Analysis of the Net Ecosystem Exchange of C0 2 in a 56-year-old Coastal Douglas-fir Stand: Its relation to Temperature, Soil Moisture and Photosynthetically Active Radiation by Tiebo Cai B . S c , Inner Mongolia Forestry College, 1993 M . S c , Inner Mongolia Forestry College, 1998 M . S c , Lakehead University, 2001 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Soil Science) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A © Tiebo Cai , January 2007 11 Abstract The primary goal of this thesis was to investigate the relationship of canopy photosynthesis (P) to photosynthetically active radiation (PAR) in a 56-year-old coastal Douglas-fir stand (DF49) located on Vancouver Island. Canopy P was calculated as daytime N E P + daytime Re, where N E P and Re are net ecosystem production of CO2 and ecosystem respiration, respectively. Half-hourly values of N E P were obtained using an E C (eddy covariance) system consisting of a 3-D sonic anemometer-thermometer and a closed-path infrared gas (CO2/H2O) analyzer, and daytime Re was inferred by obtaining the intercept of the relationship between half-hourly values of N E P and P A R . Daytime Re thus obtained was approximately 71-75% of that calculated by applying the logarithmically-transformed relationship between nighttime N E E (-NEP) and soil temperature (Ts) to daytime half hours. Values of Rio (the rate of Re at Ts = 10 °C), obtained from both annual nighttime and daytime Re - Ts relationships, increased linearly with increasing soil moisture when averaged over the active growing season (Apri l 1 -Sept 30). However, the effect of soil moisture on Re shown on the multi-year scale could not be detected on the seasonal or annual scale probably as a result of the confounding effects of other environmental factors on Re. The effective P A R (Qe) contributing to canopy P in this Douglas-fir canopy was well described as Qdo + kQw, with Qdo and Qb0 being sky diffuse and direct P A R , respectively. The parameter k, which accounts for the total scattering of Qb0 and the n o n -scattering effect (e.g., penumbral light spreading) of the solar rays, was found to be approximately 0.22 for this stand. While the Michaelis-Menten equation (the M M model) (i.e., P = aQa)AmaJ(aQlQ+Amax), where Qt0 = Qdo + Qbo) results in significant overestimation of P in sunny conditions and significant underestimation of P in cloudy conditions, its modification into P = aQel{aQe + ) (the Q e - M M m o d e l j 1 " -eliminated these systematic errors. When k - 1, the Q e - M M model reduces to the M M model. The Q e - M M model is a single big-leaf model, but it avoids the type of errors made in earlier generations of single big leaf models of canopy P , i.e., using A P A R (the total absorbed P A R by the canopy) to calculate P. The simplicity of the Q e - M M model makes it convenient to be incorporated into large-scale carbon climate models. I l l This study also shows that the widely used sun/shade model developed by de Pury and Farquhar (1997) is inadequate, mainly because the sun/shade model fails to account for the incidence angle between the solar beam and individual sunlit leaves. A s with the P modeled using the M M model, the modeled P obtained using the sun/shade model has significant systematic errors with respect to QdolQto (the ratio of Qdo to Qto). In contrast, using the Q e - M M model to estimate canopy P for this Douglas-fir stand eliminated these systematic errors with respect to Qdo/Qto- In addition, the Q e - M M model developed in this study agrees with the detailed multilayer model of canopy P developed by Norman and Arkebauer (1991) for agricultural crops (i.e., soybean and corn). iv Contents Abstract ii List of Tables vi List of Figures viii List of Symbols and Acronyms xiii Acknowledgements xvii 1 Introduction 1 2 Methodological uncertainties in estimating nighttime and daytime ecosystem respiration of a 56-year-old Douglas-fir stand from eddy covariance CO2 fluxes 7 2.1 Introduction 7 2.2 Methods 11 2.2.1 Obtaining Re - Ts relationships using nighttime N E E measurements 14 2.2.2 Obtaining Re - Ts relationships using daytime N E P measurements 16 2.3 Results and discussions 18 2.3.1 Re - Ts relationships obtained using nighttime N E E measurements 18 2.3.2 Re - Ts relationships obtained using daytime N E P measurements 23 2.3.3 Comparison of the Re - Ts relationships obtained using the nighttime and daytime methods 31 2.3.4 Estimates of the annual totals of N E P , Re and P using the nighttime and daytime methods 33 2.4 Conclusions 41 3 Comparison of different algorithms for partitioning net ecosystem exchange into its component fluxes: ecosystem photosynthesis and respiration 43 3.1 Introduction 43 3.2 Methods 49 3.2.1 Annual fits of the nighttime and daytime Re - Ts relationships 50 3.2.2 Stepwise fits of the annual nighttime and daytime Re - Ts relationships ... 50 3.3 Results 53 3.3.1 Climate and meteorological conditions 53 3.3.2 Annual fits of the Re - Ts relationships 57 3.3.3 Stepwise fits of the annual Re - Ts relationships 64 3.4 Discussion 72 3.5 Conclusions 75 4 A modification of the Michaelis-Menten equation for its application to estimating canopy photosynthesis of a coastal Douglas-fir stand 77 4.1 Introduction 77 V 4.2 Methods 84 4.3 The model 85 4.3.1 Model development 85 4.3.2 Model parameterization 98 4.3.3 Model comparisons 99 4.4 Results 100 4.4.1 Variance in P accounted for by adding fractions of Qw to Qdo 100 4.4.2 Comparisons between the M M , Q e - L U E , and Q e - M M models 103 4.4.3 Comparisons between the M M , Q e - M M and the sun/shade models 107 4.4.4 Comparisons of the performance of the Q e - M M and m - M M models 110 N 4.4.5 A case study 120 4.5 Discussion 124 4.6 Conclusions 128 5 Conclusions 130 References 137 Appendix A . The site location, E C system configuration and the PAR measurements for the 56-year-old Douglas-fir stand 153 Appendix B. Comparison of the PAR measurements made using the BF2 and LI-190SB 156 Appendix C. Inadequacies in the Sun/Shade Model Developed by de Pury and Farquhar (1997) 159 1. Lack of consideration of the angle of incidence of Qbo and the use of area-weighted A P A R to calculate P of the big sunlit and shaded leaves, respectively 159 2. Inadequacies in its scaling algorithm 169 3. Problems in its description of the geometry of light 175 4. Oversimplified representation of canopy structure 177 Appendix D. Derivation of two key equations in Norman (1980) 180 Appendix E . Comparison of the scaling algorithms used in the complete multilayer, 2-leaf multilayer, 2-leaf single-layer, M M and Q e - M M models of canopy P 185 VI List of Tables Table 2-1. Coefficients obtained for the 5 nighttime methods for DF49 in 2001 (see Figure 2-2 and text for details). Units for A and B are u,mol m"2 s"1 and °C"', respectively. Units for y() and RMSE are both jumol m"~ s" 22 Table 2-2. Coefficients obtained for the MM (Ql0: 0 - 1800 umol m"2 s"1') and LUE (Q,„: 0 - 300 umol m~~ s" ) models with the application of different daytime it* filters for DF49 in 2001 (see Figure 2-3). Units for A and B are fimol m"2 s~' and °C~ ', respectively. The values of A and B were determined using ln Red = \vxA + BTs (see Eq. (5)) ... 25 Table 2-3. Coefficients of the M M (Ql0: 0 - 1800 umol m"2 s"1) (i.e., Eq. (2)) and LUE (i.e., Eq. (6)) fits for the different months shown in Figure 2-4. Units for a and Amax are umol (CO?) umol"1 (quanta) and ujnol m"2 s~', respectively 27 Table 2.-4. Coefficients obtained for the MM (Ql0: 0 - 1800 jLimol m"2 s"1, and ut0 ) and 2 I LUE (Qio\ 0 - 300 |imol m" s" , and u00 ) models with different moving window for DF49 in 2001 (see Figure 2-5). Units for A and B are u.mol m"2 s"1 and °C~', respectively. The values of A and B were determined using ln Re(l = \nA + BT. (see Eq. (5)) 29 Table 2-5. Annual totals of the Re and P obtained using different annual nighttime and daytime Re — 7Vrelationships (see Figure 2-7 and Figure 2-8 for details). Only the nighttime half-hourly NEE measurements made in conditions where u* > 0.3 m s"1 were used in the nighttime methods. The daytime half-hourly NEP measurements made in conditions where it* < 0.3 m s"1 and Qio < 200 umol m" " s" were not used in the M M and LUE fits, and only the rest of the daytime data (i.e., not screened by the daytime u* filter) were used in both models to determine Re(( .' 37 Table 3-1. Climate conditions for the 8 years (1998 - 2005), including canopy air temperature at the 27-m height (Ta), soil temperature at the 5-cm depth (Ts), integrated water content in the 0 - 1-m depth soil layer (6), total precipitation, mean daily downwelling PAR (Ql0) (45-m height) and mean daily downwelling diffuse PAR (Q(/o) (45-m height) for the entire year and for the most active growing season (April 1 - September 30). 54 Table 3-2. The values of A and B for each year obtained from the annual nighttime (Figure 3-3) and daytime (Figure 3-4) relationships. Units for A and B are -2 -1 -1 u.mol m" s" and °C~ , respectively. The values of A and B were obtained using the logarithmic transformation o f the corresponding exponential Re-Ts relationships. The corresponding values of Rj0 and Q/o were obtained as: RW = AQW and Qw=eWB 60 Table 3-3. The coefficients (i.e., c and d) in the linear regressions between annual values of Rio and 6 and Qio and 6 (see Figure 3-5). The nighttime and daytime values of Rio and Q/o were obtained from the annual nighttime NEE I ( > - Ts (Figure 3-3) and annual daytime Reii - Ts (Figure 3-4.) relationships, respectively. Units of Rio and Qio are umol m"2 s"1 and °C"', respectively. 6 V l l (m m ) was calculated by averaging its half-hourly values of each year from April 1 to September 30 „ 63 Table 3-4. The annual totals of Re obtained (1) using the annual values of Rio and Qt0 obtained from the annual nighttime and daytime Re - Ts relationships of each individual year (see Figure 3-3 and Figure 3-4), and (2) using the annual values of Rio and Qui modelled for each individual year from the nighttime and daytime R/o - 6 and Qm - 0 relationships (see Table 3-3 and Figure 3-5). The nighttime and daytime Rio and Qi0 values were used.to calculate the nighttime and daytime half-hourly values of Re, respectively. The half-hourly values of Re were then summed to obtain the annual totals. Also shown are the means and standard deviations for the 8-year, period 64 Table 3-5. Annual totals of Re obtained using the three stepwise methods and the annual relationship method. The nighttime NEE1( - Ts and daytime Rec/ - Ts relationships were used to calculate the nighttime and daytime half-hourly values of Re, respectively, which were then summed to obtain the annual totals (see Figure 3-6 and Figure 3-7) 68 V l l l List of Figures Figure 1-1. Clouds of ash and steam from the eruption of Mt. Pinatubo on June 12, 1991.... 2 Figure 1-2. The levelling off (arrows) of atmospheric CO2 concentration after the eruptions of Mt. Agung in 1963 and Mt. Pinatubo in 1991 3 Figure 2-1. (a) The relationship between nighttime NEE measurements, representing nighttime ecosystem respiration (Ren), and soil temperature (Ts) at the 5-cm depth, (b) The relationship between the logarithmically transformed NEE and Ts. In both plots, the circles are bin averages of 100 half-hourly values, and the vertical bars are ± 1 standard deviation. The assumption of IID N(0,a 2) was met by doing the logarithmic transformation of the half-hourly nighttime NEE. The half-hourly NEE measurements are from 2001 with u* > 0.3 m s"1 (i.e., NEE , J (/? = 2472) .• 19 Figure 2-2 .The Re„ - Ts relationships obtained using 5 different nighttime methods (see text for details).20 Figure 2-3. The Re(i - Ts relationships obtained using the MM and LUE models with the application of a daytime it* filter to increasing ranges of Q,Q. The total Q,o ranges for the M M model and LUE model are 0 - 1800 umol m"2 s~' and 0 -300 umol m~~ s" , respectively. « : ;,0 i, 11,, iu0m , w.0 , and itdenotes that the daytime half-hourly NEP measurements made in calm conditions (i.e., 11* < 0.3 m s"1) were removed if QL0 < 0 pmol m"2 s"1, QL0 < 50 umol m"2 s"1, Q,o <100 umol m"2 s"1, Q,o < 200 umol m"2 s"1, and QLF, < 300 umol m~2 s"1, respectively. For example, « t f t , in the case of the M M model, means removing low it* daytime NEP measurements if Q,o < 200 umol irf~ s" and 2 I only the high it* NEP measurements associated with Q,o < 200 pmol m" s" and all the NEP measurements made when Q,() > 200 umol m"2 s"1 (regardless of their it* values) are used in the MM model fit to determine Reci. In the case of the LUE model, data for Q,0 between the upper end of the range and 300 u.mol m"" s"1 were not u* screened e.g., for n„0 values for 100 < Q,o < 300 umol m" s" were not screened. u,,0n means no daytime it* screening was applied in both the MM and LUE models, because all daytime NEP data are associated with Q,0 > 0 umol m"2 s"1 24 Figure 2-4. Daytime NEP - PAR relationships for different months of 2001. The dots in (a) - (c) are the half-hourly NEP measurements. The circles in (d) are the bin averages of 300 half-hourly NEP measurements and the vertical bars denote ± 1 standard deviation. The thin and thick lines are the respective fits obtained using the MM and LUE models to the half-hourly NEP measurements (not to the bin averages as shown in (d)). The Q,o ranges for the M M model and LUE 9 1 9 _ | model are 0 - 1800 pmol m"~ s" and 0 - 300 jamol m" s" , respectively 26 Figure 2-5. The annual Re(j - Ts relationships obtained using the MM and LUE models with moving windows of different sizes for 2001. All the moving windows were increased one day at a time and all the fits were made with the IX logarithmic transformation of Red. The total Q/0 ranges for the MM model and LUE model are 0-1800 umol m"2 s"1 and 0 - 300 u.mol in"2 s"1, respectively. ... 30 Figure 2-6. The Re-Ts relationships obtained using the LUE.model with three Ql0 ranges: Q,o < 100 umol m"2 s"1 (dotted line), Q„, < 200 umol m"2 s"1 (thin line) and Q, ID < 300 umol m"2 s"1 (dashed line). Also shown are the Rc- Ts relationships obtained using the MM model with Q,(l < 1800 umol m'2 s"1 (line with solid triangles) and Qt0 < 300 umol irf2 s"1 (line with empty triangles) and the Re -Ts relationship obtained using the nighttime logarithmic fit (the thick line), ln all the daytime Re - Ts relationships, 15-day moving window and daytime u* filter of u,0^ were used : 32 Figure 2-7. The annual cumulative NEP for 2001 obtained using different nighttime and daytime derived Re - Ts relationships. The LUE and MM model use only daytime half-hourly NEP measurements 35 Figure 2-8. Monthly totals of P for 2001 obtained using different nighttime and daytime derived Re - Ts relationships (see Figure 2-7 for the legend) 40 Figure 3-1. Seasonal changes in the 15-day averages of soil temperature (Ts) at the 5-cm . depth 55 Figure 3-2. Seasonal changes in the 15-day averages of volumetric soil water content (9) integrated from the surface to the 1-m depth. The values of field capacity (-1/3 bar) (6 =0.213 m3 m"3) and permanent wilting point (-15 bars) (6 = 0.110 m3 m"3) were taken from Black (1979) for a 26-year-old coastal Douglas fir stand 56 Figure 3-3. The annual nighttime NEE ( ( - Ts relationships for 1998 - 2005, where NEE ( I are the nighttime half-hourly NEE measurements made when u* > 0.3 m s"1. Symbols represent the bin averages of the 20 half-hourly NEE I (< values in the stratifications of half-hourly values of 0. The annual curve fits were obtained using the original half hourly NEE ( i data (not the bin averages) 58 Figure 3-4. The annual daytime Re(i - Ts relationships for 1998 - 2005 obtained using the LUE model 59 Figure 3-5. Linear regressions of R/o and Q/o on average 6 for the 0-1 m layer (see Table 3-3 for the coefficients). The nighttime and daytime R/o and Qio values were obtained using the annual nighttime NEE l ( t - Ts and annual daytime Re(/ - Ts (see Figure 3-3 and Figure 3-4) relationships, respectively. The numbers next to the data points indicate the year 62 Figure 3-6. Monthly totals of nighttime Re (i.e., Ren) obtained using the three stepwise fit methods compared with those obtained using the annual nighttime NEE ( (< - Ts relationships for 1998 - 2005 (see Figure 3-3). All Re values were calculated half-hourly and then summed to obtain monthly totals 66 Figure 3-7. Monthly totals of daytime Re (i.e., Rect) obtained using the three stepwise fit methods compared with the annual daytime Rei( - Ts relationships for 1998 -2005 (see Figure 3-4). All Re values were calculated half-hourly and then summed to give monthly totals 67 X Figure 3-8. Seasonal changes in the monthly averages of f(t) for the A15-day moving windows (see also Figure 3-6 and Figure 3-7) '. 70 Figure 3-9. Comparison of daytime daily averages of Rc, obtained using the daytime Rec/ -Ts relationships, with the corresponding nighttime daily averages of R(, obtained using the nighttime NEE | ( - Ts relationships. All the nighttime and daytime half-hourly Re values were calculated using the A 15-day stepwise fit method (see Figure 3-6 and Figure 3-7), and then averaged to obtain the corresponding nighttime and daytime daily averages 71 Figure 4-1. The dependence of modelled half-hourly light-use efficiency [g C O 2 (MJ IPARV1] on the fraction of photosynthetically active radiation (PAR) above the canopy that is from direct beam (from Norman and Arkebauer 1991). The canopy light-use efficiency is based on IPAR (intercepted PAR) and the results are for C 3 (o) and C 4 (+) canopies 81 Figure 4-2. (a) The sun/shade model aggregates all the sunlit leaves into a big hemispherical sunlit leaf (i.e., assuming the leaf angle distribution of the sunlit leaves is spherical) and uses the mean APAR (absorbed PAR) (i.e., Eq. 8) to compute the photosynthesis for all the sunlit leaves, (b) The direct PAR absorbed by an individual sunlit leaf is given by: Qh{y) = (1 -c)Qpcosy, where Qp is the PAR perpendicular to the solar beam (the dotted line) and y is the incidence angle between the beam and the normal to the leaf surface (the dashed line) 86 Figure 4-3. The relationship between f and cos 7 . y was stepwise increased from 0° to 90° in steps of 9° (dy = (9°/180°)x = 0.1571 radians). For each step, cos/ and its corresponding f (fY = smydy, Eq. (10)) were calculated (the circles). Note the / vs. cosy relationship is independent of solar elevation angle(i.e., /?), but the total LAI of the sunlit leaves is not independent of B.... 89 Figure 4-4. (a) The canopy is divided into three conceptual groups: the first group (0-L|) with all the light-limited sunlit leaves, the second group (L\ to Li) with all the light-saturated sunlit leaves, and the third group (L2 to L) with the shaded leaves, (b) The photosynthetic light response to QUl (total absorbed PAR) for the shaded leaves is linear with a slope of a. In addition to the absorption of sky diffuse PAR (i.e., Qd{ \ )) and the scattered direct PAR (i.e., Qs{ \ )), the light-limited sunlit leaves absorb limited amounts of un-scattered direct PAR (i.e., Qb]{y)), and thus its photosynthetic response can still be linear with the slope of a. The photosynthetic response of the light-saturated sunlit leaves can be described using two linear responses: the initial linear response with the slope of a and the second linear response with the slope of k0a 91 Figure 4-5. The variance in P accounted for using the Q e - M M model at three levels of ocO A Qiu. Canopy P was related to PAR using P = v , where Qx is defined aQ +A i--.v max a s Qx= Qdo + xQbo- x was increased stepwise from 0 to 1, and a corresponding coefficient of determination (i.e., r2) of the regression was calculated for each x. When x = 1, Qx - Q,Q, and when x - 0, Qx - Qao 102 XI Figure 4-6. The responses of P to Q,o, Q(io, Qui and Qe. The fitted curve in (a) was obtained using P= a~'°Am-K (i.e., the MM model) with a = 0.050 mol aQ,a + A max mol"1 and Amax ~ 24.79 |imol m"2 s"1. The arrow in (b) indicates the sharp increase in P around Q(/o of 200 umol m"" s" . The fitted curve in (d) was obtained using P= ( i . e > ) the Q t.-MM model) with a = 0.041 mol aO +A i - i ' mux mol"1, Amax = 83.38 umol m"2 s"1 and k = 0.22, r2 = 0.66, RMSE = 4.30 umol m"2 s"1. The dashed line in (d) was obtained using P = 0.030£) +1.21 (i.e., the QC-LUE model), with k = 0.23, r2 = 0.65 and RMSE = 4.38 umol m"2 s"1. Symbols represent bin averages and vertical lines indicate ±1 SD. n = 34785. All fitted curves were obtained using the original half-hourly data, i.e., not obtained using the bin-averaged data 104 Figure 4-7. Modeling errors for the MM, Q e-LUE, and Q e -MM models. Parameters for these models are given in Figure 4-6. Symbols represent bin averages and vertical lines indicate ±1 SD for the bin averages obtained using the Q e -MM model. The SD values for the other two models is similar to the corresponding values for the Q e -MM model (not shown), n = 34785 106 Figure 4-8. Modeling errors for the MM and QC-MM models with the incorporation of a temperature function for Amax, and the corresponding modeling errors using the sun/shade model. Note: the sun/shade model has built-in temperature functions to adjust the values of its Vcmax and Jmax. For the MM model, the modeled P was obtained using, P= aQ^m™f^„) w n e r e a = 0.065 mol mol"1, Amax = 26.48 umol m"2 s"1, and f(Ta) = e a with T„ = 15.56 °C, and Q = 13.71. r2 = 0.59 and RMSE = 4.75. umol m"2 s"1. For the sun/shade model: r2 = 0.55 and RMSE = 4.80 umol m"2 s"1. For the Q e -MM model, the modeled P was obtained using P - oc^e^mm^^'«^ where a = 0.053 mol r„-ru 2 mol"1, Amax = 6.7.57 umol m"2 s"1, k = 0.18, and f(Ta) = e~ n ' with T„ = 16.97 °C, and Q = 11.68. r 2 = 0.73 and RMSE = 3.86 umol m"2 s"1. Symbols represent bin averages and vertical lines indicate ±1 SD. n = 34785 109 Figure 4-9. The coefficients of determination (r") for regressions using the Q e -MM and m-MM models obtained by using 15-day moving windows (moving one day at a time) over 5 lA years of data. The average and standard deviation of the r are 0.6535 and 0.1394 for the Q e -MM model, and 0.6562 and 0.1384 for the m-MM model, respectively. Symbols represent bin averages and vertical lines indicate ±1 SD for the bin averages obtained using the Q C -MM model. The values of SD for the m-MM model are virtually identical to those for the Q e -MM model (not shown) 111 Figure 4-10. Distributions of a and Amax obtained using the 15-day moving windows for the Q C - M M model (see also Figure 4-9) 113 X l l Figure 4-11. Distr ibut ions of k obtained us ing the 15-day m o v i n g w indows for the Qc-M M model (see also Figure 4-9 and Figure 4-10) 114 Figure 4-12. (a) The relationship between A' and sin /? obtained using the Q C - M M model (see Figure 4-11). Symbols represent b in averages and vertical lines indicate ±1 S D . (b) the relationship between cr' - sin fi calculated for different values of L using o-' = l - e " A ; / - ( l - o - ) ( l - e " A ' " i ) , where = 0 .5 / s i n / ? (see E q . 21). The value o f a is assumed to be 0.1 116 Figure 4-13. The temperature response o f ad , ah, Amux,i, and A m u x b for the m - M M model obtained using 15-day m o v i n g w i n d o w s for 5 Vi years o f data (see Figure 4-9). F i l l e d circles are ad and AimiX(i, and open circles are ab and Amaxb ' 118 Figure 4-14. Distr ibut ions o f ccb I ottl and AmaxhIAmaxd for 5 Vz years o f data. The values o f ad , a h , Am„x,i, and Amaxb were obtained us ing the 15-day m o v i n g w i n d o w s for the m - M M model (see Figure 4-13) 119 Figure 4-15. Cont inuous half -hourly values o f (a) Q,o (thick line), Q(w (thin line) and QiOmdi w h i c h is the modeled Q,o in a cloudless sky using E q . B l in A p p e n d i x B (dotted line), (b) Ta (thick line) and D (thin l ine), and (c) canopy P for 6 days in the 56-year-old Douglas fir stand ( D F 4 9 ) , C a m p b e l l R ive r , B . C . Squares ( • ) are modeled P using the Q e - M M mode l , and diamonds (O) are aQ A mux modeled P using the M M model . For the Q C - M M model , P-<*Qe + An where a = 0.048 m o l mol" 1 , Amax = 67.86 u m o l m" 2 s"1, k = 0 . 1 6 , r 2 = 0.56, and R M S E = 4.82 u m o l m" 2 s"1. For the M M - m o d e l , P = aQ°A™* , where a = 0.053, Amax = 22.51 u m o l m" 2 s"1, r 2 = 0.28 and R M S E = 6.20 u m o l m" 2 s"1. Note : the measurements o f P made in a l l u* condit ions are shown in plot (c), but the measurements o f P made in ca lm condit ions (u* < 0.3 m s"1) when Qio < 200 p m o l m"" s" were excluded from regressions o f the M M and Q e -M M models 121 Figure 4-16. C a n o p y P calculated us ing the sun/shade model , (a) the Rub i sco - l imi t ed (Av) and R u B P - l i m i t e d (A,) photosynthetic rates for the b i g sunlit leaf, Psun = m'm(Av, Aj), (b) the corresponding Av and Aj for the b i g shaded leaf, Psi,d = m'm(Av, Aj), (c) the modeled P of the entire canopy (P = Psun + Psi,(i) using the sun/shade mode l (circles) and the measured P (l ines), r 2 = 0.43, R M S E = 5.54 u m o l m"~ s" . No te Av equals to zero at night in (a) but not in (b) because the fraction o f sunlit leaves at night is zero 123 X l l l List of Symbols and Acronyms cos /j average of all the cos/values of the light limited sunlit leaves cr' canopy scattering coefficient a0 empirical coefficient Kb' extinction coefficient for green leaves, Kh< = KbJ[-~(j fSun fraction of sunlit leaves ^ leaf inclination angle to the horizontal, radian or degree T optical air mass c o s /nreshoid cosine of the leaf-sun angle ( y T h r e s h o l d ) associated with Qbnreshoid £ cumulative L A I from canopy top, but mainly used as a variable in integrals A cos y T h r e s h M difference between the average of all the c o s / values of the light saturated sunlit leaves and cos y T h r e s h o l d 9* gas constant, 8.314 J K " 1 mol" 1 a variance or leaf scattering (i.e., reflected and transmitted P A R ) coefficient depending on the context a quantum use efficiency, umol (CO2) umol" 1 (quanta) s random error (residuals of a fit) 0 soil volumetric water content, m 3 m 3 P solar elevation angle, radians pa density of dry air / incidence angle between the solar beam and a normal to the leaf surface, radians fY fraction of sunlit leaf area exposed at incident angle, y f(t) time varying variable ad, ab quantum use efficient modified for diffuse P A R (ad) and direct P A R (ab), respectively, umol (CO2) umol" 1 (quanta) kQbThreshoid difference between the total un-scattered direct P A R absorbed by the light saturated sunlit leaves and Qbnreshoid, pmol m" 2 s"1 (/) a curvature parameter. A a coefficient for Re (see Eq . (3) of Chapter 2), A - R10IQ10, pmol m" 2 s"1 a an empirical coefficient used to estimate Qtomdi Ac canopy assimilation rate used in the sun/shade model, umol m" 2 s"1 Aj rate of photosynthesis limited by RuBP regeneration, umol m" 2 s"1 Ajsun RuBP-limited rate of photosynthesis for the big sunlit leaf, umol m" 2 s"1 Amax a parameter (the asymptote) used in the M M model, umol m" 2 s"1 Amaxd,Amaxb Amax modified for diffuse P A R (Amaxd) and direct P A R (Amaxb), 0 1 respectively, umol m" s" A P A R absorbed total P A R including diffuse and direct P A R , umol m" 2 s"1 Av rate of photosynthesis limited by Rubisco, umol m" 2 s"1 xiv B D DF49 dleaf dsun dsun-earth dumbra Ea Eo E B C E C Fc IID N(0, o2) hm I P A R Jmaxi k k0 ku k2 Kb Kn L,L\,L2 L A I U m M M model n N E E NEE„* N E P O L S P P A R Rubisco-limited rate of photosynthesis for the big sunlit leaf, umol m" 2 s"1 a coefficient for Re (see Eq . (3) of Chapter 2), B = (lnQ10)/10, °CX vapour pressure deficit, kPa the Douglas-fir stand planted in 1949 the diameter of a leaf, m the diameter of the sun, m the distance between the sun and the earth, m the length of the umbra, m activation energy, J mol" 1 activation energy as defined by E q (3) of Chapter 3, J mol" 1 energy balance closure which is usually expressed as (H + LE) l(Rn - G-AS/ At), where H and LE are the sensible and latent heat fluxes, respectively. Rn is the net radiation flux, G is soil heat flux and AS / At is the rate of change of energy storage in the air and biomass between the ground and the height at which H and LE are measured. Rn-G-AS/At is commonly referred to as the available energy flux, eddy covariance (technique) Half-hourly CO2 flux, umol m" 2 s"1 a storage term to account for the rate of change in CO2 in the air column beneath the E C sensors independently (i.e., random) and identically (i.e., variances are homogeneous) distributed in a normal distribution with zero mean and common variance, a 2 the measurement height (i.e., 43 m) incident (intercepted) P A R , umol m" 2 s"1 the maximum rate of electron transport for / t h leaf, umol m" 2 s"1 the fraction of Qd0 added to Qb0 to give Qe, i.e., Qe = Qdo + kQb0 a coefficient used to modify a fraction of sunlit leaves that are light limited and light saturated, respectively extinction coefficient for direct P A R assuming canopy foliage is black vertical extinction coefficient of nitrogen in a canopy cumulative L A I from canopy top (0 at the top) leaf area index, m 2 (leaf area) m" 2 (ground area) L A I for ith leaf, m 2 m" 2 empirical coefficient Michaelis-Menten model empirical coefficient net ecosystem exchange, pmol m" 2 s"1 nighttime half-hourly N E E measurements made in turbulent conditions (i.e., u* > u*,h), umol m" 2 s"1 net ecosystem production, umol m" 2 s"1 ordinary least square algorithm rate of photosynthesis (canopy-level or leaf-level), umol m" 2 s"1 photosynthetically active radiation XV Psun photosynthesis of the big sunlit leaf in the Sun/Shade (2-leaf single layer), pmol m" 2 s"1 Pi photosynthesis of / t h leaf, pmol m" 2 s"1 Qo the extra-terrestrial P A R quantum flux, 2413 pmol m" 2 s"1 Qio temperature sensitivity coefficient describing the relative increase in Re for a 10 °C increase in Ts, °Cl Qb(f) un-scattered direct P A R absorbed by a leaf with the sun-leaf angle of y 2 1 umol m" s" Qbo incident direct P A R above the canopy, pmol m" 2 s"1 Qbi(f) un-scattered direct P A R absorbed by the light-limited sunlit leaves, pmol m - V Qbajsun absorbed un-scattered direct P A R by the big sunlit leaf in the sun/shade model, u.mol m" 2 s"1 QbThreshold maximum un-scattered direct P A R absorbed by a sunlit leaf, in addition to its absorption of Qd(£) + Qs{£), to still maintain the initial linear photosynthetic response with the slope of a, pmol m 2 s"1 Q d { £ ) absorbed sky diffuse P A R at canopy depth, I, umol m" 2 s"1 Qdo incident (sky) diffuse P A R above the canopy, pmol m" 2 s"1 Qe effective amount of P A R contributing to canopy photosynthesis (Qe = Qdo + kQbo), pmol m" 2 s"1 Qp amount of P A R perpendicular to the solar beam, pmol m" 2 s"1 Qs(i ) absorbed scattered direct P A R at canopy depth, I, pmol m" 2 s"1 QSat the amount of Qta where the quantum use efficiency of absorbed light begins to decrease, pmol m" 2 s"1 Qto incident total P A R above the canopy, pmol m" 2 s"1 QtOmdi modeled Qto (total downwelling P A R above the canopy) in a cloudless' 2 1 sky, uxnol m" s" Qta absorbed total P A R , pmol m" 2 s"1 Qtat absorbed total P A R for z'th leaf, pmol m" 2 s"1 Qti incident total P A R , pmol m" 2 s"1 Qx Qx = Qdo + xQb0, used in Figure 4-5 to test the combination of Qdo and Qbo, 2 1 pmol m" s" fi,r2, rs empirical coefficients Rio standardized rate of Re at Ts = 10 °C, pmol m" 2 s"1 Re ecosystem respiration, u,mol m" 2 s*1 2 1 Red daytime Re, u,mol m" s" Ren nighttime Re, pmol m" 2 s"1 R M S E root mean square errors, pmol m" 2 s"1 for photosynthesis Rubisco ribulose-l,5-biphosphate carboxylase/oxygenase RuBP ribulose biphosphate rw(t) time (i) varying variable Sc C02 mixing ratio, mol C O 2 mol" 1 of dry air Ta air temperature, °C Ts soil temperature, °C x v i u* friction velocity, m s" U*QIOO daytime u* filter (screening), when Q T 0 < 100 umol m" 2 s"1, daytime half-hourly measurements made in u* < u*tn were not used to estimate Red- Only the daytime half-hourly measurements made when Q L 0 > 100 umol m" 2 s"1 (including all u* conditions) and when Q,o < 100 umol m" 2 s"1 with only high u* conditions were used in the N E P vs. P A R relation ship to calculate Red- Similar definitions are applied to U*QO, U*Q5O, U*Q2OO and u*Q3oo- U*QO is equivalent to applying no daytime u* filter, because all daytime data are associated with Q T 0 > 0 umol m" 2 s"1 u*tn u* threshold value, m s" Vc photosynthetic Rubisco capacity of the entire canopy, umol m" 2 s"1 Vcmaxo photosynthetic Rubisco capacity at the top of the canopy, umol m" 2 s"1 Vcsh photosynthetic Rubisco capacity of the big shaded leaf, umol m" 2 s"1 Vcsun photosynthetic Rubisco capacity of the big sunlit leaf, umol m" 2 s"1 yo empirical coefficient used in Eq . (4) of Chapter 2, umol m" 2 s"1 w ' fluctuation in vertical wind speed XVII Acknowledgements I am indebted to my supervisor, Professor Andy Black, for his academic guidance and strong support. Andy creates an open-minded research environment, which enabled me to freely explore new ideas that challenge established research models. Andy also sets a personal example for me. He is a gentleman with a humble heart. I am very grateful for the constructive suggestions from the other members of my supervisory committee: Drs. Rob Guy, T i m Oke and Mike Novak during the course of my PhD research program. Their comments greatly improved the quality of this thesis. I would like to sincerely thank the wonderful individuals in Andy 's biometeorology laboratory: Andrew Sauter, Andrew Balakshin, Armel Castellan, Christopher Schwalm, David Gaumont-Guay, Dominic Lessard, E lyn Humphreys, Gordon Drewitt, Iain Hawthorne, Joe Kidston, K a i Morgenstern, Natascha Kljun, Nick Grant, Paul Jassal, Praveena Krishnan, Rick Ketler, Scott Graham, Shawn O'Nei l l , T im Griffis, Zhong L i , Stephanie Thompson and Zoran Nesic. I learned a great deal from these friends and I really appreciate the contibutions they made in the collection of the data essential to my thesis. I greatly appreciate the postdoctoral position provided by Dr. Lawrence Flanagan at the University of Lethbridge. I would like to acknowledge the encouragement from members of Larry's research group: Chera Emrick, Nicole Geske, Jason Seabrook, Kamran Syed and Bruce Johnson. In particular, I would like to thank Nicole Geske for her kind help with the formatting of my thesis. I appreciate the financial support through a Natural Sciences and Engineering Research Council of Canada ( N S E R C ) Postgraduate Scholarship and a University Graduate Fellowship (UGF) from the University of British Columbia. Funding for the Vancouver Island research projects was from an N S E R C Strategic Grant, N S E R C , Canadian Foundation for Climate and Atmospheric Sciences ( C F C A S ) and B I O C A P Canada grants supporting the Fluxnet-Canada Research Network and an N S E R C Discovery Grant to Professor Black. Special thanks go to my parents and my brother and sisters for their love and constant support. Above all, I would like to thank my wife, Yanl i , and my- three daughters: Lujia, Joanne and Olivia . They are angels in my life. They have given me a new perspective on life. Chapter 1. Introduction 1 1 Introduction The volcanic eruption of Mt . Pinatubo (in Philippines) on June 12,1991 (Figure 1-1), the single largest perturbation in climate during the last 100 years, ejected approximately 20 mill ion tons of SO2 into the troposphere, which greatly enhanced diffuse shortwave radiation (Molineaux and Ineichen 1996) and suddenly interrupted the recent global warming trend by causing a 0.6 °C decrease in mean global surface temperature (Roboek 2002). After the eruption, the growth rate of atmospheric CO2 concentration dramatically slowed down in the early 1990s (Keeling et al. 1995). This slowdown was not purely coincidental, since an apparent levelling off of atmospheric CO2 concentration was observed following the eruption of Mount Agung (in Indonesia) in February 1963 (Bacastow 1979) (Figure 1-2). A similar pattern in the reduced rise of atmospheric CO2 concentration was also identified following the eruption of E l Chichon (in Mexico) in March 1982 after removing the confounding effect of 1982/83 E l Nino event (Keeling et al. 1995). Figure 1-1. Clouds of ash and steam from the eruption of Mt. Pinatubo on June 12, 1991. Chapter 1. Introduction 3 3901 r 3101 1 1 1 1 L-1960 70 80 90 00 Figure 1-2. The levelling off (arrows) of atmospheric C O 2 concentration after the eruptions of Mt . Agung in 1963 and Mt . Pinatubo in 1991. Chapter I. Introduction 4 One hypothesis for the levelling off of atmospheric CO2 concentration is that the eruption of Mt . Pinatubo increased the level of sky diffuse P A R (photosynthetically active radiation), which, because plant canopies use diffuse P A R more efficiently than direct P A R in photosynthesis (Roderick et al. 2001), led to a higher rate of canopy photosynthesis (P), removing more CO2 from the atmosphere (Gu et al. 2003). This hypothesis stems from the long-known observation made by plant eco-physiologists that CO2 fluxes between a plant canopy and the lower atmosphere is usually higher in cloudy conditions than in clear conditions (e.g., Price and Black 1990, Hollinger et al. 1994). But the explanations for these observations even at canopy-level are very controversial, because other environmental variables (e.g., saturation deficit, foliage temperature) are also quite different between cloudy and clear conditions (Freedman et al. 2001). Also , the "diffuse radiation" hypothesis does not reconcile the narrow tree rings observed following the Pinatubo eruption, which could be due to reduced P (Krakauer and Randerson 2003). Angert et al. (2004) concluded that the enhanced diffuse radiation following the eruption of Mt . Pinatubo was "probably only enough to compensate for the reduction in total radiation". The net downward CO2 fluxes above a plant canopy (or net ecosystem productivity, NEP) can be expressed as: P - Re (ecosystem respiration). The higher downward CO2 fluxes in cloudy conditions can reflect either higher P (likely due to higher diffuse P A R ) or lower Re (likely as a result of lower temperature). In order to rigorously address the effect of diffuse P A R on canopy P, first we have to reliably estimate P. In this study 8 years (1998 - 2005) of C 0 2 flux data from a 56-year-old Chapter I. Introduction 5 coastal Douglas-fir stand on Vancouver Island (DF49) were used to address the uncertainties in estimating canopy P and the role of diffuse and direct P A R in canopy P. Chapter 2 addressed the methodological uncertainties in estimating nighttime and daytime Re using one year (2001) of N E P measured using the eddy covariance (EC) method (e.g., Wofsy et al. 1993, Black et al. 1996). Canopy P is generally obtained as daytime N E P + daytime Re, where daytime Re has to be estimated. The errors in estimating daytime Re using both the nighttime and daytime N E P measurements were systematically discussed. Chapter 3 extended the results of Chapter 2 to provide a reliable flux-partitioning algorithm for estimating P for Chapter 4. This chapter focuses on the effect of soil moisture and phenological (seasonal) change on Re using 8-years (1998-2005) of N E P data for DF49. The algorithms for partitioning N E P into its component fluxes, P and Re used in A M E R I F L U X (Falge et al. 2002), E U R O F L U X (Reichstein et al. 2005), and F L U X N E T - C A N A D A (Barr et al. 2004) were critically reviewed. The interannual variability in the Rio and Qw values of Re was investigated and the main cause for the variability was discussed. After discussing the uncertainties in estimating P in Chapter 2 and comparing different algorithms for partitioning N E P into P and Re in Chapter 3, Chapter 4 focused on P and canopy light regime. The history of canopy photosynthesis modelling work was briefly reviewed. The systematic errors of the regular Michaelis-Menten equation aQ A (P = '" m a x ) for modelling canopy P were examined. A new form of Michaelis-Menten equation (to be referred to as the Q e - M M model hereafter) was developed for modelling canopy P. In order to evaluate the performance of the Q e - M M model and to Chapter 1. Introduction 6 assess the inadequacies of the existing models, the modelling errors in P using the Qe-M M model and the Sun/Shade model developed by de Pury and Farquhar (1997) were compared. Additionally, the Q e - M M model was compared with another modified form of the Michaelis-Menten equation used in Gu et al. (2002 & 2003). This chapter also provides a biophysical explanation for why the quantum use efficiency of direct P A R is lower than that of diffuse P A R . Chapter 5 summarizes the major results of this study, discusses the relevance of these results in the context of large-scale modelling of gross primary productivity (Ruimy et al. 1999, Stil l et al. 2004), and identifies areas for extending the findings in the three main chapters for future research. The thesis also has five appendices. Appendix A briefly shows the site location and the configuration of the E C system. Appendix B reports the calibration of the instrument used to measure diffuse P A R that is essential for the analysis in Chapter 4. Appendix C discusses the shortcomings of the Sun/Shade model developed by de Pury and Farquhar (1997). Appendix D derives the two key equations for the complete multilayer model of P developed by Norman (1980) (i.e., the C U P I D model). Appendix C and Appendix D were included, because the algorithms from both models (i.e., the Sun/Shade and the C U P I D models) have been widely used in models of canopy P. Appendix E compared the sealing algorithms of five types of canopy P models: the complete multilayer, 2-leaf multilayer, 2-leaf single-layer, M M and Q e - M M models. Comparison of the models and their validation/invalidation using multiple years of E C -derived measurements of canopy P provided insightful information about the underlying biophysical principles of these models. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 7 2 Methodological Uncertainties in Estimating Nighttime and Daytime Ecosystem Respiration of a 56-year-old Douglas-fir Stand from Eddy Covariance C0 2 fluxes 2.1 Introduction Net ecosystem CO2 exchange (NEE) is the difference between CO2 losses by ecosystem respiration (Re) and CO2 gains by canopy photosynthesis (P) and is directly measured using the eddy covariance (EC) technique (e.g., Wofsy et al. 1993, Black et al. 1996). Net ecosystem productivity (NEP) is obtained as N E P = - N E E , which is a good approximation of C sequestration because the leaching losses of dissolved organic and inorganic carbon are usually very small in forest ecosystems. P is obtained as daytime N E P + daytime Re. Daytime N E P can be directly measured using an E C system, but daytime Re has to be estimated. The most commonly used method is to infer daytime Re from nighttime E C measurements of N E E (i.e., nighttime Re). Nighttime N E E measurements made in calm conditions, as determined by a threshold friction velocity (u*th), are usually rejected (e.g., Barford et al. 2001, Morgenstern et al. 2004, Mi l le r et al. 2004), because much of the respired CO2 is likely transported horizontally (advection) rather than vertically through the E C flux measurement plane (Baldocchi 2003). Only nighttime N E E measurements made in turbulent conditions ( N E E 1 ( ) are used to develop an annual relationship with soil temperature at a shallow depth (Ts) so that nighttime Re values can be calculated to replace the rejected measurements and daytime Re values can Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 8 be estimated using daytime Ts (e.g., Black et al. 2000, Flanagan and Johnson 2005). The annual N E E u - Ts relationship is often assumed to be exponential as follows: N E E U > =AeBTs +e (1) where A and B are two empirical coefficients, and e is the random error (residual). The values of A and B are commonly determined using a non-linear ordinary least squares (OLS) algorithm (e.g., Lee et al. 1999, Falge et al. 2002, Law et al. 2002, X u and Baldocchi 2004, Reichstein et al. 2005). However, this is problematic (Morgenstern et al. 2004, Richardson and Hollinger 2005) because O L S algorithms assume (Steel and Torrie 1960) (1) the independent variable (i.e., Ts) is measured without error and (2) the residuals (i.e., e) are independently and identically distributed in a normal distribution with zero mean and common variance, a 2 . The latter assumption is often abbreviated as IID N(0, cr2). It is reasonable to assume that the half-hourly measurements of Ts are error-free, but the s 's generally do not have a common variance over the range of Ts as is shown in Figure 2- la , in which cr 2 markedly increases with Ts. On the other hand, the validity of extrapolating nighttime Re -Ts relationship to daytime has also been questioned (e.g., Wohlfahrt et al. 2005a), because light is likely to inhibit foliar mitochondrial respiration during the day, namely the K o k effect (Kok 1948, Sharp et al. 1984, Brooks and Farquhar 1985, Vi l lar et al. 1994, Atk in et al. 2000b, Wang et al. 2001, Shapiro et al. 2004), and the degree of this inhibition at the ecosystem level is largely unknown (Janssens et al. 2001). Concerned about the poor quality of nighttime N E E measurements mainly caused by the lack of nocturnal mixing and the applicability of nighttime Re to daytime, many workers (e.g., Suyker and Verma 2001, Reichstein et al. 2002a, Griff is et al. 2003, X u and Baldocchi 2004) have obtained estimates of daytime Re Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 9 using daytime N E P measurements. Daytime N E P can be expressed using the Michaelis-Menten relationship as: N E P = a g ' ° A m a x Red + s M M model (2) where a is the apparent quantum yield, Qto is the total incident photosynthetically active radiation (PAR) above the canopy, Amax is the canopy-scale maximum photosynthetic capacity, Rea- is the estimate of daytime Re, and s is the random error (residual). Eq . (2) w i l l be referred to as the M M model. The three parameters (i.e., a, Amax, and Red) are usually determined using a non-linear O L S algorithm (e.g., Suyker and Verma 2001, Reichstein et al. 2002a, Griffis et al. 2003, X u and Baldocchi 2004). But this methodology is as questionable as it is for Eq . (1). A s shown in Figure 2-4d, there are two problems. First, the e 's do not have a common variance over the full range of Qto (cr 2 increases with Qt0). Second, the s's are not independently (randomly) distributed because, as w i l l be shown in Chapter 4, Eq . (2) underestimates N E P in cloudy conditions (i.e., the predicted values of N E P using Eq . (2) are less than the bin averages in Figure 2-4d for Q,o approximately between 500 - 1000 umol m ' 2 s"1) and overestimates N E P in clear conditions (i.e., the predicted values of N E P using Eq . (2) are higher than the bin averages in Figure 2-4d for Qt0 greater than 1000 umol m" 2 s"1). Therefore, using a non-linear O L S algorithm to obtain parameters for Eq . (2) violates the assumption of IID N(0, cr 2 ) . This violation can cause potentially large errors in the estimates of annual Re, but little attention has been paid to its impact in the literature. A s pointed out by Richardson and Hollinger (2005), it is a serious concern that "relatively subtle choices in model construction and assumptions lead to what must be considered significant biases". Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 10 A n additional concern is that the length of the period for which the N E P - Qto relationship has been developed varies considerably in the literature, e.g., 1 day (Griffis et al. 2003), 3 days (Suyker and Verma 2001), 7 days (Kowalski et al. 2003, Reichstein et al. 2002a, Wohlfahrt et al. 2005a), 15 days (Lee et al. 1999) and 30 days (Falge et al. 2002, Law et al. 2002, Carrara et al. 2004). Lack of a standardized analytical procedure (e.g., the above mentioned different regression periods for the M M model) makes cross-site and cross-biome comparisons of Re very difficult. Uncertainties in the estimates of daytime Re also severely limit our understanding of ecosystem respiratory behaviour. For example, the estimates of daytime Re obtained using the M M model were reported to be lower than that obtained using the nighttime annual N E E H - Ts relationship, but this could be due to an artefact of curve fitting, and may not necessarily reflect the real effect of light inhibition on ecosystem foliar respiration. The two objectives of this chapter are to (1) report the methodological uncertainties in the estimates of Re using both the nighttime and daytime EC-measured N E E , and (2) evaluate the validity of applying the nighttime Re - Ts relationship to daytime and vice versa. In the second objective, the evidence of possible light inhibition on ecosystem foliar mitochondrial respiration w i l l be examined by comparing the nighttime and daytime Re - Ts relationships. One year (2001) of flux data for a 56-year-old coastal Douglas-fir stand (DF49) w i l l be used in this study. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 11 2.2 Methods Study site The study site is located 10 km southwest of Campbell River on the east coast of Vancouver Island, B C , Canada (49°52 'N, 125°20 'W) at an elevation of 300 m above sea level. The forest, originally planted with Douglas-fir seedlings in 1949, consists of 80% Douglas-fir (Pseudotsuga meneziesii (Mirb.) Franco), 17% western red cedar (Thuja plicata Donn ex D . Don) and 3% western hemlock (Tsuga heterophylla (Raf.) Sarg.). Its understory is sparse, mainly consisting of salal (Gaultheria shallon Pursh.), Oregon grape (Berberis nervosa Pursh), vanilla-leaf deer foot (Achlys triphylla (Smith) DC) , and a thin layer of ferns and mosses. A site survey in 1998 found that the stand density was 1100 stems ha"1, and tree height ranged from 30 m to 35 m, and the average diameter at breast height ( D B H ) was 29 cm. The soil at this site is a humo-ferric podzol with a gravelly loamy sand texture in the upper 40 cm transitioning to sand with increasing depth. The leaf area index (LAI) was estimated to be 8 ± 1 m 2 m" 2. More detailed descriptions of the site can be found in Drewitt et al. (2002), Humphreys et al. (2003), Morgenstern et al. (2004), and Humphreys et al. (2006). Measurements Morgenstern et al. (2004) described in detail the climate and eddy flux measurements at the site. Here only a short summary of these measurements is given. The E C sensors were mounted on an open-lattice 50-cm triangular tower at a height of 43 m and consisted of a 3-dimensional sonic anemometer-thermometer (SAT) (model 1012R2, Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 12 G i l l Instruments, Lymington, UK) and a closed-path infrared gas (CO2/H2O) analyzer (model LI-6262, L I - C O R , Lincoln, N E , USA). Half-hourly C 0 2 fluxes were calculated as Fc = pa w'sc ' , where pa is the mean molar density of dry air, w'sc ' is the covariance between instantaneous vertical wind speed (vv) and CO2 mixing ratio (s c ) (i.e., mol CO2 mol" 1 of dry air). The fluctuations of vv and s c i.e., vv' and sc', were calculated as the difference between the instantaneous values and the arithmetic average for the half hour. The frequency of w and sc used in the calculations of Fc was 20.83 H z after digital low-pass filtering and down-sampling of the raw signals. The rate of change in CO2 storage in the air column beneath the E C sensors was calculated as Fs = hmpaAsc/ At (Hollinger et al. 1994, Morgenstern et al. 2004), where hm is the measurement height (i.e., 43 m), Asc is the difference between sc (half-hourly average of sc) of the following and previous half-hours, and Ar = 3600 s. Half-hourly net ecosystem exchange (NEE) of C 0 2 was then calculated as N E E = Fc + Fs . Positive values of N E E correspond to CO2 losses from the ecosystem. Net ecosystem production (NEP) was calculated as - N E E . In this analysis, energy balance closure (EBC) was not applied to correct half-hourly N E E measurements. When E B C was evaluated on an annual basis for this site, the slopes of the regressions of sensible heat flux + latent heat flux vs. the available energy flux (net radiation - soil heat flux - heat storage terms) were 0.888, 0.879, 0.880, and 0.892 for 1998-2001, respectively (Morgenstern et al. 2004). The E B C correction is still a subject of debate because part of the error may arise from the measurements of net radiation (e.g., it may not be representative of the flux footprint), soil heat flux and the Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 13 heat storage terms. In addition, latent heat fluxes can be underestimated because of high frequency loss in the sampling tube as a result of dirt and water vapour adhering to the wall , which can be a worse effect than for C 0 2 fluxes. However, i f chamber measurements of soil, bole and foliage respiration were scaled up to compare with E C -derived respiration (e.g., Lavigne et al. 1997), it would likely be necessary to account for the lack of E B C (Twine et al. 2000, Barr et al. 2006). Ignoring E B C does not affect the conclusions of this thesis because the corrected N E P , Re and P would be reduced by the same fraction, i.e., about 11%. Downwelling total P A R (Qn)) was measured using a quantum P A R sensor (model LI-190SB, L I - C O R Inc) mounted at a height of 45 m. Canopy air temperature (7V) and relative humidity were measured using a relative humidity sensor (model H M P - 3 5 C , Vaisala Oyj, Helsinki, Finland) mounted at a height of 27 m. Soil temperature (Ts) was measured using copper-constantan thermocouples buried at different locations and at 5-cm depths. The above climate measurements (e.g., Ql{), Ta, and Ts) were sampled every 5 seconds and averaged over the 30-minute-interval. Curve fitting algorithm The measurements made when Q,o = 0 umol m" 2 s"1 are referred to as nighttime measurements, and those when Q,o > 0 u.mol m" 2 s"1 as daytime measurements. Coefficients of the linear and nonlinear regressions were determined using Matlab® Statistics Toolbox®. A robust least squares (RLS) algorithm was used for all the linear regressions of this analysis. In contrast to the commonly used linear O L S algorithm, the R L S algorithm uses an iteratively re-weighted least squares algorithm, with the weights Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 14 of each iteration calculated by applying the bisquare function to the residuals from the previous iteration. The R L S algorithm gives lower weight to points that do not fit well and therefore the results are less sensitive to outliers in the data as compared with linear O L S algorithm. Because the R L S algorithm of Matlab® Statistics Toolbox® is not available for non-linear regressions, the Gauss-Newton O L S algorithm was used in all nonlinear regressions of this analysis. Detailed descriptions of the linear R L S and nonlinear O L S algorithms can be found at www .math works .com. 2.2.1 Obtaining Re - Ts relationships using nighttime NEE measurements The value of u*,n for this stand was taken to be 0.3 m s"1 following the analysis of Morgenstern et al. (2004), and soil temperature at the 5-cm depth was selected as the temperature best used to predict ecosystem respiration following the analysis of Drewitt et al. (2002). Five methods were used to estimate nighttime ecosystem respiration (Ren). Method 1 assumed an exponential relationship between Ren and Ts: Ren = AeBT° exponential fit (3) Eq . (3) can also be written as Ren =i?1(lf21<(',~in)/1,>, where R10 is the standardized base rate of respiration at Ts = 10 °C, and Qio is the temperature sensitivity coefficient that describes the relative increase in Ren for a 10 °C increase in Ts. Eq. (3) and the Qw function are mathematically identical because Qw = eWB and Rw = AQW. In Method 1, the empirical coefficients A and B were determined from the annual NEE, , - Ts relationship using half-hourly fluxes and the nonlinear O L S algorithm. Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 15 Method 2 assumed a logistic relationship between Ren and Ts following Barr et al. (2004): Rn=A/(l+e(T'-w)/") + yn logistic fit (4) where A, B and yo are empirical coefficients. Similar to Method 1, the three coefficients A, B and yo were determined from the annual N E E 1 ( - Ts relationship using half-hourly fluxes and the nonlinear O L S algorithm. Method 3 used the logarithmic transformation of Eq . (3): In Ren = In A + BTs logarithmic fit (5) In Method 3, the coefficients A and B were determined from the annual ln( N E E | ( ) - T„ relationship using half-hourly fluxes and the linear R L S algorithm. After the coefficients A and B were determined, they were used in the exponential form (i.e., Eq . 3) to calculate the half-hourly Ren. Method 4 used the bin-averaged values of N E E H for every 100 half-hourly measurements of increased magnitude as was shown in Figure 2- la . The coefficients A and B were then determined for Eq . (5) by linearly fitting the annual ln(bin-averaged N E E ( I )-Ts relationship with the linear R L S algorithm. Method 5 used nightly averaged values of NEE„ which were obtained by averaging acceptable half-hourly values of N E E ] ( for each night. The minimum number required for the nightly averaging was 3. The coefficients A and B were determined using Eq. (5) by linearly fitting the annual ln(nightly averaged N E E i ( ) - Ts relationship with the linear R L S algorithm. Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 16 Once the respective coefficients for the five methods were determined, they were used to calculate the half-hourly values of Re for both calm and turbulent conditions, i.e., the original nighttime half-hourly N E E measurements made in turbulent conditions were not retained, but rather replaced by calculated Re values in order to obtain an estimate of the annual total Re. The rationale for replacing the measured N E E u w i l l be discussed later. 2.2.2 Obtaining Re - Ts relationships using daytime NEP measurements In order to reduce the inhomogeneous distribution of cr2 in the daytime N E P -Qto relationship (Figure 2-4), the M M model was modified by restricting it to low Qt0 conditions and assuming a linear relationship as follows: N E P = aQl0 - Red + s L U E model (6) Eq . (6) w i l l be referred to as the L U E (light use efficiency) model. If unspecified, the Qto interval for the L U E model is 0 - 300 umol m" 2 s"1 and the Q,o interval for the M M model 2 1 is 0 - 1800 umol m" s" . Both models use daytime measurements only. The effect of using a daytime u* threshold on the estimates of Red was tested for both the M M and L U E models using 15 days of data and advancing one day at a time (i.e., a 15-day moving window) and by removing the daytime half hourly N E P measurements made when u* < u*tn (u*th - 0.3 m s"1) conditions for increasing levels of Q,o. Five levels of Qto (i.e., u.Q , u,n , u,n , u,n , and u,n ) were used for the daytime u* screening. Taking the M M model as an example, utQ denotes that the daytime half-hourly N E P measurements made when u* < 0.3 m s"1 were removed i f Qt0 < 200 umol m" 2 s"1, and only the half-Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 17 hourly N E P measurements made when u* > 0.3 m s"1 and Qto < 200 umol m" 2 s"1 and all the half-hourly N E P measurements made when Q,0 > 200 umol m" 2 s"1 regardless of their u* values (i.e., all the daytime half-hourly N E E values associated with Qt0 of 200 - 1800 2 1 umol m" s" ) were used in the M M model fit to determine Rea-. u,Qo means that all daytime N E E values were used, i.e., no u* screening. For the L U E model, u.Q means that all the N E E measurements associated with u* < 0.3 m s"1 when Qto < 200 umol m" 2 s"1 were removed, only the half-hourly N E E measurements made in u* > 0.3 m s"1 when Q,0 2 1 < 200 umol m" s" and all N E E measurements regardless of their u* values when 200 umol m" 2 s"J< Qt0 < 300 umol m" 2 s"1 were used. Note the total P A R range for the L U E model is 0 < Qt0 < 300 umol m" 2 s"1 i f not specified otherwise. The effect of the length of the regression periods on the estimates of Red was investigated by using moving windows of six different sizes (1-, 3-, 7-, 15-, and 30-days) with the daytime u* filter of u.Q . A l l the moving windows in this analysis were started on January 1, 2001, and increased 1 day at a time. Therefore, for window sizes of longer than 1 day, the last window extended into 2002 (e.g., until January 29, 2002 for the last 30-day window). Both morning and afternoon data were used to determine the parameters in the M M and L U E models. Three different ranges of Qt0 (0 - 100, 0 - 200 and 0 -300 umol m" 2 s"1) were tested for the L U E model using the 15-day moving window and daytime u* filter of u,Q . The minimum number of daytime half-hourly N E P measurements used in the M M and L U E regressions was three. The estimates of Red for the M M and L U E models were determined using the nonlinear O L S and linear R L S algorithms, respectively. The value of Ts associated with each Red estimate is the average of the half-hourly values of Ts corresponding to the Q,o Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 18 values used in the regression. The annual Red - Ts relationships obtained using both the M M and L U E models were assumed to be exponential (i.e., Red = AeBT') and their corresponding coefficients A and B were determined using the logarithmic transformation of/?*, (i.e., \x\Red =\nA + BT). 2.3 Resu l t s a n d d iscuss ions 2.3.1 Re - Ts r e l a t i onsh ips ob ta ined u s i n g n i gh t t ime N E E measu rements A s mentioned earlier, the annual nighttime N E E i ( - Ts relationship does not have a common variance over the full range of Ts (Figure 2-la). For example, one standard deviation in the bin averaged value of N E E u at Ts = 1 °C was less than 2 pmol m" 2 s"1, but it increased to more than 8 umol m" 2 s"1 at Ts = 10 °C. In contrast, the values of one standard deviation in the annual ln( N E E u ) - Ts relationship were very similar over the full range of Ts (Figure 2-lb). The effect of these variance distributions is shown in Figure 2-2. For Ts between 8 and 13 °C, the Ren - Ts relationships obtained using the nonlinear O L S algorithm (Methods 1 and 2) gave the highest values of Ren, followed in order by the relationships obtained using the bin averaged and nightly averaged N E E I ( (Methods 4 and 5), and the relationship obtained using logarithmically transformed half-hourly values of N E E I ( (Method 3). Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 19 20r 2001 (nighttime, u.^ 0.3 m s"1) (a) - 1 5 o bin of 100 half-hourly values 10 Ui HI 5 10 7 (5 cm) (°C) 15 0 5 10 T (5 cm) (°C) 15 Figure 2-1. (a) The relationship between nighttime N E E measurements, representing nighttime ecosystem respiration (Ren), and soil temperature (Ts) at the 5-cm depth, (b) The relationship between the logarithmically transformed N E E and Ts. In both plots, the circles are bin averages of 100 half-hourly values, and the vertical bars are ± 1 standard deviation. The assumption of IID N(0,<x 2) was met by doing the logarithmic transformation of the half-hourly nighttime N E E . The half-hourly N E E measurements are from 2001 with u* > 0.3 m s"1 (i.e., NEE, , , ) (n = 2472). Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 20 Figure 2-2 .The Ren - Ts relationships obtained using five different nighttime methods (see text for details). Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 21 The order of these relationships shown in Figure 2-2 coincided with the severity of the violation of IID N(0, cr2) (i.e., in this case, the heterogeneous distribution of cr 2 ) . The variance in the original half-hourly N E E u (used in Methods 1 and 2) was most heterogeneous (Figure 2-la), followed by the bin averaged and nightly averaged N E E u (used in Methods 4 and 5) since the variance was partly reduced by the averaging. The heterogeneity in the logarithmically transformed half-hourly values of N E E u (used in Method 3) was very small (Figure 2-lb) . The heterogeneous distribution of cr2 steepened the Ren - Ts relationship because the large NEE„ values at high Ts had larger residuals than the smaller N E E u values at low Ts (Figure 2-la). The reason for this is in the O L S algorithm, the influence of the large N E E u values being magnified because their large residuals were squared, leading to incorrect higher estimates of Ren than otherwise. The Ren values obtained using the Ren - Ts relationships from the bin and nightly averaged N E E i ( (Methods 4 and 5), even with the logarithmic transformation of the averages, were higher than those obtained using the Ren - Ts relationship from the original half-hourly N E E i f with the logarithmic transformation (Method 3). This was because the effect of the large N E E u values had already gone into the averages, and could not be undone using the logarithmic transformation "after the fact". The coefficients (e.g., A and B) obtained using the 5 methods are given in Table 2-1. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 22 Table 2-1. Coefficients obtained for the five nighttime methods for DF49 in 2001 (see Figure 2-2 and text for details). Units for A and B are umol m" 2 s"1 and °C _ 1 , respectively. Units for yo and R M S E are both umol m" 2 s"1. Methods A B y0 R2 RMSE n (1) N E E = AeBT' (half-hourly) (2) N E E = A / ( l + e { T ' - W ) , B ) + y0 (half-hourly) (3) ln (NEE) = l n A + 5 T (half-hourly) (4) ln(bin averaged N E E ) = In A + BT (bin of 100 half-hourly) (5) ln(nightly averaged N E E ) = In A + BT (each night) I . 19 0.17 —- 0.40 4.02 2472 I I . 8.8 -2.02 1.57 0.39 4.09 2472 1.04 0.16 —- 0.36 4.12 2472 1.31 0.15 —- 0.82 0.92 24 1.25 0.16 —- 0.51 3.41 234 They were used to calculate Re values for all daytime and nighttime half hours, including replacing the original nighttime half-hourly values of N E E u < with model-calculated Re. On an annual basis, the summation of the half-hourly N E E i ( replacements was virtually the same as the summation of the original measured half-hourly N E E 1 ( for > the exponential fit (Method 1) ( Z ( N E E , ( m o d - N E E , , ) = -1.82 g C m" 2, where N E E „ i m o d denotes model-calculated NEE, , replacements, n = 2472) and the logistic fit (Method 2) ( Z ( N E E , „ m o d - N E E , „ ) =-0.01 g C m " 2 ) . In theory, I ( N E E „ , m o d - N E E J should be zero because it is the summation of all the residuals in the above two nonlinear O L S fits. The difference, however, became very large, i.e., Z (NEE„_ m o d - N E E , , ) = -47.34 g C m" 2, for Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 23 the logarithmic fit (Method 3) (Figure 2-2). This was because the logarithmic fit was obtained as a least squares fit to the transformed ln( N E E u ) - Ts relationship (Figure 2-lb), rather than the untransformed N E E u - Ts relationship (Figure 2-la). In our previous analysis (Morgenstern et al. 2004) for this stand and many other studies (e.g., Goulden et al. 1996a, Flanagan and Johnson 2005), the original half-hourly measurements of N E E u are retained in the dataset, and the model-calculated Re values were used only to replace nighttime half-hourly N E E measurements made in calm conditions and to estimate daytime ecosystem respiration. However, this practice is questionable. The nighttime half-hourly N E E measurements made even in turbulent conditions should be regarded as discrete (and limited number of) samples of the true ecosystem respiratory signal, and they generally do not follow a normal distribution (i.e., existence of a few extremely large values of N E E H , for example, approximately 2% of the N E E i f values are greater than 50 umol m ' 2 s"1) (Figure 2-la). In view of the IID N(0,o- 2 ) violation, the erratic behaviour inherent in the nighttime half-hourly N E E measurements (samples) made in turbulent conditions should be "logarithmically corrected" to reflect the real behaviour of whole ecosystem respiration (population). 2.3.2 Re - Ts relationships obtained using daytime NEP measurements The effect of the daytime u* filter applied to different ranges of Q,o on the Rea- - Ts relationships obtained using both the M M and L U E models is shown in Figure 2-3. The pattern of the effect of the daytime u* filter for both the M M and L U E models was similar (compare Figure 2-3a with Figure 2-3b). Note the large difference between the M M and L U E relationships. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 24 Figure 2-3. The Re(t - Ts relationships obtained using the M M and L U E models with the application of a daytime u* filter to increasing ranges of Q,o. The total Qto ranges for the M M model and L U E model are 0 - 1800 umol m" 2 s"1 and 0 - 300 umol m" 2 s"1, respectively. u,Qn, u,Q^ , u,Qm , utQ , and utQ denote that the daytime half-hourly N E P measurements made in calm conditions (i.e., u* < 0.3 m s"1) were removed i f Qto < 0 umol m 2 s"1, Qto < 50 umol m" 2 s"1, Q,o <100 pmol m" 2 s"1, Q,o < 200 pmol m" 2 s"1, and Q,o < 300 pmol m" 2 s"1, respectively. For example, u,Q^ , in the case of the M M model, means removing low u* daytime N E P measurements i f Q,o < 200 umol m" 2 s"1 and only the high u* N E P measurements associated with Qt0 < 200 umol m" 2 s"1 and all the N E P measurements made when Q,o > 200 umol m" 2 s"1 (regardless of their u* values) are used in the M M model fit to determine Rea: In the case of the L U E model, data for Ql0 between the upper end of the range and 300 umol m" 2 s"1 were not u* screened e.g., for u,Q values for 100 < Qto < 300 umol m" 2 s"1 were not screened. u» Q means no daytime u* screening was applied in both the M M and L U E models, because all daytime N E P data are associated with Q,o > 0 umol m" 2 s'1. Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 25 The coefficients for the Red - Ts relationships in Figure 2-3 are given in Table Table 2-2. Table 2-2. Coefficients obtained for the M M (Qt0: 0 - 1800 umol m" 2 s"1) and L U E (Qt0: 0 2 1 - 300 umol m" s" ) models with the application of different daytime u* filters for DF49 in 2001 (see Figure 2-3). Units for A and B are umol m" 2 s"1 and °C" \ respectively. The values of A and B were determined using \nRed = In A + BTs (see Eq . (5)). M M model L U E model A B A B 1.34 0.13 0.54 0.16 1.41 0.15 0.87 0.13 1.45 0.16 0.85 0.14 1.55 0.15 0.76 0.16 u,0 1.79 0.14 0.70 0.17 The Red values obtained using the annual Red - Ts relationships were lowest when no daytime u* screening (i.e., w„Q ) was applied, but the Red - Ts relationships quickly stabilized when u,Q was used, presumably because by that time of the day the convective boundary layer ( C B L ) was well established. To be conservative, the daytime u* filter of utQ was applied to all the subsequent analysis. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 26 Figure 2-4. Daytime N E P - P A R relationships for different months of 2001. The dots in (a) - (c) are the half-hourly N E P measurements. The circles in (d) are the bin averages of 300 half-hourly N E P measurements and the vertical bars denote ± 1 standard deviation. The thin and thick lines are the respective fits obtained using the M M and L U E models to the half-hourly N E P measurements (not to the bin averages as shown in (d)). The Q,o ranges for the M M model and L U E model are 0 - 1800 umol m" 2 s"1 and 0 - 300 umol m" 2 s"1, respectively. Chapter 2 Methodological uncertainties in estimating nighttime and daytime R e 27 The reason for the lower values of Red obtained using the L U E model compared to those using the M M model becomes clear in the analysis of N E P vs Q,o plots shown in Figure 2-4, which shows that the M M model had consistently more negative intercepts than the L U E model. A s mentioned in the Introduction of this chapter, the e 's for the M M fit did not meet the IID N(0 ,c r 2 ) assumption. For non-limiting values of Q,o (e.g., Qto > 1500 umol m" 2 s"1), a higher fraction of the diffuse P A R component led to higher canopy photosynthesis and consequently higher N E P (see Chapter 4 for details, e.g., Figure 4-7a and Figure 4-8a). Therefore, the error bars in Figure 2-4d were not completely random, because positive error bars tended to be associated with cloudy conditions and negative error bars tended to be associated with clear conditions. The coefficients of the M M and L U E fits shown in Figure 2-4 are given in Table 2-3. Table 2-3. Coefficients of the M M (Ql0: 0 - 1800 umol m" 2 s"1) (i.e., Eq . (2)) and L U E (i.e., Eq . (6)) fits for the different months shown in Figure 2-4. Units for a and Amax are umol (CO2) umol - 1 (quanta) and umol m 2 s"1, respectively. M M model L U E model a A nmax Red a Red May 0.11 27.06 8.22 0.03 2.93 July 0.18 29.16 13.55 0.05 7.53 September 0.16 23.61 9.40 0.03 3.61 May - September 0.15 26.04 10.11 0.04 4.80 Also as a result of the effect of diffuse P A R , the overall daytime N E P - Q,o relationship was more parabolic than hyperbolic with a peak in N E P at Qto approximately between 1000 - 1200 umol m" 2 s"1 where the amount of diffuse P A R was highest. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 28 However, the hyperbolic nature of the M M fit forced it to give the highest estimates of N E P for the highest values of Q,o (e.g., Qto approximately of 1800 umol m" 2 s"1), therefore the M M fit underestimated N E P for Qt0 between 500 - 1200 umol m" 2 s"1, and 9 1 overestimated N E P for Q,0 > 1200 umol m" s" . Because the frequency of the occurrence of Qto greater than 1200 umol m" 2 s"1 was significantly lower than that for Qto between 500 - 1200 umol m" 2 s"1, as indicated by the horizontal distance between the bin averages in Figure 2-4d, the overestimation of N E P for Q,o greater than 1200 umol m" 2 s"1 did not fully balance the underestimation of N E P for Qt0 between 500 - 1200 umol m" 2 s"1. The nonlinear O L S algorithm requires the summation of all residuals to be zero, i.e., overestimation + underestimation = 0. Therefore, the O L S algorithm for the M M fit had to overestimate N E P for a large part of Qt0 less than 500 umol m" 2 s"1 in order to 2 1 compensate for the lack of overestimation at Qto greater than 1200 umol m" s" , leading to an incorrect higher estimate of Rea- (more negative intercept). The larger the width of the moving windows, the more cloudy and clear conditions are likely to be included into the M M fit, thus increasing the parabolic tendency for the N E P - Q,o relationship and the severity of the violation of IID N(0, a2) assumption. Figure 2-5a shows the dramatic effect of the moving window width on the Red - Ts relationships obtained using the M M model. A s it was expected, the wider the moving windows (regression periods), the more serious the violation of the IID N(0, a2) assumption, and consequently the more incorrect enhancement for the Red - Ts curves. For example, at Ts = 15 °C, the Red value obtained using the 30-day moving window was highest, followed by that obtained using the 15-day moving window, . . . and that obtained using a 1-day moving window (i.e., on a daily basis) was lowest (Figure 2-5a). In Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 29 contrast, the Red - Ts relationships obtained using the L U E model was almost independent of the window width (Figure 2-5b), indicating its conformity to the IID N(0, cr 2 ) assumption. The 15-day moving window was chosen for all the subsequent analysis of both the M M and L U E models, because the Reet - Ts relationships tended to stabilize at moving window width of 15-days (Figure 2-5). Coefficients for the Red - Ts relationships obtained using the M M and L U E models with different moving windows are given in Table 2-4. A s a result of the incorrect enhancement of the Red - Ts curves obtained using the M M model, the value of A for the M M model was more than twice that for the L U E model. However, the value of B for the L U E model was slightly higher than that for the M M model. Table 2-4. Coefficients obtained for the M M (Ql0: 0 - 1800 umol m" 2 s"1, and utQ ) and 2 1 L U E (Qto: 0 - 300 umol m" s" , and u,Q ) models with different moving window for DF49 in 2001 (see Figure 2-5). Units for A and B are umol m" 2 s"1 and °C _ 1 , respectively. The values of A and B were determined using lnReil = In A + BTs (see Eq. (5)). M M model L U E model A B A B 1-day moving window 1.30 0.14 0.76 0.17 3-day moving window 1.38 0.15 0.60 0.19 • 7-day moving window 1.51 0.15 0.62 0.18 15-day moving window 1.55 0.15 0.76 0.16 30-day moving window 1.51 0.16 0.75 0.16 Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 30 2001 (daytime, u.Q ) Figure 2-5. The annual Red - Ts relationships obtained using the M M and L U E models with moving windows of different sizes for 2001. A l l the moving windows were increased one day at a time and all the fits were made with the logarithmic transformation of Red. The total Q,o ranges for the M M model and L U E model are 0 - 1800 pmol m" 2 s"1 and 0 - 300 umol m" 2 s"1, respectively. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 31 2.3.3 Comparison of the Re - Ts relationships obtained using the nighttime and daytime methods Figure 2-6 compares the Red - Ts relationships obtained using the L U E model for different ranges of Q,o along with the nighttime log transformed Ren values. A s the range of Qto increased, the values from the Red - Ts relationships decreased relative to the Ren -Ts relationship, i.e., for a given Ts, the corresponding Red obtained decreased as the range of Qt0 increased. But the decrease in Re from darkness to Qt0 of 0 - 100 umol m" 2 s"1 was larger than the subsequent decreases in Re for equal Qt0 ranges (e.g., decrease in Re from Qt0 of 0 - 200 umol m" 2 s"1 to Qt0 of 0 - 300 umol m" 2 s"1). Wohlfahrt et al. (2005b) surveyed many leaf-level experimental results and showed that the light inhibition on foliar respiration initially falls fast with increasing light and then stabilizes at higher P A R levels. The Red - Ts relationship obtained with the Q,0 range of 0 - 300 pmol m" 2 s"1 possibly best represents the canopy daytime dark respiration, because (1) inclusion of higher values of Q,o risks violating the statistical assumption of IID N(0, a2) as shown in Figure 2-4, (2) lower levels of Q,o may not have sufficient daytime influence since the majority of the shaded leaves deep in the canopy are still in darkness, and (3) the light 9 1 inhibition on foliar respiration is saturated at Q,o of 300 pmol m" s" at leaf-level for the majority of the plant species reported in the literature (e.g., Brooks and Farquhar 1985, Vil lar et al. 1994, Atk in et al. 2000b). Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 32 Figure 2-6. The Re - Ts relationships obtained using the L U E model with three Q,o ranges: Q,o < 100 umol m" 2 s"1 (dotted line), Q,o < 200 umol m" 2 s"1 (thin line) and Q,o < 300 pmol m" 2 s"1 (dashed line). Also shown are the Re - Ts relationships obtained using the M M model with Q,o < 1800 pmol m*2 s*1 (line with solid triangles) and Qto < 300 umol m" 2 s"1 (line with empty triangles) and the Re - Ts relationship obtained using the nighttime logarithmic fit (the thick line). In all the daytime Re - Ts relationships, 15-day moving window and daytime u* filter of u,n were used. Chapter 2 Methodological uncertainties in estimating nighttime and daytime R, 33 Also shown in Figure 2-6 are the Re - Ts relationships obtained using the M M model with Qt0 of 0 - 1800 umol m" 2 s"1 and Qto of 0 - 300 umol m" 2 s"1. A s discussed earlier, the violation of IID N(0, a2) assumption by the M M model (see also Figure 2-4) likely resulted in the former Re - Ts relationship being much higher than that obtained using the corresponding L U E model with Qto of 0 - 300 umol m" 2 s"1. The r2 and R M S E obtained for all the 15-day moving windows using the M M and L U E models (both with Qt0 of 0 - 300 umol m" 2 s"1) are 0.5434 ± 0 . 1 5 6 8 , 0.5279 ± 0.1556, and 2.7821 ± 1.3134 pmol m" 2 s"1, 2.8205 ± 1.3001 umol m" 2 s"1, respectively. Therefore, it is difficult to judge the merits of the M M and L U E models purely from a statistical point of view. The Re - Ts relationship obtained using the M M model with Qto of 0 -300 umol m" s" is also higher than the nighttime Re - Ts relationship obtained using the logarithmic transformation of nighttime half-hourly N E E (see Figure 2- lb and Figure 2-2). Thus the Re — Ts relationship obtained using the M M model even with the relatively narrow Q,o range of 0 - 300 pmol m" s" is unlikely to be correct because the foliar biomass is quite large for this Douglas-fir stand (e.g., L A I « 8) and as w i l l be discussed later, the light inhibition on foliar dark respiration is likely to result in the daytime Re - Ts relationship being lower than the nighttime Re - Ts relationship. 2.3.4 Estimates of the annual totals of NEP, Re and P using the nighttime and daytime methods Figure 2-7 shows the annual cumulative N E P calculated using different Re - Ts relationships. The annual total N E P obtained using the nighttime exponential fit was 194 g C m" 2 lower than that obtained using the nighttime logarithmic fit, and was 376 g C m" 2 Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 34 lower than that obtained using the L U E model with Qt0 range of 0 - 300 umol m" 2 s"1. The annual N E P obtained using the M M model with the 15-day moving window was approximately half of that obtained using the nighttime exponential fit. In view of the violation of IID N(0, cr 2 ) assumption, the correct nighttime Re - Ts relationship in this analysis was assumed to be derived from the nighttime annual half-hourly N E E H - Ts relationship using the logarithmic fit (Method 3), and the correct daytime Re - Ts relationship was assumed to be derived from the daytime N E P - Q,0 relationship using the L U E model with the 15-day moving window and Qt0 of 0 - 300 umol m" 2 s"1. Relationships obtained by nighttime methods other than the logarithmic fit and the daytime M M fit violated the IID N(0, cr 2 ) assumption, and therefore were considered to be incorrect. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 35 Figure 2-7. The annual cumulative NEP for 2001 obtained using different nighttime and daytime derived Re - Ts relationships. The LUE and MM model use only daytime half-hourly NEP measurements. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 36 The annual totals of Re obtained using the exponential and logistic fits were almost identical (Table 2-5), because both used the nonlinear O L S algorithm. The annual total Re obtained using the nighttime logarithmic fit was 464 g C m" 2 lower than that obtained using the nighttime exponential fit, but was 415 g C m" 2 higher than that obtained using the L U E model with Qt0 of 0 - 300 pmol m" 2 s"1. The annual total Re obtained using the M M model with the 15-day moving window was 1070 g C m" 2 higher than that obtained using the L U E model with Ql0 of 0 - 300 pmol m~2 s"1, and was even 191 g C m" higher than that obtained using the nighttime exponential fit. Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 37 Table 2-5. Annual totals of the Re and P obtained using different annual nighttime and daytime Re - Ts relationships (see Figure 2-7 and Figure 2-8 for details). Only the nighttime half-hourly N E E measurements made in conditions where u* > 0.3 m s"1 were used in the nighttime methods. The daytime half-hourly N E P measurements made in conditions where u* < 0.3 m s"1 and Qt0 < 200 umol m" 2 s"1 were not used in the M M and L U E fits, and only the rest of the daytime data (i.e., not screened by the daytime u* filter) were used in both models to determine Rea<. g C m" 2 y r 1 Re P Nighttime and daytime Re - Ts relationships Nighttime Daytime Total N E E = AeBT> (nighttime, half-hourly) 900 1186 2086 2313 N E E = A / ( l + e ( r ' - 1 0 ) / f l ) + y 0 (nighttime, half-hourly) 909 1172 2081 2299 ln(nightly averaged N E E ) = ln A + BTs (each night) 822 1061 1883 2188 ln(NEE) = ln A + BT (nighttime, half-hourly) 706 916 1622 2043 L U E model (Qt0: 0 - 200 umol m" 2 s"1, 15-day moving window, u,Q ) 555 729 1284 1856 L U E model (Qt0: 0 - 300 umol m" 2 s"1, 15-day moving window, u,n ) 525 682 1207 1809 M M model (Ql0: 0 - 1800 umol m" 2 s'1, 15-day moving window, utQ ) 997 1280 2277 2407' M M model (Ql0: 0 - 300 umol m" 2 s"1, 15-day moving window, u,Q ) 788 993 1781 2120 Best estimates in this analysis 706 682 1388 1809 Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 38 In this analysis, the correct annual total of nighttime and daytime Re was assumed to be derived from the nighttime logarithmic fit and daytime L U E fit, respectively. Therefore, the annual total of Re for 2001 was 706 (nighttime) + 682 (daytime) = 1388 g C m" 2. The annual Re obtained using the L U E fit was approximately 75% of that obtained using the nighttime logarithmic fit, indicating a 25% reduction in Re possibly as a result of the light inhibition on foliar respiration. Our soil (Jassal et al. 2005) and leaf chamber (unpublished) measurements indicated that the total foliar respiration of this closed canopy ( L A I « 8) was approximately 50% of the total Re, and thus the 25% reduction in Re suggested a 50% reduction for leaf-level foliar respiration in light relative to that in darkness. Interestingly, Gilbert Ethier at the University of Victoria (personal communication) found that leaf-level foliar respiration for the Douglas-fir shoots in the light was 50% of that in the darkness when the foliar respiration in the light was obtained using the Laisk method (see Brooks and Farquhar 1985). The 50% reduction of leaf-level respiration in light was in the middle of the published reduction range, i.e., 20 - 100% (e.g., Atk in et al. 1997, Brooks and Farquhar 1985, Vi l lar et al. 1994, Shapiro et al. 2004). The best estimate of Re in this analysis (i.e., 1388 g C m"2) was approximately 14% less than that obtained using the nighttime logarithmic fit (i.e., 1622 g C m"2) (no reduction for nighttime annual Re). The 14% reduction in annual total Re agreed very well with what has been used in other studies, such as 15% reduction hypothesized for European forests (Janssens et al. 2001), and 8 - 13% reduction modeled for a mountain meadow (Wohlfahrt et al. 2005b). Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 39 Figure 2-8 shows the seasonal variation of P obtained using the nighttime and daytime Re - Ts relationships shown in Figure 2-7. The discrepancy in the monthly totals of P obtained using the different Re - Ts relationships became larger with increasing Ts. The annual total of daytime N E P was directly measured using the E C system (i.e., 1127 g C m" 2 for 2001), so the difference in P for the different Re - Ts relationships followed that for the Re (Table 2-1). The significantly different curves in Figure 2-8 demonstrates the challenges in validating the process-based models such as C - C L A S S (Arain et al. 2002) using E C derived canopy photosynthesis. Figure 2-8. Monthly totals of P for 2001 obtained using different nighttime and daytime derived Re - Ts relationships (see Figure 2-7 for the legend). Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 41 2.4 Conclusions (1) Using a nonlinear OLS algorithm to fit nighttime N E E u - Ts relationship violates the statistical IID N(0, cr2) assumption, because the variability in half-hourly N E E u markedly increases with Ts. The Re - Ts relationships obtained using the nonlinear OLS algorithm are strongly influenced by the severity of the violation of IID N(0, cr2) and therefore are likely unreliable and incorrect. In comparison with other approaches (e.g., exponential fit, bin and nightly averaging), the logarithmic transformation of the half-hourly N E E u (i.e., ln (NEE H ) = In A + BTs) best meets the IID N(0, a2) requirements. The annual Re obtained for 2001 using the logarithmic fit was 464 g C m"2 lower than that obtained using the exponential fit. (2) When calculating the annual total nighttime respiration, half-hourly N E E measurements at night made in turbulent conditions (i.e., N E E ( 1 ) should be replaced by the estimates of Re calculated using the logarithmic fit, because the half-hourly measurements of N E E i ( are discrete (and limited) samples of ecosystem respiration and generally do not follow a normal distribution. The statistical distribution of the N E E 1 ( measurements (samples) should be "logarithmically corrected" to meet the IID N(0, cr2) requirement and to better represent the whole ecosystem respiration (population). Replacement of the original measured N E E I ( (n = 2472) with Re obtained using the logarithmic fit led to a significant increase in the annual N E P (e.g., by 47 g C m"2 for 2001). Chapter 2 Methodological uncertainties in estimating nighttime and daytime Re 42 (3) The estimates of daytime Re obtained by using the Michaelis-Menten equation to fit daytime N E P - Qt0 relationship (for the almost full range of P A R values, i.e., 0-1800 pmol m" 2 s"1) are likely overestimated, because (1) the estimates are strongly influenced by the moving window widths used as a result of the serious violation of IID N(0, cr 2 ) assumption in using the Michaelis-Menten fit and (2) they are significantly larger than log transformed nighttime values. Even restricting the Qt0 range to 0-300 umol m" 2 s"1 resulted in Re values greater than predicted using the nighttime log transformed relationship. (4) Using the L U E model to fit daytime N E P - Qt0 relationship meets the IID N(0, cr2) assumption, and the obtained daytime Re - Ts relationships are virtually independent of the widths of the moving windows. However, the main uncertainty in using the L U E model is the selection of the Qt0 ranges. In this analysis, the Qto of 0 - 300 umol m" 2 s"1 was assumed to be the Qt0 range from which the intercepts of the L U E regressions were most representative of daytime Re. (5) The annual daytime Re obtained using the L U E model (i.e., the L U E model with 15-day moving window and Qt0 of 0 - 300 pmol m" 2 s"1) was approximately 25% lower than that obtained by applying the nighttime annual N E E a < - Ts relationship (with the logarithmic transformation) to daytime. The 25% reduction was likely' caused by light inhibition of ecosystem foliar respiration. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 43 3 Comparison of Different Algorithms for Partitioning Net Ecosystem Exchange into Its Component Fluxes: Ecosystem Photosynthesis and Respiration 3.1 Introduction In order to understand the effect of environmental and biotic variables on ecosystem assimilatory and respiratory processes, it is necessary to partition the half-hourly values of NEE (NEE = Re - P) into its component fluxes: Re (ecosystem respiration) and P (canopy or ecosystem photosynthesis). As discussed in Chapter 2, the simplest and most commonly used algorithm is to develop an annual relationship between NEE M > and Ts, and then use it to calculate both nighttime and daytime half-hourly values of Re (e.g., Goulden et al. 1996b, Morgenstern et al. 2004). NEE [ ( denotes nighttime half-hourly NEE measurements made in turbulent conditions (i.e., a threshold value of «*) and Ts is the soil temperature at a shallow depth. One implicit assumption in using the annual NEE i ( - Ts relationship to estimate half-hourly Re is that Re is only a function of Ts. This underlying assumption is rarely met in any natural ecosystems. Plant stands, especially the grasslands (e.g., Flanagan and Johnson 2005) and deciduous forests (e.g., Barr et al. 2004), are usually very dynamic, with other plant and environmental factors affecting Re. Lee et al. (1999) observed significant hysteresis in the annual Re - Ts relationship for a temperate deciduous forest, which probably was caused by the seasonality of soil temperature wave penetration and litter input. There is increasing evidence that the temperature sensitivity of respiration is strongly influenced by soil Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 44 moisture (Reichstein et al. 2002b, X u and Baldocchi 2004, Flanagan and Johnson 2005). Re has also been positively related to P (e.g., Janssens et al. 2001, Hogberg et al. 2001, Bowl ing et al. 2002, Scott-Denton et al. 2005, Tang et al. 2005). In addition, there are reports of seasonal acclimation of Re to soil temperature (Atkin et al. 2000a, Luo et al. 2001, Kirschbaum 2004). The complex interactions between the factors controlling Re have hindered the development of mechanistic models for predicting ecosystem respiration (Flanagan and Johnson 2005). For example, the rapid and transient response of Re to rainfall, especially after a relatively dry period, (Irvine and Law 2002, Lee et al. 2004, X u and Baldocchi 2004, Jassal et al. 2005) cause the conventional models of soil respiration (e.g., Bunnell et al. 1977) to fail. Furthermore, it has proved to be extremely difficult even to formulate quantitative relationships between Re and its controlling factors, such as the interaction between Re and P. In order to account for the effect of other factors on Re but without developing the quantitative relationships, Falge et al. (2002) used a 30-day moving window technique to stepwise estimate half-hourly values of Re for different E C sites of F L U X N E T (http://www.fluxnet.ornl.gov/fluxnet/index.cfm ). The annual NEE I (_ - Ts relationship was assumed to follow the Arrhenius equation as follows: L _ ) Re=Rw(t)e* 2 8 3 1 6 r * + 2 7 3 - 1 6 (1) where Rw(t) is the time (t) varying Re at Ts = 10 °C, Ea is the activation energy (J mol"1) and is the gas constant (8.134 J K" 1 mol" 1). The value of Ea was first obtained using the £ t ( _ ! _ ! _ ) annual N E E , u - Ts relationship (i.e., NEE, ( < =Rwe* 2S3A6 r , + 2 7 3 1 f i ), and then held constant for the regressions of N E E I ( vs. Ts in the 30-day moving windows from which Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 45 values of Rm(t) were obtained. After the value of Rl0(t) was determined for each moving window in high u* (u* > u*th) conditions, it was used along with the obtained annual Ea value to calculate Re in low u* conditions (u* < u*,h) at night, and to calculate daytime half-hourly values of Re in all u* conditions. The regressions of N E E u vs. Ts in the 30-day moving windows were made semi-dependent on the annual N E E u > - Ts relationship by using the annual Ea value because of concern about the large noise inherent in the short-term nighttime N E E u - Ts relationship (Baldocchi 2003). The assumptions are that the Re values for a short period of time (e.g., 1 month) can be obtained by fine-tuning the annual N E E | ( - Ts relationship and the effects of other factors are relatively constant during that short period. A similar concept has been used by Barr et al. (2004) and adopted as the standard procedure for estimating Re for the Fluxnet Canada Research Network (FCRN) (http://www.fluxnet-canada.ca ). Barr et al. (2004) assumed a logistic N E E ) ( - Ts relationship: 'c l + er-Re = - » v " . (2) where rj, r2, and r3 are empirical coefficients, and rw(t) is a time varying variable. The values of the empirical coefficients (rj, r2, and r3) were obtained from the annual f nighttime N E E n - Ts relationship (i.e., NEE, , = - — r (' r _ T ) ) and were held constant for regressions of NEE, , vs. Ts in the subsequent moving windows. The value of rw(t) obtained from each moving window together with the annual values of r2, r2 and r3 obtained from the annual NEE„ - Ts relationship were then used to calculate the Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 46 nighttime half-hourly values of Re in low u* conditions and to calculate daytime half-hourly values of Re in all u* conditions. Very recently the algorithm used in Falge et al. (2002) was questioned because the annual value of Ea obtained from the annual N E E u - Ts relationship may not represent the value of Ea (i.e., the temperature sensitivity) for the short-term Re - Ts relationship (Reichstein et al. 2005). The value of Ea during the active growing season was hypothesized to be significantly higher than that during the passive growing season. Reichstein et al. (2005) replaced Eq . (1) with a similar equation developed by Lloyd and Taylor (1994) as follows: /;0(— L _ ) R^RU)(t)e 5 6 0 2 r > + 4 6 0 2 (3) where Rw(t) is the time varying Re at Ts = 10 °C, and Eo plays a similar role (i.e., determine the temperature sensitivity) as Ea in Eq. (1). In contrast to the procedure used in Falge et al. (2002), they calculated Eo in two steps: (1) a 15-day moving window technique was used to obtain values of R^(i) and E0 for consecutive 15 days, and (2) all the Eo values obtained in step (1) were averaged. The obtained averaged value of E0 was assumed to better represent the short-term temperature sensitivity of Re than the annual Eo value obtained directly from the single fit of the annual nighttime NEE„ - Ts relationship, and therefore it was held constant over the entire year to calculate half-hourly values of Re by determining a new set of Rn)(0 values in another round of moving window regressions. The common features of the above three algorithms are (1) they use O L S (ordinary nonlinear least squares) algorithms to obtain parameters from the annual Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 47 nighttime N E E u - Ts relationship, (2) they use the parameters obtained from the annual nighttime N E E U - Ts relationship to calculate half-hourly values of Re during the daytime, and (3) they obtain the half-hourly values of Re at finer time scales (e.g., 30-day moving window) by adjusting the values of either Rw(t) in Eqs. (1) and (3) or rw(f) in Eq . (2) while holding other parameters (e.g., Ea in Eq . (1)) constant. A s discussed in Chapter 2, using O L S algorithms to obtain parameters (e.g., Ea in Eq.(l)) from the annual nighttime N E E 1 ( - Ts relationship and applying them to daytime hours may cause significant errors in the estimates of daytime half-hourly' Re. More importantly, the underlying assumptions in the above three flux partitioning procedures have not been thoroughly tested. For example, obtaining one Ea value from the annual nighttime N E E 1 ( - Ts relationship and holding it constant for regressions of NEE„ vs. Ts in the 30-day moving windows may not be necessary, because the influence of E C measurement noise inherent in the nighttime NEE„ - Ts relationship can be considerably reduced i f the logarithmic transformation as described in Chapter 2 were applied. Also , adjusting the values of Rio(t) in Eq . (1) to predict half-hourly values of Re in each 30-day moving window is empirical in nature, because Eq . (1) could also be modified by obtaining an annual Rio value from the annual NEE„ - Ts relationship and holding it constant for the moving windows but with the use of a time varying Ea (Ea(t)) (i.e., M 1 ( J L_) Re = Rwe -,! 2 8 3 1 6 y ; + 2 7 3 1 ( 5 ). Furthermore, it is difficult to independently verify any of these flux-partitioning procedures since only the nighttime NEE„ - Ts relationship is used. Reichstein et al. (2005) assume that their modified procedure is "more correct" than Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 48 the one originally used in Falge et al. (2002), and than using the single fit of the nighttime annual N E E u - Ts relationship. There are still considerable gaps in our understanding of how the Rio and Qw (the relative temperature sensitivity of Re to be discussed later), especially for ecosystems with a deep rooting depth (e.g., tall forests) would respond to changes in the soil moisture regime, and to phenological (seasonal) changes in the physiological activities of the entire ecosystem (e.g., rise and fall of fine root growth). The objectives of this chapter are (1) to investigate the variability in the annual Rio and Qio values of Re and its main causes, and (2) to compare several flux-partitioning algorithms for estimating nighttime and daytime Re. The obtained half-hourly values of daytime Re obtained in this chapter w i l l be used to estimate canopy photosynthesis in Chapter 4. Objective (1) provides the rationale for objective (2), e.g., i f there are significant relationships of annual Ri0 and Qw values to soil moisture, then using a single fit of the annual nighttime N E E H - Ts relationship to estimate half-hourly values of Re is not valid. In this study, the nighttime N E E i ( - Ts relationship was used to estimate nighttime half-hourly values of Re, and the daytime Red - Ts relationship obtained from the L U E model described in Chapter 2 was used to estimate daytime half-hourly values of Re. The main hypothesis in this study is that there should exist a consistency between the nighttime N E E H - Ts relationship and daytime Red - Ts relationship. For example, i f the effect of soil moisture is evident in the nighttime N E E ; ( - Ts relationship, it is expected that its effect (although not necessarily exactly the same) is also evident in the daytime Red - Ts relationship. If the nighttime annual N E E i ( - Ts relationship overestimates/underestimates nighttime Re in certain periods of the year, then it is Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 49 expected that the daytime annual Red - Ts relationship also overestimates/underestimates daytime Re in the corresponding periods. Eight years (1998 - 2005) of EC-measured N E E data for the 56-year-old Douglas-fir stand (DF49) described in Chapter 2 are used in this study. In comparison with previous studies (e.g., Reichstein et al. 2005), this study has two advantages: (1) the long record of N E E data (i.e., 8 years) provides a rare opportunity to investigate the interannual variability in Re and its main causes, and (2) two Re - Ts relationships (i.e., nighttime and daytime, respectively) are used, and the expected consistency between the nighttime and daytime Re - Ts relationships would increase confidence in the flux-partitioning algorithms used. This chapter builds on the results from Chapter 2, and provides a flux-partitioning algorithm for estimating P for Chapter 4. 3.2 Methods 'The study site, E C CO2 flux and auxiliary meteorological measurements were described in detail in Chapter 2. Half-hourly flux measurements made when Qt0 (incident total P A R ) = 0 umol m" 2 s"1 and Qto > 0 umol m" 2 s"1 are considered to be nighttime and daytime values, respectively. In this study, the estimates of nighttime half-hourly Re were obtained using the nighttime N E E u < - Ts relationship, and the estimates of daytime half-hourly Re were obtained using the daytime Red - Ts relationship that was constructed from regressions using the L U E model. The value of u*th for this stand was taken to be 0.3 m s" 1 following the analysis of Morgenstern et al. (2004). The L U E model is N E P = aQn] - Red for Qt0 < 300 umol m" 2 s"1 with a daytime u* filter of u,Q (see Figure 2-5b of Chapter 2 for the daytime annual Red - Ts relationship obtained for 2001). Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 50 3.2.1 Annual fits of the nighttime and daytime Re - Ts relationships The method of estimating half-hourly Re using annual fits (i.e., not done stepwise) of equations describing nighttime and daytime annual (for each year separately) Re - Ts relationships to measurements was described in Chapter 2. Here only a brief summary is given. A n exponential relationship was assumed between Re and Ts as follows: Re = AeBT' annual fit method (4) where Re denotes nighttime or daytime ecosystem respiration, and A and B are two empirical coefficients. B is the relative temperature sensitivity of Re as it is equal to dR IR —-—-. Ts was taken as the soil temperature at the 5-cm depth following the analysis of d T s Drewitt et al. (2002). Eq . (4) wi l l be referred to as the annual fit method hereafter. The parameters A and B were determined using a linear regression after the logarithmic transformation of Eq . (4), i.e., In Re =\n A+ BTs (5) Eq. (4) can also be written in the Q10 form as Re =RwQwUs~U))m, where Qw and Rw are related to A and B as Qm = en)B, and Rw = AQW. After the coefficients A and B were determined using Eq . (5), they were used in Eq . (4) to calculate half-hourly values of Re. Nighttime half-hourly measurements of N E E i ( > were not retained but rather replaced by the model-calculated Re values as explained in Chapter 2. 3.2.2 Stepwise fits of the annual nighttime and daytime Re - Ts relationships Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 51 Modifications of Eq . (4) were used to stepwise fit the annual nighttime (Figure 3-3) and daytime Re - Ts (Figure 3-4) relationships. Moving windows with a window size of 15 days were used in this study and were advanced 1 day at a time. Therefore, for any given half hour, there were 15 estimates of Re obtained respectively from 15 different windows. The arithmetic average of the fifteen Re estimates was assumed to be the best estimate of Re obtained for that given half hour. Three stepwise fit methods were used in this analysis. Method 1 assumed that the Re - Ts relationship in each moving window could be approximated by modifying Eq . (4) as: Re = f(t)AeBT° A15-day method (6) where A and B are the empirical coefficients obtained from the annual (Jan 1 - Dec 31) nighttime or daytime Re - Ts relationships (as determined using Eq . (5)), and were kept constant for regressions of the 15-day moving windows. Eq . (6) w i l l be referred to as the A15-day method, where " A " indicates that the parameter " A " in Eq . (4) from the annual nighttime and daytime Re - Ts relationships was modified (in the sense that it's multiplied by f(t) or A is replaced by f(t)A). The time-varying variable f(t) for each window was obtained as follows: taking the logarithmic transformation of Eq . (6) and averaging both sides of the transformed equation gives: l n / ( 0 = lni? e - ( InA+ 57/) (7) The value of f(t) for each moving window is fixed (i.e., a single value of f(t) is obtained for each window), but the value of fit) is different for different moving windows, so In f(t) = In f(t) . Therefore, Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 52 f(t) = e,nR--Q',A+BT-) (8) In contrast with the previous practice (Falge et al. 2002, Barr et al. 2004, Reichstein et al. 2005), the value of f(t) was not directly obtained as RJ(AeBT*) using an O L S algorithm, because of the potential violation of the statistical IID N(0, cr 2 ) assumption in the Re - Ts relationships as discussed in Chapter 2. The modifier f(t) in Eq . (6) does not change the relative temperature sensitivity of Re since B is not "modified". Method 2 assumed that the Re - Ts relationship in each moving window could be approximated by modifying Eq . (4) as: Re=Aen')BT< 515-day method (9) where, similar to Method 1, A and B are the empirical coefficients obtained from the annual nighttime or daytime Re - Ts relationships and were kept constant for regressions in each moving window. Eq . (9) w i l l be referred to as the 515-day method, where " 5 " indicates that the parameter " 5 " in Eq . (4) from the annual nighttime and daytime Re - Ts relationships was modified by being multiplied by f(t). The time varying variable f(t) in a given moving window was determined by logarithmic transformation of Eq. (9) and averaging both sides of the transformed equation: / ( 0 = (lntf - In A)/BTs (10) dR IR The relative temperature sensitivity of Eq . (9) is given as: — - — - = f(i)B . dTs Method 3 assumed that the Re - Ts relationship in each moving window was exponential (i.e., Re -Ae"r'). The coefficients A and B were obtained in the same way as it was for the annual nighttime and daytime Re - Ts relationships (i.e., lnRe = \nA + BTs). Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 53 In Method 3, both A and B in the Re - Ts relationships were determined for each window rather than just A or B as in A 1 5 - and 515-day methods, respectively. Method 3 w i l l be referred to as A615-day method. 3.3 Results 3.3.1 Climate and meteorological conditions Figure 3-1 and Figure 3-2 show the seasonal variation of Ts (soil temperature at the 5-cm depth) and 6 (volumetric soil water content averaged for the 0 - 1 m depth) for the 8 years (1998 - 2005). The mean annual Ts for the 8 years was 7.45 ± 0.62 °C, with 2004 being the warmest year (8.57 °C) and 1999 being the coolest (6.59 °C) (Table 1). The 1998/1999 E l Nino/La Nina cycle led to a prolonged snow accumulation on the forest floor in the February and March of 1999, so Ts was almost constant during these two months. The sharp decrease of Ts in early March of 2002 was associated with a week of below freezing air temperature (data not shown). The mean annual total precipitation for the 8 years was 1296 ± 266 mm, with less than 25% (305 ± 100 mm) falling in the most active growing season between Apr i l and September inclusively (Table 1). Therefore, 6 was highest during the winter months, and in general decreased progressively until the middle of September when the rainy winter season generally restarted. The largest variation in 0 also occurred in September (Figure 3-2) as a result of the large variability in the month's rainfall. The mean value of the rainfall received in September for 1999 - 2003 and 2005 was 34 + 5 mm, but values for 1998 and 2004 were 6 mm and 103 mm, respectively. Chapter 3. Comparison of different algorithms for partitioning NEE into P andR, 54 Table 3-1. Climate conditions for the 8 years (1998 - 2005), including canopy air temperature at the 27-m height (Ta), soil temperature at the 5-cm depth (Ts), integrated water content in the 0 - 1-m depth soil layer (6), total precipitation, mean daily downwelling P A R (Q,0) (45-m height) and mean daily downwelling diffuse P A R (Qdo) (45-m height) for the entire year and for the most active growing season (Apri l 1 -September 30). 1998 1999 2000 2001 2002 2003 2004 2005 Mean ± S D Jan 1 - Dec 31 Mean Ta (°C) 9.10 7.66 8.21 8.09 8.47 8.48 8.77 8.33 8.39 ± 0.44 Mean Ts (°C) 8.12 6.59 7.42 7.33 7.74 8.07 8.57 8.14 7.45 ± 0.62 Mean 0 ( m 3 m"3) 0.186 0.223 0.212 0.212 0.201 0.217 0.223 0.228 0.212 ± 0 . 0 1 3 Total precipitation (mm) 1749 1613 952 1116 1113 1271 1234 1324 1296 ± 266 Qt0 (mol m" 2 d 1 ) 22.94 22.21 22.40 21.33 22.96 21.78 21.51 19.98 21.89 ± 0.98 Qd0 (mol m" 2 d 1 ) N / A N / A N / A 10.32 9.69 10.01 9.67 9.87 9.91 ± 0.27 A p r i l 1 - Sept 30 Mean Ta (°C) 14.10 11.75 12.63 12.19 12.83 13.07 13.75 12.75 12.88 ± 0.77 Mean Ts (°C) 12.15 10.07 11.17 10.76 11.36 11.54 12.40 11.65 11.39 ± 0.74 Mean #(m 3 m"3) 0.166 0.209 0.195 0.191 0.178 0.190 0.199 0.212 0.193 ± 0 . 0 1 5 Total precipitation (mm) 216 290 278 259 211 310 358 521 305 ± 1 0 0 Qt0 (mol m" 2 d"1) 37.24 34.25 34.75 32.23 36.39 34.19 34.58 30.51 34.27 ± 2.14 Qd0 (mol m" 2 d"1) N / A N / A N / A 14.74 13.63 14.34 13.90 14.15 14.15 ± 0 . 4 2 Figure 3-1. Seasonal changes in the 15-day averages of soil temperature (Ts) at the 5-cm depth. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 56 Figure 3-2. Seasonal changes in the 15-day averages of volumetric soil water content (8) integrated from the surface to the 1-m depth. The values of field capacity (-1/3 bar) (6 = 0.213 m 3 m"3) and permanent wilting point (-15 bars) (9 = 0.110 m 3 m"3) were taken from Black (1979) for a 26-year-old coastal Douglas fir stand. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 57 3.3.2 Annual fits of the Re - Ts relationships Figure 3-3 and Figure 3-4 show the annual nighttime N E E u - Ts and annual daytime Rea- - Ts relationships respectively for the 8 years (1998 - 2005). In each relationship, 9 was stratified into three levels: > 0.2 m 3 m" 3, 0.15 - 0.2 m 3 m" 3 and < 0.15 m 3 m" 3 in an attempt to detect the possible effect of 9 on Re. Figure 3-3a and Figure 3-4a show that, when 9 < 0.15 m 3 m" 3 (e.g., in September of 1998), the nighttime and daytime values of Re fell below the annual fitted curves likely as a result of the limitation of 9 on •t Re. However, caution must be exercised when interpreting the effect of 9 from this crude stratification, because of possible correlations between 9 and other environmental and biotic variables. For example, 9 > 0.2 m 3 m" 3 mainly occurs in winter and early spring, and 9 < 0.15 mainly occurs in August and September. In early spring (e.g., Apr i l ) the overall physiological activities of the stand (e.g., growth of fine roots, new shoots and soil microorganisms) presumably are more active than those in August and September, so that lower Re values in those latter two months can not be totally attributed to the effect of lower 9. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 58 Figure 3-3. The annual nighttime N E E K - - Ts relationships for 1998 - 2005, where N E E ( [ are the nighttime half-hourly N E E measurements made when u* > 0.3 m s"1. Symbols represent the bin averages of the 20 half-hourly N E E 1 ( values in the stratifications of half-hourly values of 9 (volumetric soil moisture, 0 -1 -m depth). The annual curve fits were obtained using the original half hourly N E E i ( data (not the bin averages). Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 59 Figure 3-4. The annual daytime Rea- - Ts relationships for 1998 - 2005 obtained using the L U E model. 9 is the volumetric soil moisture spatially integrated over 0 - 1-m depth. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 60 The potential significant seasonal and phenological effects (e.g., seasonal variation in the quantity and quality of both roots and soil microorganisms (Lavigne et al. 2004)) possibly masked the effect of 9 on Re in other years (Figure 3-3b-h and Figure 3-4b-h). This echoes the view of other researchers (e.g., Lee et al. 1999, Morgenstern et al. 2004, Reichstein et al. 2005) that it is extremely difficult to directly relate E C C 0 2 flux measurements made over short periods of time to other variables due to the large variability inherent in E C C 0 2 flux measurements and the complex interactions between 9 and other variables (e.g., phenology). Soi l chamber C 0 2 efflux measurements conducted at a mixed conifer forest site in Colorado showed that both Ts and 0 are important drivers of soil respiration rate, but they confound each other and function as primary controls at different timescales: Ts is a primary control seasonally, and 9 is a primary control inter-annually (Scott-Denton et al. 2003). The values of A and B for each year obtained using the annual nighttime -(Figure 3-3) and daytime (Figure 3-4) relationships are given in Table 3-2. Table 3-2. The values of A and B for each year obtained from the annual nighttime (Figure 3-3) and daytime (Figure 3-4) relationships. Units for A and B are umol 2 1 1 m" s" and °C" , respectively. The values of A and B were obtained using the logarithmic transformation of the corresponding exponential Re-Ts relationships. The corresponding values of Rio and Qw were obtained as: Ru) = AQU) and Qw - eU)B . Annual nighttime relationship Annual daytime relationship Year A B Rio Qw A B Rio Qw 1998 1.13 0.14 4.70 4.14 0.69 0.13 2.67 3.84 1999 1.02 0.17 5.73 5.64 0.53 0.19 3.49 6.60 2000 1.16 0.15 5.17 4.44 0.65 0.16 3.37 5.16 2001 1.04 0.16 5.07 4.89 0.76 0.16 3.76 4.95 2002 1.12 0.15 4.81 4.31 0.69 0.15 3.06 4.44 2003 1.05 0.15 4.70 4.48 0.33 0.22 2.92 8.87 2004 0.90 0.18 5.20 5.77 0.37 0.20 2.69 7.34 2005 0.99 0.17 5.19 5.26 0.60 0.18 3.67 6.14 Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 61 In order to minimize the influence of E C CO2 flux measurement noise and the confounding effect of other variables, the annual values of Rio and Qio obtained from the annual nighttime N E E u - Ts and annual daytime Rea- - Ts relationships of each individual year were compared in Figure 3-5. The advantage of using the annual Re - Ts relationships are (1) the range in Ts is wide enough, so Rw and Qw values can be reliably estimated (Rayment and Jarvis 2000, Lavigne et al. 2004), and (2) the effects of seasonal and phenological changes are minimized in the interannual comparison, because every year the stand goes through a similar seasonal and phenologicaLcycle (e.g., active and passive growing phases). A s w i l l be discussed later, using the annual Rw and Qw values, obtained from the single fits of the annual nighttime N E E H - Ts and daytime Rea- - Ts relationships of each individual year, to estimate half-hourly values of Re within a particular year is problematic. However, the annual Rw and Qw values most likely reflect the annually integrated composite response of Re to Ts, and therefore comparison of the annual Rw and Qw values between different years can still provide valuable insights on the overall behavior of ecosystem respiration. Figure 3-5 shows that the values of Rw and Qw obtained for the annual nighttime N E E , ( - Ts relationships increased linearly with 6, and this was also observed with the daytime annual Red - Ts relationships. The Rw - 6 and Qw - 0 relationships were all significant (p < 0.05) and their coefficients are given in Table 3-3. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 62 T 1 1 1 1 1 1 I 1 1 1 1 1 r • nighttime • daytime 0.16 0.18 0.20 0.22 average 9 (0 - 1-m depth) (m 3 m"3) (April 1 - Sept 30) 11 I I I I I I I 0.16 0.18 0.20 0.22 average 0 (0 - 1-m depth) (m 3 m*3) (April 1 - Sept 30) Figure 3-5. Linear regressions of RJO and Qw on average 0 for the 0-1 m layer (see Table 3-3 for the coefficients). The nighttime and daytime Rio and Qw values were obtained using the annual nighttime NEE ( I > - Ts and annual daytime Rea- - Ts (see Figure 3-3 and Figure 3-4) relationships, respectively. The numbers next to the data points indicate the year. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 63 Table 3-3. The coefficients (i.e., c and d) in the linear regressions between annual values of Rio and 6 and Qw and 9 (see Figure 3-5). The nighttime and daytime values of Rw and Qw were obtained from the annual nighttime N E E 1 ( > - Ts (Figure 3-3) and annual daytime Red - Ts (Figure 3-4) relationships, respectively. Units of Rw and Qw are umol m" 2 s"1 and ° C 1 , respectively. 9 (m 3 m"3) was calculated by averaging its half-hourly values of each year from Apr i l 1 to September 30. Nighttime Daytime c d r2 c d r2 12.68 2.58 0.56 19.52 -0.51 0.34 32.85 -1.47 0.66 60.45 -6.23 0.15 The Rw values obtained from the annual daytime Re(t - Ts relationships were lower than the corresponding Rw values obtained from the annual nighttime N E E ( i - Ts relationships. A s discussed in Chapter 2, the lower Rw values during the daytime were most likely the result of light inhibition of foliar mitochondrial respiration. However, the Qw values obtained from the annual daytime Red - Ts relationships were generally higher than the corresponding Qw values obtained from the annual nighttime annual NEE 1 ( > - Ts relationships. Table 3-4 shows the annual values of Re for the 8 years obtained using the Rw and Qw values modeled using the linear Rw - 9 and Qw - 9 relationships from Table 3-3. The modeled nighttime Rw and Qw values were used to calculate nighttime half-hourly values of Re, and the modeled daytime Rw and Qw values were used to calculate daytime Rw =c9 + d Qw=c9 + d Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 64 half-hourly values of Re. The nighttime and daytime half-hourly Re values were then summed to obtain an annual value of Re. In general, the relative error of the predicted annual values oiRe is small (i.e., -0.87 ± 3.58% (Mean ± SD) ) . Table 3-4. The annual totals of Re obtained (1) using the annual values of Rio and Qw obtained from the annual nighttime and daytime Re - Ts relationships of each individual year (see Figure 3-3 and Figure 3-4), and (2) using the annual values of Rw and Qio modelled for each individual year from the nighttime and daytime Ri0 - 0 and Qi0 - 0 relationships (see Table 3-3 and Figure 3-5). The nighttime and daytime Rio and Qio values were used to calculate the nighttime and daytime half-hourly values of Re, respectively. The half-hourly values of Re were then summed to obtain the annual totals. Also shown are the means and standard deviations for the 8-year period. Re(gCm2 y r 1 ) 1998 1999 2000 2001 2002 2003 2004 2005 Mean ± S D Using Rio and Qw obtained from 1339 1337 1410 1388 1345 1486 1648 1595 1443 ± individual years 121 Using Rw and Qw 1433 modelled for 1351 1289 1385 1287 1331 1485 1731 1608 + individual years 162 Relative modelling -0.87 error (%)* 0.90 -3.59 -1.77 -7.21 -1.04 -0.07 5.04 0.82 ± 3.58 Relative modelling error (%) was calculated as 100x(row 2 - row l)/row 1. 3.3.3 S tepwise fits o f the a n n u a l Re - Ts r e l a t i onsh ips The statistically significant linear Ri0 - 6 and Qw - 0 relationships shown in Figure 3-5 strongly suggest that the effect of 0 on Re must also exist within a year. The Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 65 failure to detect the effect of 6 within a given year in Figure 3-3 and Figure 3-4 may be due to the confounding effect of other factors (e.g., seasonality). The effects of 0 and other factors undermine the validity of using the annual nighttime and daytime Re - Ts relationships to estimate half-hourly values of Re, because Re is not solely dependent on Ts. The nighttime and daytime monthly values of Re calculated using the three stepwise fit methods (i.e., A15-day, 515-day and AS15-day methods) are compared with those calculated using the annual relationships in Figure 3-6 and Figure 3-7, respectively. The estimates of Re were calculated half-hourly and then summed to obtain monthly values. In general, all three stepwise fits methods gave similar results. In contrast, using the values of A and B obtained from the annual nighttime and daytime Re - Ts relationships to calculate half-hourly values of Re resulted in significant systematic errors (in comparison with the stepwise methods): underestimating Re in the active growing season (Apri l -July) and overestimating Re in the passive growing season (August - March). The patterns of underestimation and overestimation of half-hourly Re values using the nighttime and daytime methods were generally similar (e.g., compare Figure 3-6 and Figure 3-7), although the extent of under- and overestimations varied considerably among years. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 66 Nighttime o 200 100 L i i i i i i i i i i • AB15-day - annual o E O 200 h 100 J M M J S N J M M J S N J M M J S N J M M J S N Figure 3-6. M o n t h l y totals o f nighttime Re (i.e., Ren) obtained us ing the three stepwise fit methods compared w i t h those obtained us ing the annual nighttime N E E ( [ - Ts relationships for 1998 - 2005 (see Figure 3-3). A l l Re values were calculated half-hourly and then summed to obtain month ly totals. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 67 Figure 3-7. Monthly totals of daytime Re (i.e., Red) obtained using the three stepwise fit methods compared with the annual daytime Red - Ts relationships for 1998 - 2005 (see Figure 3-4). A l l Re values were calculated half-hourly and then summed to give monthly totals. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 68 The annual totals of Re obtained using the stepwise fits and annual relationships are given in Table 3-5. Table 3-5. Annual totals of Re obtained using the three stepwise methods and the annual relationship method. The nighttime N E E H - Ts and daytime Rea- - Ts relationships were used to calculate the nighttime and daytime half-hourly values of Re, respectively, which were then summed to obtain the annual totals (see Figure 3-6 and Figure 3-7). i ? e ( g C m - 2 yr-1) 1998 1999 2000 2001 2002 2003 2004 2005 Mean ± S D A15-day moving window 1350 1316 1402 1383 1367 1455 1595 1622 1436 ± 1 1 4 515-day moving window 1390 1329 1401 1388 1400 1468 1605 1650 1454 + 114 A515-day moving window 1271 1291 1434 1407 1367 1458 1570 1586 1423 ± 1 1 6 Annual relationship 1339 1337 1410 1388 1345 1486 1648 1595 1443 ± 121 The average Re for the 8 years estimated using the A15-day method (i.e., 1436 g C m" 2 yr"1) was almost identical to that estimated using the annual relationship (i.e., 1443 g 2 1 C m" yr" ). The average values of Re obtained using the 515-day and A515-day methods were 1454 and 1423 g C m" 2 yr"1, respectively. The 515-day and A515-day methods occasionally gave unrealistic monthly estimates of Re. For example, the 515-day method gave unrealistically high monthly estimates of nighttime Re in March and December of 1998 (Figure 3-6a), and the A515-day method gave an unrealistically high monthly estimate of daytime Re in December of 1999 (Figure 3-7b). These unrealistically high estimates using these two methods were probably caused by the modification of Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 69 parameter B (e.g., f(t)B in Eq . (9)). Since the A l5 -day method performed best, it was decided to use it to calculate the half-hourly values of daytime and nighttime Re in Chapter 4. The seasonal change in the monthly average values of fit) obtained for the A15-day method (Eq. (6)) is shown in Figure 3-8. In general, most of the monthly f(t) values fell between 0.5 and 1.5. The monthly f(t) values were generally greater.than 1 for the active growing season (Apri l to July) and less than 1 for the passive growing season (August - March). The seasonal trend of f(t) does not correspond well with the seasonal trend in 6 (compare Figure 3-2 and Figure 3-8). For example, 6 was highest in January (Figure 3-2), but the monthly values of f(t) in January obtained using both nighttime (Figure 3-8a) and daytime (Figure 3-8b) methods were significantly less than 1. Therefore, f(t) probably reflects more of the effect of biological activities than that of 6 on Re in January. The daytime daily average values of Re obtained during the 8 years using the A 15-day method are compared with the corresponding nighttime daily averages in Figure 3-9. The daily averages (as opposed to daily totals) were used in order to remove the effect of day length. The relationship between the daytime and nighttime daily averages was strong (r = 0.85). On average, Re during the daytime was about 30% less than at night. This reduction is likely largely due to the effect of light inhibition on canopy foliar respiration (see also Figure 3-5a and Figure 2-6). Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 70 Figure 3-8. Seasonal changes in the monthly averages of f(t) for the A15-day moving windows (see also Figure 3-6 and Figure 3-7). Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 71 (daily average, nighttime) Figure 3-9. Comparison of daytime daily averages of Re, obtained using the daytime Re(t -Ts relationships, with the corresponding nighttime daily averages of Re obtained using the nighttime N E E ( i - Ts relationships. A l l the nighttime and daytime half-hourly Re values were calculated using theA15-day stepwise fit method (see Figure 3-6 and Figure 3-7), and then averaged to obtain the corresponding nighttime and daytime daily averages. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 72 3.4 Discussion Ecosystem respiration is the sum of autotrophic (e.g., roots and foliar respiration) and heterotrophic (e.g., fungi and bacteria) respiration. The positive linear Rio - 9 and Qio - 9 relationships shown in Figure 3-5 likely reflect the control by 9 on the ecosystem respiration. Similar responses have also been reported by Reichstein et al. (2002b) for Re in two Mediterranean evergreen Holm Oak forests, and by X u and Baldocchi (2004) and Flanagan and Johnson (2005) for Re in a Mediterranean grassland in California and a mixed grassland in southern Alberta, respectively. Recent chamber measurements of soil respiration, such as those for a 60-year-old mixed hardwood stand (Savage and Davidson 2001), an 8-year-old ponderosa pine stand (Xu and Q i 2001), a 40-year-old balsam fir stand (Lavigne et al. 2004), and a mixed grass prairie (Chimner and Welker 2005), indicate that 9 is an important controlling factor for soil respiration in a wide range of ecosystems with different rooting depths. The effect of 9 on Re has significant implications for future climate change scenarios (e.g., warmer and drier climate) (Cox et al. 2000). It is a concern that Re may increase more than gross primary production in response to global warming, leading to less carbon sequestration by vegetation. The effect of 9 on Re suggests that the potentially high Re in warmer years w i l l be damped by low 9 and the potentially low Re in cooler years w i l l be enhanced by high 9, because warmer years tend to be drier and cooler years tend to be wetter. For example, Ciais et al. (2005) reported that Re for different European ecosystems significantly decreased rather than increased with temperature during the Europe-wide heat wave in 2003 as a result of its associated severe drought. Using a recent satellite normalized difference vegetation index (NDVI) data set and climate data, Angert et al. Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 73 (2005) concluded that drier summers cancel out the CO2 uptake enhancement induced by warmer springs in both mid and high latitudes, even though temperature is considered to be a major limiting factor for canopy photosynthesis in high-latitude ecosystems. The Qio values (see Figure 3-5b) obtained for this stand varied approximately from 4 to 6 for the nighttime annual fit relationship method and from 4 to 9 for the daytime annual relationship method, respectively. They are well beyond the Qw range expected for the respiratory response to temperature (1.5 - 3.0) (Tjoelker et al. 2001). In a previous analysis of CO2 flux data for the first 4 years (1998 - 2001) of E C measurements in this stand (Morgenstern et al. 2004), the high Qw values were attributed to the use of soil temperature at one depth (i.e., 5-cm) to represent the temperature of an entire ecosystem. A n additional cause of the high Qw values may be the strong phenological change in Re due to changes in respiring biomass. Qw values can be significantly overestimated i f the seasonal variation in respiring biomass is not taken into account (Lavigne et al. 2004). For example, Epron et al. (2001) calculated a Qw = 3.9 for root respiration when the change in root biomass was not taken into account, but obtained a Qw = 2.2 after accounting for the increase in fine root biomass. The effect of phenology (e.g., seasonal growth of fine roots) on Re (see Figure 3-8) has also been observed for other ecosystems, such as for a sphagnum moss (Goulden et al. 1998), and a mixed boreal spruce and pine forest (Moren and Lindroth 2000). The phenological change in respiring organisms/tissue is likely to be coupled with the seasonal change in photosynthesis and the pattern of photosynthate allocation. Janssens et al. (2001) showed that canopy photosynthesis was more important than temperature in explaining variation in Re when the Re of several European forests were compared. In the large-scale girdling experiments Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 74 of a 45-55-year-old Scots pine stand, where the stem bark was stripped to the depth of the current xylem at breast height to terminate the supply of photosynthate to roots, Hogberg et al. (2001) found that soil respiration was decreased by 40% in 5 days and 56% in 14 days. Results from these experiments showed that the supply of current photosynthate may be a key driver for soil respiration and the models of soil respiration should incorporate the effect of canopy photosynthesis and the seasonal allocation pattern of photosynthate to roots. Scott-Denton et al. (2005) conducted a similar girdling experiment in a sub-alpine forest dominated by lodgepole pine trees and showed that soil respiration rates in plots with girdled trees were reduced by 31-44% at the mid-summer respiratory maximum in comparison with control plots with non-girdled trees. Recent carbon isotope studies have also shown that a large fraction of Re comes from the metabolism of recently fixed carbohydrates (e.g., Bowling et al. 2002, McDowe l l et al. 2004). For example, Bowling et al. (2002) reported that the measured carbon isotopic composition of Re for six coniferous stands along a precipitation gradient in western Oregon could be successfully predicted using models for photosynthetic carbon isotope discrimination. Consistent with findings of Hogberg et al. (2001), Flanagan and Johnson (2005) found that the above ground biomass was a good proxy for accounting for the variation in Re of a mixed temperate grassland in southern Alberta. The three stepwise fit methods (i.e., A15-day, 515-day, and AS15-day methods) for estimating half-hourly Re agreed reasonably well (Figure 3-6 and Figure 3-7), because the 15-day moving window technique can be thought of as a smoothing interpolation approach (see also Eqs. 8 and 10), so it does not matter whether A , B or both A and B are modified. The window size of 15 days is a tradeoff between two competing requirements. Chapter 3. Comparison of different algorithms for partitioning N E E into P and Re 75 The first requirement is that it must be short enough to avoid significant changes in phenology and other environmental variables (e.g., 6). The second requirement is that it must be long enough to provide sufficient data points for the regression analysis. Window sizes of 7, 30, 60 and 90 days were also tested for the A15-day method (i.e., Eq . (6)) (data not shown). The results showed that (1) the monthly integrated values of Re obtained using the 7-day moving windows were very similar to those obtained using the 15-day moving windows, and (2) the monthly integrated values of Re obtained using window sizes longer than 15 days (i.e., 30, 60 and 90 days) gradually began to show the same underestimation and overestimation pattern observed with the annual relationship (see Figure 3-6 and Figure 3-7). The choice of the window size of 15 days was also supported by the spectral analysis of the half-hourly air temperature measurements at the site, which indicated that the time required for a significant change in the weather for the Campbell River area is 10 - 15 days (data not shown). 3.5 Conclusions (1) The annual values of Rw and Qw for the 8 years (1998 - 2005) obtained from the annual nighttime N E E U > - Ts relationships linearly increased with average 6 in the 0 to 1-m-depth soil layer. This was confirmed by the linear Rw - 9 and Qw -6 relationships obtained from the corresponding annual daytime Red - Ts relationships, suggesting a significant effect of 0 on Re. (2) The effect of 0 on Re shown at the interannual scale (see Conclusion 1) was not detected at seasonal and annual timescales probably due to the confounding Chapter 3. Comparison of different algorithms for partitioning NEE into P and Re 76 effects of other factors (e.g., phenology) which co-vary with the seasonal change in 9. (3) In comparison with the stepwise fits of the annual nighttime and daytime Re - Ts relationships, the annual nighttime and annual daytime Re - Ts relationships generally gave lower values of Re for the active growing season (Apri l - July) before any water limiting effects occurred in A u g and Sept, and larger values for the passive growing season (August - March). However, the systematic seasonal errors of using the annual Re - Ts relationships had little effect on the annual totals of Re, because the underestimation and overestimation usually were similar in magnitude. The systematic errors probably were caused by the interacting effect of 9 and other factors (e.g., phenology), which support Conclusions 1 and 2. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 77 4 A Modification of the Michaelis-Menten Equation for Its Application to Estimating Canopy Photosynthesis of a Coastal Douglas-fir Stand 4.1 Introduction The impact of the geometry of light (e.g., Kimbal l and Hand 1922, Moon and Spencer 1942, L i u and Jordan 1960, Robinson 1966, Steven 1977, McArthur and Hay 1981) on photosynthesis has been realized for a long time. Early studies largely focused on shoot-level chamber CO2 gas exchange measurements (e.g., Kramer and Decker 1944, Zelawski et al. 1973, Young and Smith 1983, Smolander et al. 1987) and theoretical canopy radiation and photosynthesis modelling work (e.g., de Wit 1965, Cowan 1968, Grace 1971, Horn 1971, Al l en et al. 1974, Sinclair et al. 1976, Goudriaan 1977, Norman 1982, Weiss and Norman 1985, Spitters et al. 1986, Goudriaan 1988). Theoretical modelling of canopy photosynthesis remains very active (Wang and Jarvis 1990, Goudriaan and van Laar 1994, de Pury and Farquhar 1997, Wang and Leuning 1998, Choudhury 2000, Roderick et al. 2001, Cohan et al. 2002). Understanding the effect of diffuse radiation on canopy photosynthesis based on field observations has been more controversial and mainly restricted to the fact that CO2 fluxes above a plant canopy on cloudy days are usually higher than on sunny days (e.g., Price and Black 1990, Hollinger et al. 1994, Hollinger et al. 1998). To some extent, this observational understanding is oversimplified and speculative (Gu et al. 1999) because other environmental variables are also different between sunny and cloudy days Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 78 (Baldocchi 1997, Lindroth et al. 1998, Freedman et al. 2000, Law et al. 2002). The first manipulative experiment attempting to overcome this observational dilemma was reported by Healey et al. (1998), who found increased biomass accumulation and radiation use efficiency for two grass canopies shaded using layers of solarweave shadecloth. Gu et al. (2002) studied the quantum use efficiencies of diffuse and direct photosynthetically active radiation (PAR) for C 0 2 fluxes above canopies of five different C 3 species. This was one of the earliest studies using eddy covariance (EC) flux measurements to investigate the effect of diffuse P A R on canopy photosynthesis. Recently, the rapid change in the global radiation environment (Stanhill and Cohen 2001) and the widespread use of the E C technique (e.g., Baldocchi 2003) rekindled interest in the impact of diffuse radiation on canopy photosynthesis and especially its effect on the terrestrial carbon cycle. One example involves the explanations suggested for the levelling off of atmospheric CO2 concentration following eruption of Mt . Pinatubo in 1992. Although the cooler temperature following the eruption was successfully used to account for the levelling off (McCormick et al. 1995, Jones and Cox 2001, Lucht et al. 2002, Robock 2002, Soden et al. 2002), Roderick et al. (2001) and Gu et al. (2003) argued that the enhanced sky diffuse radiation (Molineaux and Ineichen 1996) following the eruption could be the main reason. However, this "diffuse radiation hypothesis" was seriously challenged by the following observations: (1) the levelling off of atmospheric CO2 concentration started before the eruption (Keeling et al. 1995), (2) tree ring studies appeared not to support it (Briffa et al. 1998, Krakauer and Randerson 2003), (3) the annual cumulative carbon sequestration in 1992 at Harvard Forest (which was used to test the "diffuse radiation hypothesis") was reported to be lowest within the Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 79 1992-2000 period (Barford et al. 2001), (4) E l Chichon enhanced sky diffuse radiation (Wendler 1984, Garrison 1995) as did Mt . Pinatubo, but no obvious levelling off of atmospheric C O 2 concentration was observed (Jones and Cox 2001). Angert et al. (2004) concluded that the enhanced diffuse radiation following the eruption of Mt . Pinatubo was "probably only enough to compensate for the reduction in total radiation". In the early models of canopy photosynthesis (e.g., de Wit 1965, Norman 1980), the plant canopy was usually divided into ./V layers and in each layer the foliage was divided into sunlit and shaded leaves. Additionally, the sunlit leaves were divided into M leaf-sun angle classes to account for the incidence angles of direct P A R . Photosynthesis of the sunlit leaves from the M leaf-sun angle classes of each layer was totalled to be the photosynthetic contribution of all sunlit leaves of that layer. Canopy P was then calculated as the sum of photosynthesis of the sunlit and shaded leaves of each layer. This type of canopy P model w i l l be referred to as complete multilayer models hereafter. Subsequent development of canopy P models mainly involves simplification of the complete multilayer models. One important aspect of the simplification has been reducing the M leaf-sun angle classes for the sunlit leaves to a single average leaf-sun angle class and using the average leaf-sun angle to calculate the absorbed un-scattered direct P A R for all the sunlit leaves (e.g., Sinclair et al. 1976, Spitters 1986, Leuning et al. 1995, de Pury and Farquhar 1997). The average leaf-sun angle for the sunlit leaves with a spherical leaf inclination angle distribution is approximately 60° (see Appendix D). As shown in Appendix E , using the single average leaf-sun angle to represent the incidence angles of direct P A R for all the sunlit leaves (e.g., as in 2-leaf models, including 2-leaf multilayer and 2-leaf single-layer models) leads to systematic errors in the estimates of Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 80 canopy P with respect to the fraction of sky diffuse P A R . In other words, 2-leaf models cannot reliably predict canopy P for a mixture of sunny and cloudy days (see Figure E -l a , E - l b and E - l c ) . The lack of simple and reliable analytical methods contributes significantly to the uncertainty regarding the role of diffuse radiation in canopy photosynthesis. It remains a challenge to incorporate the effect of diffuse radiation on canopy photosynthesis into existing canopy photosynthesis models. Roderick et al. (2001) incorporated the work of Norman and Arkebauer (1991) (Figure 4-1), Anderson et al. (2000), and Choudhury (2000 & 2001) into the well-known light-use efficiency model (Monteith 1972) to accommodate the effect of diffuse radiation: P = ajQ^ ( L U E model) (1) where P is monthly average canopy photosynthesis, Qn) is monthly average incident total P A R , / is the monthly average fraction of Q,{) absorbed by the canopy, and a is monthly average photosynthetic quantum use efficiency for QlQ . Roderick et al. (2001) assumed a to be a linear function of Qdn I Qn), where Qdt) is monthly average incident diffuse P A R , as follows: a =0.0242^/(3^ + 0.012. This modification follows closely the modification of a used for a prairie ecosystem in Anderson et al. (2000), i.e., a = 0.024<2(/l) IQl{) +0.018. The L U E model is widely used for estimating regional and global carbon fluxes at monthly and annual time scales. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 81 12H gp ° > I Q v l 0 OOOOO SOYBEAN 9 -I <?8 ^ +++++CORN 2 $0.+ + 3'°- * V * b » i ZD O 6-1 C P , | p % 0 0 4 W | 1 '»l | ' "I 1 1 1 l I 1 I 0 . 0 0 .2 0 . 4 0 .6 0 . 8 1.0 FRACTION DIRECT BEAM Figure 4-1. The dependence of modelled half-hourly light-use efficiency [g C O 2 ( M J I P A R ) 1 ] on the fraction of photosynthetically active radiation (PAR) above the canopy that is from direct beam (from Norman and Arkebauer 1991). The canopy light-use efficiency is based on I P A R (intercepted P A R ) and the results are for C 3 (0) and C4 (+) canopies. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 82 A t half-hourly time scale, the hyperbolic Michaelis-Menten model is more commonly used (e.g., Wofsy et al. 1993, Morgenstern et al. 2004, X u and Baldocchi 2004, Goulden et al. 2004): p = <*C?,o4n« ( M M model) (2) where Ql0 is the half-hourly average incident total P A R on the canopy, a' is the half-hourly average quantum use efficiency, and A m a x is the half-hourly average maximum assimilation rate of the canopy. In order to incorporate the effect of diffuse P A R into the M M model, Gu et al. (2002 & 2003) extended the work of Norman and Arkebauer (1991) and Roderick et al. (2001) by modifying both a and A m a x to be linear functions of QDQ IQni> where Qd{] is half-hourly incident diffuse P A R above the canopy: a = a ^ + a ( 3 ) 0 0 A =A ®D{) i A ®M) (4\ max maxd ^ max b ^ \ ) where Qhl) is the incident direct P A R above the canopy, ad and ah are a for Qdi) and Qb0, respectively, and Ammi and Amaxh are A m a x for Qda and QM), respectively. Substituting Eqs. (3) and (4) into Eq . (2) gives a modified form of the M M model: p = (a<,Q<w + abQJ(AmmiiQd, + An .x*&o) ( m . M M model) (5) (<xdQd0 + abQm)Q,a + (AmndQdl) + AmahQM)) Although the m - M M model was considered a significant step in understanding the effect of diffuse P A R on canopy photosynthesis, it has several drawbacks: (1) it does not completely separate the roles of direct and diffuse P A R in canopy photosynthesis because Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 83 of its retention of Ql{) in the denominator of Eq . (5) (note the multicolinearity between Qto, Qw and Qdo as a result of these three quantities being related to each other as: Qto = Qw + Qdo), (2) a is tightly tied to sky conditions (ideally a should reflect actual canopy-level photosynthetic processes), (3) it does not have an explicit parameter relating to the effect of canopy structure, and (4) it is a complicated non-linear model which makes it difficult to be incorporated into global carbon - climate models (Cox et al. 2000). Additionally, in order to gain insights into the role of diffuse P A R , we have to examine the other side of the issue: the role of direct P A R . With the attention given to the role of diffuse P A R in canopy photosynthesis (Farquhar and Roderick 2003), the role of direct P A R has largely been ignored and relatively poorly understood. Gu et al. (2002 & 2003) concluded that ad was significantly greater than ah, but did not address the role of direct P A R explicitly. The objectives of this study are to (1) introduce an alternatively modified M M model (hereafter referred to as the Q e - M M model) with a focus on the photosynthetically effective radiation (i.e., Qe) within a canopy, and (2) to provide a biophysical explanation of why ah is less than ad , and (3) provide a simple algorithm to f i l l gaps in half-hourly canopy P data for the 56-year-old coastal Douglas-fir stand described earlier (i.e., DF49). This study effectively extends the concept of the M M model to half-hourly canopy CO2 fluxes by greatly reducing the errors associated with earlier versions of single big-leaf models of canopy P (e.g., Sellers et al. 1996). A potential contribution of this work is to produce algorithms that w i l l increase the accuracy of large-scale carbon - climate models. The explicit separation of diffuse and direct P A R in the Q e - M M model should Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 84 also help better understand the perturbations to the terrestrial carbon cycle caused by changes of aerosol levels. 4.2 Methods The study site, E C CO2 flux and auxiliary meteorological measurements were described in detail in Chapter 2. Downwelling total P A R (<2,„) and diffuse P A R (Qd{)) were measured respectively using a quantum P A R sensor (model LI-190SB, L I - C O R Inc) and a diffuse P A R sensor (Wood et al. 2003) (model B F 2 , Delta-T Devices, U K ) mounted at a height of 45 m. The B F 2 was installed in May 2000. The B F 2 diffuse P A R sensor measures both Ql{} and Qd0. Qm measured using the B F 2 was compared with Qlt) measured using the LI-190SB, and the agreement was very satisfactory (Qt0 (BF2) = 1.02(2(0 (LI-190SB) + 8.77, r2 = 0.98, R M S E = 61.87 umol m ' 2 s"1, n = 47644) (Figure B -1). In order to check the accuracy of the measurements of Qdo, the half-hourly Q,0 measurements from the LI-190SB made in overcast conditions were compared with the corresponding half-hourly Qdo measurements from the B F 2 . The overcast conditions were determined independently using a simple model of atmospheric attenuation of radiation (see Appendix B for details). For the overcast conditions, Q,o (BF2) = 0.96<2<o (LI-190SB) + 18.42 (r2 = 0.98, R M S E = 24.61 umol m" 2 s"1, n = 16444) and Qd0 (BF2) = 0.870,0 (LI-190SB) + 22.72 umol m" 2 s"1 (r2 = 0.96, R M S E = 31.23 umol n f 2 s"1, n = 16444) (Figure B-2). This agreement is satisfactory and falls in the technical accuracy specification (±15%) of BF2 . Approximately 10% of total P A R was classified as direct radiation by B F 2 in the overcast conditions defined in this study (see Appendix B) . This is reasonable, because by definition diffuse radiation is isotropic, but the realistic sky brightness of overcast conditions is not isotropic (uniform) (i.e., Uniform vs. Standard Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 85 Overcast Sky) (Moon and Spencer 1942). Downwelling direct PAR (Qh0) was calculated as the difference between Qin and Qdt). 4.3 The model 4.3.1 Model development Let us define the sunlit leaves of a plant canopy as the leaves that are in the gaps, receiving both direct and diffuse PAR, and the shaded leaves as the leaves that are in shade, receiving diffuse PAR only. Two-leaf models (e.g., the sun/shade model developed by de Pury and Farquhar 1997) aggregate all the sunlit leaves of a canopy (Figure 4-2a), regardless of their orientations to the solar beam, into a big sunlit leaf (group), and calculate the absorbed un-scattered direct PAR for the big sunlit leaf as: Qha_sm=(X-o-)QwKh (6) where Qba_sun is the un-scattered direct PAR absorbed by the big sunlit leaf, cr is the leaf scattering (i.e., reflected and transmitted PAR) coefficient, Qbo is the direct PAR incident on the canopy, and Kb is the extinction coefficient for direct PAR assuming that canopy foliage is "black" (i.e., total absorption of the incident PAR) and randomly distributed. The value of Kb can be obtained as: Kh =0.5/sin B (7) where B is the solar elevation angle. The factor 0.5 is the ratio of the projected area of the big hemispherical sunlit leaf (group) to its surface area (i.e., nR2 l(2nR2)) when the sun is at zenith, and the factor 1/sin B is used to adjust the projected area when the sun is at other angles (Figure 4-2a). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 86 Figure 4-2. (a) The sun/shade model aggregates all the sunlit leaves into a big hemispherical sunlit leaf (i.e., assuming the leaf angle distribution of the sunlit leaves is spherical) and uses the mean A P A R (absorbed P A R ) (i.e., Eq . 8) to compute the photosynthesis for all the sunlit leaves, (b) The direct P A R absorbed by an individual sunlit leaf is given by: Qh(j) = ( l - c r ) Q cos^ , where Qp is the P A R perpendicular to the solar beam (the dotted line) and y is the incidence angle between the beam and the normal to the leaf surface (the dashed line). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 87 Substituting Eq. (7) into Eq . (6) gives: e ta_-=a-ff)GJ,/2 (8) where Qp is the P A R perpendicular to the solar beam (Figure 4-2b), and is given as: Qp=Qh()/smB. Therefore, the A P A R (absorbed P A R ) calculated by the sun/shade model for the big sunlit leaf is simply an estimate of the averaged beam flux density in the direction of the solar beam. It cannot be used to calculate the P A R absorbed by individual sunlit leaves (Figure 4-2b). A s pointed out by Norman (1979) "In a canopy with foliage spherically distributed, there is a continuous range of flux densities from the full beam flux density (perpendicular to the incident beam) to zero (parallel to the incident beam) because of the range of leaf angles". Using the A P A R calculated with Eq . (8) to compute the photosynthesis of the sunlit leaves makes the same type of errors as using the A P A R to compute the total canopy P in single big leaf models. The solar beam is unidirectional, so the angle at which it strikes the leaf surface must be accounted for. The un-scattered direct P A R absorbed by an individual sunlit leaf can be calculated using: Qh(y) = Cl-a)Qpcosy (9) where y is the angle between the solar beam and a normal to the leaf surface, i.e., the angle of incidence (Figure 4-2b). For a spherical leaf angle distribution, the mean leaf-sun angle, y, is 57.3° (usually approximately as 60°) (see Appendix D). Therefore, Qh (/) = ( 1 _ °~)QP c o s Y = ( 1 _ CT)GP c o s 60° = (1 - o~)Q 12, which is essentially the same as the absorbed un-scattered direct P A R calculated using Eq . (8) for the big sunlit leaf (group). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 88 Let us assume the leaf angle distribution of the sunlit leaves is spherical, so the "distribution of leaf inclination angles to the horizontal is the same as the distribution of leaf-sun angles" (Norman 1980). The fraction of sunlit leaf area ( / ) exposed at incidence angle y is given by (see derivation in Appendix D): fy = sin ydy (10) Figure 4-3 shows that approximately 15% of the sunlit leaves don't absorb direct P A R at all (i.e., when c o s / = 0 or / = 90° in Eq . (9)). Approximately 45% of the sunlit leaves absorb less than 30% of Qp (i.e., cos y < 0.3 ). If we take Qp = 2000 umol m" 2 s'1 and cr = 0.1 as an example, Qb(y) < 540 umol m" 2 s"1 (calculated using Eq . (9)) when cosy < 0.3 . This means that even when the sunlit leaves could potentially receive the maximum direct P A R (i.e., Qp = 2000 umol m" 2 s"1), there is still 45% of the sunlit leaves that are likely to be light limited (i.e., the leaves absorbed less than 540 umol m ' 2 s"1 of direct P A R ) . If we take Qp = 1000 umol m - 2 s"1 and still assume that when leaves absorb less than 540 umol 2 1 m" s" un-scattered direct P A R , they are light-limited, we can calculate the cosine of the leaf-sun angles (i.e., cosy) for these light limited leaves as cosy <540/((l-cr)Q p ) = 0.6 . Figure 4-3 shows that approximately 72% of cos^ values are less than 0.6, i.e., 72% of the sunlit leaves are light-limited in this case. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 89 0.2 0.4 0.6 cosy 0.8 1.0 Figure 4-3. The relationship between / and cos^ . y was stepwise increased from 0° to 90° in steps of 9° {dy = (9°/180°);r = 0.1571 radians). For each step, c o s / and its corresponding / (fr- s m ydy, Eq . (10)) were calculated (the circles). Note the / vs. cos^ relationship is independent of solar elevation angle (i.e., /?), but the total L A I of the sunlit leaves is not independent of B. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 90 Figure 4-3 supports the statements made by de Pury and Farquhar (1997) (on their page 544) "(sunlit) leaves nearly perpendicular to the sun-beam direction have the highest absorbed irradiance (1830 - 2040 umol m ' 2 s 1 ) , and are only a small proportion of the sunlit leaves, while (sunlit) leaves parallel to the beam direction absorb only diffuse radiation (220 - 430 umol m" 2 s"1) and are a high proportion of the sunlit leaves". Figure 4-3 suggests that the photosynthesis of the sunlit leaves has to be further partitioned into a light-limited subgroup (e.g., for the parallel sunlit leaves absorbing 220 umol m - 2 s'1 P A R ) and a light-saturated subgroup (e.g., for the perpendicular sunlit leaves absorbing 1830 umol m" 2 s"1 P A R ) . Let us divide the entire canopy into three conceptual groups: the first group with all the light-limited sunlit leaves, the second group with all the light-saturated sunlit leaves, and the third group with all the shaded leaves. A l l the shaded leaves are assumed to be light-limited (Figure 4-4a). Therefore, the entire canopy P can be written as: P = P +P +P Cl\) sun _IAgluLimiled sun _l.ightSaturaled slid V / where Psim_LightLimited and Pslin_LightSaturated are the respective photosynthetic rates of the light-limited and light-saturated leaves in the sunlit group. Psna- is the photosynthetic rate of the shaded leaves. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 91 L1 -L2Y y y * * y y sunlit leaf • shaded leaf 0 0 0 0 0 0 o o o o o cz» <3> O O O O O <3> <5£> <S> <S> O " <S> }• light limited light saturated > light limited (a) (0 w 0 x: c (/) o o .c: D_ < > 0..M 0 . 0 , A Q bThresholtf N / • / 0/ slope = a /c0 = 0 slope = /c0a "saf Ota (b) Figure 4-4. (a) The canopy is d i v i d e d into three conceptual groups: the first group (O-Li) w i t h a l l the l i g h t - l i m i t e d sunlit leaves, the second group (L\ to L2) w i t h a l l the light-saturated sunlit leaves, and the third group (L2 to L) w i t h the shaded leaves. Lj, L2 and L are cumulat ive L A I . (b) The photosynthetic l ight response to Qta (total absorbed P A R ) for the shaded leaves is l inear w i t h a slope o f a . In addit ion to the absorption o f sky diffuse P A R (i.e., Qd(£)) and the scattered direct P A R (i.e., Qs(&)), the l ight - l imi ted sunlit leaves Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 92 absorb limited amounts of un-scattered direct P A R (i.e., Qbl(y)), and thus its photosynthetic response can still be linear with the slope of a. The photosynthetic response of the light-saturated sunlit leaves can be described using two linear responses: the initial linear response with the slope of a and the second linear response with the slope of k()a. The total photosynthesis of all the light limited sunlit leaves is given by: where Qd(£ ) and Qs(£ ) are the absorbed sky diffuse P A R and the scattered direct P A R at canopy depth, £ (cumulative L A I ) , respectively. QM(y) is the additional (limited) amount of un-scattered direct P A R absorbed by the light-limited sunlit leaves. The photosynthetic response of these light-limited sunlit leaves to Qta (total absorbed P A R ) is linear with a slope of a (Figure 4-4b), because the Q,a values for these sunlit leaves are not exceeding Qsal, where Qsal is the saturating level of Qta above which the quantum use efficiency of absorbed P A R is significantly reduced. The total photosynthesis of the light saturated sunlit leaves is given by:. where QbThrcshM is the maximum amount of un-scattered direct P A R (i.e., QbThreshold is the maximum of all the Qbl (y) values) absorbed by a sunlit leaf, in addition to its absorption of Qd(£) + Qs(£), to still maintain the initial linear photosynthetic response with the slope of a. The total amount of P A R absorbed by the light saturated sunlit leaves is (12) P f a[Qd (I) + Qs (I) + QhTlircshold ]d£ + (2 k{)aAQbThreshold (y)d£ (13) Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 93 Qi CO + Qs (?) + Qmnshau + ^QtnresHM (/) = G», + A<2Hv,v„„u O ) • The second integration of Eq . (13) (Figure 4-4b) reflects the photosynthetic contribution of the absorption of the un-scattered direct P A R in excess of Q h T h r e s h M (i.e., AQhThreslwld(y)), where AQ W W , ( ) W (y) is the difference between the total un-scattered direct P A R absorbed by the light saturated sunlit leaves and QhThrMd • The quantum use efficiency for AQhThreshold (y) is only k()a, because some of the absorbed &QhThreslwld(y) is dissipated as heat and used in photochemical processes other than photosynthesis (e.g., xanthophyll cycle). Let us use an example to illustrate the key points in Figure 4-4b. A s with the previous example, let us take Qp = 2000 pmol m2 s"1, cr =0.1 and also assume Qd(£) + Qs(£) pmol va'2 s" 1 throughout the canopy layers from 0 to L2 (Figure 4-4a). If the photosynthesis of an individual sunlit leaf is assumed to be saturated at Qta (total absorbed P A R ) of 700 pmol m" 2 s"1 (i.e, Qsat = 700 umol m - 2 s"1), then QhThreshM can be calculated as: QhThreshM = 700 -160 = 540 pmol m - 2 s"1. Values of QM(y) are any values that are less than QbThreshold (i.e., 540 pmol m" 2 s"1 in this case). The leaf-sun angles (i.e., y) for the light limited sunlit leaves can be calculated as y > 73° using Eq . (9) (i.e., cosy < Q h T h r e s h M /((l-cr)j2 ) = 0.3 => y > arccos(0.3) = 73°). The light saturated sunlit leaves are the sunlit leaves that receive more than 540 pmol m" s" un-scattered direct P A R . AQhThreshtM(r) = Q--°-)QP cos(y)-QhThm,told, where cosy > 0.3 . The leaf-sun angles for the light saturated sunlit leaves are y < 73°. The photosynthesis of the shaded leaves is given by: (14) Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 94 Substituting Eqs. (12), (13) and (14) into Eq . (11) gives the photosynthesis of the entire canopy: P= [a[Qd{£) + Qs(£)]d£ + £aQJy)d£ + ^aQhThreshMd£ + £kQaAQhMM(y)d£ (15) The absorbed sky diffuse P A R at £ is given by (Goudriaan and van Laar 1994): Q*V) = Q«P<eKit (16) where Kd is the extinction coefficient for Qdo and is usually approximated as 0.7. Eq. (16) is obtained as -d(Qdne~Kdl)l d£, where the minus sign indicates that Qd0 is decreasing throughout the canopy. The scattering of the solar beam (Goudriaan and van Laar 1994) can be approximated by: Q, {£) = QM)(Khe-^e - (1 - a)Khe-^) (17) where Qw is the incident direct P A R (on a horizontal plane) above the canopy, Kh is the extinction coefficient of the solar beam for green leaves. Kh = Khy]l-o~ . The last three integrations of Eq . (15) are all related to the absorption of the un-scattered direct P A R . A s shown in Eq . (9) and Norman (1980) (his Table 4), the absorption of the un-scattered direct P A R is dependent on the leaf orientation (i.e., y) rather than canopy depth (i.e., £ ). Note the fraction of sunlit leaf area is not independent of £ . Because Qhi (y) and AQhnreshiM (y) are independent of /, so we can write the last three integrations of Eq. (15), with the use of Eq . (9), as: £aQh](y)d£ = a(l-a)Qp^L[ (18a) Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 95 f2 aQbnrahMde = a(l- a)Q cos yrhreshM (L2 - L, ) (18b) jf Ka&QbThreshM (y)d£ = k0a(l - a)Qp A cos y T h r M d (L2 - L , ) (18c) where cos/ , is the average of all the c o s / values of the light limited sunlit leaves. c o s • Threshold i s t h e c o s i n e o f t h e leaf-sun angle (yThreshM) associated with QbThreshM • A cos yThreshM is the difference between the average of all the cos / values of the light saturated sunlit leaves and cosy T h r e s h M (see the definition of ^QbThreshM(y) )• The total sunlit L A I (Li) (Figure 4-4a) in a canopy is given by (Norman 1980): Lt = leK>tdl = (\-eK*)IKb (19) Let us write: Lx=k,L2 (20a) L 2 -L , = (l-k{)L2 (20b) where k\ is the fraction of the sunlit leaves that are light limited, and 1 - k\ is the fraction of the sunlit leaves that are light saturated. Substituting Eqs. (16), (17), (18) and (20) into Eq. (15) gives: P = aQd[)(l-e-Kd') + ao-'Qb0+a(l-o-)Qpk2L2 (21) where a'= l-e~K"L-(l-cr)(l-e'Kh'). a'«cr i f L is very large (e.g., L > 8). k2 = k, cos / , + (1 - k{) cos yThreshold + kQ (1 - *,) A cos yThreshM . T h e L for this stand is approximately 7 - 8, so the exponential terms in Eqs. (19) and (21) (including the exponential terms in cr') are quite small. Ignoring these exponential terms and substituting Eq . (19) (i.e., using L2 « 2sin ) into Eq . (21) gives: Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 96 P = a(Qd{j+oQh0+2k2(l-a)QpsinB) = a(Qd0 + oQh0 + 2k2(l-cr)Qh0) = ccQe Qe-LUE (22) Note sin/? disappears from Eq. 22 since QbQ = Qpsin B. Qe=Qd0 + kQb0 with k = cr + 2k2(1 - cr). The first component (i.e., cr) of k accounts for the photosynthetic contribution of scattered direct PAR, and the second component (i.e., 2k2(l-cr)) accounts for the photosynthetic contribution from the un-scattered direct PAR. In the above derivation, we considered that leaves within the canopy are either light-limited or light-saturated. In reality, leaves saturate over a narrow range of PAR as opposed to having an absolute fixed saturating point of PAR (Figure 4-4c). In order to smooth the transition from the P of the light-limited layer to that of the light-saturated layer, let us re-write Eq. (22) in its hyperbolic form: p = « (a„+^2 f c o)An ,» _ a(?A» Q e - M M model (23) aQ + A *~-e max where Amax (the asymptote) denotes the maximum rate of canopy photosynthetic assimilation. Eq. (23) will be referred to as the Q e - M M model. The magnitude ofAmax is mainly determined by temperature (see Figure 4-7c and Figure 4-8c) and the Rubisco (nitrogen) content of the leaves (e.g., Evans and Vogelmann 2003). When k = 1, the Qe-M M model becomes the regular M M model. If the LAI of a canopy is not as large as this 56-year-old Douglas-fir stand, a obtained in this case for the Q e - M M model would be the apparent quantum yield based on incident PAR as opposed to absorbed PAR. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 97 In the above derivation, the solar beam was assumed to be parallel rays, ignoring the finite angular radius of the solar disk (e.g., Horn 1971). The angular radius of the solar disk, which is 0.5°, results in a strong penumbral light spreading effect (see Appendix C), especially in coniferous stands (Miller and Norman 1971, Oker-Blom 1985, Stenberg 1998, Palmroth et al. 1999). In a sense, the existence of penumbrae in a plant canopy undermines the rationality of the pure black-and-white separation of canopy foliage into sunlit and shaded groups (Ross 1991), since the majority of the foliage can be in penumbrae (e.g., Oker-Blom 1985, Palmroth et al. 1999). Therefore, k in the Q e - M M model likely includes the penumbral light spreading effect of the solar rays. The role of penumbral light spreading on canopy P is rarely accounted for in "mechanistic" bottom-up models (e.g., the sun/shade model), because it is not existent at the leaf level and thus cannot be simply scaled up to the canopy level. In this analysis, the penumbral effect of solar rays is hypothesized to be proportional to Qb0 (i.e., part of kQh() in Eq . (23)), which is consistent with the findings in recent studies (e.g., Stenberg 1998). Alternatively, the Q e - M M model can be derived from the M M model. Substituting Eq. (3) into Eq . (2) gives: \adQd[)+ahQm) + A^ max mx (24) Rewriting Eq . (24) by factoring out ad gives the form of the Q e - M M model: iax P = (25) max Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 98 where ad and Qdn+—Qh0 correspond to the a and Q, in the Q e - M M model, cc respectively. — corresponds to k in the Q e - M M model. Comparison of Eqs. 23 and 25 reveals that the modification of Amax (i.e., A m a x = A m a x r f ^ + A m a x f e ^ - j n E q . 4) i s unnecessary, because a and A are not completely independent (they appear as a max product of aQl0Amax in the numerator of the M M model, i.e., Eq . 2). A s w i l l be shown later (e.g., Figure 4-9), the modification of a to incorporate the effect of diffuse P A R makes the modification of A unnecessary. Derivation of the Q e - M M model using the max results from Norman and Arkebauer (1991) (i.e., Figure 4-1) is given in Appendix C (i.e., Eq. (3) in this appendix). 4.3.2 Mode l parameterization In this analysis, only the measured half-hourly values of N E E (NEP) were used, i.e., gap filled values were excluded. The u* (friction velocity) threshold was chosen as u*th = 0.3 m s"1 following Morgenstern et al. (2004). In addition, the half-hourly N E E (NEP) measurements made in calm conditions (i.e., u* < u*,n) both at night and during the daytime periods when Q,0 < 200 pmol m" 2 s"1 were also excluded. It was found that the lack of nocturnal mixing extended to daytime conditions when light was very low (generally Q,o < 100 pmol m" 2 s _ 1). To be conservative, the u* filter was applied to daytime N E P measurements made in conditions when Q,o < 200 pmol m" 2 s"1 (see Chapter 2 for details). Canopy P was calculated as the sum of daytime N E P and daytime Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model • 99 ecosystem respiration (Red)- The latter was obtained using the A15-day method described in Chapter 3. The data used in this analysis were from May 2000 to December 2005. The parameters (e.g., a, Amax, and k) in the M M , Q e - M M and m - M M models were determined using the nonlinear Gauss-Newton algorithm provided by the Matlab® Statistics Toolbox®. 4.3.3 Model comparisons In order to evaluate the performance of the Q e - M M model and to assess the inadequacies of the existing models of canopy P, the Q e - M M model was compared with the M M model (Figure 4-7, Figure 4-8 and Figure 4-15), with the sun/shade model (Figure 4-8 and Figure 4-16) and with the m - M M model (Figure 4-9). Performance of the models was evaluated based on three criteria: (1) whether the model has systematic errors with respect to the change in sky diffuse P A R (e.g., Figure 4-8a), (2) whether the model has systematic errors with respect to the change in the calculated sunlit/shade fractions (which basically is a function of solar elevation angle) (e.g., Figure 4-8b), and (3) whether the model correctly responds to a change in air temperature (e.g., Figure 4-8c). The sun/shade model used in this study was directly taken from de Pury and Farquhar (1997). The numerical example given by de Pury and Farquhar (1997) in their Table 6 was reproduced before the sun/shade model was applied to the E C data, indicating the sun/shade model was coded correctly for this analysis. The three inputs to the sun/shade model for the DF49 stand were Vcmax25 (leaf-level maximum catalytic capacity of Rubisco at 25 °C) = 44 umol m ' 2 s'1 (see Warren et al. 2003, Ethier and Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 100 Livingston 2004 for the Aid curves for this stand), Kn (nitrogen extinction coefficient through the canopy) = 0.28, and L (total L A I ) = 8. The value of Kn was determined using an optimization procedure in which Kn values were increased from 0 to 0.7 in steps of 0.02. The sun/shade model was applied to the E C measurements (from May 2000 to December 2005) and the value of r2 for the regression of measured P against modeled P was computed for each value of K„. The K„ value corresponding to the maximum r2 between the measured and modelled P (i.e., K„ = 0.28) was chosen as the best estimate of Kn for this 56-year-old stand. The value of K„ is very similar to the Kn found for a wheat crop by de Pury and Farquhar (1997) (i.e., Kn = 0.713/2.4 = 0.2971, their Table 5). 4.4 Results 4.4.1 Variance in P accounted for by adding fractions of Qbo to Qdo A new variable was defined as: Qx =Qtl{)+xQm, where x is a fraction of Qb0 added to Qdo- When x = 0 , Qx = Qd{), and when x = 1, Qx = Qn). x was increased stepwise from 0 to 1 in steps of 0.01, and for each x, P was regressed against the ccQ A corresponding Q using P = x m a x to obtain a coefficient of determination (r 2) for each regression. Figure 4-5 shows that when Qt0 < 300 umol m" 2 s"1, r2 is insensitive to x. The insensitivity of r 2 to x when Qt0 < 300 umol m" 2 s"1 is expected, because canopy P tends to be light limited and Qdo is the predominant component of Q,o, therefore, adding the fraction x of Qbo to Qdo does not account for significantly more variance in canopy P. In theory, when Qt0 < 300 pmol m" 2 s"1, there is no need to distinguish between diffuse Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 101 and direct P A R , so the maximum correlation between P and Qx should occur when x = 1 (i.e., Qx = Qto). The x value corresponding to the maximum correlation between P and Qx is k, i.e., k = max(x). A s Qto increases above 300 pmol m" 2 s"1, r2 shows considerable variation with respect to x, and the general patterns are (1) Qdo accounts for more variance in P than Qt0 (e.g., when Qt0 > 900 pmol m ' 2 s"1, Qdo accounts for approximately 29% of the variance in P, while Qt0 accounts for almost no variance), and (2) r2 initially increases with x to a maximum and then significantly decreases with further increases in x. The values of x associated with the maximum r (i.e., k) are x = 0.25 and x = 0.22 for Qto between 300 - 900 pmol m" 2 s"1 and Q,o greater than 900 pmol m" 2 s"1, respectively. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 102 Figure 4-5. The variance in P accounted for using the Q e - M M model at three levels of cxO A Qto- Canopy P was related to P A R using P = x m a x , where Qx is defined as Qx= Qdo + xQbo- x was increased stepwise from 0 to 1, and a corresponding coefficient of determination (i.e., r2) of the regression was calculated for each x. When x = 1, Qx = Q,0, and when x = 0, Qx = Qd0. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 103 4.4.2 Comparisons between the M M , Q e - L U E , and Q e - M M models Figure 4-6 shows the responses of canopy P to Q,o, Qdo, Qw and Qe. A s expected, the response of P to Q,o appears to be hyperbolic, and a hyperbolic fit using the M M model accounts for 50% of the variance in P (Figure 4-6a). The response of P to Qdo is curvilinear except for the sharp increase in P around Qdo of 200 umol m" 2 s"1 (Figure 4-6b). Canopy P appears to have a very weak response to Qw (Figure 4-6c). The response of P to Qe is well described using the Q e - M M model (r2 = 0.66) (Figure 4-6d). The responses of P to Qto and Qe are both hyperbolic, but the response of P to Qe is more linear than the former as indicated by its larger value of Amax. The Amax obtained using Qe-M M model is 83.38 umol m" 2 s"1 while that for the M M model is 24.79 ixmol m" 2 s"1. In fact, a linear relationship between P and Qe using the Q e - L U E model accounts for 65% of the variance in P (Figure 4-6d). The linear fit using the Q e - L U E model has an intercept of 2 1 1.21 umol m" s" , which is possibly a consequence of lack of accounting for the transition from light-limited photosynthesis to light-saturated photosynthesis (Figure 4-4c). But the Q e - L U E model would be useful in estimating daily and monthly canopy P (data not shown), and preferable to the regular L U E model (i.e., Eq . (1)). The values of k obtained using the Q e - M M and Q e - L U E models are k - 0.22 and k - 0.23, respectively. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 104 Figure 4-6. The responses of P to Q,o, Qdo, Qt>o and Qe. The fitted curve in (a) was obtained using P = a^'{)Am» (i.e., the M M model) with a = 0.050 mol m o l 1 and Amax " G , 0 + A n , . x 2 1 = 24.79 umol m" s" . The arrow in (b) indicates the sharp increase in P around Qdo of 200 umol m" 2 s"1. The fitted curve in (d) was obtained using P = aQ^ma (i.e., the Q e - M M x^e max model) with a = 0.041 mol mol" 1, Amax = 83.38 pmol m - 2 s"1 and k = 0.22, r2 = 0.66, R M S E = 4.30 umol nf 2 s"1. The dashed line in (d) was obtained using P = 0.030£>t, +1.21 (i.e., the Q e - L U E model), with k = 0.23, r2 = 0.65 and R M S E = 4.38 umol m" 2 s"1. Symbols represent bin averages and vertical lines indicate ±1 S D . n = 34785. A l l fitted curves were obtained using the original half-hourly data, i.e., not obtained using the bin-averaged data. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 105 The errors of the M M , Q e - L U E and Q e - M M models are shown in Figure 4-7 as modelled P minus measured P. The M M model overestimates P in low Qdo conditions, and progressively underestimates P as Qdo increases. The Q e - L U E model overestimates P when Qdo < 100 umol m" 2 s"1, slightly underestimates P for Qdo between 100 and 600 umol m" 2 s"1, and then progressively overestimates P for Qdo > 600 pmol m" 2 s"1. In contrast, the Q e - M M model has the smallest modelling error with respect to Qdo- (Figure 4-7a). The systematic errors of the three models with respect to sin 8, where B is the solar elevation angle, are shown in Figure 4-7b. A l l three models overestimate P when sin B < 0.5 and underestimate P when sin B > 0.5, but the magnitude of the errors for the M M model are more than three times larger than those for the Q e - L U E and Q e - M M models. When solar elevation angle is low, e.g., sin B < 0.2, the correlation between Qdo and sin B is very strong, so the modeling errors with respect to Qdo and sin B may come from the same source. Figure 4-7c shows that the three models have very similar systematic errors with respect to canopy Ta . They all significantly overestimate P when Ta < 10 °C or Ta > 20 °C, and underestimate P between 10 °C < Ta < 20 °C, suggesting an independent effect of Ta on P, which cannot be accounted for by light. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 106 Figure 4-7. Modeling errors for the M M , Q e - L U E , and Q e - M M models. Parameters for these models are given in Figure 4-6. Symbols represent bin averages and vertical lines indicate ±1 SD for the bin averages obtained using the Q e - M M model. The S D values for the other two models is similar to the corresponding values for the Q e - M M model (not shown), n = 34785. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 107 4.4.3 Comparisons between the M M , Q e - M M and the sun/shade models In order to account for the effect of Ta on P shown in Figure 4-7c, Amax in the Qe-M M and M M models was related to Ta using a Gaussian function following June et al. -{Lckf (2004), i.e., f(Ta) = e a where Ta is half-hourly average canopy air temperature (27 m), and To and Q are empirical coefficients. Thus the Q e - M M model becomes p = aQA™J(Tu) T h e jrpj function, which is symmetric, with T0 = 16.97, and Q = 11.68 corrects most of the systematic errors in the Q e - M M model associated with Ta (Figure 4-8c) except for Ta < 0 °C. With the incorporation of the f(Ta) function, the Qe-M M model accounted for 73% of the variance in P. The modeling errors of the sun/shade model are larger even than those of the M M model with a f(Ta) function included. With the incorporation of f(Ta) into the M M model (i.e., P = aQ'»A™*f(T»} \ [t accounts for 59% of the variance in P while the sun/shade model, which includes temperature dependence of Vcmax and Jmax, only accounts for 55%. What is more unacceptable is that the sun/shade model does little to reduce the systematic errors of the M M model with respect to Qdo (Figure 4-8a). Comparing the modelling errors of the M M and Q e - M M models with respect to Qdo in Figure 4-7a and those in Figure 4-8a shows that introducing the temperature function, f(Ta), has little effect on the errors with respect to Qdo- Therefore, the systematic errors with respect to Qdo shown in Figure 4-8a for the sun/shade model cannot be caused by its built-in temperature functions for Vcmax and Jmax. These functions were fine tuned numerous times in this analysis but these fine-tunings failed to correct the systematic Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 108 errors of the sun/shade model with respect to Qdo shown in Figure 4-8a. A s discussed in the Q e - M M model development and also in Appendix C, these systematic errors of the sun/shade model shown in Figure 4-8a reflect the inadequacies in the light regime physics in the sun/shade model and the inadequacies of its algorithm for scaling Psun and Psnd from leaf-level to canopy level. Also , Figure 4-8c shows that the sun/shade model has large systematic errors with respect to Ta, indicating the failure of applying the Vcmax and Jmax temperature functions of spinach or tobacco (as the sun/shade model requires) to a Douglas-fir stand. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 109 Figure 4-8. Modeling errors for the M M and Q e - M M models with the incorporation of a temperature function for Amax, and the corresponding modeling errors using the sun/shade model. Note: the sun/shade model has built-in temperature functions to adjust the values of its Vcmax and Jmax. For the M M model, the modeled P was obtained using P = _^0JAnMf(O_ w h e r e = 0 0 6 5 ! m o l - i A = 2 6 4 8 j -2 - l d aQin+A f(T) max J V a/ / ( T B ) = e" ( J n~ ) with T0 = 15.56 °C, and Q = 13.71. r 2 = 0.59 and R M S E = 4.75 umol nf 2 s'\ For the sun/shade model: r2 = 0.55 and R M S E = 4.80 pmol m - 2 s"1. For the Q e -M M model, the modeled P was obtained using P = a ^ ' A ^ J ^ where a = 0.053 mol mol" 1, Amax = 67.57 umol m" 2 s"1, k = 0.18, and f(Ta) = e n with T0 = 16.97 °C, and Q = 11.68. r2 = 0.73 and R M S E = 3.86 umol m - 2 s"1. Symbols represent bin averages and vertical lines indicate ±1 SD. n = 34785. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 110 4.4.4 Comparisons of the performance of the Q e - M M and m - M M models In order to compare the performance of the Q e - M M and m - M M models, a moving window technique was used in the analysis following that of Gu et al. (2002). The windows were 15 days wide and moved 1 day at a time. For each window, half-hourly values of P calculated using the Q e - M M and m - M M models (with no f(Ta) included) were regressed against measured values of P . To determine performance of the models as a function of Ta, values of the r2 for the two models were averaged for 1 °C Ta bin widths for the 5 and half years of data. Figure 4-9 shows that the r associated with both the Q e -M M and m - M M models changed considerably with Ta, indicating a significant temperature effect on P (see also Figure 4-7c), especially when Ta < 5 °C. The average values of r2 for the Q e - M M and m - M M models were 0.6535 and 0.6562, respectively. The Q e - M M model accounted for as much variance in P as the m - M M model, indicating the modification of Amax in Eq. (4) is unnecessary. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 111 Figure 4-9. The coefficients of determination (r ) for regressions using the Q e - M M and m - M M models obtained by using 15-day moving windows (moving one day at a time) over 5 Vi years of data. The average and standard deviation of the r2 are 0.6535 and 0.1394 for the Q e - M M model, and 0.6562 and 0.1384 for the m - M M model, respectively. Symbols represent bin averages and vertical lines indicate ±1 SD for the bin averages obtained using the Q e - M M model. The values of SD for the m - M M model are virtually identical to those for the Q e - M M model (not shown). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 112 Figure 4-10 and Figure 4-11 show the distribution of a (Figure 4-10a), Amax (Figure 4-10b) and k (Figure 4-11) obtained using the Q e - M M model. Approximately 50% of the a values fell between 0.03 and 0.05. The distribution ofAmax was wider than that of or with roughly 27% of the Amax values being greater than 100 pmol m" 2 s"1. When Amax is very large, the Q e - M M model becomes the Q e - L U E model, i.e., cxO A l im e m a x =ccQe. The very large Amax values mainly occurred in overcast A^^aQ +Am max conditions, where the photosynthetic response to Qe was almost linear. Note: Amax > 100 0 1 1 umol m" s" does not imply that the canopy maximum photosynthetic assimilation can 2 1 exceed 100 pmol m" s" of CO2. It only means that the photosynthetic response to Qe is almost linear and the Amax needs to be very large to reduce the Q e - M M model to the Q e -L U E model. In order to derive a valid Amax reflecting the integrated measure of canopy P, the Qe range must be wide enough (e.g., using several years of data rather than 15 days of data). More than 80% of the k values were between 0.1 and 0.3. Less than 3% of k values were between 0.5 and 0.9 (Figure 4-11). The extremely low occurrence of the k values falling between k = 0.5 and k = 1.0 indicates Q,o was a very poor predictor of P 2 1 (see also the P - Qx relationship for Qto > 900 pmol m" s" in Figure 4-5). The average (n = 1995) of all k values was 0.22 ± 0.10 (average ± std). Large k values (e.g., k > 0.5) mainly occurred in overcast conditions when adding fractions of Qw didn't contribute significantly to explaining the variance in P as was shown in the x values in Figure 4-5 when Ql0 < 300 umol m - 2 s"1. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 113 60r 1 r -MM model (a) 40 h 0) D) CO c Q . 20r (b) < 0.01 0.01 - 0.03 0.03 - 0.05 0.05 - 0.07 > 0.07 a (mol mol" 1) <20 20-40 40-60 60-100100-500 >500 A max (umol m"2 s" 1) Figure 4-10. Distributions of a and Amax obtained using the 15-day moving windows for the Qe-MM model (see also Figure 4-9). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 114 Figure 4-11. Distributions of k obtained using the 15-day moving windows for the Qe-M M model (see also Figure 4-9 and Figure 4-10). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 115 The relationship between k and sin/? obtained using the Q e - M M model is shown in Figure 4-12a together with the predicted relationship between cr' calculated using a' = l-e~K"L -(l-a-)(l-e~K"L) (see Eq . (21)) and sin/? for different values ofL (Figure 4-12b). The relationship between A: and sin/? is similar in shape to the relationship between a' and sin /? for L = 8. Both have a weak dependence on sin / ? , however, the values of k are almost twice those of cr'. Figure 4-12b shows that for a given sin B, cr' is smaller for an open canopy (i.e., low L A I ) than for a closed canopy (i.e., high L A I ) . Results of our analysis of P data for a nearby 16-year-old Douglas-fir stand (L « 4) and a clear-cut with planted 4-year-old Douglas-fir seedlings (L « 2) (see Humphreys 2004 for description of the two sites) indicate values of k of 0.16 and 0.12, respectively. The k values for the three Douglas-fir sites also follow the trend predicted by the relationship of cr' to sin/? and L. A s mentioned earlier when discussing the Q e - M M model, k also includes the penumbral effect of the solar rays. It is difficult to find an exact relationship between the penumbral component of k and sin/? for canopies of different L A I . From Eqs. 30 and 31 in Denholm (1981b), it is reasonable to assume that the penumbral component of k also decreases with sin B similar in pattern to the relationship between cr' and sin / ? . Therefore, the very weak decrease of k with respect to sin B in Figure 4-12a is reasonable. Fully accounting for the scattering of Qb0 (e.g., secondary scattering) and the penumbral light spreading effect of solar rays (e.g., multi-fold penumbra) in a canopy is difficult. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 116 Figure 4-12. (a) The relationship between k and sin B obtained using the Q e - M M model (see Figure 4-11). Symbols represent bin averages and vertical lines indicate ±1 S D . (b) the relationship between a' and sin/? calculated for different values of L using a' = \-e'Kb'--(l-o-Xl-e"*"'-), where Kh =0.5/sin /J (see Eq . 21). The value of a is assumed to be 0.1. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 111 Since k appears to have a weak dependence on sin B for this 56-year-old Douglas-fir stand, using a fixed value of k (i.e., k = 0.22) as a bulk parameter in the Qe-M M model to calculate canopy P appears to be reasonable (see Figure 4-6d and Figure 4-8). The introduction of the parameter k into the M M model is useful because it provides a simple way of quantifying the effective canopy radiation regime. Furthermore, it can be easily estimated. The parameters obtained using the m - M M model are shown in relation to air temperature in Figure 4-13. On average, ah is significantly lower than ad (Figure 4-13a), but the distinction between Amaxb and Ammd is much less clear-cut (Figure 4-13b). Both ah and ad slightly increase with Ta. These results agree with the findings in Gu et al. (2002). The distribution of ocb/ad is shown in Figure 4-14a, which is similar in pattern (i.e., the most observed values are between 0.1 and 0.3) to the distribution of k obtained using the Q e - M M model (Figure 4-11). In comparison with the distribution of abl' ad , the distribution of A^^ I Am.ixd tends to shift towards higher values, for example, approximately 34% of Am3Xb / Amaxd values are greater than 0.7. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 118 Figure 4-13. The temperature response of ad, ah,Amaxd, and Amaxb for the m - M M model obtained using 15-day moving windows for 5 Vi years of data (see Figure 4-9). Fil led circles are ad and Amaxd, and open circles are ab and Amaxb. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 119 60 40 0) 3 c 4) Q_ 20 1 r m-MM model (a) (b) < 0.1 0.1 - 0.3 0.3 - 0.5 0.5 - 0.7 0.7 - 0.9 ab,ad >0.9 < 0.1 0.1 - 0.3 0.3 - 0.5 0.5 - 0.7 0.7 - 0.9 > 0.9 A JA . maxb maxd Figure 4-14. Distributions of cchl ad and Amaxbi'Amaxd for 5 Vi years of data. The values of ad , ah ,AmaXd, and Amaxb were obtained using the 15-day moving windows for the m - M M model (see Figure 4-13). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 120 4.4.5 A case study The Q e - M M and M M models were used to estimate P for a period of six days with alternating cloudy and sunny conditions. In cloudy conditions, Qdo reached 600 2 1 umol m" s" (e.g., July 29), but in sunny conditions Qdo was steady and between 200 -300 ixmol m' 2 s"1 (e.g., August 3) (Figure 4-15a). The fluctuations in Qt0 in cloudy conditions indicated the passage of clouds (e.g., July 29). Ta and D, which are highly correlated, tended to be lower in cloudy (e.g., July 29) than in sunny conditions (e.g., July 30) (Figure 4-15b). Canopy P was significantly lower in sunny (e.g., August 1) than in cloudy conditions (e.g., July 31 and August 2) (Figure 4-15c) even with comparable Ta and D (Figure 4-15b). The Q e - M M model described P reasonably well (r2 = 0.56) (Figure 4-15c), but the M M model significantly underestimated P in cloudy conditions (e.g., July 29, 31 and August 2) and significantly overestimated P in sunny conditions (e.g., August 1 and 3) (Figure 4-15c), and as a result, the M M model accounted for only 28% of the variance in P. The r2 obtained using the m - M M model was the same as that for Q e - M M model, and the values of P calculated using the two models were almost identical (data not shown). Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 121 2000 Figure 4-15. Continuous half-hourly values of (a) Q,o (thick line), Qdo (thin line) and QtOmdi which is the modeled Q , 0 in a cloudless sky using Eq. B l in Appendix B (dotted line), (b) Ta (thick line) and D (thin line), and (c) canopy P for 6 days in the 56-year-old Douglas fir stand (DF49), Campbell River, B.C. Squares (•) are modeled P using the Qe-M M model, and diamonds (O ) are modeled P using the M M model. For the Q e - M M ccO A model, P = — ^ ' ™* , where a = 0.048 mol mol"1, Amax = 67.86 umol m"2 s"1, k = 0.16, r2 = 0.56, and RMSE = 4.82 umol m"2 s"1. For the MM-model, P = aQ<"A™ t where a = 0.053, Amax = 22.51 umol m"2 s"1, r2 = 0.28 and RMSE = 6.20 umol m"2 s"1. Note: the measurements of P made in all u* conditions are shown in plot (c), but the measurements of P made in calm conditions (u* < 0.3 m s:1) when Q t 0 < 200 pmol m"2 s"1 were excluded from regressions of the M M and Q e - M M models. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 122 The modeled canopy P for the sunlit and shade leaves using the sun/shade model for the same six days is shown in Figure 4-16. It is clear that Psun is always limited by its photosynthetic capacity (i.e., Av) (Figure 4-16a), which agrees with the findings of de Pury and Farquhar (1997) (their Figure 11). The value of Av is driven by VcmaX25 (which is a function of Ta), Kn (which is assumed to be constant in this study) and Kb (which is a function of solar elevation angle), and that is why the diurnal change of Av for the sunlit leaf is smooth (see Eq . 22 in de Pury and Farquhar 1997). A s is discussed in detail in Appendix C, that P of the sunlit leaves is always Rubisco-limited (i.e., decoupled from the amount of P A R the sunlit leaves actually absorbed) is questionable, because a high proportion of the sunlit leaves are oriented approximately parallel to the solar beam and are light limited (i.e., not Rubisco-limited). On the other hand, Psnd tends to be RuBP-limited (i.e., A , < Av). However when Qd0 is high, for example, during the noon hours on the three cloudy days (July 29, 31 and August 2), Psnd also becomes Rubisco-limited (i.e., Av < A/) and during these noon hours the P of the entire canopy becomes Rubisco-limited, i.e., has nothing to do with the P A R incident on the canopy. The modeled values of P during these noon hours are questionable and are a direct result of the flaws in the scaling algorithm of the sun/shade model (see Appendix C for details). The bottom shaded leaves should always be light-limited for this dense canopy, i.e., cannot be Rubisco-limited as predicted by the sun/shade model. The sun/shade model accounted for approximately 43% of the variance in canopy P (Figure 4-16c), which is less satisfactory than the performance of the Q e - M M model. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 123 Figure 4-16. Canopy P calculated using the sun/shade model, (a) the Rubisco-limited (Av) and RuBP-limited (Aj) photosynthetic rates for the big sunlit leaf, Psll„ = min(A v , Aj), (b) the corresponding Av and Aj for the big shaded leaf, Pshd = min(A v , Aj), (c) the modeled P of the entire canopy (P = Psm + Pshd) using the sun/shade model (circles) and the measured P (lines), r2 = 0.43, R M S E = 5.54 umol m" 2 s"1. Note Av equals to zero at night in (a) but not in (b) because the fraction of sunlit leaves at night is zero. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 124 4.5 Discussion The models presented in this study are closely related. If A m a x d = Am.Mb, then the m - M M model (Eq. (5)) becomes the Q e - M M model (Eqs. (23) and (25)). If Amax in the Q e - M M model is infinitely large, the Q e - M M model reduces to the Q e - L U E model (Eq. (22)). If k = 1 in the Q e - M M model, it becomes the M M model (Eq. (2)). The m - M M model has two more variables (i.e., Qto and Amaxb) than the Q e - M M model, but does not account for significantly more variance in P than the latter (Figure 4-9). Therefore, the modification of Amax to be a function of Qd0IQM appears to be unnecessary (Eq. (4)). Even from a computational perspective, the modification of Amax (i.e., 4™ = A ™ X ( / + A n a x h ^ " ) f ° r m e model is unnecessary because a and Amax Qti) Qto appear as a product in the numerator of the M M model. Also, the modification of Amax is not supported by the modelling in Norman and Arkebauer (1991) because their model, Cupid, used an M M model with fixed values of a and Amax (see Eq. (11) in Norman 1980) to estimate P of the sunlit leaves in different leaf-sun angle classes and P of the shaded leaves at different canopy depths. The Cupid model doesn't assign an Amaxb for direct PAR and an A m a x d for diffuse PAR, respectively. The average value of k for this Douglas-fir forest is approximately 0.22 (Figure 4-6d and Figure 4-11). k reflects the magnitude of the scattering as well as non-scattering effects (e.g., the penumbral effect) of the solar beam. The scattering of the solar beam in a plant canopy (e.g., Forseth and Norman 1993, Goudriaan and van Laar 1994, Campbell and Norman 1998) depends on many factors, such as foliar optical properties (Gausman and Allen 1973), leaf angular distribution (Campbell and Norman 1989), and the Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 125 structure of the canopy (Miller 1967, Idso and de Wit 1970, Lemeur 1973, Lang et al. 1985, Campbell 1986, Chen et al. 1997, Ross and Ross 1998). Scattered P A R has been reported to be as high as sky diffuse P A R within a deciduous canopy (Hutchison and Matt 1976) and to be significant beneath a coniferous canopy (Black et al. 1991). Penumbrae caused by the solar rays homogenize the light distribution and significantly reduce the completely shaded area (i.e., umbra) (e.g., Denholm 1981a, Stenberg 1998). Jarvis and Leverenz (1983) found that the photosynthetic light response was significantly more linear at canopy level than at leaf level for Sitka spruce possibly as a result of the scattering and penumbral component of the solar beam which leads to "a fairly uniform light distribution with the majority of leaf surfaces at intermediate quantum flux densities". The penumbrae in a Scots pine canopy simulated using a Monte Carlo technique were found to occur more frequently than full sun (i.e., gaps) and full shade (i.e., umbrae) (Oker-Blom 1985). Palmroth et al. (1999) investigated the distribution of direct sunlight on a plane shaded by a Scots pine shoot situated at varying distances using a multipoint P A R measurement system, and found that the distribution changed from clearly bimodal (full sun - full shade) to the one concentrated around the mean (penumbral irradiance) as the shoot was moved further away from the multipoint P A R measurement system. The heterogeneity and complexity of canopy structure makes it difficult to both reasonably measure (e.g., Black et al. 1991, Palmroth et al. 1999) and model (Oker-Blom 1985, Stenberg 1998) the full extent of the scattering and non-scattering effects of the solar beam in a plant canopy. The Q e - M M model may provide a new approach to study the radiation regime in a canopy (i.e., the estimation of the magnitude of k). The advantage of this approach is that half-hourly E C CO2 flux Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 126 measurements are made over a large flux footprint, so it effectively gives an integrated measure of the canopy radiation regime. Gu et al. (2002) found that the light use efficiency for direct beam (i.e., ab) was significantly lower than that for diffuse P A R (i.e., ad) for canopies of five different C 3 species. This study supports that conclusion because the application of the Q e - M M model indicates that ab is only a fraction k of ad (i.e., ab = kad ) (see Eq . (25)). In this study, k is hypothesized to be the effective fraction of Qb0 contributing to canopy photosynthesis. Gu et al. (2002) found that the five different C 3 stands had different ratios of ab to ad , likely reflecting differences in canopy structure and leaf photosynthetic and optical characteristics. The m - M M model focuses on the light use efficiency (i.e., a = a d ^ - + a b ^ - ) while the Q e - M M model focuses on light (i.e., Qe = Qd() + kQb0), S o Qm since it is light that drives canopy photosynthesis. The advantage of focusing on light is that we can add a fraction of Qb0 to Qd0 (i.e., Qx - Qd0 + xQb0 in Figure 4-5) to investigate to the maximum correlation between P P F D and canopy P. We cannot do this in the case of a , i.e., by adding a fraction of ab to ad, since the two quantities are not additive. The Q e - M M model suggests that the separation of canopy foliage into sunlit and shaded groups is not important (i.e., sin (3 is not finally required in Eq . (22)), because Qe can be reasonably assumed to be isotropic and consequently the whole canopy can be treated as a single big leaf. The Q e - M M model is a single big-leaf model, but it avoids the type of errors made in the earlier single big-leaf models of canopy P (Amthor 1994, Lloyd et al. 1995, Sellers et al. 1996) and therefore makes it particularly suitable for regional and global scale carbon balance modelling. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 127 In this study, the temperature effect on P was determined using an empirical Gaussian function (i.e., f(Ta) = e n ) (see Figure 4-8), and no effort was made to separate the effect of air temperature (Morgenstern et al. 2004) from that of D on P (e.g., Anthoni et al. 2002, Goulden et al. 2004). The Q e - M M model developed in this study is a simple top-down model of canopy P. A l l its parameters can be easily inferred from E C measurements (e.g., Figure 4-6d and Figure 4-8), and they provide a useful integrated measure of canopy photosynthetic behavior. The bottom-up models (e.g., de Pury and Farquhar 1997), built from detailed mechanistic representations of leaf-level processes and scaled up to the canopy level, are much more complex. A s pointed out by Jarvis (1993), bottom-up models are often more susceptible to errors in inputs (because the selection of parameter values is difficult a priori) and scaling assumptions than their top-down counterparts which are constrained to the 'realm of observations'. Consequently, bottom-up models do not necessarily guarantee better accuracy (Anderson et al. 2000) (see also the comparison of the performance of the Q e - M M model with that of the sun/shade model in Figure 4-8). For example, in most bottom-up models, the leaf angle distribution is assumed to be random and clumping is not considered (i.e., leaves are treated as randomly distributed elements analogous to the randomly distributed molecules in a solution, so Beer's law of light attenuation can be applied to a canopy). In reality, however, the needles are regularly arranged on a shoot and the clumping factor for a coniferous stand can be as low as 0.4 (Campbell and Norman 1998). There are large uncertainties regarding how to incorporate the clumping factor into existing bottom-up models. Another example is that the effect of penumbra cannot be simply scaled up from the leaf-level to the canopy-level because it does not exist at the leaf-level. When the Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 128 bottom-up models become very compl ica ted , it is diff icult to do sensit ivity tests for the mode l parameters. V o l c a n i c eruptions (Hoecker et a l . 1985, O l m o et a l . 1999, Dut ton and Bodhaine 2001), forest fires (Wotawa and Trainer 2000, Page et a l . 2002), b iomass burn ing (Dennis et a l . 2002, Pan et a l . 2004), urban air po l lu t ion (Wese ly and L ipschu tz 1976, A g u a d o 1990, N i c h o l 1997, Lamanna and Golds te in 1999, K o b a y a s h i et a l . 2004), and dust storms (Husar et a l . 2001) a l l mod i fy the sky diffuse radiation regime i n different ways , and therefore exert significant impacts on the regional and global terrestrial carbon cyc le ( N i y o g i et a l . 2004). The increased aerosol load ing f rom natural and anthropogenic sources can lead to both g lobal d i m m i n g (Stanhi l l and C o h e n 2001) and global w a r m i n g (T immermann et a l . 1999). H o w the two processes interact to affect the g loba l terrestrial carbon cyc le requires further invest igat ion (Farquhar and Rode r i ck 2003). The Q e - M M mode l presented i n this study cou ld be used as a s imple diagnostic tool for studies o f the impact o f diffuse radiation on gross pr imary product ion o f terrestrial ecosystems. 4.6 C o n c l u s i o n s (1) A canopy can be treated as a single b i g leaf to estimate its photosynthesis w i t h the ctQ A replacement o f Q,o in the M i c h a e l i s - M e n t e n ( M M ) mode l (i.e., P = — "' m a x ) w i t h " £ ? , . . + 4 ™ cxO A_ Qe-Qd»+kQm (i.e., P = — ^ ^ i a x , referred to as the Q e - M M model) , k is the ccQ +A >^e max fraction o f Qbo added to Qdo, and was approximately 0.22 for this Douglas- f i r stand. It is hypothesized that the value o f k reflects the magnitude o f scattering and non-scattering (e.g., the penumbral l ight-spreading) effects o f the solar rays. Chapter 4. Development of a one-big-leaf model of canopy P: the Qe-MM model 129 (2) The quantum yield for direct P A R (ah) is only fraction k of that for diffuse P A R (ad) because the effective flux of direct P A R for canopy P is approximately kQw-(3) The M M model significantly overestimates canopy P in sunny conditions, and significantly underestimates canopy P in cloudy conditions. The Q e - M M model has no systematic errors with respect to Qdo, and with the incorporation of the effect of temperature on P, accounted for 73% of the variance in P (derived half-hourly E C measurements for DF49 from May 2000 to December 2005). (4) The modification of A m a x (i.e., A m d x = A m a x „ ^ + A m a x b ^ ) in the m - M M model fcJrO Js£/0 (i.e., Eq . (4) by Gu et al. 2002) appears to be unnecessary. The Q e - M M model is demonstrated to be almost identical to the m - M M model in terms of estimating canopy P for this coastal Douglas-fir stand, but it significantly reduces the complexity of modelling canopy P. (5) The EC-derived half-hourly values of canopy P for the DF49 do not support the sun/shade model developed by de Pury and Farquhar (1997) (see Figure 4-8a) because the sun/shade model fails to address the heterogeneity of the light environment within the big sunlit leaf (group) (see Appendix C for details). Chapter 5. Conclusions 130 5 Conclusions This study has examined the effect of soil temperature (Chapter 2), phenology and soil moisture on ecosystem respiration (Chapter 3), and the role of direct and diffuse P A R in canopy photosynthesis (Chapter 4) of a 56-year-old coastal Douglas-fir stand (DF49) on Vancouver Island. This chapter summarizes and discusses the major findings of the study. (1) Respiration at night (REN) is best estimated using the relationship between the logarithm of half-hourly measurements of N E E and temperature rather than the exponential relationship because the former best meets the IID N(0 ,cr 2 ) requirements. (2) The estimates of REA- obtained by fitting the Michaelis-Menten equation (i.e., N E P = aQ"A™* -R ) to half-hourly E C measurements of N E P during the daytime (i.e., full range of P A R ) were found to be strongly influenced by the length of the regression periods used (e.g., 3-day vs. 30-day moving windows). They were considered to be unreliable. Reasons for this are (a) the variability of the daytime half-hourly E C measurements of N E P significantly increases with increasing Q,0, and (b) the residuals from the M M fit are not entirely random because negative residuals tend to associate with cloudy conditions and positive residuals with clear conditions. Thus, using the Michaelis-Menten equation to obtain a daytime N E P - Qt0 relationship severely violates the statistical IID N(0 ,cr 2 ) assumption. This is similar to the problem of using an O L S algorithm (i.e., the exponential relationship) for the nighttime NEE„ - Ts relationship to Chapter 5. Conclusions 131 determine Ren (nighttime Re). These estimates of Red are also considered unreliable because they are significantly greater than estimates obtained using the logarithmically transformed relationship between nighttime N E E and soil temperature to daytime half hours. Light inhibition of foliar respiration is expected to cause daytime Re to be less than nighttime Re at the same temperature. Even restricting the P A R range to 0-300 pmol m'2 s"1 resulted in Red estimates greater than those estimated from the nighttime relationship so it was concluded that regardless of P A R range use of the M M relationship overestimated daytime Re-(3) In contrast to the use of the M M model, using the L U E model (i.e., N E P = aQa) -Red) applied to P A R < 300 umol m2 s 1 to obtain a daytime N E P -Qto relationship provided plausible estimates of daytime Red. This is because the estimates were virtually independent of the moving window widths used and the violation of the statistical IID N(0,cr 2 ) assumption was eliminated. The relationship provided half-hourly values of Red that were less (28% less at 5 °C, 26% less at 10 °C and 23% less at 15 °C) than those calculated using the nighttime logarithmic relationship. (4) The annual totals of daytime Re obtained using the L U E model were approximately 25% less than that obtained by applying the nighttime NEE 1 ( < - Ts relationship to determine daytime Re. This was observed for all the 8 years (1998 - 2005) studied. The reduction is most likely caused by the light inhibition on ecosystem foliar respiration, which is supported by an independent leaf-level study at the same site. Chapter 5. Conclusions 132 (5) The values of R10 and Q10 for the 8 years (1998 - 2005) obtained from the eight annual nighttime N E E | ( - Ts relationships linearly increased with increasing 0 (soil volumetric moisture content averaged from the surface to the to 1-m depth). However, the effect of 9 on Re evident on the interannual scale could not be detected on the seasonal or annual scale, probably as a result of the confounding effects of other environmental and biotic factors (e.g., the phenology and dependence of Re on P) on Re. (6) Using annual nighttime and daytime Re - Ts relationships to estimate nighttime and daytime half-hourly Re values, respectively underestimated Re for the active growing season (April - July), and overestimated Re for the passive growing season (August - March). However, the systematic errors of using annual relationships had little effect on the estimation of annual totals of Re, because the underestimation and overestimation were similar in magnitude. The three stepwise fit methods developed to overcome the errors associated with using annual relationships agreed reasonably well . However, they do not provide any mechanistic understanding of Re, and they should be viewed more as methods of interpolating Re from nighttime turbulent conditions to nighttime calm conditions, and from daytime daily averages of Re (obtained using the L U E model) to daytime half-hourly Re estimates. (7) Canopy P can be described by replacing the Q,o in the M M model (i.e., P= a®'t)A7 ) with Qe=Qdl)+kQhi) (i.e., P= a^A™ , referred to as the Q e - M M model), k, which is the fraction of Qbo added to Qdo to obtain an estimate of effective canopy radiation (Qe), was found to be approximately 0.22 for this Chapter 5. Conclusions 133 Douglas-fir stand. The value of k reflects the magnitude of scattering and non-scattering effects of the solar beam. The Q e - M M model developed in this study is consistent with the findings of Norman and Arkebauer (1991). (8) The M M model significantly overestimates canopy P in sunny conditions, and significantly underestimates it in cloudy conditions. In contrast, the Q e - M M model has no systematic errors with respect to Qdo, and with the incorporation of an empirical function for the effect of air temperature on P, it accounted for 73% of the variance in P over a 8-year period for this 56-year-old Douglas-fir stand. (9) This study showed that the sun/shade model developed by de Pury and Farquhar (1997) performed as poorly as the regular M M model. Like the M M model, the sun/shade model also has systematic modeling errors with respect to Qdo, mainly because it does not take into account the effect of the leaf inclination angle distribution and uses LAI-weighted A P A R (absorbed P A R ) to calculate the P of the sunlit leaves. The evidence for the light inhibition on ecosystem foliar respiration (Chapter 2) in other stands should be examined. M y hypothesis is that as L A I decreases, the nighttime N E E H > - Ts relationship wi l l converge with the daytime Red - Ts relationship obtained using the L U E model, because as L A I decreases, the proportion of Re due to foliar respiration decreases and the effect of light inhibition of foliar respiration decreases accordingly. Humphreys (2004) already showed that in a recently clearcut-harvested Douglas-fir stand (i.e., a very low L A I stand), soil respiration fluxes obtained using a portable soil chamber were similar to values of Re calculated using nighttime N E E Chapter 5. Conclusions 134 measurements, but for this 56-year-old Douglas-fir stand, Re was significantly greater than soil respiration. Therefore, it is highly likely that ecosystem foliar respiration in this 56-year-old Douglas-fir stand is large. Without accurately accounting for the effect of light inhibition on ecosystem foliar respiration, calculations of the regional and global carbon balances (e.g., Ciais et al. 2005) w i l l likely be in large error. The exact mechanism for light inhibition on foliar respiration is still debatable (Pinelli and Loreto 2003), but it is generally accepted that foliar dark respiration is reduced in light relative to that in darkness (Sharp et al. 1984, Brooks and Farquhar 1985, Vi l lar et al. 1994, Shapiro et al. 2004). Additional leaf-level measurements are needed to address in-depth questions, such as the seasonal change in the effect of light inhibition and how it is affected by other environmental variables (e.g., leaf temperature, light intensity and soil moisture). The effect of 6 on Re discussed in Chapter 3 also merits further investigation and the same analysis used here (i.e., both nighttime and daytime N E P were used to estimate Re) can be easily extended to other ecosystems. It is a little surprising that the sensitivity of the annually obtained Qw to 0 in this deep-rooting coastal Douglas-fir ecosystem is almost as high as that in a mixed grassland with shallow-rooting depth (Flanagan and Johnson 2005). The values of R10 and Qw obtained from the annual nighttime and daytime Re - Ts relationships are integrated measures of Rc over the entire year, so they provide little detailed information about the linkage between P and Re and the partitioning between the heterotrophic and autotrophic ecosystem respiration. Continued modeling efforts using soil respiration (Jassal et al. 2005) and 1 3 C isotope (Ponton et al. 2006) measurements in this stand wi l l provide valuable insights on the coupling between Chapter 5. Conclusions 135 P and Re and the partitioning of Re between the heterotrophic and autotrophic components. The Q e - M M model presented in Chapter 4 has considerable potential to be incorporated into large-scale carbon climate models (e.g., Ruimy et al. 1999, Sti l l et al. 2004). This analysis only focused on modifying the M M model, but the concept of Qe (i.e., the photosynthetically effective P A R in the canopy) can be applied to other forms of equations that are also frequently used to describe the leaf-level photosynthetic response to light in the literature. For example, the photosynthetic response to light at leaf-level can be described by a general quadratic equation as: 0P2 - (aQ0 + A m a x )P + aQl{,Amax = 0 (1) where a, Qt0 and Amax are the apparent quantum use efficiency, incident total P A R and maximum assimilation rate, respectively. <j> is a curvature parameter (Ogren 1993). Eq . (1) can easily be modified for its application at canopy level by replacing Q,0 in Eq . (1) with Qe: 0Pi-(aQe+AmJP + aQeAmas=O (2) where <j), P, a, and Amax have the same meanings as in Eq . (1) except for at canopy scale. It is desirable to extend the methodology of Chapter 4 to other stands, so the characteristics of k can be systematically investigated before the Q e - M M model can be reliably applied at large scales. It is well-accepted that the evapotranspiration of a canopy can be approximated using the big leaf model described by the Penman-Monteith equation (e.g., Jarvis and McNaughton 1986) with a "canopy conductance" representing the entire canopy and the water transport in the soil-plant-atmosphere continuum can also be reasonably described Chapter 5. Conclusions 136 by resistors and capacitors representing the hydraulic resistance and water storage of soil and plant tissues (e.g., Jones 1992). However, it is generally accepted that estimation of canopy P requires, at minimum, a 2-leaf model (e.g., the sun/shade model in de Pury and Farquhar 1997). A n important contribution of this analysis is the development of the Qe-M M model, which provides an option of retaining the single big leaf concept to estimate canopy P. The Q e - M M model is particularly easy to couple with the Penman-Monteith equation, the soil-plant-atmosphere liquid water transfer equations, and the biochemical equations of leaf photosynthesis (e.g., Farquhar et al. 1980). References 137 References Aguado, E . , 1990. Effect of advected pollutants on solar radiation attenuation: Mojave Desert, California. Atmospheric Environment, 248: 153-157. Al len , L . H . , Stewart, D . W . and Lemon, E.R. , 1974. Photosynthesis in plant canopies: effect of light response curves and radiation source geometry. Photosynthetica, 8: 184-207. Amthor, J.S., 1994. Scaling CO2 - photosynthesis relationships from the leaf to canopy. Photosynthesis Research, 39: 321-350. Anderson, M . C . , Norman, J . M . , Meyers, T.P. and Diak, G.R., 2000. A n analytical model for estimating canopy transpiration and carbon assimilation fluxes based on canopy light use efficiency. Agricultural and Forest Meteorology, 10: 265-289. Angert, A . , Biraud, S., Bonfils, C , Buermann, W . and Fung, I., 2004. CO2 seasonality indicates origins of post-Pinatubo sink. Geophysical Research Letters, 31: doi: 10.1029/2004GL019760. Angert, A . , Biraud, S., Bonfils, C , Pfenning, C .C . , Buermann, W. , Pinzon, J., Tucker, C.J . and Fung*, I., 2005. Drier summers cancel out the C 0 2 uptake enhancement induced by warmer springs. Proceedings of the National Academy of Sciences, 102: 10823-10827. Anthoni, P . M . , Unsworth, M . H . , Law, B . E . , Irvine, J. , Baldocchi, D .D. , Van Tuyl , S. and Moore, D. , 2002. Seasonal differences in carbon and water vapor exchange in young and old-growth ponderosa pine ecosystems. Agricultural and Forest Meteorology, 111: 203-222. Arain, M . A . , Black, T .A . , Barr, A . G . , Jarvis, P .G. , Massheder, J . M . , Verseghy, D . L . and Nesic, Z. , 2002. Effects of seasonal and interannual climate variability on net ecosystem productivity of boreal deciduous and conifer forests. Canadian Journal of Forest Research, 32: 878-891. Atkin , O.K. , Edwards, E.J . and Loveys, B.R. , 2000a. Response of root respiration to changes in temperature and its relevance to global warming. New Phytologist, 147: 141-154. Atkin , O.K. , Evans, J.R., Ba l l , M . C . , Lambers, H . and Pons, T .L . , 2000b. Leaf respiration of snow gum in the light and dark: Interactions between temperature and irradiance. Plant Physiology, 122: 915-923. Atkin , O .K. , Westbeek, M . H . M . , Cambridge, M . L . , Lambers, H . and Pons, T .L . , 1997. Leaf respiration in light and darkness. Plant Physiology, 113: 961-965. References 138 Bacastow, R., 1979. Dip in the atmospheric CO2 level during the mid-1960's. Journal of Geophysical Research, 84: 3108-3114. Baldocchi, D . , 1997. Measuring and modeling carbon dioxide and water vapour exchange over a temperate broad-leaved forest during the 1995 summer drought. Plant, Cel l and Environment, 20: 1108-1122. Baldocchi, D .D. , 2003. Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Global Change Biology, 9: 479-492. Barford, C C , Wofsy, S . C , Goulden, M . L . , Munger, J.W., Pyle, E . H . , Urbanski, S.P., Hutyra, L . , Saleska, S.R., Fitzjarrala, D . and Moore, K . , 2001. Factors controlling long- and short-term sequestration of atmospheric CO2 in a mid-latitude forest. Science, 294: 1688-1691. Barr, A . G . , Black, T .A . , Hogg, E . H . , Kljun, N . , Morgenstern, K . and Nesic, Z. , 2004. Inter-annual variability in the leaf area index of a boreal aspen-hazelnut forest in relation to net ecosystem production. Agricultural and Forest Meteorology, 126(237-255). Barr, A . G . , Morgenstern, K . , Black, T .A . , McCaughey, J .H. and Nesic, Z . , 2006. Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of the CO2 Flux. Agricultural and Forest Meteorology, In press. Bjorkman, O., Boardman, N . K . , Anderson, J . M . , Thorne, S.W., Goodchild, D.J . and Pyliotis, N . A . , 1972. Effect of light intensity during growth of Atriplex patula on the capacity of photosynthetic reactions, chloroplast components and structure. Carnegie Institution Year Book, 71: 115-135. Black, T . A . , 1979. Evapotranspiration from Douglas fir stands exposed to soil water deficit. Water Resources Research, 15(1): 164-170. Black, T .A . , Chen, J . - M . , Lee, X . and Sagar, R . M . , 1991. Characteristics of shortwave and longwave irradiances under a Douglas-fir stand. Canadian Journal of Forest Research, 21: 1020-1028. Black, T .A . , Chen, W.J . , Barr, A . G . , Arain, M . A . , Chen, Z. , Nesic, Z. , Hogg, E . H . , Neumann, H . H . and Yang, P . C , 2000. Increased carbon sequestration by a boreal deciduous forest in years with a warm spring. Geophysical Research Letters, 27(9): 1271-1274. Black, T .A . , den Hartog, G. , Neumann, H . H . , Blanken, P.D. , Yang, P . C , Russell, C , Nexic, Z. , Lee, X . , Chen, S.G., Staebler, R. and Novak, M . D . , 1996. Annual cycles of water vapour and carbon dioxide fluxes in and above a boreal aspen forest. Global Change Biology, 2: 219-229. References 139 Bowling, D.R. , McDowel l , N . G . , Bond, B .J . , Law, B . E . and Ehleringer, J.R., 2002. 1 3 C content of ecosystem respiration is linked to precipitation and vapor pressure deficit. Oecologia, 131(1): 113-124. Briffa, K . R . , Jones, P.D. , Schweingruber, F . H . and Osborn, T.J. , 1998. Influence of volcanic eruptions on Northern Hemisphere summer temperature over the past 600 years. Nature, 393: 450-455. Brooks, A . and Farquhar, G .D. , 1985. Effect of temperature on the CO2/O2 specificity of ribulose-l,5-bisphosphate carboxylase/oxygenase and the rate of respiration in the light. Planta, 165: 397-406. Bunnell, F . L . , Tait, D . E . N . , Flanagan, P .W. and van Cleve, K . , 1977. Microbial respiration and substrate weight loss. I. A general model of the influence of abiotic variables. Soil B i o l . Biochem., 9: 33-40. Campbell, G.S., 1986. Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution. Agricultural and Forest Meteorology, 36: 317-321. Campbell, G.S. and Norman, J . M . , 1989. The description and measurement of plant canopy structure. In: G . Russell, B . Marshall and P .G . Jarvis (Editors), Plant canopies: their growth, form and function. Cambridge University Press, Cambridge, pp. 178. Campbell, G.S. and Norman, J . M . , 1998. A n introduction to environmental biophysics. Springer-Verlag, New York, 286 pp. Carrara, A . , Janssens, I .A., Yuste, J .C. and Ceulemans, R., 2004. Seasonal changes in photosynthesis, respiration and N E E of a mixed temperate forest. Agricultural and Forest Meteorology, 126: 15-31. Chen, J . M . , Rich, P . M . , Gower, S.T., Norman, J . M . and Plummer, S., 1997. Leaf area index of boreal forests: Theory, techniques, and measurements. Journal of Geophysical Research, 102(D24): 29429-29443. Chimner, R A . and Welker, J . M . , 2005. Ecosystem respiration responses to experimental manipulations of winter and summer precipitation in a Mixedgrass Prairie, W Y , U S A . Biogeochemistry, 73(1): 257-270. Choudhury, B.J . , 2000. A sensitivity analysis of the radiation use efficiency for gross photosynthesis and net carbon accumulation by wheat. Agricultural and Forest Meteorology, 101: 217-234. Choudhury, B.J . , 2001. Modeling radiation- and carbon-use efficiencies of maize, sorghum, and rice. Agricultural and Forest Meteorology, 106: 317-330. References 140 Ciais, P., Reichstein, M . , Viovy , N . , Granier, A . , Oge'e, J., Allard6, V . , Aubinet, M . , Buchmann, N . , Bernhofer, C. , Carrara, A . , Chevallier, F., Noblet, N . D . , Friend, A . D . , Friedlingstein, P., Gru'nwald, T . , Heinesch, B . , Keronen, P., Knohl , A . , Krinner, G. , Loustau, D. , Manca, G . , Matteucci, G. , Miglietta, F., Ourcival, J . M . , Papale, D. , Pilegaard, K . , Rambal, S., Seufert, G . , Soussana, J.F., Sanz, M . J . , Schulze, E .D . , Vesala, T. and Valentini, R., 2005. Europe-wide reduction in primary productivity caused by the heat and drought in 2003. Nature, 437: 529-533. Cohan, D.S. , X u , J., Greenwald, R., Bergin, M . H . and Chameides, W . L . , 2002. Impact of atmospheric aerosol light scattering and absorption on terrestrial net primary productivity. Global Biogeochemical Cycles, 16: doi:10.1029/2001GB001441. Cowan, I.R., 1968. The interception and absorption of radiation in plant stands. Journal of Applied Ecology, 5(2): 367-379. Cox, P . M . , Betts, R . A . , Jones, C D . , Spall, S .A. and Totterdell, I.J., 2000. Acceleration of global warming due to carbon-cycle feedbacks in a coupled climate model. Nature, 408: 184-187. de Pury, D . G . G . and Farquhar, G.D. , 1997. Simple scaling of photosynthesis from leaves to canopies without the errors of big-leaf models. Plant, Cel l and Environment, 20: 537-557. de Wit , C.T., 1965. Photosynthesis of leaf canopies. Cent, for Agric . Publ. and D o c , Wageningen, 57 pp. Denholm, J .V. , 1981a. The influence of penumbra on canopy photosynthesis I. Theoretical considerations. Agricultural Meteorology, 25: 145-166. Denholm, J .V. , 1981b. The influence of penumbra on canopy photosynthesis II. Canopy of horizontal circular leaves. Agricultural Meteorology, 25: 167-194. Dennis, A . , Fraser, M . , Anderson, S. and Al len , D. , 2002. A i r pollutant emissions associated with forest, grassland, and agricultural burning in Texas. Atmospheric Environment, 36: 3779-3792. Drewitt, G .B . , Black, T .A . , Nesic, Z. , Humphreys, E.R. , Jork, E . M . , Swanson, R., Ethier, G.J. , Griffis, T. and Morgenstern, K . , 2002. Measuring forest floor C 0 2 fluxes in a Douglas-fir forest. Agricultural and Forest Meteorology, 110(4): 299-317. Dutton, E . G . and Bodhaine, B . A . , 2001. Solar irradiance anomalies caused by clear-sky transmission variations above Mauna Loa: 1958-99. Journal of Climate, 14: 3255-3262. Epron, D. , Le Dantec, V . , Dufrene, E . and Granier, A . , 2001. Seasonal dynamics of soil carbon dioxide efflux and simulated rhizosphere respiration in a beech forest. Tree Physiology, 21: 145-152. References 141 Ethier, G.J . and Livingston, N . J . , 2004. On the need to incorporate sensitivity to C O 2 transfer conductance into the Farquhar-von Caemmerer-Berry leaf photosynthesis model. Plant Cel l and Environment, 27(2): 137-153. Evans, J.R. and Vogelmann, T.C. , 2003. Profiles of 1 4 C fixation through spinach leaves in relation to light absorption and photosynthetic capacity. Plant, Cel l and Environment, 26: 547-560. Falge, E . , Baldocchi, D. , Tenhunen, J. , Aubinet, M . , Bakwin, P., Berbigier, P., Bernhofer, C , Burba, G. , Clement, R., Davis, K . J . , Elbers, J .A. , Goldstein, A . H . and Grelle, A . , 2002. Seasonality of ecosystem respiration and gross primary production as derived from F L U X N E T measurements. Agricultural and Forest Meteorology, 113:53-74. Farquhar, G . D . and Roderick, M . L . , 2003. Pinatubo, diffuse light, and the carbon cycle. Science, 299: 1997-1998. Farquhar, G.D. , von Caemmerer, S. and Berry, J .A. , 1980. A biochemical model of photosynthetic C O 2 assimilation in leaves of C 3 species. Planta, 149: 78-90. Flanagan, L . B . and Johnson, B . G . , 2005. Interacting effects of temperature, soil moisture and plant biomass production on ecosystem respiration in a northern temperate grassland. Agricultural and Forest Meteorology, 130: 237-253. Forseth, I .N. and Norman, J . M . , 1993. Modell ing of solar irradiance, leaf energy budget and canopy photosynthesis. In: D.O. Hal l , J . M . O . Scurlock, H .R . Bolhar-Nordenkampf, R . C . Leegood and S.P. Long (Editors), Photosynthesis and Production in a Changing Environment: a Field and Laboratory Manual, pp. 207-219. Freedman, J . M . , Fitzjarrald, D.R. , Moore, K . E . and Sakai, R . K . , 2000. Boundary layer clouds and vegetation - atmosphere feedbacks. Journal of Climate, 14: 180-197. Freedman, J . M . , Fitzjarrald, D.R. , Moore, K . E . and Sakai, R . K . , 2001. Boundary layer clouds and vegetation - atmosphere feedbacks. Journal of Climate, 14: 180-197. Garrison, J., 1995. A n evaluation of the effect of volcanic eruptions on the solar radiation at six Canadian stations. Solar Energy, 55: 513-525. Gausman, H . W . and Al len , W . A . , 1973. Optical parameters of leaves of 30 plant species. Plant Physiology, 52: 57-62. Goudriaan, J., 1977. Crop micrometeorology and a simulation study. Cent, for Agric . Publ. and D o c , Wageningen, 249 pp. Goudriaan, J., 1988. The bare bones of leaf-angle distribution in radiation models for canopy photosynthesis and energy exchange. Agricultural and Forest Meteorology, 43: 155-169. References 142 Goudriaan, J. and van Laar, H . H . , 1994. Modell ing potential crop growth processes -textbook with exercises. Kluwer Academic Publishers, Amsterdam, 238 pp. Goulden, M . L . , Mil ler , S.D., Rocha, H.R.d . , Menton, M . C . , Freitas, Ff.C.d., Figueira, A . M . E . S . and Sousa, C .A .D .d . , 2004. Diel and seasonal patterns of tropical forest C 0 2 exchnage. Ecological Applications, 14: S42-S54. Goulden, M . L . , Munger, J.W., Fan, S . - M . , Daube, B . C . and Wofsy, S.C., 1996a. Measurements of carbon sequestration by long-term eddy covariance: methods and a critical evaluation of accuracy. Global Change Biology, 2: 169-182. Goulden, M . L . , Munger, W. , Fan, S . M . and Daube, B . C . , 1996b. Measurements of carbon sequestration by long-term eddy covariance: Methods and a critical evaluation of accuracy. Global Change Biology, 2: 169-182. Goulden, M . L . , Wofsy, S.C., Harden, J.W., Trumbore, S.E., C r i l l , P . M . , Gower, S T . , Fries, T., Daube, B . C . , Fan, S . - M . , Sutton, D.J . , Bazzaz, A . and Munger, J.W., 1998. Sensitivity of boreal forest carbon balance to soil thaw. Science, 279: 214-217. Grace, J., 1971. The directional distribution of light in natural and controlled environment conditions. Journal of Applied Ecology, 8(1): 155-164. Griffis, T.J., Black, T .A . , Morgenstern, K . , Barr, A . G . , Nesic, Z. , Drewitt, G .B . , Gaumont-Guay, D . and McCaughey, J .H. , 2003. Ecophysiological controls of the carbon balance of three southern boreal forests. Agricultural and Forest Meteorology, 117: 53-71. Gu, L . , Baldocchi, D. , Verma, S.B., Black, T A . , Vesala, T., Falge, E . M . and Dowty, P.R., 2002. Advantages of diffuse radiation for terrestrial ecosystem productivity. Journal of Geophysical Research, 107: 10.1029/2001JD001242. Gu, L . , Baldocchi, D .D. , Wofsy, S.C., Munger, J.W., Michalsky, J.J., Urbanski, S.P. and Boden, T .A . , 2003. Response of a deciduous forest to the Mount Pinatubo eruption: enhanced photosynthesis. Science, 299: 2035-2038. Gu, L . , Fuentes, J .D. and Shugart, H . H . , 1999. Responses of net ecosystem exchanges of carbon dioxide to changes in cloudiness: Results from two North America deciduous forests. Journal of Geophysical Research, 104: 31421-31434. Healey, K . D . , Rickert, K . G . , Hammer, G . L . and Bange, M . P . , 1998. Radiation use efficiency increases when the diffuse component of incident radiation is enhanced under the shade. Australian Journal of Agricultural Research, 49: 665-672. Hoecker, W . H . , Flowers, E . C . and Cotton, G.F. , 1985. Variation of direct beam solar radiation in the United States due to the E l Chichon debris cloud. Bulletin American Meteorology Society, 66: 14-19. References 143 Hogberg, P., Nordgren, A . , Buchmann, N . , Taylor, A .F .S . , Ekblad, A . , Hogberg, M . , Nyberg, G . , Ottosson-Lofvenius, M . and Read, D J . , 2001. Large-scale forest girdling shows that current photosynthesis drives soil respiration. Nature, 411: 789-792. Hollinger, D . Y . , Kelliher, F . M . , Byers, J .N. , Hunt, J.E., McSeveny, T . M . and Weir, P .L. , 1994. Carbon dioxide exchange between an undisturbed old-growth temperate forest and the atmosphere. Ecology, 75(1): 134-150. Hollinger, D . Y . , Kelliher, F . M . , Schulze, E . -D . , Bauer, G . , Arneth, A . , Byers, J .N. , Hunt, J.E., McSeveny, T . M . , Kobak, K . I . , Milukova, I., Sogatchev, A . , Tatarinov, F., Varlargin, A . , Ziegler, W . and Vygodskaya, N . N . , 1998. Forest-atmosphere carbon dioxide exchange in eastern Siberia. Agricultural and Forest Meteorology, 90: 291-306. Horn, H.S. , 1971. The adaptive geometry of trees. Princeton University Press, New Jersey, 144 pp. Humphreys, E.R. , 2004. Net ecosystem production of three coastal Douglas-fir stands at different stages of development after harvesting. Ph.D. Thesis, University of British Columbia, Vancouver, 155 pp. Humphreys, E.R. , Black, T .A . , Ethier, G.J. , Drewitt, G .B . , Spittlehouse, D . L . , Jork, E . -M . , Nesic, Z. and Livingston, N . J . , 2003. Annual and seasonal variability of sensible and latent heat fluxes above a coastal Douglas-fir forest, British Columbia, Canada. Agricultural and Forest Meteorology, 115: 109-125. Humphreys, E.R. , Black, T .A . , Morgenstern, K . , Cai , T., Drewitt, G .B . , Nesic, Z . and Trofymow, J .A. , 2006. Carbon dioxide fluxes in coastal DoUglas-fir stands at different stages of development after clearcut harvesting. Agricultural and Forest Meteorology: In press. Husar, R . B . , Tratt, D . M . , Schichtel, B . A . , Falke, S.R., L i , F., Jaffe, D. , Gasso, S., G i l l , T., Laulainen, N.S . , L u , F., Reheis, M . C . , Chun, Y . , Westphal, D. , Holben, B . N . , Gueymard, C , McKendry, I., Kuring, N . , Feldman, G.C. , McCla in , C , Frouin, R.J. , Merr i l l , J., Dubois, D. , Vignola, F., Murayama, T., Nickovic, S., Wilson, W . E . , Sassen, K . , Sugimoto, N . and Malm, W . C . , 2001. Asian dust events of Apr i l 1998. Journal of Geophysical Research, 106(D16): 18317-18330. Hutchison, B . A . and Matt, D.R. , 1976. Beam enrichment of diffuse radiation in a deciduous forest. Agricultural Meteorology, 17: 93-110. Idso, S.B. and de Wit, C.T., 1970. Light relations in plant canopies. Applied Optics, 9(1): 177-184. Irvine, J. and Law, B . E . , 2002. Contrasting soil respiration in young and old growth ponderosa pine. Global Change Biology, 8: 1183-1194. References 144 Janssens, I .A., Lankreijer, H . , Matteucci, G . , Kowalski , A . S . , Buchmann, N . , Epron, D. , Pilegaard, K . , Kutsch, W. , Longdoz, B . , Griinwald, T., Montagnani, L . , Dore, S., Rebmann, C. , Moors, E J . , Grelle, A . , Rannik, U . , Morgenstern, K . , Clement, R., GuSmundsson, J., Minerbi, S., Berbigier, P., Ibrom, A . , Moncrieff, J., Aubinet, M . , Bernhofer, C. , Jensen, N .O . , Vesala, T., Granier, A . , Schulze, E . -D. , Lindroth, A . , Dolman, A . J . , Jarvis, P .G. , Ceulemans, R. and Valentini, R., 2001. Productivity and disturbance overshadow temperature in determining soil and ecosystem respiration across European forests. Global Change Biology, 7: 269-278. Jarvis, P .G. , 1993. Prospects for bottom-up models. In: J.R. Ehleringer and C B . Field (Editors), Scaling Physiological Processes Leaf to Globe. Academic Press, San Diego, pp. 115-126. Jarvis, P .G . and Leverenz, J .W., 1983. Productivity of temperate, deciduous and evergreen forests. In: O .L . Lange, P.S. Nobel, C B . Osmond and H . Zeigler (Editors), Encyclopedia of Plant Physiology. Springer, Berlin, pp. 233-280. Jarvis, P .G . and McNaughton, K . G . , 1986. Stomatal control of transpiration: scaling up from leaf to region. Advances in Ecological Research, 15: 1-49. Jassal, R., Black, A . , Novak, M . , Morgenstern, K . , Nesic, Z . and Gaumont-Guay, D . , 2005. Relationship between soil C 0 2 concentrations and forest-floor C 0 2 effluxes. Agricultural and Forest Meteorology, 130(3-4): 176-192. Jones, C D . and Cox, P . M . , 2001. Modeling the volcanic signal in the atmospheric CO2 record. Global Biogeochemical Cycles, 15(2): 453-465. Jones, H . G . , 1992. Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology. Cambridge University Press, 413 pp. June, T., Evans, J.R. and Farquhar, G.D. , 2004. A simple new equation for the reversible temperature dependence of photosynthetic electron transport: a study on soybean leaf. Functional Plant Biology, 31(3): 275-283. Keeling, C D . , Whorf, T.P., Wahlen, M . and van der Pflicht, J., 1995. Interannual extremes in the rate of rise of atmospheric carbon dioxide since 1980. Nature, 375: 666-670. Kimbal l , H . H . and Hand, I.F., 1922. Daylight illumination on horizontal, vertical, and sloping surfaces. Monthly Weather Review, 50(12): 615-628. Kirschbaum, M . U . F . , 2004. Soil respiration under prolonged soil warming: are rate reductions caused by acclimation or substrate loss? Global Change Biology, 10: 1-8. Kobayashi, H . , Matsunaga, T., Hoyano, A . , A o k i , M . , Komori , D . and Boonyawat, S., 2004. Satellite estimation of photosynthetically active radiation in Southeast Asia: References 145 Impacts of smoke and cloud cover. Journal of Geophysical Research, 109: D04102, doi: 10.1029/2003JD003807. Kok , B . , 1948. A critical consideration of the quantum yield of Chlorella photosynthesis. Enzymology, 13: 1-56. Kowalski , S., Sartore, M . , Burlett, R., Berbigier, P. and Loustau, D . , 2003. The annual carbon budget of a French pine forest (Pinus pinaster) following harvest. Global Change Biology, 9: 1051-1065. Krakauer, N . Y . and Randerson, J.T., 2003. Do volcanic eruptions enhance or diminish net primary production? Evidence from tree rings. Global Biogeochemical Cycles, 17(4): 1118, doi:10.1029/2003GB002076. Kramer, P.J. and Decker, J.P., 1944. Relation between light intensity and rate of photosynthesis of loblolly pine and certain hardwoods. Plant Physiology, 19: 350-358. Lamanna, M . S . and Goldstein, A . H . , 1999. In situ measurements of C2-C10 volatile organic compounds above a Sierra Nevada ponderosa pine plantation. Journal of Geophysical Research, 104: 21247-21262. Lang, A . R . G . , Xiang, Y . and Norman, J . M . , 1985. Crop structure and the penetration of direct sunlight. Agricultural and Forest Meteorology, 35: 83-101. Lavigne, M . , Ryan, M . and Anderson, D. , 1997. Comparing nocturnal eddy covariance measurements to estimates of ecosystem respiration made by scaling chamber measurements. Journal of Geophysical Research, 102: 28977-28986. Lavigne, M . B . , Foster, R.J . and Goodine, G. , 2004. Seasonal and annual changes in soil respiration in relation to soil temperature, water potential and trenching. Tree Physiology, 24: 415-424. Law, B . E . , Falge, E . , Gu, L . , Baldocchi, D .D. , Bakwin, P., Berbigier, P., Davis, K . , Dolman, A . J . , Falk, M . , Fuentes, J.D., Goldstein, A . , Granier, A . , Grelle, A . , Hollinger, D. , Janssens, I A . , Jarvis, P., Jensen, N .O. , Katul, G. , Mahl i , Y . , Matteucci, G. , Meyers, T., Monson, R., Munger, W. , Oechel, W. , Olson, R., Pilegaard, K . , Paw, K . T . , Thorgeirsson, H . , Valentini, R., Verma, S., Vesala, T., Wilson, K . and Wofsy, S., 2002. Environmental controls over carbon dioxide and water vapor exchange of terrestrial vegetation. Agricultural and Forest Meteorology, 113(1-4): 97-120. Lee, X . , Fuentes, J.D., Staebler, R . M . and Neumann, H . H . , 1999. Long-term observation of the atmospheric exchange of C 0 2 with a temperature deciduous forest in southern Ontario, Canada. Journal of Geophysical Research, 104(13): 15975-15984. References 146 Lee, X . , W u , H.-J . , Sigler, J., Oishi, C . and Siccama, T., 2004. Rapid and transient response of soil respiration to rain. Global Change Biology, 10(6): 1017-1026. Lemeur, R., 1973. A method for simulating the direct solar radiation regime in sunflower, Jerusalem artichoke, corn and soybean canopies using actual stand structure data. Agricultural Meteorology, 12: 229-247. Lindroth, A . , Grelle, A . and Moren, A . - S . , 1998. Long-term measurements of boreal forest carbon balance reveal large temperature sensitivity. Global Change Biology, 4: 443-450. L i u , B . Y . H . and Jordan, R .C . , 1960. The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Solar Energy, 4(3): 1-19. Lloyd, J., Grace, J., Miranda, A . C . , Meir , P., Wong, S.C., Miranda, H.S. , Wright, I.R., Gash, J .H.C. and Mclntyre, J., 1995. A simple calibrated model of Amazon rainforest productivity based on leaf biochemical properties. Plant, Cel l and Environment, 18: 1129-1145. Lloyd, J. and Taylor, J .A. , 1994. On temperature dependence of soil respiration. Functional Ecology, 8: 315-323. Lucht, W. , Prentice, I.C., Myneni, R .B . , Sitch, S., Friedlingstein, P., Cramer, W. , Bousquet, P., Buermann, W . and Smith, B . , 2002. Climatic control of the high-latitude vegetation greening trend and Pinatubo effect. Science, 296: 1687-1689. Luo, Y . , Wan, S., Hui , D . and Wallace, L . L . , 2001. Acclimatization of soil respiration to warming in a tall grass prairie. Nature, 413: 622-625. McArthur, L . J .B . and Hay, J.E., 1981. A technique for mapping the distribution of diffuse solar radiation over the sky hemisphere. Journal of Applied Meteorology, 20: 421-429. McCormick, M . P . , Thomason, L . W . and Trepte, C.R. , 1995. Atmospheric effects of the Mt . Pinatubo eruption. Nature, 373: 399-404. McDowel l , N . G . , Bowling, D.R., Schauer, A . , Irvine, J., Bond, B .J . , Law, B . E . and Ehleringer, J.R., 2004. Associations between carbon isotope ratios of ecosystem respiration, water availability and canopy conductance. Global Change Biology, 10(10): 1767-1784. Mil ler , E . E . and Norman, J . M . , 1971. A sunfleck theory for plant canopies. 1. Lengths of sunlit segments along a transect. Agron. J., 63: 735-738. Mil ler , J .B., 1967. A formula for average foliage density. Australian Journal of Botany, 15: 141-144. References 147 Mil ler , S.D., Goulden, M . L . , Menten, M . C . , Rocha, H.R.d. , Freitas, H.C.d . , Figueira, A . M . E . S . and Sousa, C .A .D .d . , 2004. Biometric and micrometeorological measurements of tropical forest carbon balance. Ecological Applications, 14(4): S114-S126. Molineaux, B . and Ineichen, P., 1996. Impact of Pinatubo aerosols on the seasonal trends of global, direct and diffuse irradiance in two northern mid-latitude sites. Solar Energy, 58: 91-101. Monteith, J., 1972. Solar radiation and productivity in tropical ecosystems. Journal of Applied Ecology, 9: 747-766. Moon, P. and Spencer, D .E . , 1942. Illumination from a non-uniform sky. Trans. Ilium Eng. S o c , 37: 707-726. Moren, A . - S . and Lindroth, A . , 2000. CO2 exchange at the floor of a boreal forest. Agricultural and Forest Meteorology, 101(1-14). Morgenstern, K . , Black, T .A . , Humphreys, E.R., Griffis, T.J. , Drewitt, G .B . , Cai , T., Nesic, Z. , Spittlehouse, D . L . and Livingston, N . J . , 2004. Sensitivity and uncertainty of the carbon balance of a Pacific Northwest Douglas-fir forest during an E l Nino /La Nina cycle. Agricultural and Forest Meteorology, 123: 201-219. Nichol , J., 1997. Bioclimatic impacts of the 1994 smoke haze event in southeast Asia . Atmospheric Environment, 31(8): 1209-1219. Niyogi , D. , Chang, H . - L , Saxena, V . K . , Holt, T., Alapaty, K . , Booker, F., Chen, F., Davis, K . J . , Holben, B . , Matsui, T., Meyers, T., Oechel, W . C . , Sr., R . A . P . , Wells, R., Wilson, K . and Xue, Y . , 2004. Direct observations of the effects of aerosol loading on net ecosystem CO2 exchanges over different landscapes. Geophysical Research Letters, 31: doi:10.1029/2004GL020915. Norman, J., 1982. Simulation of microclimates. In: J .L. Hatfield and I.J. Thomason (Editors), Biometeorology in Integrated Pest Management. Academic Press, New York, pp. 65-99. Norman, J . M . , 1979. Modeling the complete crop canopy. In: B . J . Barfield and J.F. Gerber (Editors), Modification of the aerial environment of plants. American Society of Agricultural Engineers, St. Joseph, pp. 249-277. Norman, J . M . , 1980. Interfacing leaf and canopy light interception models. In: J.D. Hesketh and J .W. Jones (Editors), Predicting Photosynthesis for Ecosystem Models. C R C Press, Boca Raton, pp. 49-67. Norman, J . M . and Arkebauer, T.J., 1991. Predicting canopy light-use efficiency from leaf characteristics. In: J. Hanks and J. Ritchie (Editors), Modeling Plant and Soil Systems. Agronomy Monograph. A S A - C S S A - S S S A , pp. 125-143. References 148 Ogren, E. , 1993. Convexity of the photosynthetic light response curve in relation to intensity and direction of light during growth. Plant Physiology, 101: 1013-1019. Oker-Blom, P., 1985. Photosynthesis of a Scots pine shoot: simulation of the irradiance distribution and photosynthesis of a shoot in different radiation fields. Agricultural and Forest Meteorology, 34: 31-40. Oker-Blom, P., 1986. Photosynthesis of a Scots pine shoot: simulation of the irradiance distribution and photosynthesis of a shoot in different radiation fields. Agricultural and Forest Meteorology, 34: 31-40. Olmo, F.J. , Tovar, J., Alados-Arboledas, L . , Okulov, O. and Ohvril , H.O. , 1999. A comparison of ground level solar radiative effects of recent volcanic eruptions. Atmospheric Environment, 33: 4589-4596. Page, S.E., Siegert, F., Rieley, J.O., Boehm, H . - D . V . , Jaya, A . and Limin , S., 2002. The amount of carbon released from peat and forest fires in Indonesia during 1997. Nature, 420: 61-65. Palmroth, S., Palva, L . , Stenberg, P. and Kotisaari, A . , 1999. Fine scale measurement and simulation of penumbral radiation formed by a pine shoot. Agricultural and Forest Meteorology, 95: 15-25. Pan, Z. , Segal, M . , Arritt, R .W. and Takle, E.S., 2004. On the potential change in solar radiation over the US due to increases of atmospheric greenhouse gases. Renewable Energy, 29: 1923-1928. Pinelli , P. and Loreto, F., 2003. 1 Z C 0 2 emission from different metabolic pathways measured in illuminated and darkened C 3 and C 4 leaves at low, atmospheric and elevated C 0 2 concentration. Journal of Experimental Botany, 54: 1761-1769. Ponton, S., Flanagan, L . B . , Alstad, K . P . , Johnson, B . G . , Morgenstern, K . A . I . , Kljun, N . , Black, T A . and Barr, A . G . , 2006. Comparison of ecosystem water-use efficiency among Douglas-fir forest, aspen forest and grassland using eddy covariance and carbon isotope techniques. Global Change Biology, 12(2): 294-310. Price, D.T. and Black, T .A . , 1990. Effects of short-term variation in weather on diurnal canopy C 0 2 flux and evapotranspiration of a juvenile Douglas-fir stand. Agricultural and Forest Meteorology, 50: 139-158. Rayment, M . B . and Jarvis, P .G. , 2000. Temporal and spatial variation of soil CO2 efflux in a Canadian boreal forest. Soil Biology and Biochemistry, 32: 35-45. Reichstein, M . , Falge, E . , Baldocchi, D. , Papale, D . , Aubinet, M . , Berbigier, P., Bernhofer, C , Buchmann, N . , Gilmanov, T., Granier, A . , Grunwald, T., Havrankova, K . , Ilvesniemi, Ff., Janous, D. , Knohl , A . , Laurila, T., Lohila, A . , Loustau, D. , Matteucci, G. , Meyers, T., Miglietta, F., Ourcival, J . - M . , Pumpanen, J., Rambal, S., Rotenberg,- E. , Sanz, M . , Tenhunen, J., Seufert, G. , Vaccari, F., References 149 Vesala, T., Yakir , D . and Valentini, R., 2005. On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm. Global Change Biology, 11(9): 1424-1439. Reichstein, M . , J.D., T., Roupsard, O., Ourcival, J . - M . , Rambal, S., Miglietta, F., Peressottis, A . , Pecchiari, M . , Tirone, G . and Valentini, R., 2002a. Severe drought effects on ecosystem C 0 2 and H 2 0 fluxes at three Mediterranean evergreen sites: revision of current hypothesis? Global Change Biology, 8: 999-1017. Reichstein, M . , Tenhunen, J.D., Roupsard, O., Ourcival, J . M . , Rambal, S., Dore, S. and Valentini, R., 2002b. Ecosystem respiration in two Mediterranean evergreen Holm Oak forests: drought effects and decomposition dynamics. Functional Ecology, 16(1): 27-39. Richardson, A . D . and Hollinger, D . Y . , 2005. Statistical modeling of ecosystem respiration using eddy covariance data: Maximum likelihood parameter estimation,and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models. Agricultural and Forest Meteorology, 131: 191-208. Robinson, N . , 1966. Solar Radiation. Elsevier Pub. Co., New York, 347 pp. Robock, A . , 2002. The climatic aftermath. Science, 295: 1242-1244. Roderick, M . L . , Farquhar, G.D. , Berry, S.L. and Noble, I.R., 2001. On the direct effect of clouds and atmospheric particles on the productivity and structure of vegetation. Oecologia, 129: 21-30. Ross, J., 1991. Introduction. In: J. Ross (Editor), Photon-Vegetation Interactions-Applications in Optical Remote Sensing and Plant Ecology. Springer-Verlag, pp. 1-7. Ross, J. and Ross, V . , 1998. Statistical description of the architecture of a fast growing wil low coppice. Agricultural and Forest Meteorology, 91: 23-37. Ruimy, A . , Kergoat, L . , Bondeau, A . , Bondeau, A . , Churkina, G . , Cramer, W. , Colinet, G. , Collatz, J., Dedieu, G. , Emanuel, W. , Esser, G . , Field, C., Francois, L . and Friend, A . , 1999. Comparing global models of terrestrial net primary productivity (NPP): analysis of differences in light absorption and light-use efficiency. Global Change Biolology, 5(sl): 56-64. Savage, K . E . and Davidson, E . A . , 2001. Interannual variation of soil respiration in two New England forests. Global Biogeochemical Cycles, 15(2): 337-350. Scott-Denton, L . E . , Rosenstiel, T . N . and Monson, R . K . , 2005. Differential controls by climate and substrate over the heterotrophic and rhizospheric components of soil respiration. Global Change Biology, 11: 1-12. References 150 Scott-Denton, L . E . , Sparks, K . L . and Monson, R . K . , 2003. Spatial and temporal controls of soil respiration rate in a high-elevation, subalpine forest. Soil Biology & Biochemistry, 35: 525-534. Sellers, P.J., Randall, D . A . , Collatz, G.J. , Berry, J .A. , Field, C . B . , Dazlich, D . A . , Zhang, C , Collelo, G .D . and Bounoua, L . , 1996. A revised land surface parameterization (SiB2) for G C M s . Part I: Model formulation. Journal of Climate, 9/4: 676-705. Shapiro, J.B., Griffin, K . L . , Lewis, J .D. and Tissue, D.T. , 2004. Response of Xanthium strumarium leaf respiration in the light to elevated C 0 2 concentration, nitrogen availability and temperature. New Phytologist, 162(2): 377-386. Sharp, R .E . , Matthews, M . A . and Boyer, J.S., 1984. K o k effect and the quantum yield of photosynthesis: light partially inhibits dark respiration. Plant Physiology, 75: 95-101. Sinclair, T.R., Murphy, C . E . and Knoerr, K . R . , 1976. Development and evaluation of simplified models for simulating canopy photosynthesis and transpiration. Journal of Applied Ecology, 13: 813-829. Smolander, H . , Oker-Blom, P., Ross, J., Kellomaki, S. and Lahti, T., 1987. Photosynthesis of a Scots pine shoot: test of a shoot photosynthesis model in a direct radiation field. Agricultural and Forest Meteorology, 39: 67-80. Soden, B.J . , Wetherald, R.T., Stenchikov, G . L . and Robock, A . , 2002. Global cooling after the eruption of Mount Pinatubo: a test of climate feedback by water vapor. Science, 296: 727730. Spiders, C.J.T., Toussaint, H . A . J . M . and Goudriaan, J., 1986. Separating the diffuse and direct component of global radiation and its implications for modeling canopy photosynthesis. Part I. components of incoming radiation. Agricultural and Forest Meteorology, 38: 217-229. Stanhill, G . and Cohen, S., 2001. Global dimming: a review of the evidence for a widespread and significant reduction in global radiation with discussion of its probable causes and possible agricultural consequences. Agricultural and Forest Meteorology, 107: 255-278. Steel, R . G . D . and Torrie, J .H. , 1960. Principles and Procedures of Statistics. McGraw-H i l l , New York, 481 pp. Stenberg, P., 1998. Implications of shoot structure on the rate of photosynthesis at different levels in a coniferous canopy using a model incorporating grouping and penumbra. Functional Ecology, 12: 82-91. Steven, M . D . , 1977. Standard distributions of clear sky radiance. Quarterly Journal of the Royal Meteorological Society, 106: 57-61. References 151 Sti l l , C.J. , Randerson, J.T. and Fung, I .Y., 2004. Large-scale plant light-use efficiency inferred from the seasonal cycle of atmospheric CO2. Global Change Biolology, 10(8): 1240-1252. Suyker, A . E . and Verma, S.B., 2001. Year-round observations of the net ecosystem exchange of carbon dioxide in a native tallgrass prairie. Global Change Biology, 7(3): 279-289. Tang, J., Baldocchi, D . D . and X u , L . , 2005. Tree photosynthesis modulates soil respiration on a diurnal time scale. Global Change Biology, 11: 1298-1304. Timmermann, A . , Oberhuber, J. , Bacher, A . , Esch, M . , Latif, M . and Roeckner, E . , 1999. Increased E l Nino frequency in a climate model forced by future greenhouse warming. Nature, 398: 694-697. Tjoelker, M . G . , Oleksyn, J. and Reich, P .B. , 2001. Modell ing respiration of vegetation: evidence for a general temperature-dependence Q10. Global Change Biology, 7: 223-230. Twine, T.E. , Kustas, W.P. , Norman, J . M . , Cook, D.R. , Houser, P.R., Meyers, T.P., Prueger, J .H. , Starks, P.J. and Wesely, M . L . , 2000. Correcting eddy-covariance flux underestimates over a grassland. Agricultural and Forest Meteorology, 103: 279-300. Vil lar , R., Held, A . A . and Merino, J., 1994. Dark leaf respiration in light and darkness of an evergreen and a deciduous plant species. Plant Physiology, 107: 421-427. Wang, X . , Lewis, J., Tissue, D. , Seemann, J. and Griffin, K . , 2001. Effects of elevated atmospheric C 0 2 concentration on leaf dark respiration of Xanthium strumarium in light and in darkness. Proceedings of the National Academy of Sciences, U S A , 98: 2479-2484. Wang, Y . - P . and Leuning, R., 1998. A two-leaf model for canopy conductance, photosynthesis and partitioning of available energy I: Model description and comparison with a multi-layered model. Agricultural and Forest Meteorology, 91: 89-111. Wang, Y . P . , 2000. A refinement to the two-leaf model for calculating canopy photosynthesis. Agricultural and Forest Meteorology, 101: 143-150. Wang, Y . P . and Jarvis, P .G. , 1990. Effect of incident beam and diffuse radiation on P A R absorption, photosynthesis, and transpiration of sitka spruce - A simulation study. Silva Carelica, 15: 167-180. Warren, C.R., Ethier, G.J. , Livingston, N .J . , Grant, N.J . , Turpin, D . H . , Harrison, D . L . and Black, T .A . , 2003. Transfer conductance in second growth Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) canopies. Plant, Cel l and Environment, 26: 1215-1227. References 152 Weiss, A . and Norman, J . M . , 1985. Partitioning solar radiation into direct and diffuse, visible and near-infrared components. Agricultural and Forest Meteorology, 34: 205-213. Wendler, G. , 1984. Effects of the E l Chichon volcanic cloud on solar radiation received at Fairbanks, Alaska. Bulletin American Meteorological Society, 65(3): 216-218. Wesely, M . L . and Lipschutz, R .C . , 1976. A method for estimating hourly averages of diffuse and direct solar radiation under a layer of scattered clouds. Solar Energy, 18: 467-473. Wofsy, S.C., Goulden, M . L . , Munger, J.W., Fan, S . M . , Bakwin, P.S., Daube, B . C . , Bassow, S.L. and Bazzaz, F . A . , 1993. Net exchange of CO2 in a mid-latitude forest. Science, 260: 1314-1317. Wohlfahrt, G . , Anfang, C , Bahri, M . , Haslwanter, A . , Newesely, C , Schmitt, M . , Dro'sler, M . , Pfadenhauer, J.r. and Cernusc, A . , 2005a. Quantifying nighttime ecosystem respiration of a meadow using eddy covariance, chambers and modelling. Agricultural and Forest Meteorology, 128: 141-162. Wohlfahrt, G. , Bahn, M . , Haslwanter, A . , Newesely, C . and Cernusca, A . , 2005b. Estimation of daytime ecosystem respiration to determine gross primary production of a mountain meadow. Agricultural and Forest Meteorology, 130: 13-25. Wood, J., Muneer, T. and Kubie, J., 2003. Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration. Journal of Solar Energy Engineering, 125: 43-48. Wotawa, G . and Trainer, M . , 2000. The influence of Canadian forest fires on pollutant concentrations in the United States. Science, 288: 324-328. X u , L . and Baldocchi, D .D. , 2004. Seasonal variation in carbon dioxide exchange over a Mediterranean annual grassland in California. Agricultural and Forest Meteorology, 123(1-2): 79-96. X u , M . and Q i , Y . , 2001. Spatial and seasonal variations of Q10 determined by soil respiration measurements at a Sierra Nevadan forest. Global Biogeochemical Cycles. Young, D.R. and Smith, W . K . , 1983. Effect of cloudcover on photosynthesis and transpiration in the subalpine understory species Arnica Latifolia. Ecology, 64(4): 681-687. Zelawski, W. , Szaniawski, R., Dybczynski, W . and Piechurowski, A . , 1973: Photosynthetic capacity of conifers in diffuse light of high illuminance. Photosynthetica, 7(4): 351-357. Appendix A. The site, EC system, and diffuse PAR measurements 153 Appendix A. The Site Location, EC System Configuration and the PAR Measurements for the 56-year-old Douglas-fir Stand Anaham Lake Soda Creek Ot CWanko Fork*, A | e x i 5 creek Williams Lake »o T t t a U k e Hance°v». 1 5 0 H o u s e " @ -30km 330mi „ _ . 100 Mile House Dog Creek O Nemiah Valley c Lone Butte Big Bar CreekQ Clinton cf V fi-ll oo t^ J3ofd Bridge Fa Bratorne --. c~ ® @ a Pembertort J.ytton , y/Campbell River " ^ ^ ^ M i j p o w e l l River Tahsis Gold River Nootka ^ B , a c k C r e e k o C o U r t e m * Madeira Park-u Vancouver . W. / T \ Vancouver V - £ > " M C ' / N a n a i m o Chilliwack -Burnaby *JJ t^^ ^^ —^ Squam-sh North Bend i p Cumberland Boat Basin' f ^ ^ l 0 Port Alberm LantTv*! ». • Ahousat Tofino Ucluelet BE Kildonan North Cowichan D e"a a Custer .^Bellmgharn _ Saanich . . . . . . jgi .-- Concrete .Victoria Q 20- .« NeahBay Colwood Stanwood Mount Vernon -Port Angeles - M U k * e o 1 Bamtseld • Port R e n f r e w C 2006 MapQuest. In* Kalaloch Brinnon cattle Figure A - l . Location of the 56-year-old Douglas-fir stand (DF49) on the east coast of Vancouver Island. The red star indicates the town of Campbell River. Map was obtained from http://www.mapquest.com/maps/. Appendix A. The site, EC system, and diffuse PAR measurements 154 Figure A - 2 . View of the 56-year-old Douglas-fir stand on Vancouver Island. The (eddy covariance) system consists of a 3-D sonic anemometer and a closed-path infrared gas analyzer. Appendix A. The site, EC system, and diffuse PAR measurements 155 Figure A - 3 . Half-hourly values of total and diffuse P A R were measured using a L I -190SB quantum sensor and a Delta-T B F 2 sensor, respectively. Appendix B. Quality check for the diffuse PAR measurements made using BF2 156 Appendix B. Comparison of the PAR Measurements Made Using the BF2 and LI-190SB. Since B F 2 measures both Q,0 and Qdo using the same algorithm (see Wood et al. 2003 for details), its half-hourly measurements of Qto were compared with those measured using LI-190SB in order to obtain an indirect quality check for its Qdo measurements (Fig. A l ) . In addition, the quality of B F 2 Qdo measurements were directly checked by their comparison with LI-190SB Q,0 measurements made in overcast conditions (Fig. A2) . The overcast conditions were determined as follows. First, we adopted a simple model from Campbell and Norman (1998) to predict Q,0 in a cloudless sky, e „ w , = « U s i n / ? ( B l ) where Qtomdi is the modelled Q,0 in a cloudless sky, Q0 is the extra-terrestrial P A R quantum flux (2413 pmol m" 2 s'1, converted from the solar constant of 1367 W m"2), B is the solar elevation angle, a is an empirical coefficient (taken as 0.86 for this stand), and r is the optical air mass. The value of r was calculated as 1/sin B. Second, the overcast and sunny conditions were defined as Q,o (LI-190SB)/<2,0mrf/ < 0.5, and Q,0 (LI-190SB)/<2,0mrf/ > 0.9, respectively. The rest of the half-hourly measurements were loosely classified as the partly cloudy conditions. Appendix B. Quality check for the diffuse PAR measurements made using BF2 157 Figure B - l . Relationship between the half-hourly values of Q,o from B F 2 and those from LI-190SB for the 56-year-old Douglas-fir stand (DF49) in Campbell River. In order to reduce the figure size, only one tenth of the measurements were plotted (i.e., the half-hourly measurements were decimated for the plotting). Appendix B. Quality check for the diffuse PAR measurements made using BF2 158 2000 Figure B-2. Relationship between the half-hourly values of Quo measured using B F 2 from May 2000 to December 2005 and the corresponding half-hourly values of Qto measured using LI-190SB (see also Fig . A l ) . In overcast conditions, Qdo (BF2) = 0.87Qto (LI-190SB) + 22.72 (r2 = 0.96, R M S E = 31.23 umol m" 2 s"1, n = 16444) (the thin line). In sunny conditions, a hyperbolic equation was used to fit the relationship between Qdo and Qto, i.e., Qd0 =b.85£, ( )337.11/(0.85e, (1 +337.11) (r2 = 0.49, R M S E = 84.89 umol m" 2 s"1, n = 21021) (the thick curve). In order to reduce the figure size, the half-hourly Qdo and Q,o measurements in overcast, partly cloudy and sunny conditions were all decimated for the plotting. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 159 Appendix C. Inadequacies in the Sun/Shade Model Developed by de Pury and Farquhar (1997) 1. Lack of consideration of the angle of incidence of Qbo and the use of area-weighted A P A R to calculate P of the big sunlit and shaded leaves, respectively. The sun/shade model defines the sunlit leaves as those in the gaps, receiving both Qbo (direct beam P A R ) and Qdo (diffuse P A R ) regardless of their angles of orientation with respect to the solar beam. This is not correct, because as de Pury and Farquhar (1997) point out (their page 544) "(sunlit) leaves nearly perpendicular to the sun-beam direction have the highest absorbed irradiance (1830 - 2040 umol m" 2 s"1), and are only a small proportion of the sunlit leaves, while (sunlit) leaves parallel to the beam direction absorbed only diffuse radiation (220 - 430 umol m" 2 s"1) and are a high proportion of the sunlit leaves". This statement echoes the view of Norman (1980) (his page 60) "Although leaves oriented nearly perpendicular to the solar beam have the highest photosynthetic rate per unit leaf area, they have the lowest rate per unit soil area because relatively few leaves are so oriented in a canopy with a spherical leaf distribution." In fact, as pointed out by Norman (1979) (his page 254) "In a canopy with foliage spherically distributed, there is a continuous range of flux densities from the full beam flux density (perpendicular to the incident beam) to zero (parallel to the incident beam) because of the range of leaf angles." The continuous distribution of the incident beam flux density for sunlit leaves shown in the Figure 10 of Norman (1979) is reproduced here as Figure C - l . Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 160 de Pury & Farquhar (1997) Q,,-(W/m2) Figure C - l . Comparison of the distribution of the total incident P A R (Qti) on the sunlit leaves at L (total-LAI) = 0.1 modelled by Norman (1979) (the solid line) (i.e., the continuous photon flux densities as a result of leaf-sun angles) with the value obtained using the sun/shade model of de Pury and Farquhar (1997) (the filled circle) (i.e., the average incident P A R for the big sunlit leaf formed by grouping all sunlit leaves together). The direct P A R incident on the big sunlit leaf was calculated as: Qhojncidem = KbQbi) = 0-52feo / s i n P > where Qw is the direct downwelling P A R above the canopy, Kb is the extinction coefficient for Qw, and B is the solar elevation angle. The incident sky diffuse P A R was calculated as Qd = Qdl)e~KiL. Using QM - 427 W m" 2, sin B = 0.95, Qd0 = 128 W m" 2, Kd = 0.7 and L = 0.1 from Table 2 of Norman (1979), Qb0 .ncidal = 225 W m2, and Qd = 119 W m" 2. Qti for the big sunlit leaf is Qd + QMJnciden, =119 + 225 = 344 W m" 2. The un-scattered Qw absorbed by the big sunlit leaf is ( l -cr )Qha i n c j d m l . The fraction of sunlit leaves at canopy depth £ (cumulative L A I ) is given by fsun = e~K"f • Therefore, the total absorbed un-scattered Qw by the sunlit leaves (on the basis of ground area) is given by: IC1 - ^)e„,_,,,,vte,, fsjil = I (1 - a)KhQme-K»ldl = QM) (1 - a)(l - eK+ ), which is Eq. (20b) of de Pury and Farquhar (1997), where the term fSmdl is used as a weighting factor. Disregarding the continuous distribution of direct P A R within the sunlit leaves and using only the averaged direct P A R (i.e., Qm iiwidenl) to calculate the P of the sunlit leaves (see the above integration) makes the same type of errors as using Q,o to calculate P of the entire canopy. The latter is often implemented in the single big leaf models of canopy P. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 161 This means that Psun (photosynthesis of the big sunlit leaf) has to be further partitioned into a light-limited fraction (e.g., for the sunlit leaves receiving 220 pmol m 2 s"1) and a light-saturated fraction (e.g., for the sunlit leaves receiving 1830 pmol m" 2 s"1). Similarly, on partly cloudy days (e.g., Qdo = 900 pmol m" 2 s"1), the top shaded leaves are light-saturated while the bottom shaded leaves are light-limited, and we have to separate the top light-saturated shaded leaves from the bottom light-limited shaded leaves. Unfortunately, the sun/shade model aggregates all the sunlit leaves into one big sunlit leaf (group) and all the shaded leaves into one big shaded leaf (group), and treats each big leaf (group) as a homogenous photosynthetic entity. The A P A R (absorbed P A R ) for the big sunlit leaf is calculated using their Eq . 20 with the weighting of LAIsuniit (the L A I for the sunlit leaves). The A P A R for the big shaded leaf is calculated using their Eq. A26 or Eq. 21 with the weighting of LAIsnaded (the L A I for the shaded leaves). Using the sunlit/shaded LAI-weighted A P A R to calculate Psm and PShaded (photosynthesis of the big shaded leaf) while disregarding the distinctively different photosynthetic responses within each big leaf (group) (e.g., some parallel sunlit leaves are light-limited and some perpendicular sunlit leaves are light saturated) makes the same type of errors as using LAI-weighted A P A R to calculate the P of the entire canopy. In this sense, the errors of the sun/shade model in modelling canopy P are likely worse than those of the single big leaf models, because it uses A P A R twice (i.e., once for the big sunlit and once for the big shaded leaf). Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 162 1.4 Ratio of diffuse to total irradiance Ratio of direct to total irradiance Figure C-2. The contrast in the relationship between L U E and fractions of diffuse/direct irradiance: the hyperbolic relationship predicted by the sun/shade model (a) and the linear relationship predicted by the C U P I D model (b). The labels and units are preserved as in their original papers. In plot (a), Ac is the gross canopy photosynthetic assimilation modeled for a wheat crop. "The fraction of diffuse irradiance was varied by changing the atmospheric transmission coefficient but with constant total irradiance" (page 547 of de Pury and Farquhar 1997). In plot (b), the canopy light-use efficiency [g CO2 (MJ IPAR)" ] ] is based on I P A R (intercepted P A R ) and results are for a C 3 (o) and C 4 (+) canopies. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 163 Using A P A R to calculate Psun and Pshaded led to the mistake shown in their Figure 7b (reproduced here in Figure C-2a), the validity of which has long been questioned (Cohan et al. 2002). Their Figure 7b sharply contrasts with the findings in Norman and Arkebauer 1991 (reproduced here in Figure C-2b) and Choudhury (2000). The response of canopy P for a wheat crop predicted by the sun/shade model to QdolQto in Figure C-2a when QdolQto < 0.5 mainly reflects the response of the shaded leaves. Their sunlit leaves are not responsive to QdolQto at all (i.e., almost always Rubisco-limited as shown in their Figure 11 (reproduced here as Figure C-3), contradicting their statement that a high proportion of the sunlit leaves receive Qdo and are light-limited. When QdolQto > 0.5 (e.g., on partly cloudy and overcast days), the sun/shade model is no longer responsive to the changes in the fraction of diffuse irradiance (Figure C-2a), because the big shaded leaf in the model also switches to being Rubisco-limited, and the P of the entire canopy is incorrectly predicted to be decoupled from the radiation it receives. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 164 CM i £ o £ a. 40 30 20 0 A/Sun / ' - A s // 1 (de Pury & Farquhar 1997) i i i i 600 1200 1800 Canopy absorbed irradiance (Limol nrr2 s - 1 ) Figure C-3. Reproduction of Figure 11 of de Pury and Farquhar (1997) showing the response of the photosynthesis (Ac) of the big sunlit leaf to absorbed irradiance predicted using the sun/shade model. Ajsim and Avs,m are the modelled electron-transport-limited and Rubisco-limited rates of photosynthesis of the big sunlit leaf, respectively. Ac is taken as the minimum of AjSun and Avsun. Symbols and units are preserved as in the original paper. They say on their page 551 that "It is apparent that the sunlit leaves are usually Rubisco-limited (Avsun < AjSun), except when the absorbed irradiance is very low. The fraction of leaves in the sunlit fraction increased from 0% at low irradiance to 56% at the maximum solar elevation". In other words, photosynthesis of the big,sunlit leaf (group) is always limited by its nitrogen content and has little to do with the irradiance it absorbed. For this wheat canopy, the fraction of sunlit leaves can go as high as 56% as they suggested, which means the photosynthesis of 56% of the leaves in this wheat canopy has nothing to do with the irradiance absorbed. This contradicts the fact that a high proportion of sunlit leaves are parallel to the solar beam and their photosynthesis is light-limited (i.e., electron-transport-limited rather than Rubisco-limited). Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 165 In addition, the photosynthetic Rubisco capacity for the big sunlit leaf (Vcsim) is calculated by the sun/shade model using (their Eq . (22)): where Vcmaxo is the photosynthetic Rubisco capacity at the top of the canopy, I is the cumulative L A I from canopy top, and K„ and Kb are the extinction coefficients for the nitrogen and direct solar beam, respectively. The formulation for Vcsun is problematic, because (1) the nitrogen gradient (i.e., Kn) in a canopy is more in a horizontal (i.e., related to leaf age) rather than in a vertical direction (Warren and Adams 2001, Rayment et al. 2002), and (2) it is difficult to scale Vcmaxo from leaf-level to Vcsun at canopy level. For example, using Vcmax0 = 40 pmol m" 2 s"1 and Kn = 0.1 could give the same Vcsun as using 2 1 Vcmaxo = 80 pmol m" s" and Kn = 0.7, therefore Vcmaxo can be parameterized in infinite number of ways as long as its combination withi£„ gives the same VcSlin. In that sense, the leaf-level Vcmax0 in the sun/shade model is not scalable. It can be easily shown that the Q e - M M model results from assuming that quantum efficiency in the M M model increases linearly with the diffuse P A R fraction. Replacing a in the M M model with a = a0(mQd() IQt{) + n) (i.e., using a linear relationship between a and QdolQto suggested by Figure C-2b), gives: p _ g„(/»6rf„/6„)+^)6toAn.x ( 1 ) where m and n are two empirical coefficients for the generalized linear relationship between a and QdolQto- Further expanding the terms in Eq. (1) gives: Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 166 a„ (m + n)(Qd0 + —^- QM ) A m a x P = m±R (2) an(m + n)(Qdi) +—— QM)) + Amm m + n n Let ax =a0(m + n) and k = , then Eq . (2) becomes the Q e - M M model: m + n P = «•(&.)+*&oH,., = g i 6 A « ( 3 ) cc,(Qd,+kQm) + A_ ccQ+A^ where Qe = Qdo + kQw- In fact, the Q e - M M model supports the statement made by de Pury and Farquhar (1997) that a high proportion of the sunlit leaves are parallel to the solar beam and therefore receive mainly diffuse P A H . Thus, it is not surprising that the sun/shade model performed as poorly as the regular M M model (Figure C-4). A s we might have expected, the Q e - M M model has virtually no systematic modeling errors in P with respect to QdolQto- The sun/shade and the M M models both systematically overestimate P in clear conditions and systematically underestimate P in cloudy conditions (Figure C-4). Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 167 Figure C-4. The relative modelling errors of P for a 56-year-old Douglas-fir stand (DF49) obtained using the M M , sun/shade and Q e - M M models. The relative errors of P are calculated as: (PmM - Pmeasurement)lpmeasurement, where P m d l is the half-hourly values of P modeled using the aforementioned three models, and Pmeasurement is the EC-derived half-hourly values of canopy P. Symbols represent bin averages and vertical lines indicate ±1 SD. n = 18,196. This figure is the same as Figure 4-8a in Chapter 4 except that (1) the x axis was changed from Qdo to QdolQto, (2) the y axis was changed to the relative errors of 2 1 P, and (3) only P m d \ and Pmeasurement values greater than 10 umol m" s" were bin averaged. Refer to Figure 4-8a for further details. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 168 We can calculate the coefficient k for the soybean crop (Figure C-2b) by using its relationship between light use efficiency and the ratio of incident diffuse to incident total PAR. Let us rewrite k = n/(m+n) (in Eq. (3)) as: n(m + n) + n-n(m + n) ,„ .n-mn/(l-n) k = -> L i L = „ + (!_„) v L (4) m + n m + n Comparing Eq. (4) with the expression for k given by Eq. (22) of Chapter 4 (i.e., k = cr + (1- cr)(2A:2), where a is the leaf scattering coefficient) shows that n = <7 (5a) and n-mn/(l-n) m + n = 2k2 (5b) where k2 = k,cosy, + Q-~k,) cos yThreshold + ki)(l-ki)AcosyThKshnld given by Eq. (21) in Chapter 4. k2 reflects the fraction of the photosynthetic contribution from the light-limited sunlit leaves (A:,cosy) and that from the light-saturated sunlit leaves (mainly kAcosyj^Mj). From Eq. (5a) and (5b), we can see that the intercept (i.e., cc{)n) and slope (i.e., ai}m) in the linear relationship of a = aa(mQdQIQia +n) (see Eq. (1)) reflect the magnitude of the scattered solar beam in the canopy (i.e., n = a) and the photosynthetic contribution of the sunlit leaves by absorbing un-scattered solar beam, respectively. Let us take the values of light use efficiency for the soybean (the C 3 plant) canopy of Figure C-2b as an example. When QdolQto = 0.1, light use efficiency (a )= 0.02 mol mol"1 by converting the 4 g C02/(MJ IPAR) (i.e., 4 g C02/(MJ IPAR) = 4 g C02/(MJ IPAR) x (1/44 mol C0 2 g"1 C0 2) x (1/4.6 MJ IPAR mol"1 photons IPAR) = 0.02 mol C0 2 Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 169 mol"1 photons IPAR). When QdolQto = 0.9, a = 0.054 mol mol"1 by converting the 11 g C02/(MJ IPAR). Therefore, using a = a0(mQd() /Ql0+n), we have: a()(0Am + n) = 0.020 (6a) a0 (0.9m + n) = 0.054 (6b) Dividing Eq. (6b) by Eq. (6a) gives: (0.9m + n)/(0.1m + n) = 2.7 (7) From Eq. (5a), n = a and the latter is given as 0.15 in the Table 2 of Norman (1980) (i.e., leaf transmittance = 0.05 and leaf reflectance = 0.10). Substituting n = 0.15 into Eq. (7) gives m = 0.41. Substituting m = 0.41 and n = 0.15 into Eq. (6a) or (6b) gives or,, = 0.10. The k value for the soybean canopy can then be calculated as k = n/(m + n) = 0.15/(0.41 + 0.15) = 0.27. 2. Inadequacies in its scaling algorithm The sun/shade model assumes that the P of the big sunlit leaf or the big shaded leaf is either Rubisco-limited or RuBP-limited, ignoring the frequent crossing over of the two limitation curves (Figure C-5). The scaling algorithm used in the sun/shade model is shown in Figure C-5a. The defect of this scaling algorithm has been pointed out by Wang (2000) for the big sunlit leaf. It is difficult to correct this defect because of the uncertainty in determining L\. Actually this scaling algorithm is problematic for the big shaded leaf as well (see Figure 4-16b in Chapter 4). For example, on partly cloudy days, the top shaded leaves are Rubisco-limited, while the bottom shaded leaves are RuBP-limited. The correct algorithm in the sun/shade model should have been (as shown in Figure C-5b): first integrate the Rubisco-limited curve from 0 to L\, then integrate the RuBP-limited curve fromZi toL, and finally sum the two integrations. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 170 , Figure C-5. (a) The scaling algorithm used in the sun/shade model. Integrations of the Rubisco-limited and RuBP-limited curves from 0 to L gives the photosynthetic rates associated with the two limiting processes, respectively. The minimum of the above two integrations is taken as the actual canopy P by the sun/shade model, (b) The correct algorithm for integrating the two limiting processes with the consideration of the crossover point (L\). Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 111 It is worth noting that the big sun and the big shade leaves of the sun/shade model have little correspondence with the sun and shade leaves in the regular plant physiological context. The photosynthetic Rubisco capacity of the big sun (Vcsm) and shade (ycsh) leaves were shown in Figure 10 of de Pury and Farquhar (1997) (reproduced here as Figure C-6a). The Vcsh at night was over 200 pmol m" 2 s"1 while during the day was less than 100 pmol m" 2 s"1, and Vcsh was greater than Vcsun in the early morning (i.e., 6-9 am) and late afternoon (15 - 18 pm) periods (Figure C-6a). The perfect symmetry in the diurnal variation in Vcsh and Vcslin is an artifact of the model. It merely reflects that "the division of the leaves into sunlit or shaded fractions is changing", and has no real physiological meaning, defeating one of the purposes of doing bottom up models of canopy P. The photosynthetic light responses for the sun and shade leaves defined in regular physiological context (Bjorkman et al. 1972) are shown in Figure C-6b. A s a result of the acclimation to (chronic) growth irradiance, the sun leaf (i.e., grown in high light) generally has higher photosynthetic capacity than the shade leaf (i.e., grown in low light). A s mentioned earlier, the sun/shade model failed to account for the crossing over of the Rubisco- and RuBP-limitation curves (Figure C-5). In fact, the scaling algorithm of the sun/shade model is also problematic within each limitation curve even i f we disregard the crossing over. Let us assume that we have a canopy with only three leaves, marked by #1, #2 and #3 respectively in Figure C-6b. Their photosynthesis per unit leaf area can be calculated using Eq. (5) of de Pury and Farquhar as (the term (Ci - T*)/(4Ci +8r*) fo rP , was ignored for simplicity): 0P-(aQ,+J )P + aQ J =0 . (8) r i \ >£s\ai max// i >^tm maxi V / Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 172 where P „ Q,ai and Jmaxi are the photosynthetic rate, total absorbed P A R and maximum electron transport rate for the / t h leaf (i = 1, 2, and 3) per unit leaf area, respectively, a is the quantum use efficiency which is assumed to be the same for all three leaves. ^ is a curvature parameter. Therefore canopy P per unit ground area can be obtained as: p=ipA (9) 2=1 where L , is the L A I for the ilb leaf which is used to convert P , from leaf area basis to ground area basis and P , is obtained from Eq . (8) as: P = }! . Eq . (9) is used in the multi-layer 2<f> models of canopy P (e.g., Eq . (13) of Norman 1980). However, the sun/shade model calculates canopy P of the three leaves as follows (see Eqs. (20) and (22) of de Pury and Farquhar 1997): 0._»g=ilQJ'l (10a) i=l W ^ i X a x A (10b) Canopy P is then obtained by substituting Eqs. (10a) and (10b) into Eq . (8) by conceptually condensing the three leaves into one big leaf, i.e., (ccQ, ,. +J ,. )-J(aQ, h. +J hf-46aQ h. J ~ Comparison of the P obtained using Eq. (9) and Eq . (11) shows the difference in the scaling algorithms between Norman (1980) and de Pury and Farquhar (1997). Using Eq . (11) to calculate canopy P with Jmax_bi8 and Qta_biS as bulk parameters for the aggregated Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 173 big leaf is invalid, because the photosynthetic light responses for the three leaves are different and nonlinear. In the example given in Figure C-6b, leaves #1, #2, and #3 are approximately at the photosynthetic saturating point, near the saturating point, and near the light-limited point, respectively. Even if all the three leaves are located on the linear portions of their respective photosynthetic curves, using Eq . (11) to calculate canopy P still doesn't have a sound mathematical basis, because the three leaves have three Jmax values (i.e., Jmaxi, i = 1, 2, 3) as opposed to having one common Jmax value and have three different L A I values (i.e., L „ i = 1, 2, 3). The sun/shade model assumes leaf level maximum electron transport rate (Jmax) decreases with cumulative L A I (Figure 5 of de Pury and Farquhar is reproduced here as Figure C-6c). A s a result, leaves at different canopy depths have different photosynthetic light responses curves (i.e, different Jmax values) similar to the leaves #1, #2 and #3 shown in Figure C-6b. Using (10a) and (10b) to calculate canopy P involves averaging the irradiance and R u B P capacity profiles, respectively. Thus, it makes the same type of errors in calculating canopy P as the single models of canopy P. Furthermore, hypothesizing an exponential decrease of Jmax with canopy depth is not completely valid, because Jmax was found to be highly related to leaf age and its gradient is very significant in the horizontal direction. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 174 Figure C-6. Comparison of the sun and shade leaves defined by de Pury and Farquhar (1997) and those defined byBjdrkman et al. (1972). The photosynthetic Rubisco capacity for the sun (VcSun) and shade (Vcsh) leaves (Vc = Vcsun + Vcsn) in de Pury and Farquhar (1997) is simply driven by the L A I of the sunlit and shaded fractions of the canopy (a) and has no real physiological meaning. The sun and shade leaves defined in Bjdrkman et al. (1972) are the leaves grown in high light and low light environment, respectively (b). A s a result of the acclimation to the growth irradiance, the leaves grown in high light have higher photosynthetic capacity than the leaves grown in low light. The three filled circles in (b) represent three leaves in a canopy with different photosynthetic capacities and different L A I values (see the example in the main text). The sun/shade model assumes that leaf-level Jmax decreases exponentially with canopy depth (c) and as a result, there is a Jmax profile for the canopy. Therefore, even i f the three leaves (i.e., #1, #2 and #3) in (b) are on the linear portions of their respective photosynthetic light response curves, their Imax values cannot be simply summed up with the multiplication of their respective L A I values to obtain the total photosynthesis of the three leaves (i.e., using Eq . 10b in the main text) because the photosynthetic responses for each of three leaves are very different and nonlinear. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 175 3. Problems in its description of the geometry of light The sun/shade model assumes that the solar beam is composed of parallel rays (Figure C-7a) and consequently divides the canopy foliage as either purely black (sunlit leaves) or purely white (shaded leaves). This representation of the solar beam wi l l severely distort the predicted light environment in a canopy, particularly for a coniferous canopy with small needles. The algorithm should have taken into account the finite size of the solar disk and accounted for the significant effect of penumbrae. A s shown in Figure C-7b, Aabc is similar to Aade, and from the similarity of the two triangles, the shadow length (umbra) can be calculated as: dumbm = 100dieaf since the ratio dsim.earth to dsun is, to a good approximation, 100. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 176 Figure C-7. The shadow of a leaf. In (a), the solar rays are assumed to be parallel in the sun/shade model. In (b) and (c), the shadow cast by a leaf is divided by geometry into the completely shaded umbra and partially shaded penumbra. A Douglas-fir needle is approximately 1 mm wide, so its umbra is no wider than 10 cm. In this schematic, only the shadow of one leaf is shown. In a deep coniferous stand, the umbra and penumbra cast by millions of needles overlap (i.e., multi-fold penumbra) and greatly reduce the heterogeneity in canopy radiation. Note that i f the leaf were replaced by the moon, a total solar eclipse would be observed in the region of the umbra and a partial solar eclipse would be observed in the region of the penumbra. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 111 4. Oversimplified representation of canopy structure. The sun/shade model assumes that the leaves in a canopy are randomly distributed (Figure C-8a) in a manner similar to the randomly moving molecules in a solution, so the Beer's law of light attenuation can be strictly applied to the canopy. But in reality, leaves are clumped (grouped) at several levels: shoots (Figure C-8b), branches, whorls and tree crowns (Figure C-8c), and even groups of trees (Oker-Blom 1986, Chen et al. 1997). The effect of clumping on the measurement of canopy L A I is particularly significant for coniferous stands. For example, for a mature Southern Old Black Spruce (SOBS) stand (part of the B E R M S project), the L A I obtained using the LAI-2000 plant canopy analyzer was approximately 2.3 (i.e., the effective L A I , Le, is 2.3), while that obtained using allometic relationships was 6.3 (see Table 3 of Chen et al. 1997). After accounting for the woody components and clumping effect onLe, the optical L A I was adjusted to 3.9, which is still 40% lower than the allometic L A I . A n y uncertainties in the measurements of canopy L A I w i l l translate into large errors in canopy P obtained using the sun/shade model, because the model is very sensitive to canopy L A I . Also , the clumping of foliage has a significant effect on the sunlit leaf area distribution and P of the foliage in the lower canopy. It remains a great challenge to properly incorporate the effect of clumping on P into the bottom up models of canopy P (e.g., the sun/shade model). Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 178 . (a) (b) (c) (Oker-Blom 1986) Figure C-8. Conceptual models of canopy structure (Oker-Blom 1986). (a) the needles are assumed to be randomly distributed in a canopy as described by the sun/shade model. In reality, the needles are clumped (grouped) into shoots (b) and the shoots are further clumped into tree crowns (c). The clumping of conifer needles at several levels (e.g., shoot- and crown-level) introduces large uncertainties in the canopy L A I obtained using optical methods (e.g., LAI-2000 plant canopy analyzer) and also changes the distribution of sunlit leaf area, both of which w i l l cause great difficulty in parameterizing the sun/shade model and affect its accuracy. Although the Q e - M M model was developed assuming that leaves are randomly distributed in the canopy, the canopy L A I is not a parameter for the Q e - M M model. Thus the Q e - M M model is not susceptible to the errors in the measurements of L A I , and can be used as a simple top down model to study whole canopy photosynthetic behaviour. Appendix C. Inadequacies in the Sun/Shade model (de Pury and Farquhar 1997) 179 In conclusion, the sun/shade model fails to account for the additional non-linearity in P of the big sunlit and shaded leaves, thus making errors as large as those resulting from using single big leaf models. Interestingly, in order to solve the one non-linearity of P of the single big leaf model, the use of the sun/shade model introduces two non-linearities, one for the big sunlit leaf and the other for the big shaded leaf. In order to correct the additional non-linearity in P within the sunlit and shaded leaves, the sun/shade model w i l l become a 4-leaf model, and i f we consider the frequent crossovers in the Rubisco-limited and RuBP-limited rates (Figure C-5b), it w i l l become a 8-leaf model. Furthermore, i f we consider the penumbral effect of the solar beam (Figure C-7b) and the clumping of needles and leaves (Figure C-8c), plus the eventual coupling of the P model with a stomatal conductance model, the two-leaf model becomes very difficult to correct. On the other hand, the extension of the findings of Norman and Arkebauer (1991) (Figure C-2b) leads to a simple modification of the M M model (i.e., the Q e - M M model). Direct (e.g., Anderson et al. 2000) or indirect (e.g., Gu et al. 2002) applications of Norman and Arkebauer's findings have been made over a wide range of ecosystems, such as deciduous forests, coniferous forests, grasslands, and agricultural crops. The success of the Q e - M M model (Figure C-4) in this analysis shows that the findings of Norman and Arkebauer (1991) are valid for a 56-year-old coastal Douglas-fir stand as well . Appendix D. Derivation of two key equations in Norman (1980) 180 Appendix D. Derivation of Two Key Equations in Norman (1980) The multilayer model of canopy photosynthesis developed by Norman (1980) remains the state of the art in canopy photosynthesis modeling. There are two key statements in his model. The first is (on his page 57) "For a canopy with a spherical leaf angle distribution, the fraction of sunlit leaf area exposed at various angles to the sun is independent of solar zenith angle and given by (his Eq . (7), which was rewritten as Eq . (10) in Chapter 4)": fr=sinydy (1) where / is the angle between a sunlit leaf's normal and the solar beam. The second key statement is (on his page 57) "The distribution of leaf inclination angles to the horizontal is the same as the distribution of leaf-sun angles (for a canopy with a spherical leaf angle distribution)". The objective of this appendix is to show the above two key statements graphically. Understanding the above two statements is the key to understand the theory presented in Chapter 4. 1. Derivation of / = sin ydy First let us consider the distribution of the sunlit leaf surface area on a hemisphere. We do this because the leaves with a spherical inclination angle distribution can be arranged exactly to form a sphere (Figure D- l a ) (see also Figure 4-2a). Appendix D. Derivation of two key equations in Norman (1980) 181 Figure D - l . In this schematic, the sun is positioned at the vertical for the sake of convenience. The absolute position of the sun is not a concern because here we are dealing with a sphere (formed by all the sunlit leaves), (a) The leaf area (dS) covered between angle y and y + dy and azimuth angle dy/. dS is obtained as the product of its width (R sin ydy/) and its length (Rdy). (b) The leaf inclination angle to the horizontal (0) equals the angle of incidence, i.e., the angle between the solar beam and leaf normal (y ), because y + rj = 90° and <j> + rj = 90°. The line ac, which is tangent to the hemisphere at the location of the leaf, is parallel to the leaf assuming the leaf is infinitesimally small compared to R. Appendix D. Derivation of two key equations in Norman (1980) 182 We w i l l consider only the upper hemisphere, because the relationships derived for the upper hemisphere hold for the lower hemisphere as well . Also , because the angle distribution of all the sunlit leaves is spherical, the absolute position of the sun doesn't matter any more. For the sake of convenience, let us assume the sun is at vertical as shown in Figure D - l a . The surface area (dS ) of sunlit leaves covered between angle / and y + dy and azimuth angle dy/ is given by: dS = (R sin ydy/)(Rdy) (2) where R is the radius of the hemisphere. The first term (i.e., Rsinydi//) and the second term (i.e., Rdy) on the right hand side of Eq . (2) are the width and length of dS, respectively. The total leaf area covered between y and y + dy over the hemisphere can be obtained by integrating Eq . (2) with respect to y/ from 0 to 2n , i.e., S = ^(R sin ydy/)(Rdy) = 2nR2 sin ydy (3) Thus, the fraction of sunlit leaves exposed at angle between y and y + dy is given by: _ 2nR2 sin ydy t y ~ 2^R2 = sinydy (4) where the term 2nR2 in the denominator of Eq. (4) is the total surface area of the hemisphere, i.e., half the total area of sunlit leaves in the spherical leaf angle distribution. Appendix D. Derivation of two key equations in Norman (1980) 183 2. Showing that "the distribution of leaf inclination angles to the horizontal is the same as the distribution of leaf-sun angles for a canopy with a spherical leaf angle distribution" Let us assume that the leaf inclination angle to the horizontal is (/> as shown in Figure D - l b , and the angle between the solar beam and the leaf's normal, i.e., the angle of incidence, is y. It is reasonable to assume that the leaf is infinitesimally small in comparison with the radius (i.e., R ) of the hemisphere, so the line passing through the leaf's surface (i.e., line ac) can be approximated as the tangent to the hemisphere at that point. Therefore, A s pointed out by Norman (1980) (on his page 57), "The sunlit leaves in the-canopy must be divided into leaf classes that are distinguished by various angles between the leaf normal and the direction of the sun" because the solar beam is unidirectional. Eqs. (4) and (6) are very important, because Eq . (4) allows us to calculate how much the sunlit leaf area is exposed at angle y and Eq . (6) allows us to calculate the beam flux density in that leaf angle class (i.e., y) using Eq. (9) of Chapter 4 (i.e., Qb(y) ~ ( l _ c r ) Q p cos^ , which is essentially the same as the Eq. (9) of Norman (1980)). Refer to Table 4 of Norman (1980) for a worked out example. (5) Then we have: y = <j> (6) Appendix D. Derivation of two key equations in Norman (1980) 184 Using Eqs. (4) and (6), we also can calculate the mean leaf inclination angle of a canopy with spherical leaf angle distribution as: </> = y = ^ / s i n ydy = (sin / - / cos y)\() = 1 (radian) = 57.3° (i.e., 180/tf) (7) where <f> and / are mean angles of <f> and / , respectively. In the integral of Eq . (7), the term sin ydy can be thought of as a weighting factor of / . Therefore, the mean leaf inclination angle is 57.3° for a spherical leaf angle distribution. Appendix E. Comparison of the scaling algorithms of different models of canopy P 185 Appendix E. Comparison of the Scaling Algorithms Used in the Complete Multilayer, 2-leaf Multilayer, 2-leaf Single-layer, MM and Qe-MM Models of Canopy P The objective of this appendix is to compare the scaling algorithms used in complete multilayer (e.g., Norman 1980, Norman and Arkebauer 1991), 2-leaf multilayer (e.g., Sinclair et al. 1976, Spitters 1986, Goudriaan and van Laar 1994, Leuning et al. 1995) and 2-leaf single-layer (e.g., de Pury and Farquhar 1997, Wang and Leuning 1998) models of canopy P with the two single leaf models discussed in this thesis: the M M and Qe-MM models. Each type of the aforementioned models has the same scaling algorithms, although the details within each type models can differ greatly. For example, the 2-leaf single-layer model of Wang and Leuning (1998) has a stomatal conductance sub-model and uses a Michaelis-Menten equation to describe the rate of electron transport while that of de Pury and Farquhar (1997) doesn't have a stomatal conductance sub-model and uses a quadratic equation to describe the rate of electron transport, but the scaling algorithms for the two 2-leaf single-layer models are the same. In this analysis, the only difference between the complete multilayer, 2-leaf multilayer and 2-leaf single-layer models is their scaling algorithms. In other aspects of these models (e.g., leaf-level photosynthetic characteristics), they share the same initial parameters or equations. Also , the effects of stomatal conductance and temperature on canopy P have been ignored in this analysis. Complete multilayer models divide the plant canopy into N layers, and in each layer, the foliage is further divided into sunlit and shaded leaves. In addition, the sunlit Appendix E. Comparison of the scaling algorithms of different models of canopy P 186 leaves of each of the N layers are divided into M leaf inclination angle classes. The scaling algorithm of the complete multilayer model (see Eqs. (12) and (13) and Table 4 of Norman (1980)) can be described as: N M N P = fr^sunj +T, P^ jLSM_i complete multilayer model (1) i=l j=l /=1 where N is the total number of canopy layers (e.g., N = 5), M is the total number of leaf inclination angle classes of the sunlit leaves, and / . is the midpoint angle of each leaf - class (for M = 5, y} = 9°, y2 = 27°, y5 = 81°), fy is the fraction of sunlit leaf area M with leaf angle y. where ^fr =1- Py is the photosynthesis of sunlit leaves with leaf angle y.. Lsunj and Lshdj are the L A I of the sunlit and shaded leaves of the z t h layer, respectively. Pshdj is the photosynthesis of the shaded leaves of the / t h layer. Shaded leaves of each layer only absorb diffuse P A R and scattered direct P A R . Sunlit leaves, in addition, absorb un-scattered direct P A R . Two-leaf multilayer models of canopy P divide the canopy into N layers and in each layer the foliage is divided into sunlit and shaded leaves as in complete multilayer models. However, these models don't further divide the sunlit leaves of each layer into M leaf inclination angle classes. Instead, they reduce the M leaf angle classes of the sunlit _ nil leaves to a single mean leaf inclination angle class (i.e., y = ^ fyy. = 57.3° « 60°, see Appendix D for details). The scaling algorithm of 2-leaf multilayer models can be mathematically described as: • P = I X „ _ + 2-leaf multilayer model (2) Appendix E. Comparison of the scaling algorithms of different models of canopy P 187 where P s l i n _ i is the photosynthesis of the sunlit leaves of the ilh layer. Two-leaf single-layer models further simplify 2-leaf multilayer models of P. Let us assume that leaf-level photosynthesis (Pieaf) can be described using the Michaelis-a Q A Menten equation as: P,, = '" , where a , Q,a and Amax are the quantum use efficiency, total absorbed P A R and maximum photosynthetic capacity, respectively. For the sake of simplicity, let us scale P; e f l / to canopy P using fixed values of a and Amax as it was in Norman (1980) (his Eq . (11)), so different leaves of the canopy have different rates of photosynthesis simply as a result of the differences in their Q,a. According to the scaling algorithm of 2-leaf single-layer models (see Eqs. (20) and (21), and Table 6 of de Pury and Farquhar (1997) for details), canopy P can be described as: P = Psl,„+P,.l, 2-leaf single-layer (3a) H sMfsM^\A_fsuS£)dl P~=-r ~ L (3b) . II 0 ps„ = - T - - ^ 4 (3c) (I 0 where P s u n and PShd are the photosynthesis of the big sunlit and shaded leaves (or groups), respectively. L is the total canopy L A I and £ is the cumulative L A I from canopy top. Qta_sim(£) a n d Qta_shd(i) are the total absorbed P A R by the sunlit and shaded leaves at canopy depth I, respectively. fsim(C) and fshd(t) are the fractions of sunlit and shaded leaves at canopy depth I, respectively. fsm(t) + fsi,A^) = 1- ^ m e plant canopy is Appendix E. Comparison of the scaling algorithms of different models of canopy P 188 divided into infinitesimally small layers (i.e., N is infinitely large), we can write Eq. (2) in its integral form using Eqs. (4a)-(4d): ,L„ =PmW„(*) = P„W„W* (4a) N-xo to*p*< i=P^)L,A?) = PiAOfsM^ (4b) (V->oo Pun (?) = (0An« / ( « & , _ „ (I) + ) (4c) PM O = ( * ) 4 n „ / « * (0 + A n . ) (4d) Substituting Eq. (4) into Eq. (2) yields: Therefore, 2-leaf single-layer models of canopy P are not exactly the integral versions of the 2-leaf multilayer models (compare the Eqs. (3b) and (3c) with the first and second integrals of (5), respectively). Of course, if we substitute Qla sun(£) and Qla shd(t) with the corresponding light penetration equations from Spitters (1986) or Goudriaan and van Laar (1994), it is almost impossible to obtain an analytical solution for the integrals of Eq. (5). The scaling algorithms of the complete multilayer, 2-leaf multilayer and 2-leaf single layer models of canopy P are compared in Figure E - l . In this example, the three a n A models scaled P. , = " to canopy P using Eqs. (1), (2) and (3), respectively. The comparison of the complete multilayer and 2-leaf multilayer models was made in the same manner as it was with the comparison of Case 1 and Case 2 in Norman (1980). Eq. (3) is an extremely simplified version of the Sun/Shade model developed by de Pury and Farquhar (1997). Table 4 of Norman (1980) and Table 6 of de Pury and Farquhar (1997) Appendix E. Comparison of the scaling algorithms of different models of canopy P 189 give detailed descriptions of the complete multilayer and 2-leaf multilayer models, and the 2-leaf single layer models, respectively. A hypothetical plant canopy is used here with the initial parameters for the complete multilayer, 2-leaf single layer and 2-leaf multilayer models given as: a (leaf scattering coefficient for P A R ) = 0.15, L (total canopy L A I ) = 8, a = 0.06 mol mol" 1 and Amax = 20 umol m" 2 s"1. This hypothetical canopy has a perfect spherical leaf inclination angle distribution (also see Appendix D) with no clumping of its leaves, so the assumptions of the models can be fully met. The values of Qdo and Qt0 are the half-hourly diffuse and total P A R measurements (n = 4219) taken from the data set for the 56-year-old Douglas-fir stand (DF49) for the period of Apr i l 1 - September 31, 2004. For the multilayer layer model, the hypothetical canopy was split into 80 layers with an L A I increment of 0.1, and the leaf inclination angles of the sunlit leaves were divided into 45 angle classes (i.e., yx = 1°, y2 = 3 ° , . . . y45 = 89°). The parameters of the M M and Q e - M M models were obtained by fitting the M M and Q e - M M models respectively to the total canopy P obtained using the complete multilayer model. The cxO A fitted M M model is: P = — m a x with a = 0.054 mol mol" 1 and Amax = 50.81 umol « £ ? „ , + A n a x 2 1 m" s" . The term Qto of the M M model is the incident total P A R above the canopy, i.e., Qto = Qdo + Qbo- The fitted Q e - M M model is: P = aQ<A™ with a = 0.052 mol mol" 1, «0 t .+A™x Amax = 103.64 umol m" 2 s"1, k = 0.46 and Qe = Qd0 + kQb0. Figure E - l a shows that P s u n obtained using the 2-leaf multilayer and 2-leaf single layer models has significant systematic errors with respect to QdolQto (the fraction of sky diffuse P A R ) . When QdolQto is close to 1, the relative errors of Psun are close to zero for the 2-leaf multilayer models, because when the incoming irradiance has no direct P A R , Appendix E. Comparison of the scaling algorithms of different models of canopy P 190 ignoring the leaf-sun angles (i.e., ignoring the incidence angles of solar beam) obviously has little consequence for estimating Psun. But when it is in clear conditions (e.g., QdolQto = 0.15), the relative errors of Psim for the 2-leaf multilayer models can be as high as 8% as a result of using a mean leaf inclination angle class to calculate Psun. The relative errors of Psun of the 2-leaf single layer models have a similar trend with respect to QdolQto as those of the 2-leaf multilayer models, but the errors of Psun of the 2-leaf single layer models don't go to zero even when QdolQto approximates 1, i.e., when QdolQto = 1, the 2-leaf single layer models still make approximately 5% errors for Psun. Pshd calculated using the complete multilayer and 2-leaf multilayer models are the N same (i.e., the term ^Pshd tLshd , of Eqs. (1) and (2)). A s a result of the scaling i=i algorithms used in the 2-leaf single layer models (i.e., compare Eq . (3c) with the second integral of Eq . (5)), their relative errors of Pshd are strongly dependent on QdolQto and are as large as 18% (Figure E - lb ) . Interestingly, the relative errors of Psun of the 2-leaf single layer models decrease with QdolQto (Figure E- la ) while their relative errors of Psnd increase with QdolQto (Figure E- lb ) , so the relative errors of total canopy P of the 2-leaf single layer models are almost independent of QdolQto (Figure E - l c ) . The maximum and minimum relative errors of the total canopy P for the M M , 2-leaf single layer, 2-leaf multilayer and Q e - M M models are 12.17% (-11.46%), 11.42% (8.07%), 5.07% (0.04%) and 1.03% (-2.86%), respectively (Figure E - l c ) . Numbers in the brackets are the minimum relative errors. The 5% relative errors of P for the 2-leaf multilayer models are consistent with what was reported in Sinclair et al. (1976), but Sinclair et al. (1976) didn't mention these errors are systematic with respect to Qdo/Qto-Appendix E. Comparison of the scaling algorithms of different models of canopy P 191 Figure E - l d shows the direct comparison of canopy P modeled using the complete multilayer model and P obtained by fitting the Q e - M M model to P values of the former. P ( Q e - M M model) = LOOP (complete multilayer model) - 0.14, r2 = 0.9956, R M S E = 0.5666 pmol m" 2 s"1 and n = 4219. The magnitude of the relative errors of the 2-leaf multilayer and 2-leaf single-layer models may change with total canopy L A I and leaf-level photosynthetic characteristics (e.g., leaf-level Amax), but the trend of the relative errors for these two types of 2-leaf models shown in Figure E - l a , E - l b and E - l c remain the same (date not shown).. In summary, i f we take the complete multilayer models of canopy P as the reference, both the 2-leaf multilayer and 2-leaf single layer models have systematic errors in P with respect to Qdo/Qto as a result of the averaging or simplifying schemes used in those models, although the errors of the latter type are much larger. Total P A R (i.e., Q^) has to be separated into its diffuse and direct components for serious modeling of canopy P . Diffuse P A R (including scattered direct P A R ) can be reasonably assumed to be isotropic and thus is relatively straightforward to be modeled in a canopy. One of the most interesting parts of models of canopy P is to calculate the absorbed un-scattered direct P A R by the sunlit leaves as pointed out by de Wit (1965, his page 16) "To calculate canopy photosynthesis it has to be known what fraction of the light is intercepted at what angles". Ignoring the incidence angles between the sunlit leaves and the solar beam and using a mean incidence angle to calculate Psun is over-simplistic. The excellent agreement between P of the complete multilayer model and P obtained by fitting the Q e - M M model (Figure E - l d ) demonstrates that the Q e - M M model is a promising alternative to the 2-leaf models. Appendix E. Comparison of the scaling algorithms of different models of canopy P 192 Figure E - l . The relative errors of P obtained using the 2-leaf single layer and 2-leaf multilayer, and M M and Q e - M M models. The relative errors of P are calculated as: (p,ndi ~ PcompicJ I Pmmpic,e > w h e r e Pmdi is P modeled using the aforementioned four canopy P models, and Pcomplete is the corresponding P calculated using the complete multilayer model (see main text for details). In plots (a)-(c), symbols represent bin averages and vertical lines indicate ±1 SD. In plot (c), the SD for the 2-leaf multilayer model is too small to be discerned while the SD for the M M model is ignored for the clarity of the plot. The SD of the M M model is approximately 5 times larger than those of the Q e - M M model. Qdo and Qt0 are the sky diffuse P A R and total P A R incident above the plant canopy, respectively. In plot (d), the open circles represent modeled half hourly values of total canopy P.
- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Analysis of the net ecosystem exchange of CO₂ in a...
Open Collections
UBC Theses and Dissertations
Featured Collection
UBC Theses and Dissertations
Analysis of the net ecosystem exchange of CO₂ in a 56-year-old coastal Douglas-fir stand : its relation… Cai, Tiebo 2007
pdf
Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.
Page Metadata
Item Metadata
Title | Analysis of the net ecosystem exchange of CO₂ in a 56-year-old coastal Douglas-fir stand : its relation to temperature, soil moisture and photosynthetically active radiation |
Creator |
Cai, Tiebo |
Publisher | University of British Columbia |
Date Issued | 2007 |
Description | The primary goal of this thesis was to investigate the relationship of canopy photosynthesis (P) to photosynthetically active radiation (PAR) in a 56-year-old coastal Douglas-fir stand (DF49) located on Vancouver Island. Canopy P was calculated as daytime NEP + daytime R[sub e], where NEP and R[sub e] are net ecosystem production of CO[sub 2] and ecosystem respiration, respectively. Half-hourly values of NEP were obtained using an EC (eddy covariance) system consisting of a 3-D sonic anemometer-thermometer and a closed-path infrared gas (CO[sub 2]/H[sub2]O) analyzer, and daytime R[sub e] was inferred by obtaining the intercept of the relationship between half-hourly values of NEP and PAR. Daytime R[sub e] thus obtained was approximately 71-75% of that calculated by applying the logarithmically-transformed relationship between nighttime NEE (-NEP) and soil temperature (T[sub s]) to daytime half hours. Values of R[sub 10] (the rate of R[sub e] at T[sub s] = 10 °C), obtained from both annual nighttime and daytime R[sub e] – T[sub s] relationships, increased linearly with increasing soil moisture when averaged over the active growing season (April 1 - Sept 30). However, the effect of soil moisture on R[sub e] shown on the multi-year scale could not be detected on the seasonal or annual scale probably as a result of the confounding effects of other environmental factors on R[sub e]. The effective PAR (Q[sub e]) contributing to canopy P in this Douglas-fir canopy was well described as Q[sub d0] + kQ[sub b0], with Q[sub d0] and Q[sub b0] being sky diffuse and direct PAR, respectively. The parameter k, which accounts for the total scattering of Q[sub b0] and the non-scattering effect (e.g., penumbral light spreading) of the solar rays, was found to be approximately 0.22 for this stand. While the Michaelis-Menten equation (the MM model) (i.e., P = αQ[sub t0])A[sub max]/(αQ[sub t0]+A[sub max]), where Q[sub t0] = Q[sub d0] + Q[sub b0]) results in significant overestimation of P in sunny conditions and significant underestimation of P in cloudy conditions, its modification into P = αQ[sub e])A[sub max]/(αQ[sub e]+A[sub max]) (the Q[sub e]-MM model) eliminated these systematic errors. When k = 1, the Q[sub e]-MM model reduces to the MM model. The Q[sub e] - MM model is a single big-leaf model, but it avoids the type of errors made in earlier generations of single big leaf models of canopy P, i.e., using APAR (the total absorbed PAR by the canopy) to calculate P. The simplicity of the Q[sub e]-MM model makes it convenient to be incorporated into large-scale carbon climate models. This study also shows that the widely used sun/shade model developed by de Pury and Farquhar (1997) is inadequate, mainly because the sun/shade model fails to account for the incidence angle between the solar beam and individual sunlit leaves. As with the P modeled using the MM model, the modeled P obtained using the sun/shade model has significant systematic errors with respect to Q[sub d0]/Q[sub t0] (the ratio of Q[sub d0] to Q[sub t0]). In contrast, using the Q[sub e]-MM model to estimate canopy P for this Douglas-fir stand eliminated these systematic errors with respect to Q[sub d0]/Q[sub t0]. In addition, the Q[sub e] -MM model developed in this study agrees with the detailed multilayer model of canopy P developed by Norman and Arkebauer (1991) for agricultural crops (i.e., soybean and corn). |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2011-01-20 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0100335 |
URI | http://hdl.handle.net/2429/30753 |
Degree |
Doctor of Philosophy - PhD |
Program |
Soil Science |
Affiliation |
Land and Food Systems, Faculty of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
Download
- Media
- 831-ubc_2007-266908.pdf [ 10.09MB ]
- Metadata
- JSON: 831-1.0100335.json
- JSON-LD: 831-1.0100335-ld.json
- RDF/XML (Pretty): 831-1.0100335-rdf.xml
- RDF/JSON: 831-1.0100335-rdf.json
- Turtle: 831-1.0100335-turtle.txt
- N-Triples: 831-1.0100335-rdf-ntriples.txt
- Original Record: 831-1.0100335-source.json
- Full Text
- 831-1.0100335-fulltext.txt
- Citation
- 831-1.0100335.ris
Full Text
Cite
Citation Scheme:
Usage Statistics
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
data-media="{[{embed.selectedMedia}]}"
async >
</script>
</div>
Our image viewer uses the IIIF 2.0 standard.
To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0100335/manifest