 0.81 1.29 1.10 0.64 * b1 not different from 1.00 or b0 not different from 0.00 at =0.05  DF49 r2 0.86 0.87 0.94 0.97 0.97  RMSE 3.56 2.73 0.87 0.60 0.65  b1 1.68 0.83 0.91 1.00* 1.00*  b0 -2.80 -1.41 0.38 0.08* -0.02*    134  Figure 5.5 Constraint functions for (a-d) SS-C models (e-h) SS-C-NLR models and (i-l) ESC-NLR. Effects include effects of (a,e,i) increasing standardized absorbed photosynthetically active radiation, Qa′; (b,f,j) sub-optimal temperature, T; (c,g,k) high vapour pressure deficit, Δe; (d,h,l) declining relative soil water content, θr.  Parameter estimates for the ES-C-NLR model were set by compromising between estimates of , , and  from the SS-C-NLR models. Visual inspection of the SS-C-NLR models suggested that dfrost was underestimated perhaps because the response of g to frost events was highly variable. Impacts of θr varied between sites (Figure 5d, 5h). HDF88 exhibited a substantially higher sensitivity to θr as manifested through a higher value of Φ. Both SS and ES models explained a significant fraction of the variance of monthly mean Pg (Table 5.6). The SS models, comprising linear functions of Qa, alone, explained between 80 and 86 % of the variation of Pg, however, they consistently overestimated Pg. Inclusion of NLR (SS-NLR) decreased the bias and reduced errors, but did not improve the level of 135  explained variance. Integrated on a monthly time scale, the SS-C models explained between 85 and 94 % of the variation of observed values across sites (Figure 5.6a-c and Table 5.6). The SS-C-NLR models exhibited slight improvement in determination coefficients over the SS-C models, explaining 85 to 97 % of the variation (Figure 5.6d-f). Adding NLR to the models improved the RMSE by 32, 30, and 31 % at HDF00, HDF88, and DF49, respectively. The level of explanation using the ES-C-NLR models remained high, while the RMSE substantially increased at HDF00 and HDF88 as a consequence of positive model biases (Figure 5.6g-i and Table 5.6). The SS-C-NLR models were collectively able to explain 96 % of the variation in observed annual Pg across the sites (Figure 5.7). The model explained a significant degree of the annual variation at HDF00, where FPAR increased two-fold over the period of measurement (Table 5.3). The model showed less ability to match inter-annual variability of Pg at HDF88 and DF49. Inclusion of f(H) was the main factor allowing the SS-C-NLR model to match increased Pg observed during 2004 and 2005 at DF49. Daily and 30-day moving average residuals from the SS-C-NLR models are shown in Figure 8. Positive residuals reflect model under-prediction, while negative residuals reflect model over-prediction. Increasing trend in the residuals at HDF00 was apparent, ranging from large over-prediction in the initial years following planting to large under-prediction, particularly during peak summer, over the last two measurement years. Predictions at HDF88 also showed increase in residuals between 2002 and 2006, perhaps suggesting a discrepancy between multi-annual trend in actual and estimated L.  136  Figure 5.6 Observed versus predicted monthly mean daily gross photosynthesis (Pg) based on (a-f) site-specific and (g-h) ecosystem-specific parameterization. Dashed line marks 1:1 relationship.  137  Figure 5.7 Observed and predicted annual total Pg using an ecosystem-specific model at HDF00 (squares), HDF88 (triangles) and DF49 (circles) for all compete years of measurement between 1998-2006. Dashed line marks 1:1 relationship.  Frost events are indicated by blue shading in Figure 5.8. Moving average residuals tended to respond to frost occurrence, for example, during the winter of 2004-2005, which corresponded with lasting over-prediction of Pg at HDF88 and DF49. Periods of drought, defined here by θr < 0.4, are indicated by red shading. Despite fitting of f(θr) at each site, the models were unable to fully account for impacts of water stress, as indicated by correspondence between negative residual events that commonly occurred during periods of low θr. Manipulation of θth and Φ (not shown) was able to improve agreement during these periods, however, it was generally found to occur at the expense of agreement during periods absent of drought. Overall, the SS-C-NLR models were able to match much of the variation that occurred on daily and synoptic time scales (Figure 5.9). For example, the model was able to match high Pg during early March, 2001 (Figure 5.9b) and low Pg during October, 2003 (Figure 5.9c). 138  The daily time series also highlights instances where agreement broke down, for example, during three consecutive days during early April, 2001 (Figure 5.9b). Systematic biases, spanning for weeks at a time, commonly occurred during mid-to-late summer. For example, the model failed to match declining productivity during July-August followed by high productivity during mid-August through September, 2005. In 2006, the model appeared unable to fully match low productivity during periods in August and September.  Figure 5.8 Daily and 30-day moving average residuals (observed minus SS-C-NLR) Pg.  5.6 Discussion 5.6.1 Predictions of g and Pg Comparison with multi-site and multi-year observations is a powerful way to evaluate PEMs. The calibration exercise was not perfectly suited to evaluate the predictive skill of the model, but was rather designed to identify the upper capacity for predictions, given knowledge of 139  driving variables and process representation (i.e., model structure). Explained variance in monthly estimates of Pg was similar to that reported by Law et al. (2000) for Pinus ponderosa (R2 = 0.67), Xiao et al. (2005) in a mixed coniferous (Picea rubens, Tsuga canadensis) forest (R2 = 0.92), Yuan et al. (2007) for a wide range of 28 ecosystems (average R2 = 0.87), and Mäkelä et al. (2008) for several European ecosystems (R2=0.86). The ES model was able to explain a significant degree of variability in annual Pg across sites, however, the model was unable to fully match variation within sites (Figure 5.7). The mean absolute error in annual Pg exceeded the standard deviation, which suggests that further improvements are needed to accurately monitor and detect climate-induced variations at the annual time scale. Loss of predictive skill between the SS- and ES-type models may have been caused by either variation in the physiological response to climatic forcing, or it may simply reflect over fitting of the SS-type models. The younger two stands experienced a more convex optimum in f(T), while different responses to f(θr) could not be explained solely by soil properties using a simple soil parameterization scheme, such as that developed by Landsberg and Waring (1997). The relative influences of f(Qa′) and f(Δe) also differed between sites, with greater influence of f(Δe) at HDF00 relative to the other two sites. These differences are not necessarily physiological in nature, as parameters were derived from numerical optimization rather than mechanistic understanding. As a consequence, improved explanation of variance may be achieved through unrealistic parameter combinations. We attempted to limit the parameters to a plausible range using constrained nonlinear regression. With more unknown than known parameters in a model, future  140  calibration efforts may benefit from moving towards inversion of EC records (Reichstein et al. 2003; Knorr and Kattge 2005).  Figure 5.9 Daily and 10-day moving average (black curves) observed and (grey curves) SSC-NLR simulated Pg at DF49.  141  Figure 5.10 Relationship between daily gross photosynthetic efficiency (g) and abovecanopy air temperature (T). Curves show Eq. 5 fitted separately to November-March (light shade) and April-September (dark shade) by applying σ = 6.0, Ea = 65 KJ mol-1, and Topt equivalent to long-term mean T during each respective season (indicated by triangles).  Inter-annual variability of modelled Pg was highly sensitive to the parameterization of constraint functions. Subtle changes in the temperature-response function, for example, changed year-to-year variation in total Pg. Despite prescription of L at HDF00 based on MODIS reflectance measurements, which should have accounted for the contribution of invading pioneer vegetation, the SS and ES models were unable to match the increasing multi-annual trend in observed g. This may exemplify the difficulty in estimating L and Qa in open-canopy stands, or perhaps accounting for unmodelled processes, such as root development. Although process-based models commonly assume constant L in evergreen 142  needleleaf forest ecosystems, results obtained across the Douglas-fir chronosequence suggest that seasonal phenology has a moderate influence on Qa in juvenile stands, such as HDF88, which can lead to substantial errors in estimates of g from EC data.  5.6.2 Model processes Long-term productivity is highly sensitive to parameterization of g max (Ruimy et al. 1999; Law et al. 2000; Yuan et al. 2007). Estimates of g max at HDF88 and DF49 were similar to 3.14 g C MJ -1 previously reported at the DF49 (Coops et al. 2007) and those reported for stands of Pinus sylvestris and Picea abies using a similar model (Mäkelä et al. 2008). Mean daily and monthly estimates of g also corresponded closely with those generalized for evergreen needleleaf forests (Heinsch et al. 2006; Xiao et al. 2005). Non-climatic influences on g max are scarcely measured and are commonly absent or poorly defined in PEMs, which attempt to explain as much spatial variation of Pg as possible under the control of climate and physiological convergence (Goetz and Prince 1998). Yet, these processes likely exhibit high enough variation to confound processes that cause environmental stress and, therefore, need to be carefully considered in efforts to uncover convergence and calibrate models. All sites in this study were in close proximity to each other, such that between-site differences in g max could be attributed to non-climatic factors (assuming negligible influence of microclimatic differences). Correlation between g max and foliar nitrogen concentration reported across six different ecosystems by Mäkelä et al. (2008) suggests that nutrient availability may be a major factor contributing to variation in g max. Variation in εg max may 143  also be influenced by species composition. For example, there is a greater abundance of western hemlock (Tsuga heterophylla) at DF49 (Humphreys et al. 2006), which is more tolerant of shade and high tree density than Douglas-fir, and may therefore enhance stand productivity (Chen and Klinka 2003). We took the approach of channelling all non-climatic effects on Pg through adjustment of g max  based on a function of the FR (Eq. 5.13). These processes, therefore, impose a constant  upper limit of g over the time-scales investigated here and do not represent seasonal, multiannual, or decadal dynamics in nutrient availability. The advantage of using site index to scale non-climatic effects is that it is widely available from forest inventories, however, this approach then requires inclusion of  in Eq. 5.12 and Eq. 5.13 because site index is a partial function of climate. Further knowledge of  may be gained over a broader biological and climatological sample through regional calibration and data-model fusion of EC and inventory measurements (e.g., Schaefer et al. 2008). In this study, we found that  ~ 0.3 was consistent with field measurements and produced reasonable predictions across all sites using the ES-C-NLR model. This implies that productivity of Douglas-fir in locations with equivalent climate may vary, on average, by 70 % based on site fertility, while stands with equivalent site fertility may vary across the range of the species by 30 % in response to spatial variation of climatic conditions. Setting  to 0.3 in Eq. 5.13 and projecting estimates to a site index of 50 in Eq. 5.12, yielded g max = 4.42 g C MJ-1, which may serve as an informed estimate of the landscape-representative maximum value for Douglas-fir.  144  5.6.3 Environmental drivers The relationship between daily Qa and εg was relatively consistent within sites and stronger than the effects of other environmental variables. Inclusion of NLR improved predictions of Pg by reducing RMSE and changing f(Δe) to within levels that are consistent with previous studies of stomatal regulation (Meinzer 1982; Price and Black 1990). Monthly mean εg declined linearly with increasing Qa′, suggesting that the nonlinearity is substantially dampened, but remains a significant (linear) driver on a monthly time scale. Correlation between εg and the directionality of incident radiation has been commonly reported in forest ecosystems (Hollinger et al. 1994; Gu et al. 2002; Jenkins et al. 2007; Chasmer et al. 2008; Cai et al. 2009). At the leaf- and shoot-level, NLR is caused by a varying combination of chloroplast CO2 concentration and carboxylation capacity (Lambers et al. 1998). Above limiting levels of irradiance, photosynthesis is limited by regeneration of RuBP (Baldocchi and Harley 1995). As a result, light saturation can be an important characteristic of Pg in forest ecosystems regardless of Qd/Qt. However, apparent insensitivity of NLR to photosynthetic parameters, such as Pmax in multi-layer canopy radiative transfer models, implies that other factors, such as Qd/Qt, may be the main cause. Hollinger et al. (1994) found that the apparent quantum yield was significantly greater on days with predominantly diffuse radiation relative to days with clear-sky conditions, which may have contributed to higher daily values of εg and total CO2 uptake during the former radiation regime. However, they also stated that this effect was secondary to the reduction of εg associated with increasing Qa, which is consistent with experimental model runs shown in Figure 5.3a-c. Simulations undertaken by Knohl and Baldocchi (2008) show that 145  enhancement of canopy photosynthesis under exceedingly overcast conditions is eventually counteracted by decreasing Qt, resulting in a negative effect annually. Alton et al. (2005) similarly report a small increase in g associated with increased Qd in a Siberian Pinus sylvestris stand that does not result in significant overall increases in Pg. Although modelbased experiments presented in Figure 5.3 suggested that increase in Qd/Qt enhances Pg even when Qt is held constant, supporting empirical evidence is lacking. Measurements of photosynthesis from shoots in the upper canopy level of a Picea abies stand during overcast- and clear-sky conditions by Urban et al. (2007) suggest that differences in photosynthetic efficiency at the canopy-scale are closely mimicked by differences at the leafscale. Experimentation with a detailed radiative transfer model, applied here to DF49 likewise, suggested that all canopy layers respond to Qd/Qt (Figure 5.3). Chasmer et al. (2008) analyzed g across a boreal chronosequence of Pinus banksiana, where much like at HDF00, the characteristic increase in g during periods of high Qd/Qt was equally apparent in regenerating stands with low canopy cover (i.e., L < 1.0 m2 m-2). Hence, there is a basis for representing NLR in forest canopies by setting g as a function of Qa, while setting Qa as a function of Qd/Qt. This is consistent with the view of Sinclair and Muchow (1999) that absolute deviations in Qa are the primary driver of daily εg and Jarvis et al. (1976), who state “needles in different parts of a canopy are exposed to large differences in irradiance which is the dominant conditioning environmental influence.” It is worthwhile noting, however, that although the effect of Qd/Qt on radiation extinction can be found empirically as in this study, calculation of Qa from the Beer-Lambert model is largely insensitive to changes in k when L > 3.0 m2 m-2. 146  Inclusion of NLR strays from a principal objective of minimizing process complexity in PEMs. However, PEMs are increasingly popular tools used to study regional carbon cycle dynamics and it is clear from this study and others (Turner et al. 2003; Lagergren et al. 2005; Ibrom et al. 2008) that absence of NLR may limit the ability to simulate short-term temporal dynamics. Although it is unclear whether this leads to large errors in long-term simulations, it severely limits the ability to evaluate the uncertainty in model parameters and process representation by means of comparison with EC measurements. We have explored a means of accounting for NLR by constraining g based on a standardized index, Qa′. Transformation of Qa from absolute units to relative units is effectively an analogue of the clearness index, which integrates both the strong correlation between Qt and Qd/Qt and covariation with θ. The method enabled the model to sustain a linear relationship between annual total Pg and Qa, necessary to match previously reported relationships between irradiance and biomass increments across landscapes (McMurtrie et al. 1994), while improving representation of temporal variability of Pg within individual stands. The former assumption constrains Pg to increase linearly with Qa from the origin. However, recent studies have suggested that the relationship on annual and longer time scales may be better described with a positive offset (e.g., Bergh et al. 2005, Figure 5.3). Presence of an offset causes hyperbolic behaviour of efficiency that is consistent with the NLR of Pg within stands. Hence, whereas McMurtrie et al. (1994) proposed that NLR caused efficiency to decline more-or-less universally, more recent evidence suggests that efficiency declines variably across stands as a linear function of Qd/Qt . This has important implications for modelling the forest carbon balance with PEMs in regions where the radiation regime varies due to terrain shading and latitude.  147  The method does not require new variables, but only knowledge of the seasonal climatology of Qt. It does, however, require knowledge of the sensitivity γ. Parameterization of γ may prove challenging in continental climates, where the seasonal εg-Qa′ relationship is confounded by phenology and dormancy. For example, the relationship between efficiency (derived from net primary production) and Qa′ in boreal Pinus sylvestris L. and Picea abies (L.) Karst. (Lagergren et al. 2005) bears little resemblance to those found in this study. Although further investigation of spatiotemporal variation in photosynthetic light saturation (e.g., Cai et al. 2009) may allow for effective parameterization of γ, this degree of model complexity may not be justified and may warrant replacement of the LUE approach, altogether, with a conventional (i.e., Michaelis-Menton) light-response function (Ibrom et al. 2008). A considerable proportion of the variability in daily Pg could be explained by environmental stresses. On a daily time scale environmental controls generally appeared significant, although weak possibly due to noise in the measurement system and unmodelled variability. Unlike observations in continental locations (Krishnan et al. 2008), the temperature-response function in these temperate ecosystems was bimodal, with distinct values of Topt during the cold and warm seasons (Figure 5.10). The cold-season transformation was not explicitly considered in the model calibration undertaken here. Observed values of Topt during winter and summer closely corresponded with the long-term mean T during each respective season. There was strong evidence to suggest that high temperatures have a negative effect on Pg. Although the magnitude of the heat stress effect remains highly uncertain due to confounding effects of Δe and Qa, it is supported by the presence of a negative effect in the cold-season response curve (when Δe and Qa both tend to be low). It is additionally supported by the high 148  degree of predictive skill that was attained by all models when heat stress was accounted for through inclusion of Eq. 5.5 (in addition to effects of Δe and Qa). Apparent plasticity in acclimation to mean site T and rigidity during the transition between winter and summer regimes may provide insight into the long-term growth response of temperate evergreen coniferous forests to warming trends. Ultimately, this supports inclusion of a nonlinear temperature response curve in PEMs rather than a linear increasing function. Analysis of daily total Pg, preceded by subfreezing temperature, indicated a high degree of tolerance to chilling stress and freeze/thaw cycles. Pg declined steadily with decreasing temperature and exhibited no clear evidence of additional frost damage. Similar to measurements above a Pinus ponderosa forest (Law et al. 2000), canopy photosynthesis persisted during days preceded by freezing temperatures. We chose to increase dfrost in the ES model in order to more accurately match major freeze/thaw events, however, there was considerable variation in the ability to match observed reductions. It is assumed that low soil water availability, commonly when θr < 0.4, forces a closure in stomata. Evaluation of daily (observed minus predicted) residuals from the SS-C-NLR models clearly showed that Pg was strongly influenced by θr at each of the sites (Figure 5.8). Smoothing daily time series helped to clarify the effects of and θr on Pg, showing a more distinct response on multi-day (‘synoptic’) rather than daily time scales. When the environmental constraint functions were removed, as is the case with the SS-NLR models, their effects were apparent from the increasing correspondence between anomalies in Pg and with the shaded regions (θr < 0.4). Hence, consideration of water stress improved the ability to predict Pg. Differences between years in the response to water stress may have been  149  caused either by spatial discrepancies between measurements near the tower and the footprint-weighted conditions or unmodelled variability in water availability. The spring of 2004 and 2005 was substantially warmer with higher GDD across sites and inclusion of f(H) was instrumental in simulating systematically higher Pg. This was a major contributor to increased observed and modelled annual Pg during 2004 and 2005 (Figure 5.7). However, high GDD during the spring of 1998 led to similarly high prediction of Pg, which was not fully expressed by the measurements. The models were unable, however, to fully account for low productivity during some springs, including 1999 at DF49 and 2002 at HDF88.  5.6.4 Concluding remarks In this study, EC measurements in three Douglas-fir stands of varying age, soil fertility, and soil type were used to calibrate a PEM and understand the relative influences of site conditions and environmental stress on Pg. The main findings of this study are summarized as follows: A significant degree of explained variation in Pg derived from EC measurements across three stands of Douglas-fir suggests that a simple ecosystem-specific PEM is a useful tool to simulate variability of Pg across large spatial and temporal domains; NLR was the dominant driver of daily variation of εg and Pg; Inclusion of NLR significantly improved predictions of Pg over that of conventional PEMs in which Pg is set as a linear function of Qa; Inter-annual variability of Pg was associated with variation in the upper limit of Pg, which persisted for seasons at a time. This persistence was partially explained by a model based on antecedent effects of cumulative heat availability;  150  Periodic occurrence of drought had a significant impact on inter-annual variability of Pg, however, simple functions of θr and Δe were unable to consistently explain Pg responses.  151  Chapter 6: Modelling environmental controls on productivity in temperate-maritime forests 6.1 Synopsis This chapter compares variation of tree productivity predicted by the 3-PG model with available field measurements from eddy covariance and permanent forest inventories in coastal Douglas-fir forests. The comparisons suggest that representation of environmental stress in light-use efficiency (LUE) models is limited by (1) decoupling between absorbed photosynthetically active radiation (Qa) and leaf area index (L), which leads to underestimation in dense forest canopies; (2) unrealistic expression of the effects of temperature (T), and atmospheric carbon dioxide concentration (Ca) on gross photosynthetic light-use efficiency (εg); (3) inaccurate coupling between photosynthesis and stomatal conductance and; (4) exclusion of ‘non-stomatal’ regulation of photosynthesis.  6.2 Introduction Stemwood rapidly accumulates following stand-replacing disturbance, making it a large and dynamic carbon (C) reservoir in forest ecosystems. Lacking spatially-continuous measurements of stemwood carbon (Csw), estimates must be extrapolated from sample plots to the landscape using age-class yield models (AYMs) (Kurz et al. 1995; Hudiburg et al. 2009; Böttcher et al. 2008; Waterworth et al. 2007). The advantage of AYMs over more mechanistic approaches, or process-based models (PBMs), is that the prediction uncertainty can be quantified from the measurement and sampling errors of the inventory. However, as AYMs are developed to represent average historical conditions and use datasets that are infrequently repeated, they are not well equipped to study potential impacts of environmental  152  change on productivity (Wensel and Turnblom 1998; Kurz et al. 2009; Metsaranta and Lieffers 2009). Several strategies have been developed to incorporate environmental sensitivity into AYMs. One approach is to use statistical response functions of climate to correct the inventory, itself (Nigh 2006; Monserud et al. 2006). Environmental factors can also be directly incorporated into the model to produce hierarchical frameworks (Bernier et al. 1999; Raulier et al. 2000), or hybrid models (HMs) (Makele et al. 2000), defined here as those models that depend on a combination of local measurements and physically-based functions of varying degrees of mechanistic representation. The 3-PG model is a hybrid that simulates Csw using a unique combination of allometric equations, empirical functions of stand age and site fertility, and knowledge of the physiological controls on productivity (Landsberg and Waring 1997). Semi-empirical representation of biophysical processes in the model reflects a number of key simplifying assumptions derived from reduction of more mechanistic biogeochemical ecosystem models (Landsberg and Gower 1997). Resulting simplification of the model makes it an ideal candidate for operational use. The model is widely used to predict productivity and yield across forested landscapes (Coops et al. 2005; Hirsch et al. 2004; White et al. 2006) and has undergone extensive testing in short-rotation Eucalyptus plantations (Sands and Landsberg 2002; Almaeida et al. 2004; Landsberg and Sands 2004; Stape et al. 2004; Nightingale et al. 2008), naturally-regenerating Eucalyptus (Coops et al. 1998; Tickle et al. 2001a; White et al. 2000), and temperate conifer forests (Coops and Waring 2001; Swenson et al. 2005; Coops 2000; Law et al. 2000). 153  Considerable uncertainty remains in the sensitivity of tree productivity to environmental factors, including atmospheric carbon dioxide (CO2), air temperature (T), and hydrological conditions such as atmospheric vapour pressure deficit (Δe) and precipitation (P), and solar irradiance. Laboratory experiments and eddy-covariance measurements provide a wealth of information pertaining to key biophysical processes; however, these data sources only provide insights into short-term responses, ranging from immediate environmental stress to seasonal weather anomalies. Inventory measurements of live stemwood growth (Gsw) provide a valuable additional constraint that spans decades and a wide range of contemporary climates. In this study, the 3-PG model was applied to temperate-maritime coniferous forests in southwest British Columbia, Canada, to (1) re-evaluate representation of environmental stress by comparing model algorithms with observations at eddy-covariance flux towers and (2) describe the capacity to reproduce observed patterns of productivity at eddy-covariance flux towers and permanent forest-inventory plots.  6.3 Data 6.3.1 Eddy covariance A description of eddy-covariance flux measurements is given in Chapter 5.  6.3.2 Inventory measurements A description of permanent forest inventory plots is provided in Chapter 2.  154  6.4 Representation of environmental stress in 3-PG 3-PG employs a hybrid approach between empirical growth and yield models and processbased biosphere models. Several key processes are simulated based on knowledge of the underlying biophysical principles, while most often maintaining reliance on local observations to account for site “fertility rating”; the logic being that process-based models lack the input variables necessary to skillfully predict intrinsic factors that contribute to variability in productivity, such as nutrient dynamics and soil quality. The model simulates productivity, carbohydrate allocation, and tree mortality. To simulate the net C balance, additional algorithms are required to account for decomposition of dead C pools and C emissions and removals associated with disturbance. Each model simulation tracks a onedimensional forest stand, represented by a single homogeneous cohort of trees, characterized by a stem density a single (“big-leaf”) foliage layer with leaf area index, L, and mean breastheight diameter, DBH. In this version of the model, live-tree C pools consist of stemwood (Csw), foliage (Cf), branches and bark (Cb), coarse roots (Crc), and fine roots (Crf), which are revised slightly to be compatible with CBM-CFS3 (Kurz et al. 2009). Required meteorological variables included monthly mean shortwave irradiance (Sg) mean air temperature (T), total days with frost (F), mean daytime vapour pressure deficit, (Δe), and total precipitation (P).  6.4.1 Net primary production The concept of light-use efficiency (LUE) is widely used in models of NPP to circumvent explicit calculation of leaf energy balance and biochemical reactions (Monteith 1972; 155  Monteith 1977; McMurtrie et al. 1994; Landsberg and Waring 1997). The approach arose from the observation that across-site variation of annual crop dry-mass production is a linear function of irradiance (Monteith 1972; Monteith 1977), which was subsequently re-worked into a form to model NPP (or Pg) in various ecosystem types and on various time scales (Potter et al. 1993; McMurtrie et al. 1994; Landsberg and Waring 1997; Yuan et al. 2007) by treating the canopy as a single leaf, giving it recognition as a ‘big leaf’ model (Sinclair 1976; Norman 1980; Sellers et al. 1992; de Pury and Farquhar 1997). The approach assumes that autotrophic respiration (Ra) is a fixed proportion of gross primary production (Pg), such that NPP is a fixed proportion of Pg (defined by carbon use efficiency; CUE) and that Pg increases with absorbed photosynthetically active radiation (Qa) at a rate defined by gross photosynthetic light-use efficiency (εg): NPP  CUE	 																																																																																																																 6.1   																																																																																																																																											 6.2  The assumption of constant CUE within a species appears to be a valuable simplification that works well in most circumstances (Waring 1998; Delucia et al. 2007). There is some indication that CUE may vary seasonally and with stand age; however, these patterns cannot be fully identified without further measurements of Ra. In conventional LUE models, Qa is derived from adjusting total photosynthetically active irradiance above the canopy (Qt) to account for irradiance that passes through canopy according to Beer’s law: 1  1  1  exp    																																																																														 6.3  156  where k is the extinction coefficient, L is the leaf area index of the canopy. Eq. 6.3 assumes that all Qt that does not pass through the canopy is absorbed. Gross photosynthetic light-use efficiency is modelled with multiplicative constraint functions as:              																																																																																					 6.4  where εg max is the theoretical maximum gross photosynthetic light-use efficiency, and subsequent constraint functions recognize that, under natural conditions photosynthesis operates below maximum capacity, reflecting resource limitations and environmental stress, including functions for nutrient availability, f(N), stand age, f(A), sub-optimal temperature stress, f(T), frost damage, f(F), and water stress, f(W).  6.4.2 Canopy LUE and Qa The theoretical maximum gross photosynthetic light-use efficiency (εg max) was described as a constant 0.030 mol C mol-1 quanta for C3 plants (Landsberg and Waring 1997), which is consistent with apparent quantum yield (α), with more commonly reported units of 0.125 mol CO2 mol-1 quanta (Ehleringer and Björkman 1977; Luo et al. 2000; Singsaas et al. 2000). Although the theoretical maximum value is largely constant, variable estimates are frequently reported due to difficulties in isolating the marginal value under natural conditions. Precise measurements at optimal temperatures and 325 mol CO2 mol-1 air suggest a value of 0.073 mol C mol-1 quanta for C3 plants and a 14% increase between 300 and 400 mol CO2 mol-1 air (Ehleringer and Björkman 1977). The initial assumption of universality was quickly relaxed by following applications of the model that raised εg max by various degrees in order to match field observations of 157  productivity (Law et al. 2000; Waring and McDowell 2002; Sands and Landsberg 2003; and everyone thereafter). This has commonly been described as the “canopy” maximum gross photosynthetic light-use efficiency. The justification for raising εg max, for example to 0.056 mol C mol-1 quanta (Coops et al. 2007; Hember et al. 2010), or more generally in creating a “canopy”-scale version of the parameter, is that it was necessary in order to allow studies to achieve high levels of explained variance in comparisons with Pg from newly available eddycovariance measurements (e.g. Yuan et al. 2007; Hember et al. 2010). Consider an example at the DF49 flux tower, where mean annual Pg is 2024 g C m-2 yr-1 (Chen et al. 2010) and mean annual Qa is 1231 MJ quanta m-2 yr-1. Converting the universal value of εg max to 1.65 g C MJ-1 quanta and ignoring canopy attenuation gives a potential mean annual Pg = 2031 g C m-2 yr-1, which implies negligible environmental stress. Boosting εg max to 0.050 mol C mol-1 quanta alleviates the problem, producing a more realistic value of Pg = 3385 g C m-2 yr-1. The discrepancy suggests that there is something fundamentally wrong with the canopy scaling technique used in LUE models. εg max is one of few parameters in LUE models that possesses physical dimensions and yet it must be tuned beyond reason in order to match observations. The discrepancy arises because εg max is inherently a leaf-scale parameter that is being applied on a canopy (i.e., per-unit-ground-area) basis (Luo et al. 2000). Eq. 6.3 reflects the average radiation load for a single planar photosynthesizing surface (leaf class) within the canopy. Yet, to quote de Pury and Farquhar (1997), “numerical integration of photosynthesis for each leaf class yields canopy photosynthesis,” or:  ,  ,  																																																																																																																								 6.5  158  where Pg,l and Qa,l are leaf-level photosynthesis and absorbed photosynthetically active irradiance for vertical canopy layer, l. Pg, l can be simulated according to a nonrectangular hyperbolic light-response curve:  ,  1 	α 2Θ  ,    α  ,    4	α    	Θ  ,  																																			 6.6  where Pg max is maximum leaf-level photosynthetic capacity, and  is a constant describing the convexity. In this way, multi-layer models perceive canopy Qa differently from big-leaf models. In big-leaf models, the product of leaf-level values of εg and canopy-average radiation load approximates the average leaf-level flux as opposed to the integrated canopy flux. Previous modelling studies proposed that, if photosynthesis scales spatially with irradiance within canopies, Eq. 6.5 simplifies to a form closely related to Eq. 6.3 (Sellers et al. 1992; Sands 1995). However, the scaling technique appears to be inconsistent in with multi-layer integrations in a hypothetical scenario characterized by a dense coniferous forest canopy under typical irradiance (Figure 6.1). In this scenario, transmittance declines with canopy depth according to Beer’s law and k is set to 0.5. When the Pg max parameter is set to decline equivalently (i.e., to acclimate to irradiance at each depth within the canopy) in explicit simulations with a multi-layer model, predicted canopy Pg is significantly lower than that derived from the analytical scaling solution given by Eq. 6.3 (Figure 6.1b). Consistent with Sellers et al. (1992), the scenario suggests that photosynthesis in the lower half of dense canopies, say l > 4 m2 m-2, does not contribute to canopy Pg (i.e., net leaf-level CO2 assimilation of zero). Questions of whether dense forests invest in foliage with negative C  159  balance under the pretext of resource optimality, or whether this reflects vestigial foliage are overshadowed by evidence that vertical decline in net photosynthesis does not parallel attenuation of irradiance in dense forest canopies (Bond et al. 1999; Lewis et al. 2000; Urban et al. 2007). Bond et al. (1999) reported that Pg max plateaus at approximately 50% of that under high irradiance in dense coniferous stands. Lewis et al. (2000) observed 27-36% declines in light-saturated photosynthesis over the depth of foliage in old-growth Douglas-fir and western hemlock. They did not report estimates of transmittance, or the irradiance at each measurement position, however, Beer’s attenuation coefficients for irradiance ranging between 0.4 and 0.6 combined with L = 8.7 m2 m-2 suggest a decline of irradiance over the measured profile that is significantly greater than that of Pg. Values of k for photosynthesis (as opposed to Qt), consistent with results from Lewis et al. (2000) would lie somewhere in the range between 0.23 and 0.35 (Figure 6.1b). The concept that photosynthetic capacity acclimates to irradiance is invalid in observations for dense forest stands; however, this is irrelevant because the analytical scaling solution used in LUE models does not appear to behave as though it did (Figure 6.1). The scaling approach used in LUE models lacks the capacity to represent variation in canopy Pg that would be expected by variation in L according to Eq. 6.5. When εg max is set to a realistic leaflevel value, Eq. 6.3 and Eq. 6.4 would be suitable for a big-leaf canopy with L of 1.0 m2 m-2, while they will underestimate canopy-scale Qa by a factor of L minus a correction of attenuation in Qa and photosynthetic capacity with canopy depth.  160  12  25  (a)  (b)  Canopy P (μmol m−2 s−1)  8  6  20 Range implied by Lewis et al. (2000) 15  Analytical scaling solution  g  Vertical canopy layer  10  4  2  0  10  Multi−layer integration  5  0 0  0.5 2  1  1.5  2  0.2  0.3  −2  LAI (m m ), transmittance  0.4  0.5  0.6  0.7  0.8  0.9  k  Figure 6.1 Comparison between analytical solutions for scaling leaf-level photosynthesis to a dense forest canopy (L = 8.7, and clumping index 0.7) using multi-layer models (Norman 1980) and light-use efficiency models (Sellers et al. 1992; Sands 1995; Landsberg and Sands 2011) (a) vertical leaf area profile (L of 1-m thick canopy layers) (bars) and associated transmittance of irradiance for a hypothetical forest canopy with spherical leaf angle distribution (k = 0.5), (b) relationships between canopy gross primary production (Pg) calculated with a nonrectangular hyperbolic light-response function assuming incident photosynthetically active radiation of 600 mol quanta m-2 s-1, a maximum photosynthetic capacity at the top of the canopy of Pg max = 10 mol CO2 m-2 s-1, constant convexity ( = 0.85) and constant apparent quantum yield (α = 0.125 mol CO2 mol-1 quanta) and extinction coefficient, k. The solid circle marks the analytical solution from Sands 1995 (discussed in Landsberg and Sands 2011 and used in 3-PG). Square symbols mark solutions using a multilayer radiative transfer scheme from Norman (1980) under varying rates of extinction of Pg max  between k = 0.2 and 0.8. The rectangle denotes the region of extinction implied by results from Lewis et al. (2000).  The directionality of Qt also has a strong effect on Qa at the scale of leaves (Oker-Blom 1985; Urban et al. 2007) and canopies (Price and Black 1990; Hollinger et al. 1994; Gu et al. 2002). Under clear skies, direct (“beam”) radiation (Qb) constitutes a larger fraction of Qt and is 161  focused on leaf surface angles normal to solar incidence on sunlit fractions of the canopy (Cai et al. 2008). Diffuse radiation (Qd), in contrast, constitutes an increasing proportion of Qt with increasing cloud cover and is more uniformly distributed across leaf surface angles and canopy depths. For a given value of Qt, increase in the fraction of diffuse radiation (Qd/Qt) increases the radiation load for a substantial proportion of foliage that is radiationlimited, leading to enhancement of Pg, whereas a decrease of Qd/Qt increases the radiation load on sunlit foliage, which is more likely to be radiation-saturated, resulting in little enhancement (Knohl and Baldocchi 2008; Cai et al. 2008). The effect of Qd/Qt on Qa is evident from the hyperbolic dependence of apparent estimates of εg on Qt (i.e., when Qa is calculated according to Eq. 6.3) (Raulier et al. 2000; Makela et al. 2008; Chasmer et al. 2008), which occurs in part because Qd/Qt is inversely dependent on Qt. While the effect of Qd/Qt on Pg is strong on hourly and daily time scales, it is substantially ‘masked’ by other factors over longer time integrations. Several LUE models have recently incorporated the effect in various ways (Turner et al. 2006; Makela et al. 2008; Cai et al. 2008). Cai et al. (2008) demonstrated that the directionality of Qt may be predicted by assuming that only a fraction of incident beam radiation, kb1, is available for photosynthesis. It is worth pointing out that light-response functions based entirely on Qd (i.e., with kb1 = 0) retain some curvature (Figure 6.1). Although the cause of the curvature is not well understood, it may be accounted for by additionally considering different rates of attenuation of diffuse and beam irradiance, kd and kb, respectively:  ,  	exp      ,  	exp    																																																								 6.7  162  where Qd,0 and Qd,0 are the diffuse and direct PAR above the canopy (at l = 0). To achieve this, Qd/Qt can be estimated using the “clearness index” approach according to: 1 1  exp  /  																																																																																							 6.8  where So is extraterrestrial shortwave irradiance at the top of the atmosphere, Sg/So is known as clearness index, and b1 and b2 are fitted parameters. So was calculated using equations reported by Jin et al. (2004), requiring input of latitude and day-of-year.  6.4.3 Water stress In the original version of 3-PG (herein referred to as “LW97”), the water balance is solved for a single soil layer, with the soil water holding capacity defined by root zone depth and hydraulic properties (field capacity (fc) and wilting point (wp)) that are prescribed according to a look-up-table of discrete soil texture classes. Volumetric soil water content of the root zone (θ) is determined by the balance between precipitation (P) and evapotranspiration (ET), including canopy transpiration (Et) and evaporation of canopy interception (Ei). Mean daytime net radiation (Rn) is calculated from a linear relationship with Sg (Jarvis et al. 1976). Aerodynamic conductance of water vapour (ga) is set constant for evergreen needleleaf forest canopies (Landsberg and Waring 1997). Evaporation from each surface is quantified according to the Penman-Monteith equation (Landsberg and Sands 2011). Absent from the original version, simulation of ground evaporation (Eg) was added to give the model flexibility to simulate the soil water balance in open stands during early regeneration following disturbance. To simulate Eg, transfer functions were calibrated to derive groundlevel values of Rn, daytime vapour pressure deficit, Δe, and ga based on attenuation of above163  canopy values with increasing L (Schulze et al. 1994; Granier et al. 1999). Ground conductance of H2O was calculated as a function θr (Wu et al. 2000). Canopy conductance of H2O (gc) is simulated according to:      																																																																																																																				 6.9  where gc max is a prescribed maximum canopy conductance, and fgc(W) reflects a constraint function that represents water stress: min  ∆ ,  																																																																																																						 6.10  As opposed to the to Lohammar equation (Eq. 5.8), effects of vapour pressure deficit (Δe) are represented according to an exponential function: Δ  exp  	Δ 																																																																																																																				 6.11  and effects of relative soil water content (θr) are quantified according to Eq. 5.10. This methodology reflects a simplification of the Jarvis-Stewart multiple-constraint model (Jarvis 1976; Stewart 1988). The performance of the Jarvis-Stewart functions to simulate gc was evaluated by fitting several different function combinations to estimates of daily values of gc derived from inverting eddy-covariance measurements of ET using the Penman-Monteith equation (Humphreys et al. 2003; Blanken and Black 2004; Bernier et al. 2006). The analysis was conducted using continuous eddy-covariance, meteorological, and soil moisture records at HDF00, HDF88, and DF49 (see Chapter 5 for site descriptions). The models were fitted 164  according to nonlinear least-squares regression for dry days between May and September. Calibrating the model separately at each stand in the chronosequence, the most powerful constraints consistently included an inverse hyperbolic function of Δe (Lohammar et al. 1980; Lindroth and Halldin 1986), a hyperbolic function of Sg (Stewart 1988), and a sigmoidal function of r (Denmead and Shaw 1962; Landsberg and Waring 1997). Although the effect of Sg was omitted from the original version of 3-PG, I chose to include it for the present analysis. A model was then fitted simultaneously to all stands in the chronosequence to develop a ‘global’ model using the average initial parameters from the above site-specific models. I first tested a model wherein gc max was set as a nonlinear function of L (Kelliher et al. 1995; Spittlehouse 2003), which was consistent with a weak across-stand relationship found between mid-summer L and gc max measurements above old (DF63) and young (DF71) stands at Dunsmuir Creek (Price and Black 1990; Kelliher et al. 1995) and the chronosequence data used here (Humphreys et al. 2003; Humphreys et al. 2006) (Figure 6.2a). According to this methodology, gc max for specific stand was defined according to:    	 	exp  																																																																																																											 6.12  where gs is leaf-level stomatal conductance (i.e., gc at L = 1.0 m2 m-2) and kgL reflects attenuation due to shading with canopy depth (Kelliher et al. 1995). The curve in Figure 6.2a corresponds with gs = 0.00475 m s-1 and kgL = 0.087. Optimization failed to converge using this model and visual analysis indicated that differing estimates of predicted gc max, assumed to occur due to variation with L across stands, did not correspond with a unified response function of Sg. As an alternative strategy, I tested a global model where gc max was set constant across stands, while Sg was replaced with a variable 165  describing the absorption of solar irradiance, Sa = Sg [1 - exp(-k L)], where k was set to 0.5 (as in Chapter 5) and L is prescribed based on site measurements. This model exhibited improved performance because it led to unified constraint functions that performed well at each test site (Figure 6.2b-d). It is interesting to note that gc max is also constant in LW97. One notable exception was the divergence in the ‘modifier’ for Sa at HDF00 and to a lesser extent at HDF88 (Figure 6.2b). This likely reflects the fact that L was set constant at each site and future development of the model needs to try to resolve these divergences by accounting for seasonal variation in L and its effect on Sa. With this model convention (characterized by a universal gc max of 0.0190 m s-1) allows for consistent constraint functions to account for water stress (Figure 6.2c-d). The hyperbolic response of gc to Δe was strong and consistent at all sites. The degree of physical realism in this relationship is difficult to interpret, however, because Δe is a variable in the Penman-Monteith equation (which introduces across-equation correlation). Nevertheless, the hyperbolic function derived here from eddy-covariance measurements is consistent with those from other methods (Leuning et al. 1995; Oren 1999; Katul et al. 2009). In 3-PG, gc responds to Δe exponentially according to a rate coefficient, kg. In all known program scripts of 3-PG, a single value of kg is used in the response functions of gc and Pg despite acknowledgement of differing values, with kg being lower for Pg (Landsberg and Waring 1997). Applying kg = 0.05 (Waring and McDowell 2002; Coops et al. 2007), 3-PG did not accurately match the observed patterns of gc at DF49 (Figure 6.2c).The optimal fit of the exponential function at DF49 occurred at kg = 0.17, which closely agrees with kg = 0.19 proposed by Landsberg and Waring (1997). The fitted exponential model was not fully able to match the curvature and continued to approach zero, while observations reached an 166  asymptote at high Δe. The fitted Jarvis-Stewart model performed better, but also underpredicted gc at high Δe (Figure 6.2c).  (a)  (b) 24  HDF88  1.0  DF49  c  0.8  DF71  16  12  Relative g  −1  gc (mm s )  20  HDF00  0.6  0.4  8  DF63  4  DF49 HDF88 HDF00  0.2  0  0 0  1  2  3  4  5 2  6 −2  7  8  9  10  0  5  10  (c)  20  25  30  (d) 1.0  0.8  0.8  Relative g  c  1.0  c  Relative g  15  Sa (MJ m−2 d−1)  L (m m )  LW97 k = 0.05  0.6  g  0.4  LW97 kg = 0.19  0.2  0.6  0.4  0.2  0  LW97 Sand  0 0  2  4  6  8  10  Δe (hPa)  12  14  16  18  0  0.2  0.4  0.6  0.8  1.0  θr  Figure 6.2 Controls on canopy conductance of H2O (gc) in stands of Douglas-fir; (a) relationship between estimates of maximum canopy conductance of H2O (gc max) and leaf area index (L) across stands of Douglas-fir located on Vancouver Island; (b) relative gc versus absorbed solar irradiance, Sa = Sg [1-exp(-k L)], (observed gc divided by modelled gc while holding Sa at 45.0 MJ m-2 d-1) (c) relative gc versus vapour pressure deficit (Δe) (observed gc divided by modelled gc while holding Δe at 1.0 hPa); (d) relative gc versus relative soil water content (θr) (observed gc divided by modelled gc while holding θr at 1.0). Symbols in panels b-d indicate sample quantiles  2×S.E.. Solid curves in panels b-d indicate constraint functions of the Jarvis-Stewart model derived from the global fit. Dashed curves in panel c indicate exponential equations used in LW97 with kg = 0.19 and kg = 0.05. 167  The effect of r on gc was similar at all sites and closely matched the expected response function proposed by Landsberg and Waring (1997) for soils with a ‘sandy’ soil texture class. As r decreased below 0.45, observations of relative gc remained higher than the expected response at DF49, suggesting that deficiencies in the above strategy to isolate the effect, or that unmodelled processes influence the relationship, or that roots may extend below the lowest soil moisture probes (1.0 m), leading to underestimation of r at that site. A similar phenomenon has been noted as a possible cause of discrepancy between eddy-covariancebased estimates of canopy Et and soil water balance at other sites (Bernier et al. 2006). In 3-PG, the effect of water stress on photosynthesis, distinguished herein by fPg(W), is attributed entirely to ‘stomatal’ control of CO2 diffusion between the laminar boundary layer and the sub-stomatal cavity and set equivalent to that of fgc(W), thus giving a general expression of water stress: 																																																																																																										 6.13 To assess the behaviour of f(W) as it pertains to Pg, an additional set of models were fit to half-hourly estimates of Pg derived from partitioning of daytime eddy-covariance CO2 flux measurements. The models consisted of a Michaelis-Menten function of Qa, adjusted by an Arrhenius function of T and an exponential function of Δe (Winner et al. 2004). The training sample was limited to periods when r > 0.40 between May and September. In the same manner as for the above model of gc, the effect of θr on Pg was isolated from model residuals, standardized, and stratified across a gradient in r (Figure 6.3a). No model was developed at HDF00 as half-hourly Qd/Qt was not measured. Impacts of r on gc and Pg were compared in relative terms by plotting each response across a gradient in r (Figure 6.3b). At the HDF88 168  site, decline of relative Pg was similar to that of relative gc, while at the DF49 site, decline was over-predicted by the response function for ‘sandy’ soil texture class between r of 0.40 and 0.20, before re-approaching the expected function at r < 0.15. Equivalent relative responses of gc and Pg to r at the HDF88 site supports the use of a unified response function in 3-PG (i.e., equivalent relative effects on gc and Pg). A unified response, however, was less evident at DF49, where rates of decline differed between gs and Pg. With respect to the correlation between Pg and Δe, kg = 0.05 closely agreed with the estimate from fitted half-hourly predictions at the DF49 site and reflects an intermediate effect between responses previously reported for other conifer forests (Figure 6.3c). The exponential function proposed by Landsberg and Waring (1997) and the linear function used by Chen et al. (1999) overestimate the fitted constraint, while the MODIS satellite photosynthesis product (MOD17) for evergreen needleleaf forests underestimates (overestimates) the constraint at low (high) Δe (Heinsch et al. 2003). Inferring the effect of Δe on f(W) from a single model fitted to residual Pg is hazardous given that (1) the causal mechanism is actually – but not necessarily restricted to – gc rather than Δe and (2) there is strong interdependence between Δe and other driving variables (e.g., T) which can lead to error in parameter estimation of the half-hourly model of Pg. To further isolate the relationship from the influence of T, the Pg model was re-run at the DF49 site using only the Michaelis-Menten submodel to remove dependence on Qa, isolating the relationship between (observed minus predicted) residuals and Δe for narrow (1.0 ºC) temperature classes between 4.0 and 26.0 ºC, and excluding periods when r was below 0.40. Figure 6.3c shows the relationships between relative Pg and Δe at four different temperature 169  classes (each symbol representing sample quantiles (see Wilks 1995, pg 22) - the mean of 1/10th the sample size). Significant correlation was consistently found for the unstratified (raw) variables within each subsample between temperatures of 10.0 and 24.0 ºC.  1.0  (a)  1.0  0.8  Relative Pg  0.8  Relative Pg  (b)  0.6  0.6  0.4  0.4  0.2  0.2  0  LW97  0 0  0.2  0.4  0.6  0.8  1.0  0  0.2  θr 1.0  0.6  0.8  1  0.8  1  Relative Gc 1.0  (c)  (d)  0.8  Relative Pg  0.8  Relative Pg  0.4  0.6 T=24°C  0.4  LW97  0.6  0.4  T=20°C  0.2  0.2  T=18°C T=14°C  0  0 0  5  10  15  Δe (hPa)  20  25  30  0  0.2  0.4  0.6  Relative Gc  Relative gc  Figure 6.3 Comparison between observations and model predictions of water stress at Douglas-fir flux towers including relationships between (a) relative gross primary production (Pg) and relative soil water content (θr) at DF49 (solid circles) and HDF88 (open diamonds) (b) relative Pg and relative gs in response to perturbation in θr (c) relative Pg and vapour pressure deficit (Δe) at DF49 (d) relative Pg and relative gc in response to a perturbation in Δe at DF49. Symbols indicate observations stratified across sample quantile classes of the independent variable (Wilks 1995). All sampling constrained to the friction velocity > 0.35 m s-1. Curves labeled “LW97” indicate the values used in the 3-PG model.  170  The behaviour illustrated in Figure 6.3c is consistent with other observations, with decreasing sensitivity of Pg to Δe with increasing T in controlled chamber measurements (Dai et al. 1992), and slight non-linearity in the Δe-response at each temperature (Katul et al. 2009). Within each temperature class, relative Pg was inversely correlated with Δe, while the average relative Pg simultaneously increased with increasing average T (and Δe) for each class. For comparison, recent parameterisations of 3-PG with kg = 0.05 (upper solid curve in Figure 6.3c) correspond well with the observed relationship at 20 ˚C, whereas values appropriate for matching gc (e.g., kg = 0.17; lower solid curve in Figure 6.3c) would drastically under-predict Pg. Reasons for this behaviour become more apparent when gc is perceived as the causal agent of the relationship between Pg and Δe. Using the well-constrained relationship between gs and Δe from the Jarvis-Stewart model (Figure 6.2), gc(Δe) can be back-calculated from observations, converted to relative gc, and plotted against relative Pg for each temperature class (Figure 6.3d). Patterns match the expected response of Pg when a linear relationship is assumed between Pg and supply of CO2 under varying gc (Katul et al. 2009; Medlyn et al. 2011). I used the following empirical relationship for fPg(W) developed by Anderson et al. (2000):    /  																																																																																																																																6.14  where Ci is the intercellular CO2 concentration, Ca is the ambient CO2 concentration, and γn is the nominal level of operation (Anderson et al. 2000). The ratio, Ci/Ca was then modelled according to Katul et al. (2009) as:  171  C C  1  1.6	WUE C  /  ∆e  /    																																																																																									 6.15  where water-use efficiency (WUE) is the ratio of Pg to Et or the inverse of the ‘cost’ of transpiration (Hari et al. 1986). When γn = 0.80 and WUE is prescribed to increase with gc to accommodate the behaviour of observations, semi-empirical models (Leuning 1990; Collatz et al. 1991; Wang and Leuning 1998), and optimality theory (Cowan 1977; Hari 1986; Arneth et al. 2002; Katul et al. 2009; Medlyn et al. 2011), the function closely matches the observed relationships at DF49 (Figure 6.3d). When WUE is set constant, Eq. 6.15 exhibits a remarkable ability to reproduce the salient features of variability in Pg. To attain strong agreement, however, the model requires an iterative solution, or some degree of simplification, such as replacing the right-hand term, Δe1/2 f(θr), with the Jarvis-Stewart model of gc. Indeed, this appears to be a valuable potential way to incorporate the curvilinear relationship between gc and Pg into models like 3-PG without use of interaction. Re-expressing the response as a function of relative gc implies that the decreasing sensitivity of Pg to Δe as Δe increases reflects a combination of changing WUE and operation at different regions of Ci/Ca (i.e., different regions of the CO2 assimilation-Ci response). Intuitively, WUE would be expected to decline as water stress increases, however, WUE simultaneous increases as thermal stress is alleviated (see Section 6.4.4). The relationship breaks down at high gs (low Δe) as Ci/Ca  γn and Pg transitions from being ribulose 1-5 bisphosphate (RuBP)-saturated to RuBP-limited, which can be represented empirically according to γn (Anderson et al. 2000) or explicitly in biochemical models (Farquhar and von Caemmerer 1982). From this analysis it is assumed that the marginal effect of gs on Pg can be inferred from Eq. 6.15 (e.g., under light-saturated conditions and at T  Topt), which is largely 172  consistent with values of kg currently used in 3-PG to optimize predictions of Pg. Failure to isolate the effect for a specific WUE will contaminate the relationship. The main consequence of adopting Eqs. 6.14 and 6.15 over that of the approach in 3-PG is that fPg(W) increases asymptotically, as opposed to linearly, with increasing gc in response to a perturbation in Δe. Asymptotic behaviour is clearly demonstrated by many studies (Meinzer 1982; Dai et al. 1992; Fisher et al. 2007; Maseyk et al. 2008). This is also consistent with a nearly linear relationship between Pg and Δe (Fites and Teskey 1988; Leuning 1995; Dang et al. 1997; Winner et al. 2004; Katul et al. 2009). If ga is assumed to be high, then it may be possible that curvature might be explained by Fickian diffusion; unlike H2O, the CO2 gradient across stomata increases as conductance decreases, feeding back on Ci. Although many studies suggest a more curvilinear relationship between Pg and Ci, this could reflect failure to account for internal conductance (gi) in earlier gas-exchange measurement techniques (Ethier and Livingston 2004). Formualation over a wide range of temperatures also tends to ‘linearize’ the relationship between Pg and gc. Eqs. 6.14 and 6.15 introduce differences in the relative impacts of water stress on gc and Pg depending on whether the stress originates in the root zone or surface layer. The reasons for this are not entirely clear. If it is assumed that the radical behaviour of Pg(θr) at mid-levels of θr at DF49 was caused by different spatial representativeness of the soil moisture and eddycovariance measurement systems (Bernier et al. 2006), then results may support the representation of soil water stress in 3-PG – soil water resistance imposes equivalent relative effects on gc and Pg. This does not necessarily mean, however, that the effect on Pg reflects a direct response to gc (Sharkey et al. 1984; Schulze 1986). Soil water resistance may impose reduction in plant water potential (ψp) and hydraulic conductance (Kp) within the root-shoot173  leaf pathway that either reduces internal CO2 conductance (gi) and chloroplast carbon dioxide concentration (Cc), or directly disrupts metabolism (Grassi and Magnani 2005; Schulze et al. 2006; Flexas et al. 2008), leading to inhibition of Pg (Wong et al. 1985; Dang et al. 1997), while the effect of root signaling to close stomata could reflect an evolutionary response to avoid unnecessary transpiration under diminished photosynthetic capacity (Schulze 1986; Schulze et al. 2006). The same can be said for effects of Δe, although the component that is ‘stomatal’ in nature is relatively well constrained (Oren et al. 1999). Application of the idea that ψp affects Pg was applied by Williams et al. (1996), who proposed that stomata operate to optimize Pg above a threshold ψp at which point stomatal closure is imposed to avoid damaging or irreversible loss of Kp. However, as in 3-PG and conventional biochemical models, the approach assumes that the effect on Pg is stomatal in nature, which fails to explain apparent non-stomatal effects (Wong et al. 1985). Evidence of independent responsiveness of gc to Sg is still apparently debated (Morrison and Jarvis 1981; Landsberg and Sands 2011). The semi-empirical couplings are specific cases of optimality theory (Collatz et al. 1991; Leuning 1995; Medelyn et al. 2011), while the optimality model and the Jarvis-Stewart model are conceptually indistinguishable – plants have evolved to minimize the cost of transpiration per unit C gained. Using Sg as an independent variable in the Jarvis-Stewart model as opposed to coupling with Pg (Eq. 6.15) does not have significant implications for model skill inferred from comparisons with present-day eddy-covariance CO2 flux records, but is generally not used in simulations over widely varying Ca. Yet, the only rationale for the emergent behaviour in optimality models is that it appears to match most salient features of contemporary variability, which is only partially reassuring. In practical terms, use of the Jarvis-Stewart model avoids the need for 174  iterative solutions for the coupled model, although Leuning’s model provides a quadratic solution, while quadratic solutions also exist for optimality theory (Arneth et al. 2002; Medelyn et al. 2011). In 3-PG, the consequence of assuming Δe exerts equivalent relative effects on gc and Pg prohibits simultaneous optimization of Et and Pg (Figure 6.4). In the specific case of Douglas-fir forest stands analyzed here, operators must choose between optimizing Et by setting kg ~ 0.17, or optimizing Pg by setting kg ~ 0.07. These stated optima are specific to maximum canopy-scale stomatal conductance of 0.0200 m s-1 and εg max = 3.00 g C MJ-1 quanta (estimates that allow the LW97 version of 3-PG to match canopy gc and Pg at DF49 well) and will improve slightly by tuning either value in potentially unrealistic ways. An important consideration is that the choice to optimize Pg will be inhibited by the error in simulation of Et, which exacerbates the error in the soil water modifier of Pg. As shown in Figure 6.4, prediction of Pg under normal operation of the model exhibits a lower potential skill and at an intermediate (unrealistic) value of kg. This is because Et is uninhibited by high Δe, rapidly depleting soil water and producing unrealistically low θr, which then feeds back on Pg through f(θr). The problem can be alleviated by turning the soil water modifier off (Figure 6.4), but this then defeats the purpose of representing the soil water balance. In some situations, the problem can also be alleviated by optimizing for Et and then increasing εg max to compensate, or optimizing for Pg and increasing gc max. Although this allows the bias in Et or Pg to be removed, the resulting effect of Δe on Pg is physically inconsistent and prohibits accurate representation of environmental stress. Reducing gc max is a compelling solution, as lowering gc max from 0.020 m s-1 to 0.012 m s-1 can appear physically realistic, however this is  175  only because 3-PG does not include a modifier to adjust gs based on Sg (or photosynthesis as in optimality models).  0.8  0.6  MEC  Et  Pg without f(θr)  0.4  Pg with f(θr)  0.2  0  −0.2 0.025  0.050  0.075  0.100  0.125  0.150  0.175  0.200  0.225  0.250  Sensitivity to vapour pressure deficit  Figure 6.4 Divergent optima in the model efficiency coefficients (MECs) of monthly (circles) gross primary production and (triangles) evapotranspiration across a gradient in the coefficient, kg, that controls reduction of stomatal conductance and photosynthesis. Solid circles indicate the MEC for gross primary production when the model is run normally, while open circles indicate the MEC for gross primary production when simulated soil water stress is turned off. Observations are from the DF49 flux tower. MECs of 1.00 imply perfect agreement between models and observations, MECs of 0.00 imply model skill equivalent to use of the mean observation.  6.4.4 Thermal stress The temperature sensitivity of α and Pg max can be analyzed by estimating light-response functions for specific temperature classes at the DF49 flux tower (Figure 6.5). It is advantageous to first remove known dependence of Pg on Δe using an exponential function (see Section 6.4.3) as well as dependence on Qd/Qt by using only Qd (as opposed to Qt) as shown in Figure 6.5b. At Qd = 200 mol m-2 s-1, α increases exponentially with T over the 176  observed range at DF49 in accordance with the Arrhenius equation (Eq. 5.5), ranging from near 0.00 to 0.60 mol CO2 mol-1 quanta at T = 30 ˚C (Figure 6.6a). Canopy α exceeds the marginal leaf-level value by as much as six times. Consistent with previous measurements by Humphreys et al. (2006) and Chen et al. (2006), measurements taken from ten transects in May 2009 at the DF49 flux tower suggested that average L is 8.7  1.6 m2 m-2 (S.D.) across the tower footprint. Multiplying the marginal leaf-level α = 0.125 mol CO2 mol-1 quanta by L = 8.7 and setting parameters for the Arrhenius equation to characteristic values for RuBP regeneration (σ = 2.0; Ea = 65000 J mol-1; Topt = 36 ˚C) over-predicts field measurements of canopy α across all temperatures. Lowering L to 5.6 gives a stronger fit (Figure 6.6). This reduction of 35% (or ‘effective’ L) may reflect canopy shading and the combination of extinction in Qd and photosynthetic capacity (Lewis et al. 2000), or limiting Ca. Experimentation with Beer’s law suggests that the 35% reduction below expected α can be fully explained by radiation extinction with the extinction coefficient of k = 0.52 (very close to a spherical leaf angle distribution). Hence, L and photosynthetic capacity affect canopyscale observations of α. The temperature response of α is similar to that of RuBP regeneration in biochemical models (e.g., Farquhar and von Caemmerer 1982), while there is no evidence of decline in α due to increasing diversion of energy towards oxygenation over the range of observed temperatures. This contradicts observations of quantum yield of net photosynthesis, which have expressed decline with increasing temperature due to O2 inhibition (Ehleringer and Björkman 1977; Monson 1982; Brooks and Farquhar 1985; McMurtrie et al. 1992).  177  Consistent with a wide range of studies, including laboratory experiments (Berry and Bjorkman 1980; Way and Oren 2010), dendrochronologies (Chen et al. 2010b), eddycovariance, and inventory plots (Rehfeldt et al. 1999; Reich and Oleksyn 2008; Nedlo et al. 2009; Clark et al. 2007; Wang et al. 2010), the temperature response function of Pg max at DF49 suggests that photosynthetic capacity declines above an optimal temperature (Figure 6.6b). Lacking a strong understanding of what causes the decline above optimal T, most studies are careful not to attribute it necessarily to temperature. For example, Barber et al. (2000) described the inverse correlation between tree growth and summer temperature as a form of “temperature-induced drought stress”. In many dendrochronologies, drought indices are found as strong indicators of the decline, while drought conditions tend to covary with T. Part of the photosynthetic decline at high T is assumed to reflect a response to stomatal regulation of gas diffusion. Lloyd et al. (2008) describes this as the “indirect” response to warming. Although details regarding the underlying mechanisms remain unclear, the general magnitude and behaviour of indirect effects of Δe and θr on photosynthesis as they range across temperature are only partially constrained by empirical observation. Stratifying temperature-response functions of Pg at the DF49 flux tower by narrow classes of Δe and holding irradiance constant indicates that T, itself, may not be responsible for reducing Pg max at temperatures above 10 ˚C as implied by Figure 6.6b (Figure 6.7). Direct analysis of observed Pg indicates that, while overall average levels of Pg decline with increasing Δe, Pg continues to exhibit positive correlation with T (Figure 6.6a). Removing the effects of stomatal regulation according to the empirical modifiers of gs, f(Δe) and f(θr) introduced earlier suggests that stomatal regulation accounts for a significant proportion of the decline (Figure 6.7b and 6.7c), but fails to fully account for declines below the marginal 178  T-response function expected based on the Arrhenius equation (Figure 6.7d). The observations and f(Δe)-corrected observations both exhibited strong correlation with T (Figure 6.7 and Table 6.1). Although disruption was apparent, the relationships remained significant with additional correction for f(θr). For the observations, temperature sensitivity (T) declined from 1.58 to 0.82, however, the decline appeared to be explained by f(Δe) and f(θr) (Table 6.1).  (a)  Pg (μmol CO2 m−2 s−1)  30  (b)  30  20°C 30°C 15°C 25°C 10°C  25  20  15°C 20°C 10°C  25  30°C  25°C  20  5°C 5°C  15  10  15  10  0°C  5  0°C  5  0  0 0  500  1000 −2  Qt (μmol m  1500 −1  s )  2000  0  100  200  300  400  500 −2  Qd (μmol m  600 −1  700  800  900  s )  Figure 6.5 Light-response analysis of gross primary production (Pg) derived from partitioned eddy-covariance CO2 flux measurements above a mature Douglas-fir canopy and with the response to vapour pressure deficit empirically removed and stratified by 5 ˚C classes of air temperature: (a) incident total photosynthetically-active radiation (Qt) and (b) incident diffuse photosynthetically-active radiation (Qd). All sampling constrained to u* > 0.35 m s-1.  179  2  0.8  −2  0.092  L=8.7 m m  0.7  0.081  0.6  0.069  0.5  0.058  0.4  2  −2  0.046  L=5.6 m m 0.3  0.035  0.2  0.023  0.1  0.012  0  0 0  10  20  T (°C)  30  40  45  5.2  (b) 40  4.62  35  4.04  30  3.46  25  2.89  20  2.31  15  1.73  10  1.15  5  0.58  0  Pg max (μmol CO2 m−2 s−1) / L  0.104  Pg max (μmol CO2 m−2 s−1)  α (μmol CO2 μmol−1 quanta)  0.115  (a)  α (μmol CO2 μmol−1 quanta) / L  1 0.9  0 0  10  20  30  40  T (°C)  Figure 6.6 Temperature-response functions at the DF49 flux tower: the coefficient representing (a) apparent quantum yield (α) and an Arrhenius fit and (b) maximum gross primary production (Pg max) and a parabolic fit. Values on the right axes of each panel reflect scaling to per unit leaf area assuming L = 8.7.  Consistent positive correlation with T suggests that effects of O2 inhibition do not explain declines in photosynthesis at higher temperatures at the DF49 flux tower. There are no known studies that tested for direct negative effects of temperature on Pg at other eddycovariance flux towers so it is unclear whether this behaviour is unique among these types of data. However, the fact that at least one site indicates no direct heat stress raises the question of whether the alternative explanation – that photosynthesis does decline in direct response to increasing temperature (e.g., Monson et al. 1982) – proves causality. Unpublished experimentation with a biochemical model (Farquhar and von Caemmerer 1982) with semiempirical stomata-photosynthesis coupling (Wang and Leuning 1998) suggests that Rubisco kinetic constants need to be drastically tuned from the default parameters proposed by Wullschleger (1993) and Bernacchi et al. (2002) in order to reproduce this behaviour (not shown). 180  50  50  (b) 45  40  40  Δe = 2 hPa  Pg (μmol CO2 m  −2  35  Δe = 6 hPa  30  Δe = 10 hPa  25  Δe = 18 hPa  20 15  Pg (μmol CO2 m−2 s−1)  45  −1  s )  (a)  35 30 25 20 15  Δe = 14 hPa Δe = 22 hPa  10  10  5  5 0  5  10  15  20  25  30  0  5  10  T (°C) 50  25  30  (d)  45  45  Marginal f(T) 40  −1  Pg (μmol CO2 m−2 s−1)  40  s )  20  50  (c)  35  −2  Pg (μmol CO2 m  15  T (°C)  30 25 20 15  Without f(Δe) and f(θr)  35 30 25  Without f(Δe) 20 15  Observed 10  10  5  5  0 0  5  10  15  T (°C)  20  25  30  0  5  10  15  20  25  30  T (°C)  Figure 6.7 Temperature (T)-response functions of gross primary production (Pg) derived from hourly eddy-covariance measurements at the DF49 flux tower. Curves are stratified by 4-hPa classes of vapour pressure deficit (Δe) with Qt = 1200  200 mol quanta m-2 s-1 and u* > 0.35 m s-1 (a) observations, (b) observations adjusted to remove vapour pressure deficit effects on Pg (i.e., multiplied by 2-exp(-0.07Δe)), (c) observations with effects of both Δe and relative soil water content, f(θr), removed and (d) comparison between the observed temperature response function, and those expected in the absence of f(Δe) and f(θr), and the theoretical maximum (“marginal f(T)”) at Qd = 200 mol quanta m-2 s-1. Symbols indicate nine temperature quantiles within each Δe class for visual inspection only; raw data indicate significant positive correlation between hourly Pg and T within each class (P < 0.01).  181  It is unclear whether operators of similar biochemical models make adjustments to those parameters, as they are commonly not disclosed. It is unclear whether earlier analysis of the temperature sensitivity of photosynthetic quantum yield using gas-exchange measurements gave consideration to whether Et and ψp were controlled over experimental ranges of T, which in retrospect is of considerable importance granted that the experimentation was based on analysis of Ci, rather than Cc. Monson et al. (1982) regulated Δe, but did not disclose experimental responses for E or ψp.  Table 6.1 Temperature sensitivity (T) (i.e., slope coefficients) derived from regression relationships between gross primary production (Pg) and air temperature (T) at six different classes of vapour pressure deficit (Δe) (4-hPa class width) at the DF49 flux tower. N indicates number of half hour measurements in each regression. Bold coefficients are statistically different from zero at the 99% confidence level. Δe class (hPa)  Mean T (˚C)  N  T Observations (mol CO2 ˚C-1)  T Observations+f(Δe) (mol CO2 ˚C-1)  2 6 10 14 18 22 Mean:  7.5 12.8 17.7 20.4 23.4 25.6  288 1494 711 330 142 67  1.58 1.19 0.84 0.49 0.88 0.82 0.96  1.62 1.48 1.20 0.81 1.58 1.47 1.36  T Observations +f(Δe) +f(θr) (mol CO2 ˚C-1) 1.74 1.80 1.54 1.49 3.67 1.62 1.98  The temperature sensitivity of Pg max in Figure 6.6b could be linked to other bottlenecks involving ribulose 1-5, bisphosphate carboxylase/oxygenase (Rubisco) activity, constraints on photosynthetic metabolism and growth, or non-stomatal constraints on CO2 diffusion (Jones 1985; Downton et al. 1988; Warren et al. 2004; Grassi and Magnani 2005; Flexas et al. 2008). Remarkably, if these unknown constraints on Pg max were alleviated, photosynthetic 182  efficiency would hypothetically increase by roughly a factor of 4.5 as T increased from 20˚C to 36˚C (Figure 6.6a).  6.5 Evaluation of 3-PG simulations 3-PG was evaluated based on comparisons with eddy-covariance CO2 flux measurements and permanent forest inventory measurements. Results pertain to operation of the widely-used version of the model with parameters borrowed from previous studies (Table 6.2).  Table 6.2 Species-specific parameters describing environmental stress in the LW97 version of 3-PG model (adjusted to include temperature sensitivity according to Sands and Landsberg 2002). Symbol εg max  Value 3.0  Tmin Topt Tmax gc max  -2.0 20.0 40.0 0.018  Units g C MJ-1 quanta ˚C ˚C ˚C m s-1  kg  0.07  -  Description Canopy maximum gross photosynthetic light use efficiency Minimum temperature for photosynthesis (Waring and McDowell 2002) Optimum temperature for photosynthesis (Waring and McDowell 2002) Maximum temperature for photosynthesis (Waring and McDowell 2002) Canopy-scale maximum stomatal conductance of H2O (Waring and McDowell 2002) Sensitivity of canopy-scale stomatal conductance to vapour pressure deficit  6.5.1 Stand development and tree C dynamics Although the focus of this study was to analyze representation of environmental stress and its impacts on the prediction of stand productivity, all components of the model, including development of the stand (i.e., L and DBH), were tested to ensure they were functioning properly. The model was manually calibrated to ensure matches with a variety of available observations derived from eddy-covariance measurements (Morgenstern et al. 2004; Humphreys et al. 2006), soil chamber measurements (Jassal et al. 2007), and groundplot 183  measurements (Trofymow et al. 2007; Trofymow et al. 2008) within the area of the DF49 flux tower. Figure 6.8 shows all the main diagnostics for stand development in the model. Simulations refer strictly to the DF49 site; however, to facilitate comparison, the flux tower chronosequence was superimposed at the respective year for comparison purposes. To focus only on the behaviour of stand development, inter-annual variability due to environmental stress was temporarily excluded from simulations by applying the mean annual cycle of monthly weather recorded at DF49, 1998-2006.  (a) 20 15 10 5 0  12  Tree density (stems ha )  14  1600  1  NPP (Mg C ha−1 yr−1)  g  P (Mg C ha−1 yr−1)  25  (b)  10 8 6 4 2 0  (c)  1200 800 400 0  Roots  8  −1  6  2  0.3  10  0.2  Branch+Bark  0.1  Foliage  (e)  (f)  BA (m ha )  0.4  Stemwood  L (m2 m−2)  Allocation fraction  80  (d)  4 2 0  0.5  −1  yr )  −1  50  60  (Mg C ha−1)  (j) Aboveground  200 150  dw  100  C  50  Roots  0  (k)  50 40 30 20 10 0  1950  1970  1990  2010  Time, years  2030  2050  4  (i)  3 2 1 0  Turnover (Mg C ha−1 yr−1)  0  ag  −1  (Mg C ha )  Psw (Mg C ha  100  sw  1  150  0  C  20 0  (h)  (Mg C ha−1)  (g) 1.5  250  40  200  C  BAI (m2 ha−1 yr−1)  2  60  1950  1970  1990  2010  Time, years  2030  2050  3  Roots  (l)  2.5 2 1.5 1  Foliage  0.5 0 1950  1970  1990  2010  2030  2050  Time, years  Figure 6.8 Demonstration of 3-PG model simulations of stand-level tree development and carbon dynamics for a chronosequence of Douglas-fir plantations near Campbell River, British Columbia. Simulations were conducted with site information and disturbance history for the DF49 flux tower (Morgenstern et al. 2004; Trofymow et al. 2008) and run with the 1998-2006 mean monthly climate to demonstrate model behaviour in the absence of inter184  annual variability. Relevant measurements are shown for comparison: (a) annual total gross primary production (Pg); observations derived from eddy-covariance flux measurements at HDF00, HDF88 and DF49 superimposed on time according to the stand age of each measurement record; (b) net primary production (NPP); circle symbol: DF49 estimate from Jassal et al. (2007); square symbol: DF49 estimate from Schwalm et al. (2007); (c) stand density; initial estimate: Humphreys et al. (2006); 2002 estimate: mean  S.D. from twelve 0.04-hPa National Forest Inventory groundplot measurements (Trofymow 2008); (d) annual 3-PG allocation fractions for branch and bark, roots, foliage, and stem carbohydrate allocation fractions; (e) total leaf area index (L): downward triangles: HDF00 measurements; upward triangles: HDF88 measurements; 2002 DF49 estimates: triangle: Black (2008); square: Chen et al. (2006); 2009 DF49 estimate: mean  S.D. from ten 200-m transects distributed over the DF49 footprint; (f) basal area: circle symbols: age-class means derived from permanent sample plots with site class 35 m (SC35) leading with Douglas-fir in coastal British Columbia; (g) SC35 basal area increment: open symbols: gross basal area increment; closed symbols: net basal area increment; (h) stemwood carbon; square symbol: 2002 estimate derived from groundplot mean  S.D.; circle symbols: age-class means from SC35 permanent sample plots; (i) solid curve and open circles: stemwood growth; dashed curve and closed circles: net stemwood production; (j) aboveground and belowground tree carbon; observed aboveground tree carbon: groundplot mean  S.D.; (k) standing dead wood carbon; observations: groundplot mean  S.D.; (l) foliage and root turnover; observed foliage turnover: mean annual estimate from periodic measurements conducted at 27 traps at DF49 between 2002 and 2005 (Trofymow 2007).  As in other analyses (Landsberg et al. 2003; Landsberg et al. 2005), the model shows a strong capacity to reproduce the salient features of variability in the development of Douglasfir stands, including coherency between the different measurement systems. It is interesting to note that the only solution to match all diagnostics indicates that NPP during the measurement period at DF49 was approximately 950 g C m-2 yr-1, which is only slightly 185  above estimates from Jassal et al. (2007). It is also interesting to note that the model closely matched average observations of Pg (Figure 6.8a) and NPP (Figure 6.8b), yet tended to overpredict Csw (Figure 6.8h) and aboveground carbon (Figure 6.8i). Consistent with findings of positive historical trends in tree growth highlighted in Chapter 3, this may have occurred because the model was run with 1998-2007 average weather variables from the tower, which likely reflected more ideal growing conditions than the 1949-2007 average climate.  6.5.2 Gross primary production Much like results from Chapter 5, the prognostic simulations with 3-PG showed strong ability to simulate monthly Pg at the DF49 flux tower (R2=0.95, RMSE=1.0 g C m-2 d-1), but limited ability to match interannual variability (Figure 6.9). The relationship between observed and predicted annual Pg was not significant (P = 0.21, R2 = 0.17).  2300 2250  Observations −1  yr )  2200  Annual Pg (g C m  −2  2150 2100 2050 2000 1950  3-PG  1900 1850 1998  2000  2002  2004  2006  Time, years  Figure 6.9 Comparison between observed (closed circles) and 3-PG (open circles) predicted annual gross primary production (Pg) at the DF49 flux tower.  186  6.5.3 Stemwood growth Applying the 3-PG model to permanent sample plots of Douglas-fir (n = 621), simulations exhibited some agreement with observed decadal fluctuations, but underpredict the long-term trend in Gsw that is observed from the sample by approximately 50% (Figure 6.10).  Age−detrended Gsw (Mg C ha  −1  −1  yr )  3−PG LW97 0.6  (a)  0.4  Observations 0.2  3-PG  0  −0.2  −0.4 1960 1965 1970 1975 1980 1985 1990 1995  Time, years  Figure 6.10 Comparison of observed (solid) and 3-PG predicted (open symbols) periodic annual stemwood growth (Gsw) at inventory plots of coastal Douglas-fir. Both observations and predictions were detrended to remove variance explained by stand age (see Chapter 3 for details).Solid and dashed lines indicate best-fit trend lines using ordinary least-squares regression.  6.6 Discussion A continuum of modelling approaches exists to simulate NPP, ranging from simple regression models to complex process-based models. One of the most important features to define model complexity is whether the model program employs ‘vectorization’ or ‘loops’. The main implication is that a vectorization of the problems under question will take 187  microseconds to run, while looping will take seconds, marking the difference between being able to efficiently test model structure and calibration through numerical optimization. 3-PG includes a monthly loop, which in terms of challenges in usage, means that it is much closer to coupled land-surface models than to much simpler fitted statistical models. Given the addition of computational (and operational) expenses, looping needs to be justified based on the gains in model skill, flexibility, and physical realness. 3-PG loops for two reasons: the soil water balance and stand development. The latter need not be simulated on a monthly time step, whereas the former requires a monthly time step at a minimum. Unless the above problems with representation of water stress can be resolved, there is no justification for running the model within a monthly loop. Although it is clear from analysis at DF49 that canopy Pg is strongly linked with L, the advantages of decoupling the two parameters also has clear advantages. In a fully coupled system, early stand development (i.e., as Cf increases from 1.0 or 84.0 g C m-2 following natural regeneration or planting) can be highly unstable. “Sun” leaves likely dominate canopy Pg during early regeneration. When the two are coupled, decadal climate variability can also cause drastic changes in canopy productivity on multi-annual to decadal time scales. Despite the interest in these types of mechanisms (specifically the contribution of L-induced feedbacks to climate change, CO2 fertilization, and N fertilization), they would prohibit use of the model in many instances. 3-PG exhibits an inability to reproduce interannual variability of Pg at eddy-covariance flux towers and decadal variability of Gsw at permanent sample plots, which are important benchmarks to validate this type of model prior to forecasting. A literature review of model predictive skill suggests that these challenges are not specific to 3-PG or this study area (e.g., 188  Coops 1998; Tickle et al. 2001; Almaida et al. 2004; Sands and Landsberg 2002; Stape et al. 2004; Miehle et al. 2006; Miehle et al. 2009; Dye et al. 2004; Esprey et al. 2004; Paul et al. 2007; Peng et al. 2002; Peng et al. 2009; Schmid et al. 2006; Pietsch et al. 2005; Harkonen et al. 2010; Weiskittel et al. 2009; Duursma et al. 2007). Indeed, HMs convey a general inability to substantially improve model predictive skill relative to growth and yield models, while PBMs rarely attempt to make such comparisons. A major objective behind including process-based modelling in AYMs should be to improve the accuracy of model predictions. In the context of simulations in Canada, this specifically means removing the temporal bias that is apparent in 3-PG simulations (Figure 6.9), which would also be expected to occur in growth and yield models, through explicit representation of the factors driving systematic trends in Gsw and Msw. The 3-PG model remains a strong candidate for such applications, but suffers from deficiencies in the representation of environmental stress that currently inhibits the ability to achieve the aforementioned objective. Some of the deficiencies arise from the design simplifications that arose through model reduction and scaling techniques, while others clearly express unresolved debate about the physiological mechanisms controlling plant productivity. Below is an outline of these key processes:    The LUE algorithm is decoupled from L, simulating the average absorbed photosynthetically active radiation of a single leaf class, which is incompatible with the theoretical value of εg max, while use of “canopy” values underestimates the actual value of εg max by an order of magnitude in dense stands. Setting εg max unrealistically  189  low, allows operators to achieve good fits to observations made under current conditions, but prohibits realistic representation of transient responses to warming.    εg is dependent on the directionality of irradiance and, in particular, the amount of diffuse irradiance. This has important effects on the spatial distribution of Pg in complex terrain. Assuming a linear relationship between Qt and Pg will significantly underestimate Pg in regions affected by topographic shading.    3-PG does not represent variability in Ca, despite strong evidence that it is in limiting supply.    The temperature sensitivity of εg in Douglas-fir reflects thermal effects on RuBP regeneration, while declines at high temperature reflect processes that appear to be only indirectly related to temperature (i.e., ‘non-stomatal’ water stress). The parabolic temperature-response function in 3-PG will allow operators to match the contemporary spatial response of growth; however, the model will attribute declines in productivity in response to transient warming above the optimum to temperature.    Vapour pressure deficit imposes different relative effects on stomatal conductance and photosynthesis. Assuming equivalent relative effects in the 3-PG model prohibits simultaneous optimization of canopy Pg and Et. Favouring optimization of Pg at the expense of Et must take care to ensure error in Et does not restrict skill in predictions of Pg by affecting the soil water balance.  190  Chapter 7: Conclusion 7.1 Summary of findings This thesis investigated historical patterns of variability in forest productivity, including individual focus on tree stemwood growth (Gsw), mortality (Msw), and gross primary production (Pg) in temperate-maritime forests of southwest British Columbia, Canada. The observations were used to: (1) address the scope of the problem facing inclusion of environmental sensitivity into forest resource management by further elucidating the magnitude of past trends and variability; (2) attribute observed patterns to specific biophysical processes and; (3) develop and test a combination of empirical and process-based models. These results provided interesting new insights into the recent state of forest productivity in southwest BC and strategies to anticipate future responses to environmental change. Major conclusions of the thesis are summarized below:    Increased tree growth: Applying a creative analysis technique developed by Caspersen et al. (2000) to a large permanent forest inventory in southwest BC, I found evidence that observations of net stemwood production (Psw) increased between 45 and 60% since the end of the Little Ice Age. The assertion of long-term enhancement was further supported by significant positive trends in Gsw (0.60% yr-1) and Psw (0.44% yr-1) for the more recent measurement period.    Recent trends in tree growth were driven by environmental changes: Statistical analyses aimed at modelling historical variability indicated that both climate, including long-term trends in summer temperature and precipitation and other factors, likely consisting of a combination of increasing atmospheric carbon dioxide (CO2) 191  and nitrogen deposition (Nd), were responsible for historical growth increases. As a consequence, representation of direct climatic controls on Gsw would, therefore, not allow models to match observed trends. These findings suggest that environmental changes introduce substantial bias in conventional age-class yield (ACY) models by contaminating age-response functions that are fit to chronosequences that span a systematic change in environmental conditions.    Increases in drought-induced tree mortality offset a significant proportion of historical growth enhancement: Variation in Msw formed wave-like fluctuations that were closely linked with increases in drought stress. Positive trends in Msw reduced the effect of growth enhancement on Psw by offsetting approximately half of the enhancement of Gsw.    Production efficiency models (PEMs) do not exhibit the ability to reproduce observed environmental sensitivity: Development and testing of PEMs suggest that lack of coupling with nutrient availability and CO2 as well as simplifications in the representation of direct physiological stresses limit the capacity to match key benchmarks, including inter-annual variability in eddy-covariance measurements of Pg and decadal variability in periodic measurements of Gsw and Msw from permanent forest inventories.  These findings present new evidence of growth enhancement acting on a sub-continental scale to contribute to increasing evidence of strong environmental effects on worldwide forest productivity (Denman et al. 2007). These findings are important because  192  environmental sensitivity of global forest NPP constitutes a major source of uncertainty in future atmospheric CO2.  7.2 Observations of tree productivity Proliferation of the eddy-covariance technique has led to a wealth of data available for estimating Pg, ecosystem respiration (Re), and net ecosystem production (NEP), which has by extension led to a much improved understanding of the C cycle of forest and peatlands in Canada and elsewhere. These data have been nothing short of revolutionary in the development and parameterization of forest C cycle models. Although the partitioning of Pg and Re is generally accepted practice by the scientific community, there is no established method of deriving net primary production (NPP) from eddy-covariance datasets without extensive additional ancillary measurement systems. Although a large body of research exists on the behaviour of net primary production (NPP), aspects of its variability, principally including sensitivity to environmental change, continues to be a critical knowledge gap in understanding the terrestrial biosphere (Denman et al. 2007) and an obstacle in forecasting yields (BC-FML 2010). The standard method of observing NPP, therefore, continues to consist of setting up ecological plots (e.g., Grier and Logan 1977; Harcombe et al. 1990; Phillips and Gentry 1994). The main advantage of this strategy is that placement of plots is controlled and typically done with specific objectives in mind. This is an important consideration when the objectives include identification of environmental sensitivity. For example, van Mantgem et al. (2009) specifically sought to identify the relative contributions of intrinsic and extrinsic factors in driving positive trends in demographic tree mortality throughout the Pacific 193  Northwest. They noted that this would be challenging with a sample undergoing directional succession, instead opting to develop a sample that minimized this problem by selecting oldgrowth stands in the steady-state phase. These challenges associated with sample design were apparent in tree productivity trends reported for ecological plot networks in the tropics when they incurred heavy criticism by the scientific community for not fully addressing various intrinsic factors as possible causes (Condit 1997; Gloor et al. 2009). In the present study, observations of Gsw and Msw were derived from an industry-based forest inventory, which permitted sufficient temporal sampling to analyze trends and sensitivity to individual environmental variables. A challenge associated with the use of industry-based inventories is that plot placement was not negotiable. As an implication, the error is difficult to assess quantitatively. Paraphrasing Ung et al. (2009) as an example, “black spruce growing in warm areas with high growing degree days are generally confined to poor-quality sites.” The implication is that it is very plausible that other influential factors covary with environmental variables and therefore contaminate model fits. Both Ung et al. (2009) and Crookston et al. (2005) also voiced concerns that uneven sampling of the climate space could also lead to errors in model parameterization. This is a legitimate concern in the sample of plots in southwest British Columbia, as there is a high degree of climatic redundancy in placement of plots (especially for western hemlock). As a practical constraint, this meant that the overwhelming majority of analyses focused on relationships with climate anomalies, which do not necessarily demand full spatial coverage of the species range in order to identify signals. Although no attempt was made here to extrapolate to the region, such exercises can also be influenced by sampling errors, including the “majestic forest effect” in particular (Condit et 194  al. 1997). Despite all these sources of error, regional inventories provide a detailed look at past and current patterns with unprecedented spatial and temporal coverage. The ability to understand individual environmental effects on tree productivity in the field, including estimation of the sensitivity (direction and magnitude) in addition to simply correlation, depends on the ability to identify the marginal responses (i.e., when all other factors are controlled). Both sampling deficiencies and imperfect experimental designs inflate the probability of making Type II (false negative) statistical errors. Only with thousands of census intervals do the climate signals become identifiable, whereas analysis of individual plots or ecological plot networks will be inhibited by small sample size. The expansive temporal sampling in addition to reasonably strong spatial sampling in the BC inventory provided a powerful dataset for analyzing past tree productivity. Although the U.S. inventory clearly exceeds the BC inventory in spatial sampling, there is only one census interval measurement per plot in the Pacific Northwest U.S. Forest Service dataset and oneto-three census interval measurements per plot in the eastern U.S. database. It is unclear if permanent sample plot programmes in other regions include similar levels of temporal sampling. Another distinguishing feature of permanent sample plots is the plot area, which is typically much less than the footprint of eddy-covariance flux towers, but still greater than tree-level measurements. This poses unique challenges for modelling. For example, I suspect that much of the work to calibrate models using eddy-covariance flux towers are, at least partially, scale-dependent. It is remarkable that the coefficient of variation of annual Pg estimated from flux towers in evergreen, coniferous forest ecosystems is typically below 15%, while the periodic mean annual coefficient of variation for Gsw at inventory plots is 44% (see Chapter 195  2). This is at least somewhat consistent with the continued increase in the magnitude of relative variation moving from plot-level to tree-level measurements, where dendrochronology frequently shows annual coefficient of variations exceeding 100% when a tree is ‘released’ or ‘supressed’ by neighbouring trees.  7.3 Modelling tree productivity Combining information from eddy-covariance flux towers (Morgenstern et al. 2004), ancillary measurements that are representative of the footprint fluxes (e.g., Trofymow et al. 2007; Trofymow et al. 2008; my leaf area index measurements), and regional forest inventories provides a powerful way to constrain model predictions. I found many challenges in achieving model simulations that explained all available observations, although 3-PG does show strong potential to do so (Chapter 6), yet it is this type of coherency analysis that elucidates problems with model structure. Although temporary inventory plots were not available for use in this study, I am inclined to believe that, from a modelling perspective and a general perspective of understanding forest ecosystems, permanent sample plots are more valuable. A major deficiency in the BC inventory is the lack of plots in old-growth forest stands. Without similar levels of sampling as for younger age classes in the current dataset, modelling dynamic steady-state processes that dominate the growth phase must be achieved largely through theoretical considerations. Although the simplest models are sought, the reality is that environmental sensitivity appears to be defined by a large number of nonlinear and interrelated relationships. As a consequence, multivariate statistical models can be just as complex (parameter-wise) as process-based models. Conversely, simpler models based on two explanatory variables, say 196  representing temperature and drought (e.g., Crookston et al. 2005), may not necessarily be realistic enough to account for decadal patterns, such as those identified in Chapter 3 and 4. A major lesson learned from fitting statistical models to Gsw and Msw was that traditional methods of numerical optimization can be prohibitively difficult and unreliable. Consistently through the analyses in Chapters 3 and 4, optimizing models to fit collective samples provided no assurance that the models were unbiased with respect to the sample domain, or larger domains. Minimisation of the error from the collective sample of Gsw, for example, based on functions of stand age, temperature and precipitation, did not ensure that the solution produced a model that was unbiased with respect to each explanatory variable. Hence, visual inspection of model residuals is absolutely critical. The reasons for this are not entirely clear. Part of the problem with multivariate statistical models is the prevalence of local minima due to poor initial parameter estimates in conventional minimisation problems, or priors in nonparametric methods. Another source of error may arise from serial dependence and lack of representation of mixed effects in collective samples. It is worth noting here that nonlinear mixed-effects models were successfully applied for all multivariate statistical models in Chapter 3 and 4, yet exhibited virtually no difference in results and did not appear to alleviate any of the above problems with optimization. This also means that conventional validation methods (e.g., comparison between observed and predicted monthly Pg at flux towers as in Wang et al. 2011) can give overly pessimistic impressions of model skill. For example, if it is possible to achieve R2 values in excess 0.95 in comparisons with flux towers and also exhibit no ability to reproduce regional decadal patterns, then the opposite can also be true. Although validation exercises with all available data should be encouraged, it is possible to put too much emphasis on the R2. 197  7.4 Future directions Multivariate statistical models present considerable potential in modelling Gsw and Msw over large study domains. The approach is simple to apply and well constrained by observations. As a result, the method is also highly dependent on the availability of permanent forest inventories to calibrate the model. Although the above section outlined several challenges in model calibration, a promising strategy exists in multi-objective optimization within a Bayesian framework, which allows the operator to prioritize bias reduction and customize the accuracy with respect to specific variables. Development of such models was limited here by the relatively narrow climatic subspaces of the investigated species; however, this is currently being alleviated by merging the BC inventory with U.S. inventories. Multivariate statistical models exhibit considerable flexibility in how they are driven. The current study presented stand-alone models, while the compatibility with process-based models is a compelling possibility. This strategy is exemplified by the ECOLEAP modelling framework (Bernier et al. 1999) and the InTEC model (Chen et al. 2003). As a strategy to reduce complexity in process-level representation, both models calibrated multivariate statistical models based on a subset of simulations derived from biochemical models. This strategy circumvents many of the problems arising from model reduction and scaling techniques used in hybrid forest productivity models, while reflecting the emergent properties associated with the latest advances in the representation of plant physiology in biochemical models.  198  Although it is clear from low coefficients of determination reported for relationships between tree productivity and environmental variables in Chapters 3 and 4 that incorporation of environmental sensitivity will not appreciably improve model precision (i.e., improve the ability to estimate the specific tree productivity of a given stand type at a given location and time), results highlight both the need and ability to account for temporal biases in the form of long-term trends in Gsw and Msw that appear to be driven by environmental changes. Despite this, there is virtually no emphasis on elucidating and correcting temporal biases in studies of model validation of forest yields (Sterba and Monserud 1997). This is an important and realistic objective to improve (or at least understand the uncertainty of) predicted tree productivity in the CBM-CFS. Although the BC and U.S. inventories provide substantial coverage of species found in Canada, the success of this type of approach depends on the existence and accessibility of inventories in Canada’s other major ecozones. Interactions between environmental variables are a critical area of research that is needed to understand future responses of tree productivity. Recent advancements in the understanding of non-stomatal water stress and general connections between photosynthesis and plant water relationship suggest that difficulties in simulating tree productivity at least partially reflect incomplete physiological understanding and that more laboratory experimentation is needed to understand what accounts for the unexplained gap in Figure 6.6d and specifically how those mechanisms modulate CO2 fertilization.  199  References Acker, S., Halpern, C., Harmon, M., Dyrness, C., 2002. Trends in bole biomass accumulation, net primary production and tree mortality in Pseudotsuga menziesii forests of contrasting age. Tree Physiology, 22, 213-217. Adams, H.D., Guardiola-Claramonte, M., Barron-Gafford, G.A., Villegas, J.C., Breshears, D.D., Zou, C.B., Troch, P.A., Huxman, T.E., 2009. Temperature sensitivity of droughtinduced tree mortality portends increased regional die-off under global-change-type drought. 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Yuan, W., Liu, S., Zhou, G., Zhou, G., Tieszen, L.L., Baldocchi, D., Bernhofer, C., Gholz, H., Goldstein, A.H., Goulden, M.L., Hollinger, D.Y., Hu, Y., Law, B.E., Stoy, P.C., Vesala, T., Wofsy, S.C., 2007. Deriving a light use efficiency model from eddy covariance flux data for predicting daily gross primary production across biomes. Agricultural and Forest Meteorology, 143, 189–207.  221  Appendix A: Estimation of historical vapour pressure deficit Vapour pressure deficit (Δe) is defined as the difference between the maximum and the actual partial pressure of H2O of the atmosphere: ∆  																																																																																																																																		 A1  where es(T) is the saturation vapour pressure at the ambient air temperature (T) and ea is the actual vapour pressure. Continuous direct measurements of Δe only became available at airport climate stations after 1953. To overcome the lack of direct measurements prior to 1953 and sparseness thereafter, most ecological studies (e.g., Landsberg and Waring 1997; Kicklighter et al. 1999; McGuire et al. 2000) use models based on daily minimum (Tmin) and maximum (Tmax) air temperature to predict Δe (Thornton et al. 1997; Kimball et al. 1997; Landsberg and Sands 2011); the logic being that Tmin and Tmax are available from a much larger number of stations with records that extend back well before humidity measurements began. Saturation vapour pressure (in kPa) is accurately predicted from temperature (Landsberg and Sands 2011): 0.61078	e  .  	 /  .  																																																																																																 A2  Vapour pressure (ea) is then predicted by assuming daily Tmin is approximately representative of the dew-point temperature (Td). As Td remains fairly constant throughout the day, we can assume ea ~ es(Tmin), which substituting into Eq. A1 gives: ∆  																																																																																																																						 A3  222  Kimball et al. (1997) investigated properties of the error in this model, reporting seasonality in the difference between observed and predicted estimates and a general degradation of accuracy at arid sites. As long-term trends in forest productivity are significantly influenced by variability in Δe, I further investigated the assumption of long-term stationarity in the relationship between Tmin and Td, suspecting that warming trends in Tmin may not necessarily reflect equivalent trends in Td. Non-stationarity in the difference between Tmin and Td was tested on the basis of whether a significant long-term, linear trend existed in the residual (Tmin minus Td) according to least-squares regression. Trends were then tested for the residual (observed minus predicted) time series of Δe. As productivity is primarily influenced by conditions during summer, the analysis of trends was conducted on annual time series of summer (June-JulyAugust) mean variables. Table A1 lists long-term trend coefficients for Tmin, Td, and Tmin – Td for climate stations located at Airports across Canada. The first nine stations were located within the study area of coastal British Columbia, while remaining stations were selected to represent the rest of southern Canada. Sample sizes ranged from 28 to 43 years. Residuals were weakly autocorrelated and normally distributed. The standard error (S.E.) of the coefficients was derived from bootstrap resampling. For all stations together, just 53% of the stations that were tested exhibited trend in the difference between Tmin and Td (Table A1). Likewise, 53% of stations that were tested exhibited trend in residual Δe, and two of the significant trends were negative (both located in central Canada) (Table A2). 223  Trends were more common in coastal British Columbia, however, where seven of nine tests indicated significant positive trend in both Tmin - Td and residual (observed minus predicted) Δe. Throughout coastal British Columbia, Tmin increased over the records, while Td did not. This led to overpredictions of ea. By extension, model predictions of Δe largely exhibited insignificant, negative trends, while actual measurements of Δe indicated significant positive trends at approximately 50% of the stations.  224  Table A.1 Trend statistics for observed summer (June-July-August) average minimum air temperature (Tmin), dew-point temperature (Td) and the difference. N is the sample size (i.e., number of years in annual time series), trends are expressed as the slope coefficient b integrated over 50 years (˚C/50yr), P is the correlation probability, and S.E. is the standard error. Bold values mark statistical significance.  Prince Rupert BC Terrace BC McInnes Is BC. Cape Scott BC Port Hardy BC Tofino BC Vancouver Int. BC Abbotsford BC Nanaimo BC Lynn Lake AB Fort Nelson BC Prince George BC Fort Smith BC Watson Lake YT Fort St. John AB Cold Lake AB Saskatoon SK Thompson MB Kenora ON Kapuskasing ON Val-D’Or QC Bagotville QC Ottawa ON Fredericton NB Sydney NS Sept-Iles QC Goose NL Deer Lake NL Wabush Lake QC Lansdowne House ON Kuujjuarapik QC Moosonee ON Churchill MB  N 41 43 42 36 43 43 43 43 43 28 43 43 43 43 43 42 43 29 43 43 41 43 43 43 43 43 43 31 35 37 39 40 43  Tmin P <0.001 0.188 0.365 0.004 <0.001 0.005 <0.001 <0.001 <0.001 0.370 0.183 <0.001 0.204 0.476 0.089 0.227 0.643 0.507 0.067 0.069 0.640 0.096 0.033 0.020 0.372 0.374 0.072 0.133 0.401 0.856 0.215 0.329 0.619  b 1.89 0.64 0.41 1.59 1.45 1.30 1.59 2.48 3.36 1.04 0.47 1.46 0.81 0.33 0.78 -0.64 -0.24 0.61 1.35 1.08 0.21 0.94 1.08 1.17 0.52 0.40 -0.85 -1.32 0.72 -0.06 0.81 0.63 -0.35  S.E. 0.78 0.88 0.58 0.94 0.73 0.88 0.97 0.66 0.68 1.65 0.80 0.60 1.30 0.69 0.81 0.90 1.27 3.05 1.37 1.51 1.10 0.91 0.98 0.87 0.84 0.74 0.79 2.01 1.24 1.80 1.50 1.87 1.13  Td P 0.076 0.898 0.904 0.220 0.264 0.097 0.410 0.452 0.163 0.604 0.186 0.031 0.350 0.594 0.815 0.708 0.900 0.265 0.237 0.949 0.680 0.526 0.277 0.140 0.129 0.815 0.033 0.090 0.557 0.161 0.828 0.185 0.533  b 0.86 0.03 0.04 0.73 0.41 0.55 0.36 0.27 0.54 0.74 -0.71 -1.08 -0.55 0.32 0.17 0.33 0.03 1.32 -0.85 0.00 -0.31 0.38 0.55 0.73 -0.84 -0.04 -0.92 -1.84 -0.40 -1.09 -0.13 -0.85 -0.28  S.E. 0.98 0.73 0.81 0.96 0.74 0.79 1.30 0.99 0.67 2.16 1.21 1.06 1.50 1.48 1.11 1.36 1.56 2.43 1.44 1.19 1.35 0.96 1.07 0.92 0.86 0.85 0.74 2.19 1.04 1.69 1.16 1.26 1.58  Tmin minus Td P b <0.001 1.14 0.17 0.64 0.085 0.31 <0.001 0.99 <0.001 1.07 0.002 0.66 0.001 1.07 <0.001 2.06 <0.001 2.79 0.510 0.50 0.003 1.21 <0.001 2.56 <0.001 1.44 0.983 -0.09 0.222 0.60 0.013 -0.83 0.636 -0.25 0.514 -0.45 <0.001 2.19 <0.001 1.22 0.122 0.51 0.069 0.47 0.098 0.59 0.177 0.35 <0.001 1.22 0.132 0.48 0.818 0.09 0.632 0.33 0.007 1.11 0.002 1.08 0.022 1.10 0.003 1.63 0.693 0.10  S.E. 0.41 0.85 0.28 0.26 0.40 0.38 0.60 0.54 0.60 1.42 0.83 0.90 0.56 0.87 1.05 0.76 1.64 1.15 1.07 0.58 0.72 0.52 0.59 0.65 0.43 0.77 0.54 1.05 0.67 0.72 0.76 1.09 0.56  225  Table A.2 Trend statistics in summer (June-July-August) mean near-surface atmospheric vapour pressure deficit (Δe). N is the sample size (i.e., number of years in annual time series), trends are expressed as the slope coefficient b integrated over 50 years (hPa/50yr), P is the correlation probability, and S.E. is the standard error. Bold values mark statistical significance. Observed  Prince Rupert BC Terrace BC McInnes Is BC. Cape Scott BC Port Hardy BC Tofino BC Vancouver Int. BC Abbotsford BC Nanaimo BC Lynn Lake AB Fort Nelson BC Prince George BC Fort Smith BC Watson Lake YT Fort St. John AB Cold Lake AB Saskatoon SK Thompson MB Kenora ON Kapuskasing ON Val-D’Or QC Bagotville QC Ottawa ON Fredericton NB Sydney NS Sept-Iles QC Goose NL Deer Lake NL Wabush Lake QC Lansdowne House ON Kuujjuarapik QC Moosonee ON Churchill MB  N 41 43 42 36 43 43 43 43 43 28 43 43 43 43 43 42 43 29 43 43 41 43 43 43 43 43 43 31 35 37 39 40 43  P 0.018 0.564 0.850 0.005 0.007 0.049 0.192 0.109 0.399 0.041 0.058 0.28 0.310 0.960 0.444 0.394 0.061 0.304 0.028 0.140 0.274 0.126 0.537 0.793 0.011 0.406 0.731 0.765 0.016 0.078 0.001 0.808 0.028  b 0.72 -0.56 -0.03 0.58 0.71 0.87 0.84 1.42 0.76 2.58 1.42 2.54 0.59 0.00 0.75 -0.63 -1.87 1.28 2.15 0.97 0.71 1.09 -0.61 0.19 1.37 0.33 0.31 -0.33 1.72 1.21 1.64 -0.21 1.04  Predicted S.E. 0.76 3.34 0.62 0.68 0.69 1.43 1.88 2.60 3.51 2.38 1.27 1.95 1.53 1.01 1.52 1.72 2.57 2.08 1.60 1.11 1.65 1.53 2.05 1.05 0.95 1.29 0.83 1.55 1.23 1.36 0.74 1.17 0.78  P 0.636 0.249 0.315 <0.001 0.789 0.648 0.495 0.919 0.079 0.031 0.491 0.579 0.429 0.528 0.732 0.637 0.197 0.193 0.901 0.804 0.903 0.225 0.119 0.995 0.731 0.538 0.800 0.344 0.051 0.270 0.001 0.096 0.028  b -0.13 -0.78 -0.22 -0.49 -0.10 0.22 -0.31 -0.18 -1.37 1.69 0.33 0.52 -0.28 0.23 0.10 0.28 -0.73 1.31 -0.03 0.08 0.07 0.70 -0.70 0.00 -0.09 -0.17 0.09 -0.70 0.86 0.63 0.89 -1.12 0.83  S.E. 0.84 2.72 0.60 0.42 0.92 1.45 1.24 2.96 2.72 1.73 0.84 1.35 0.95 0.94 0.84 1.14 1.25 1.66 1.05 0.93 1.29 1.15 1.17 0.89 0.72 0.90 0.78 1.62 0.77 0.84 0.42 1.10 0.76  Observed minus predicted P b <0.001 0.77 0.385 0.35 0.400 0.16 <0.001 1.04 <0.001 0.77 0.004 0.66 0.003 1.03 <0.001 1.53 <0.001 2.21 0.234 0.62 0.005 1.10 <0.001 1.92 0.002 1.01 0.297 -0.34 0.277 0.36 0.003 -0.83 0.031 -1.30 0.989 0 <0.001 2.09 0.001 0.87 0.066 0.77 0.128 0.46 0.508 0.20 0.613 0.17 <0.001 1.42 0.066 0.55 0.724 0.11 0.497 0.49 0.014 0.87 0.066 0.80 0.034 0.71 0.026 1.02 0.674 0.07  S.E. 1.00 1.05 0.52 0.57 0.65 0.94 1.34 1.17 1.39 1.00 0.58 0.77 0.58 0.86 0.75 0.52 1.54 0.99 0.83 0.53 0.66 0.64 0.79 0.50 0.46 0.86 0.46 0.96 0.54 0.92 0.65 0.74 0.53  226  

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