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Vertical distribution of carbon dioxide, water vapour, momentum and energy exchange within and above… Emmel, Carmen 2014

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Vertical distribution of carbon dioxide,water vapour, momentum and energyexchange within and above a foreststand affected by the mountain pinebeetlebyCarmen EmmelA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Atmospheric Science)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)March 2014c? Carmen Emmel 2014AbstractThe mountain pine beetle (MPB) has killed vast areas of pine forest inBritish Columbia, Canada converting forests from carbon sinks to sources.Different management options for these forests exist ranging from notreatment to complete removal of the infested forest (clearcut). The MPBattack and the following management alter the microclimate and carbonbalance of affected stands.An intensive field campaign was conducted in the summer of 2010 in anaffected forest without treatment in the interior of British Columbia. Eddycovariance, radiation, temperature, humidity and carbon dioxide (CO2)measurements were made at seven heights on a tower within and above thecanopy. This dissertation assessed the impact of the MPB attack and thestructure of the disturbed canopy on the contribution of various vegetationlayers (ground, secondary structure, overstory) to exchanges of CO2, watervapour (H2O), momentum and sensible heat.Previous research has shown that forests without treatment canreturn to being carbon sinks faster than clearcut sites. It was hypoth-esized that the rich secondary structure (mostly immature trees thatsurvived the beetle attack) was responsible for this fast recovery. Thecurrent dissertation showed that canopy layers in this sparse and open-canopy stand were aerodynamically well coupled with the atmosphere aboveand allowed 60 % of photosynthetically active radiation to reach the ground.Given these favorable light conditions, the secondary structure wasindeed responsible for a large proportion of the CO2 uptake; however, theunderstory (< 1 m high) contributed at least equally to the CO2 uptake. Adissimilarity in the vertical distribution of sources and sinks of CO2, H2Oand sensible heat was found. The dissimilarity between CO2 and H2O wascaused by the differences in water use efficiency of the different vegetationlayers.iiAbstractGradient-diffusion theory (K-theory) applicability was examined in orderto guide modeling of stand microclimates and growth conditions. Momen-tum flux (shear stress) could be adequately determined using K-theory andan adjusted length scale. In the case of the other scalars, the use of K-theorywas found to be problematic due to counter-gradient fluxes, the inability toresolve gradients and fluxes and/or source scales.iiiPrefaceI was the lead investigator, responsible for the design of the field campaign,data collection, data analysis, as well as paper and thesis manuscriptcomposition. Contributions of others are indicated below.A version of Chapter 2 has been published as: Emmel, C., Paul-Limoges,E., Black, T. A., & Christen, A.: 2013, Vertical Distribution of Radiationand Energy Balance Partitioning Within and Above a Lodgepole Pine StandRecovering from a Recent Insect Attack. Boundary-Layer Meteorology,149(2), 133163. A version of Chapter 3 has been submitted for publicationto Agricultural and Forest Meorology (Emmel, C., Paul-Limoges, E.,Bowler, R., Black, T. A., & Christen, A.: Vertical Distribution of CarbonDioxide Sources and Sinks in a Recovering Mountain Pine Beetle-AttackedLodgepole Pine Stand).Andreas Christen and T. Andrew Black were the supervisory authors,and were involved throughout the project with the design of the studyand the manuscript composition. Eugenie Paul-Limoges helped with thecollection of the data and was supervised by myself. Rebecca Bowlermade leaf-level CO2 assimilation measurements under my supervision andprovided species-specific leaf area indices. The LiDAR-derived leaf areaindex data used in Chapters 2 and 3 was provided by Thomas Hilkerand Nicholas Coops (The University of British Columbia). The NFI dataused in the same two chapters was provided by Tony Trofymow (PacificForestry Centre). Rick Ketler and Zoran Nesic were involved with thetechnical design of the field campaign. Kate Liss, Adrian Leitch andAndreas Christen performed and analyzed the sonic field intercomparisonmeasurements, of which parts are presented in the uncertainty discussionin Chapter 4. Selected figures have been redrawn by the Cartographer ofthe Geography Department, Eric Leinberger.ivTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . vList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of acronyms and symbols . . . . . . . . . . . . . . . . . . xxviiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . xxxviiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and state of knowledge . . . . . . . . . . . . 31.1.1 Carbon and carbon dioxide . . . . . . . . . . . . . 31.1.2 Mountain pine beetle . . . . . . . . . . . . . . . . 51.1.3 Energy balance in canopies . . . . . . . . . . . . . 71.1.4 Turbulent exchange in and above canopies . . . . 81.1.5 Eddy-covariance technique . . . . . . . . . . . . . 122 Vertical distribution of radiation and energy balance par-titioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.1 Conceptual framework . . . . . . . . . . . . . . . 182.2.2 Field campaign . . . . . . . . . . . . . . . . . . . 232.2.3 Quality control and data analysis . . . . . . . . . 312.3 Results and discussion . . . . . . . . . . . . . . . . . . . . 37vTable of contents2.3.1 Spatial variability of canopy structure and radi-ation . . . . . . . . . . . . . . . . . . . . . . . . . 372.3.2 Radiative exchange . . . . . . . . . . . . . . . . . 402.3.3 Energy balance partitioning . . . . . . . . . . . . 442.4 Summary and conclusions . . . . . . . . . . . . . . . . . . 603 Vertical distribution of carbon dioxide sources and sinks 623.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 623.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.1 Measurement site . . . . . . . . . . . . . . . . . . 643.2.2 Instrumentation . . . . . . . . . . . . . . . . . . . 653.2.3 Analysis and corrections . . . . . . . . . . . . . . 713.3 Results and discussion . . . . . . . . . . . . . . . . . . . . 763.3.1 Climatic conditions . . . . . . . . . . . . . . . . . 763.3.2 CO2 fluxes over the course of the campaign . . . . 773.3.3 Diurnal cycle and flux profiles . . . . . . . . . . . 773.4 Comparison of eddy-covariance and ecophysiological ap-proaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.4.1 Ecophysiological results . . . . . . . . . . . . . . . 833.4.2 Comparison . . . . . . . . . . . . . . . . . . . . . 873.5 Water use efficiency . . . . . . . . . . . . . . . . . . . . . 933.6 Summary and conclusions . . . . . . . . . . . . . . . . . . 964 Flux-gradient relationships within and above the canopy 984.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 984.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 1044.3.1 Measurement site . . . . . . . . . . . . . . . . . . 1044.3.2 Instrumentation . . . . . . . . . . . . . . . . . . . 1054.3.3 Calibration . . . . . . . . . . . . . . . . . . . . . . 1084.3.4 Uncertainties . . . . . . . . . . . . . . . . . . . . . 1124.3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . 1154.4 Results and discussion . . . . . . . . . . . . . . . . . . . . 1184.4.1 Zero-plane displacement height and roughnesslength . . . . . . . . . . . . . . . . . . . . . . . . . 1184.4.2 Profiles of scalars and corresponding fluxes . . . . 1194.4.3 Gradient and counter-gradient transport . . . . . 1284.5 Comparison to surface-layer predictions . . . . . . . . . . 1404.5.1 Stability functions . . . . . . . . . . . . . . . . . . 1404.5.2 Eddy diffusivity . . . . . . . . . . . . . . . . . . . 146viTable of contents4.6 Summary and conclusions . . . . . . . . . . . . . . . . . . 1555 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.2 Implications . . . . . . . . . . . . . . . . . . . . . . . . . 1615.3 Technical improvements and potential future work . . . . 161Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165AppendicesA Photographs of the field site and instrumentation . . . 184B Appropriateness of single rotation, double rotation andplanar fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198C Heat flux plate intercomparison . . . . . . . . . . . . . . . 205D Comparing the WPL correction to eddy fluxes based onmixing ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . 208E Vertical profile of tree volume and surface . . . . . . . . 213E.1 Tree taper . . . . . . . . . . . . . . . . . . . . . . . . . . 213E.2 Tree volume fraction . . . . . . . . . . . . . . . . . . . . . 215E.3 Tree surface fraction . . . . . . . . . . . . . . . . . . . . . 216F Energy balance closure and turbulence thresholds . . . 218G Species-specific leaf area index . . . . . . . . . . . . . . . 224H NEP partitioning . . . . . . . . . . . . . . . . . . . . . . . . 227H.1 Non-rectangular hyperbolic fit using daytime NEP . . . . 227H.2 Linear fit under low-light conditions . . . . . . . . . . . . 228H.3 Q10 model based on nighttime data . . . . . . . . . . . . 233H.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 234I Supporting figures and tables from pressure calibration 238J Mixing ratio uncertainties due to propagation of pressureuncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 241J.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 241viiTable of contentsJ.2 Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . 241J.2.1 Water vapour mixing ratio . . . . . . . . . . . . . 241J.2.2 Carbon dioxide mixing ratio . . . . . . . . . . . . 242J.3 Summary and conclusions . . . . . . . . . . . . . . . . . . 243K LI-840 IRGA calibration . . . . . . . . . . . . . . . . . . . 244L Energy balance of the thermocouple wire . . . . . . . . 250M The effect of directional wind shear on calculations ofReynolds stress . . . . . . . . . . . . . . . . . . . . . . . . . 251N Eddy diffusivity profiles using different scaling combina-tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256viiiList of tables2.1 Instrumentation installed on the scaffold tower . . . . . . 252.2 Instrumentation installed in the ground. . . . . . . . . . . 262.3 Stand density, average tree height (H) and average di-ameter at breast height (DBH) of trees that end in eachlayer separated into dead and living, small and largetrees. These numbers do not account for seedlings,saplings and understory broadleaf plants. . . . . . . . . . 302.4 Thresholds for threshold check of turbulence data. . . . . 332.5 Average cell LAI, RMSE and nRMSE in comparison toSspatial for each measurement site. For the plot sitesweighting factors are given, which are used in the cal-culation of Sspatial. . . . . . . . . . . . . . . . . . . . . . . 402.6 Number of cases with unstable, neutral and stable con-ditions that were used in the daytime (Sin above thecanopy > 5 W m?2), nighttime (Sin above the canopy= 0) and 24-h analysis. . . . . . . . . . . . . . . . . . . . 442.7 Energy balance closure (EBC, in %) during nighttime atall seven levels (z/h) when using no threshold and whenusing different u? thresholds. The number of records(N) included in the analysis for each threshold is alsoshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.1 Selected instrumentation installed on the scaffold tower . 683.2 Source/sink strength in the three vegetation layers(understory, secondary structure and overstory)determined using the eddy-covariance (EC) and theecophysiological approaches (EP), and photosyntheticand respiratory flux divergence determined using theEC measurements and the LL method . . . . . . . . . . . 93ixList of tables4.1 Instrumentation and measurements conducted at eachof the seven levels (1.2-, 2.7-, 7.6-, 11.9-, 16.5-, 21.0-and 26.8-m heights). One instrument of each type wasinstalled at each level except the LI-840 IRGA wherethere was only one instrument installed at the bottomof the tower, which sampled air sequentially from eachlevel through synflex tubing. . . . . . . . . . . . . . . . . . 1074.2 Properties of six canopies of which the horizontal meanwind and shear stress profiles are shown in Fig. 4.5 . . . . 1194.3 Root mean square error (in m2 s?1) of measured KMcompared to predicted KM for the four scaling combi-nations described in Fig. 4.2 for three stability regimes. . 1534.4 Same as Table 4.3 but for KH . . . . . . . . . . . . . . . . 1534.5 Same as Table 4.3 but for KE . . . . . . . . . . . . . . . . 1544.6 Same as Table 4.3 but for KC . . . . . . . . . . . . . . . . 154A.1 ID, tree species, status and bole circumference at breastheight for all trees on which bole respiration measure-ments were performed. . . . . . . . . . . . . . . . . . . . . 195B.1 Rotation angles for planar fit . . . . . . . . . . . . . . . . 200B.2 Linear fit coefficients and correlation coefficients for u?w?of double rotation vs. planar fit and single rotation vs.planar fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 204C.1 New calibration factors (in W m?2 mV?1). . . . . . . . . 207E.1 Number (Nt), average height and average DBH of deadtrees by layer they end in. . . . . . . . . . . . . . . . . . . 214E.2 Number (Nt), average height and average DBH of livetrees by layer they end in. . . . . . . . . . . . . . . . . . . 214E.3 Bole volume fractions (?tree, m3 m?3) for each layer andtree status in 2006. . . . . . . . . . . . . . . . . . . . . . . 216E.4 Bole surface area fractions (BAI, m2 m?2) for each layerand tree status in 2006. . . . . . . . . . . . . . . . . . . . 217F.1 Visually determined u? thresholds when using u? at thesame level (u?,z) and above the canopy (u?,top) for theseven measurement levels. . . . . . . . . . . . . . . . . . . 219F.2 Visually determined ?w thresholds when using ?w at thesame level (?w,z) and above the canopy (?w,top). . . . . . 219xList of tablesG.1 Average species specific data from MPB-03: tree diam-eter at breast hight (DBH), plant density, foliage mass,specific leaf area (SLA) and leaf area index (LAI) (fromBowler et al., 2012). Numbers in brackets are standarddeviations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 225G.2 Contributions of broadleaf and coniferous vegetation tothe three vegetation layers. . . . . . . . . . . . . . . . . . 226H.1 This table contains the fitting parameters of the non-rectangular hyperbolic functions for each level deter-mined based on half-hourly averaged data using PARzand PARtop. It also gives the root mean square error(RMSE) of the data compared to the fitted lines. . . . . . 233H.2 This table contains the fitting parameters (slope and R= -intercept) of the linear fit for each level determinedbased on 30-min averaged low-light-level daytime dataeither using PAR at each level (PARz) or PAR abovethe canopy (PARtop). It also gives the root mean squareerror (RMSE) of the data compared to the fitted lines. . . 234H.3 This table contains the mean and standard deviation(STD) of nighttime NEPz. . . . . . . . . . . . . . . . . . . 236I.1 Slopes and offsets from linear regression and coefficientsof determination for z/h = 0.14 to 1.05 compared topressure at z/h = 1.34. . . . . . . . . . . . . . . . . . . . . 240I.2 Height corrections and the total calibration offset (offsetfrom linear fit + height correction) for the pressure ateach level . . . . . . . . . . . . . . . . . . . . . . . . . . . 240M.1 Absolute and relative root mean square deviation(RMSD) of u?w? from results of Eq. M.3. . . . . . . . . . . 254xiList of figures1.1 Normalized wind speed (a) and momentum flux(b) reported from different measurement studies inforest canopies under mainly neutral or unstableconditions. The wind profile shows a typical inflectionpoint at the top of the canopy. The momentum fluxdecreases rapidly with depth into the canopy andstays approximately constant above. Details about thestudies are given in Table 4.2 in Chapter 4. LAI is theleaf area index. . . . . . . . . . . . . . . . . . . . . . . . . 101.2 Side view (a) and plan view (b) of the footprint [modi-fied with permission after Oke et al. (in prep.)]. . . . . . . 141.3 Photograph of an EC system showing an ultrasonicanemometer CSAT3, an open-path gas infrared ana-lyzer (IRGA) LI-7500 and a thermocouple (photographtaken by Andreas Christen). . . . . . . . . . . . . . . . . . 142.1 Schematic of levels and layers. A level is a measurementheight, while a layer is a stratum between two measure-ment heights. Level, layer midpoint and canopy heightsas well as stand structure [understory (0 ? 1 m), sec-ondary structure (1 ? 8 m) and overstory (8 ? 20 m)]height are indicated. . . . . . . . . . . . . . . . . . . . . . 192.2 Photograph of the mountain-pine-beetle-attacked standadjacent to the Crooked River Regional Park. This pho-tograph was taken on 12 July 2010 from the top of themeasurement tower (30 m) in a south-west direction. . . . 23xiiList of figures2.3 Map of a 200 m ? 200 m domain (black grid with 40m ? 40 m cells) centered on the flux tower showingcanopy LAI (colours) with a 5-m resolution, the 24-habove-canopy cumulative flux footprint (white contourlines), the three plots where ground-level Sin was mea-sured and the three positions of the roving tripod. Thewind rose at bottom left shows the average 24-h wind-direction distribution above the canopy during the fieldcampaign. . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.4 Average diurnal cycles of radiation fluxes and air tem-perature for the period from 13 July 2010, 16:00 PSTto 3 August 2010, 15:30 PST: a) Sin and Sout at the1-m height and above the canopy, Sspatial at the groundand extraterrestrial shortwave irradiance (Sext), b) Linand Lout at the 1-m height and above the canopy, c) netradiation at all levels with radiation measurements andd) air temperature at all levels and just-below-the-barkbole temperature for a dead tree at 1.3-m height. . . . . . 412.5 Ensemble-averaged diurnal courses of QH , QE and QS+QG at z/h = 0.06 and z/h = 1.34 for the time periodfrom 13 July 2010, 16:00 PST to 3 August 2010, 15:30PST. The diurnal courses of Q? at the two heights areshown in Fig. 2.4. . . . . . . . . . . . . . . . . . . . . . . 462.6 Ensemble-averaged daytime flux densities of all energybalance terms for the time period from 13 July 2010,16:00 PST to 3 August 2010, 15:30 PST. Numbers in thebars are the relative contribution of each component tothe energy balance of the given level in %. The residualis calculated as Q? +QH +QE +QS +QG. . . . . . . . 472.7 Ensemble-averaged daytime divergences of net radiationand the turbulent fluxes (a) and rates of change of stor-age (b) for the time period from 13 July 2010, 16:00PST to 3 August 2010, 15:30 PST. ?QG/?z was ?7.72W m?3 in the lowest layer. . . . . . . . . . . . . . . . . . 482.8 Average Bowen ratio (?) at 08:00, 11:00, 14:00 and 17:00PST and ensemble-averaged daytime Bowen ratio i.e.,(daytime total QH)/(daytime total QE). . . . . . . . . . . 522.9 Same as Fig. 2.6 but for nighttime. . . . . . . . . . . . . . 542.10 Same as Fig. 2.7 but for nighttime. ?QG/?z was 6.22W m?3 in the lowest layer. . . . . . . . . . . . . . . . . . 55xiiiList of figures2.11 Same as Fig. 2.6 but showing averaged 24-h profiles.Averaged daily total flux densities (MJ m?2 day?1) arealso indicated on the x-axis at the top. . . . . . . . . . . . 582.12 Same as Fig. 2.7 but showing averaged 24-h pro-files. Averaged daily total flux-density divergences(MJ m?3 day?1) are also indicated on a secondaryx-axis at the top. ?QG/?z was ?3 W m?3 or ?0.26MJ m?3 day?1 in the lowest layer. . . . . . . . . . . . . . 593.1 Photograph of the forest structure in the MPB-attackedstand: dead mature pine trees, sparse living secondarystructure and widespread ground coverage in the under-story. This photograph was taken on 9 July 2010 justbefore the start of the field campaign close to the tower. . 663.2 Average profile of LiDAR-derived leaf area density(LAD) (blue) in 2006 and assumed LAD of living vege-tation in 2010 as used in the ecophysiological approachbased on on-ground destructive LAI measurements(green). Below the 3-m height (z/h = 0.15) LAD basedon LiDAR data cannot be determined since the signalcannot be separated from ground returns. . . . . . . . . . 673.3 (a) Half-hourly averages of above-canopy photosynthet-ically active radiation (PAR), (b) half-hourly averagesand daily average air temperature Ta at the 6-m heightdetermined from HMP measurements, (c) half-hourlyaverages of vapour pressure deficit (D) at the 6-m heightdetermined from HMP measurements, (d) half-hourlyaverages of soil temperature (Ts) at the 0.025-m depth,(e) half-hourly averages of volumetric soil water con-tent (?s) at the 0.1-m depth and daily total precipita-tion, and (f) daily (24-h) average evaporative fraction(QE/(QE +QH)) and Bowen ratio (?) above the standfor the three-week period of the campaign in 2010. . . . . 78xivList of figures3.4 Ensemble-averaged half-hourly profiles of incomingphotosynthetically active radiation (PAR) normalizedby PAR above the canopy (PARtop) at 05:00 (105?mol m?2 s?1, 9.3 ? solar altitude), 08:00 (847?mol m?2 s?1, 34.9 ?), 11:00 (1483 ?mol m?2 s?1,53.7 ?), 14:00 (1350 ?mol m?2 s?1, 47.3 ?), 17:00 (729?mol m?2 s?1, 23.4 ?) and 20:00 (40 ?mol m?2 s?1,?0.9 ?). Ensemble-averaged PARtop and solar altitudevalues are given in parentheses. Sketches if treesand bushes indicate where the understory, secondarystructure and overstory layers where located. . . . . . . . 793.5 Half-hourly averages of NEEz over the course of thecampaign in 2010 just above the understory (z/h =0.06), at the top of the secondary structure (z/h = 0.6)and above the canopy (z/h = 1.34). . . . . . . . . . . . . 803.6 Ensemble-averaged diurnal cycle of (a) CO2 molefraction (c, measured with LI-840 and expressed as?mol mol?1 moist air), (b) standard deviation of thevertical wind velocity (?w), (c) measured CO2 fluxdensity (Fc), (d) rate of CO2 storage change (?Fs)below each level and (e) air-column-storage correctedCO2 flux density (NEEz) at the seven levels. . . . . . . . 813.7 (a) Ensemble-averaged air-column storage correctedflux profiles at different times of the day: 00:00, 04:00,08:00, 12:00, 16:00, 20:00 PST. The red hexagon showsthe spatially and temporally averaged soil respirationmeasured with the portable chamber system, whichwas used as the lower boundary condition for CO2source strength calculations of the lowest layer. (b)Ensemble-averaged daytime and nighttime profiles ofCO2 source strength. All profiles were determined fromEC measurements. . . . . . . . . . . . . . . . . . . . . . . 84xvList of figures3.8 (a) Ensemble-averaged daytime gross photosynthetic(P ) and respiratory (R) flux density (cumulative Por R for ecosystem below z/h) using the followingpartitioning methods: linear fit to low-light leveldaytime data (LL) using PAR at each level (PARz)and using PAR above the canopy (PARtop), fitting anon-rectangular hyperbolic function (NRHF) usingPARz and PARtop, and partitioning based on averagenighttime (NT) data. The red hexagon shows thespatially and temporally averaged soil respiration mea-sured with the portable chamber system, which wasused as the lower boundary condition for respiratoryflux divergence calculations for the lowest layer. (b)Flux divergence of P and R based on LL using PARz.All profiles were determined from EC measurements. . . . 853.9 Measured (symbols) and fitted (solid lines) light re-sponse relationships for foliar net assimilation rate of(a) conifer trees (Aco) and (b) understory broadleaf veg-etation (Abr). Solid lines are the fitted light responsecurves for D = 0.5 (black), 1.5 (purple), 2.5 (red), 3.5(yellow) and 4.5 kPa (green). (c) Dependence of livebole respiration (Rb,l) on bole temperature (TB). Thesolid line is a linear fit using a logarithmic transformation. 863.10 Half-hourly NEE contributions (?NEEz) over thecourse of the campaign in 2010 of the three vegetationlayers ((a) understory, (b) secondary structure and(c) overstory) determined using the eddy-covariance(EC) and ecophysiological (EP) approaches and (d)NEE determined using the two approaches. Someindividual values of measured Fc that were larger than10 ?mol m?2 s?1 and smaller than -15 ?mol m?2 s?1are not shown. Two days at the bginning of thecampaign were not used for the comparison because ofmissing bole temperatures. . . . . . . . . . . . . . . . . . . 88xviList of figures3.11 Ensemble-averaged diurnal cycle of the NEE contribu-tions (?NEEz) of the three vegetation layers ((a) under-story, (b) secondary structure and (c) overstory) deter-mined using the eddy-covariance (EC) and ecophysio-logical (EP) approaches and (d) NEE determined usingthe two approaches for the period 15 July to 15 August2010. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.12 Ensemble-averaged vertical distribution of CO2 sourcesand sinks (Sc) summarized for the three vegetation lay-ers based on (a) the eddy covariance approach and (b)the ecophysiological approach. . . . . . . . . . . . . . . . 913.13 Ensemble-averaged daytime (a) P and E and (b) WUEand WUEi over the entire campaign. (c) Ensemble-averaged daytime WUE and WUEi for the first (14 to20 July), second (21 to 27 July) and third week (28 Julyto 3 August) of the campaign. . . . . . . . . . . . . . . . . 954.1 Predictions of the stability functions (?) for the surfacelayer. The stability functions for sensible heat (?H),latent heat (?E) and CO2 (?C) are expected to behavethe same way. The stability function predictions formomentum (?M ) differ under unstable conditions from?H , ?E and ?C , while they are all the same for stableconditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.2 The four combinations of scaling types (global and lo-cal) and scaling height types. . . . . . . . . . . . . . . . . 1054.3 Pressure at the six levels after the calibration coeffi-cients including the height offsets were applied. Red:z/h = 0.06, orange: z/h = 0.14, light green: z/h =0.38, dark green: z/h = 0.60, turquoise: z/h = 0.83,blue: z/h = 1.05 , black: z/h = 1.34. . . . . . . . . . . . . 1104.4 LI-840 IRGA mc measurements of the CO2 span gasbefore and after the calibration and actual CO2 spangas concentrations. CO2 span gas concentrations variedover the course of the campaign. . . . . . . . . . . . . . . 111xviiList of figures4.5 Ensemble averaged profiles of the horizontal mean windspeed (u) normalized by the wind speed at canopyheight (u(h)) and ensemble averaged profiles of shearstress (?) normalized by ? at z/h = 1.34 (?top) for3-h periods of the day and four stability regimes. Thenormalization values are given in coloured numbers.Numbers in brackets are number of half hours includedin the statistics of each profile. The grey lines areprofiles determined in other studies, which were notseparated by time, but were mainly measurementsunder unstable or neutral conditions. . . . . . . . . . . . . 1234.6 Ensemble averaged height of inflection point (zinfl) nor-malized by the canopy height (h) for 3-h periods (a)and for different stability conditions (b). Numbers be-low bars give the number of half-hours included in thecalculations of the boxplot. . . . . . . . . . . . . . . . . . 1244.7 Ensemble averaged profiles of the potential temperature(?) and sensible heat flux (QH) for 3-h periods of the dayand different stability regimes. Numbers in brackets arenumber of half hours included in the statistics of eachprofile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.8 Ensemble averaged profiles of the H2O mixing ratio(mq) and latent heat flux (QE) for 3-h periods of theday and different stability regimes. Numbers in brack-ets are number of half hours included in the statisticsof each profile. . . . . . . . . . . . . . . . . . . . . . . . . 1264.9 Ensemble averaged profiles of the CO2 mixing ratio (mc)and CO2 flux (Fc) for 3-h periods of the day and differ-ent stability regimes. Numbers in brackets are numberof half hours included in the statistics of each profile. . . 1274.10 Ensemble-averaged relative frequencies of occurrence ofshear stress corresponding to counter-gradient (red) andgradient diffusion (blue) for each hour of the day andthe six layers. White areas show the relative frequencyof half hours when either the flux or the wind gradientwas smaller than the uncertainties and gradient diffu-sion conformity could not be determined reliably. Redand blue numbers give the ensemble-averaged 24-h rela-tive frequency (in %) of occurrence of counter-gradientand gradient fluxes, respectively. . . . . . . . . . . . . . . 130xviiiList of figures4.11 Same as Fig. 4.10 but for sensible heat flux. . . . . . . . . 1314.12 Same as Fig. 4.10 but for H2O flux. . . . . . . . . . . . . 1324.13 Same as Fig. 4.10 but for CO2 flux. . . . . . . . . . . . . 1334.14 Kinematic shear stress (?/?) vs. horizontal mean windspeed gradient (?u/?z) for the six layers and differ-ent stability conditions. Each point represents one 30-min average. Counter-gradient transport occurred whenpoints lie in the top left or the bottom right quadrant.Grey bands around the zero lines are uncertainty bands.The four numbers in the corners show how many 30-minvalues lie in each quadrant including the uncertaintybands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1364.15 Same as Fig. 4.14 but for kinetic sensible heat flux(QH/(?cp)) and mean potential temperature gradients(???/?z). . . . . . . . . . . . . . . . . . . . . . . . . . . 1374.16 Same as Fig. 4.14 but for water vapour flux (QE/?)and mean H2O density gradients (???q/?z). . . . . . . . 1384.17 Same as Fig. 4.14 but for CO2 flux (Fc) and mean CO2density gradients (???c/?z). . . . . . . . . . . . . . . . . 1394.18 Stability functions for shear stress, where red crossesare 30-min averaged results from this study, while blackdots are bin averaged results from this study and theblack line is the surface-layer prediction. . . . . . . . . . . 1424.19 Same as Fig. 4.18 but for sensible heat flux. . . . . . . . . 1434.20 Same as Fig. 4.18 but for H2O flux. . . . . . . . . . . . . 1444.21 Same as Fig. 4.18 but for CO2 flux . . . . . . . . . . . . . 1454.22 Measured (red) and predicted (grey) eddy diffusivitiesfor shear stress (KM ) for three stability regimes. Theprediction uses the local scaling and the adjusted zs(combination IV). The numbers in brackets are thenumber of half hours included in the analysis. . . . . . . . 1484.23 Same as Fig. 4.22 but for KH . . . . . . . . . . . . . . . . 1494.24 Same as Fig. 4.22 but for KE . . . . . . . . . . . . . . . . . 1504.25 Same as Fig. 4.22 but for KC . . . . . . . . . . . . . . . . . 1514.26 Median values of KM , KH , KE and KC under unstable,neutral and stable conditions for the six layers. Notethat different scales are used on the x-axis . . . . . . . . . 152xixList of figuresA.1 Photographs of the three vegetation layers: (a) under-story vegetation, (b) secondary structure and (c) over-story vegetation. . . . . . . . . . . . . . . . . . . . . . . . 184A.2 Panorama view (360 ?) of the MPB-attacked lodgepolepine stand adjacent to Crooked River Provincial Park(MPB-03) taken from the top of the flux tower (30 m).Photograph provided by Dr. Thomas Hilker. . . . . . . . 185A.3 Photograph of MPB-attacked lodgepole pine standadjacent to Crooked River Provincial Park (MPB-03)taken from the top of the flux tower (30 m) on 12 July2010 in a west direction. . . . . . . . . . . . . . . . . . . . 186A.4 Photograph of the measurement tower with the sevenmeasurement levels equipped with eddy-covariance sys-tems, inlets for the closed-path infrared gas analyzerand radiometers. In the center part of the tower therain gauge (TE525M, Campbell Scientific (CSI), Logan,Utah) can be seen. Just below the top of the tower, apropeller-vane anemometer (model 05103 R.M. YoungInc., Traverse City, MI) was installed. Photograph wastaken from south of the tower. . . . . . . . . . . . . . . . 187A.5 Eddy-covariance systems at the seven levels lookingfrom the tower towards the west. . . . . . . . . . . . . . . 188A.6 Box containing the closed-path infrared gas analyzer(LI-840) and a CR1000 datalogger. . . . . . . . . . . . . . 189A.7 Photograph of the eddy-covariance system at the z =1.2-m height showing the open-path infrared gas ana-lyzer (LI-7500, LI-COR Inc., Lincoln, Nebraska), theultrasonic anemometer (CSAT3, CSI) and the thermo-couple. The funnel of inlet for the closed-path (LI-840,LI-COR) infrared gas analyzer and the solenoids con-nection for the supply of the calibration gas. . . . . . . . . 190xxList of figuresA.8 A sample of the radiometer used in the field campaign:(a) four-component net radiometer (CNR-1, Kipp & Zo-nen B.V., Delft, The Netherlands (K&Z)) and quan-tum sensors (SQ-110, Apogee Instruments Inc., Logan,Utah) installed on tripod, (b) two four-component netradiometers (CNR-1) during the in-field radiometer in-tercomparison at the beginning of the field campaign(one was later installed on the tripod, while the otherone stayed at the tower top) and one quantum sensor(LI-190, LI-COR), which was continuously installed atthe tower top, (c) net radiometer (NR Lite, K&Z) in-stalled at the 2.7-m height and (d) pyranometer (CM5,K&Z) installed on the ground. . . . . . . . . . . . . . . . 191A.9 Hemispherical photographs taken at the ground pyra-nometer locations (P1A to P3C), the tripod locations(T1 to T3) and the tower. The tower photograph wastaken in the summer of 2007 by Mathew Brown. Allother photographs were taken in July 2010. . . . . . . . . 192A.10 (a) Manual portable chamber system equipped with aclosed-path infrared gas analyzer (LI-800, LI-COR) anda temperature and relative humidity probe (HMP35CF,CSI) using an opaquely covered chamber while measur-ing bole respiration. (b) The clear chamber while mea-suring at a soil location. The quantum sensor attachedto the system can also be seen in this photograph. . . . . 193A.11 All trees on which bole respiration measurements wereperformed. The numbers refer to the tree codes givenin Table A.1. . . . . . . . . . . . . . . . . . . . . . . . . . 194A.12 All soil locations where soil respiration measurementswere performed. The numbers refer to the soil collarID, where the roman number indicates to which of thesix plots the collar belongs. Photographs of I-1, I-2 andIII-3 were taken at the end, while all other photographswere taken at the beginning of the field campaign. . . . . 196A.13 (a) The portable photosynthesis system (LI-6400, LI-COR) and (b) the attached transparent cuvette andquantum sensor. . . . . . . . . . . . . . . . . . . . . . . . 197xxiList of figuresA.14 Location of bole temperature measurements. Greentape covers the entry holes for the bole thermocouples.All thermocouples were connected to a multiplexer lo-cated in the white box. . . . . . . . . . . . . . . . . . . . . 197B.1 Wind inclination (?) vs. wind direction (WD) at theseven levels (a: 1.2 m, b: 2.7 m, c: 7.6 m, d: 11.9 m,e: 16.5 m, f: 21.0 m and g: 26.8 m) before any rotationor planar fit was applied. Wind direction is directionrelative to magnetic geographic North. Each dot is a30-min average from 14 July to 3 August 2010. . . . . . . 199B.2 Same as Fig. B.1 but after planar fit was applied . . . . . 199B.3 Photograph of the lower half of the measurement towershowing the wooden roof structure installed close to thelevel at the 7.6-m height. The photograph is taken fromWest of the tower looking East. The photograph wastaken by the author. . . . . . . . . . . . . . . . . . . . . . 201B.4 (a - g) Momentum flux (u?w?) based the three rotationapproaches (green: single rotation, red: double rotationand black: planar fit) at the seven levels (a: 1.2 m, b:2.7 m, c: 7.6 m, d: 11.9 m, e: 16.5 m, f: 21.0 m andg: 26.8 m) on 24 July 2010. (h) Half-hourly averagedhorizontal wind (u) measured at the seven levels (red:1.2 m, orange: 2.7 m, light green: 7.6 m, green: 11.9 m,turquoise: 16.5 m, blue: 21.0 m and black: 26.8 m) onthe same day. . . . . . . . . . . . . . . . . . . . . . . . . . 202B.5 (a - g) Kinematic momentum flux (u?w?) determinedwith double rotation vs. planar fit (blue: linear fit) andu?w? determined with single rotation vs. planar fit (red:linear fit) at the seven levels (a: 1.2 m, b: 2.7 m, c: 7.6m, d: 11.9 m, e: 16.5 m, f: 21.0 m and g: 26.8 m). Everydot stands for a 30-min period between 14 July and 3August 2010. The lines are linear regressions fitted tothe red and blue dots. . . . . . . . . . . . . . . . . . . . . 203C.1 Insulated sand chamber used to calibrate heat fluxplates. The chamber was heated by a central heaterplate powered by an Anatek 50V/1A power supply.Photograph taken by Trevor Baker. . . . . . . . . . . . . . 205xxiiList of figuresC.2 Voltage measured by the each HFP plotted against thereference HFP heat flux (QG,ref) for (a) F239in, (b)F239out, (c) F579in and (d) F579out. The equationsof the linear regression and the correlation coefficients(R2) are also shown. . . . . . . . . . . . . . . . . . . . . . 207D.1 Comparison of the latent heat flux density based on in-stantaneous mixing ratio (QE,inst) and using the WPLcorrection (QE,WPL). Each dot stands for one half hour.The black lines show the 1:1 line. The equations ofthe linear regressions and the Pearson correlation coef-ficients are also given. . . . . . . . . . . . . . . . . . . . . 211D.2 Comparison of the CO2 flux density based on instanta-neous mixing ratio (Fc,inst) and using the WPL correc-tion (Fc,WPL). Each dot stands for one half hour. Theblack lines show the 1:1 line. The equations of the linearregressions and the Pearson correlation coefficients arealso given. . . . . . . . . . . . . . . . . . . . . . . . . . . . 212F.1 Half-hourly energy balance closure (EBC, black crosses)for all seven levels plotted against the equivalent of thefriction velocity at the same level (u?,z), showing closureranging from 0.5 to 1.5. The red lines show the u?,zthresholds as listed in Table F.1. . . . . . . . . . . . . . . 220F.2 Half-hourly energy balance closure (EBC, black crosses)for all seven levels plotted against the friction velocityabove the canopy (u?,top), showing closure ranging from0.5 to 1.5. The red lines show the u?,top thresholds aslisted in Table F.1. . . . . . . . . . . . . . . . . . . . . . . 221F.3 Half-hourly energy balance closure (EBC, black crosses)for all seven levels plotted against the standard devia-tion of the vertical wind at the same level (?w,z), show-ing closure ranging from 0.5 to 1.5. The red lines showthe ?w,z thresholds as listed in Table F.2. . . . . . . . . . 222F.4 Half-hourly energy balance closure (EBC, black crosses)for all seven levels plotted against the standard devi-ation of the vertical wind above the canopy (?w,top),showing closure ranging from 0.5 to 1.5. The red linesshow the ?w,top thresholds as listed in Table F.2. . . . . . 223xxiiiList of figuresH.1 Daytime NEPz plotted against PARz for all seven levels.Crosses are 30-min averaged data and dashed lines arethe corresponding fits for the 30-min averaged data. . . . 229H.2 Daytime NEPz plotted against PARtop for all seven lev-els. Crosses are 30-min averaged data and dashed linesare the corresponding fits for the 30-min averaged data. . 230H.3 Low-light level daytime NEPz plotted against PARz forall seven levels. Crosses are 30-min averaged data andsolid lines are the corresponding linear fits for the 30-min averaged data. . . . . . . . . . . . . . . . . . . . . . . 231H.4 Low-light level daytime NEPz plotted against PARtopfor all seven levels. Crosses are 30-min averaged dataand solid lines are the corresponding linear fits for the30-min averaged data. . . . . . . . . . . . . . . . . . . . . 232H.5 Nighttime NEPz plotted against Ta for all seven levels.Crosses are 30-min averaged data and solid lines are thecorresponding Q10 fits for the 30-min averaged data. . . . 235H.6 Respiratory (R) flux density profiles (cumulative R forecosystem below z/h) based on 30-min averaged datadetermined with the following partitioning methods:(a) partitioning based on average nighttime (NT) data,fitting a non-rectangular hyperbolic function (NRHF)using (b) PARz and (c) PARtop as well as linear fitto low-light-level daytime data (LL) using (d) PARat each level (PARz) and (e) using PAR above thecanopy (PARtop). Error bars are standard deviationsdetermined with the bootstrapping analysis. (f) showsall R profiles in one plot. . . . . . . . . . . . . . . . . . . 237I.1 Pressure (p) at the six levels before any calibration wasapplied. Orange: z/h = 0.14, light green: z/h = 0.38,dark green: z/h = 0.60, turquoise: z/h = 0.83, blue:z/h = 1.05 , black: z/h = 1.34. . . . . . . . . . . . . . . . 238I.2 Correlation between the pressure at each level and thepressure at z/h = 1.34. Shown are half-hourly averages. . 239K.1 Slope (top) and offset (bottom) determined with twopoint calibrations for each half hour for CO2. Time isin PST and tickmarks are placed at noon. . . . . . . . . . 245xxivList of figuresK.2 Half-hourly averaged battery voltage (VB) and shortwave irradiance above the canopy (Sin,top). Time is inPST and tickmarks are placed at noon. . . . . . . . . . . 245K.3 CO2 slope (left) and offset (right) from the two-pointcalibrations vs. the battery voltage (VB). The blacklines are the fitted curves described by Eqs. K.1 andK.2, respectively. . . . . . . . . . . . . . . . . . . . . . . . 246K.4 H2O offset from the intercomparison of LI-840 IRGAH2O zero gas measurements with the battery voltage(VB). The black line is the fitted curve described byEq. K.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248K.5 LI-840 IRGA mq measurements of the H2O zero gasbefore and after the calibration was applied. The redline is the zero line. . . . . . . . . . . . . . . . . . . . . . . 248M.1 Schematic showing how the two vertical shear compo-nents act on a horizontal plain. . . . . . . . . . . . . . . . 252M.2 Rotation of wind direction (WD) expressed as the differ-ence between WD at each level and WD at z/h = 1.34(WDtop). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253M.3 Magnitude of the kinematic shear stress withoutv?w? (|u?w?|) plotted against the same includingv?w? (?u?w?2+ v?w?2) at the seven levels. Each dotrepresents a 30-min averaged measurement. The blackline is the 1:1 line. . . . . . . . . . . . . . . . . . . . . . . 254M.4 Same as Fig. M.3 but using the same scale for all levels. . 255N.1 Measured (red) and predicted (grey) eddy diffusivitiesfor wind shear (KM ) using global scaling and zs = z(combination I). The numbers in brackets are the num-ber of half hours included in the analysis. . . . . . . . . . 257N.2 Same as Fig. N.1 using local scaling and zs = z (com-bination II). . . . . . . . . . . . . . . . . . . . . . . . . . . 257N.3 Same as Fig. N.1 using global scaling and zs = ze (com-bination III). . . . . . . . . . . . . . . . . . . . . . . . . . 258N.4 Measured (red) and predicted (grey) eddy diffusivitiesfor sensible heat (KH) using global scaling and zs = z(combination I). The numbers in brackets are the num-ber of half hours included in the analysis. . . . . . . . . . 258xxvList of figuresN.5 Same as Fig. N.4 using local scaling and zs = z (com-bination II). . . . . . . . . . . . . . . . . . . . . . . . . . . 259N.6 Same as Fig. N.4 using global scaling and zs = ze (com-bination III). . . . . . . . . . . . . . . . . . . . . . . . . . 259N.7 Measured (red) and predicted (grey) eddy diffusivitiesfor latent heat (KE) using global scaling and zs = z(combination I). The numbers in brackets are the num-ber of half hours included in the analysis. . . . . . . . . . 260N.8 Same as Fig. N.7 using local scaling and zs = z (com-bination II). . . . . . . . . . . . . . . . . . . . . . . . . . . 260N.9 Same as Fig. N.7 using global scaling and zs = ze (com-bination III). . . . . . . . . . . . . . . . . . . . . . . . . . 261N.10 Measured (red) and predicted (grey) eddy diffusivitiesfor CO2 (KC) using global scaling and zs = z (combi-nation I). The numbers in brackets are the number ofhalf hours included in the analysis. . . . . . . . . . . . . . 261N.11 Same as Fig. N.10 using local scaling and zs = z (com-bination II). . . . . . . . . . . . . . . . . . . . . . . . . . . 262N.12 Same as Fig. N.10 using global scaling and zs = ze(combination III). . . . . . . . . . . . . . . . . . . . . . . 262xxviList of acronyms and symbolsSpecial notationsSymbol Description? Prime denotes deviation from the half-hourly mean? Prefix denoting the difference between a quantity at two adja-cent measurement heights?? Overbar denotes half-hourly averagesEC Subscript to denote results determined with the eddy covarianceapproachEP Subscript to denote results determined with the ecophysiologi-cal approachref Subscript to denote the measurements of a reference sensorAcronymsAcronym Description UnitsBAI Bole surface area m2 m?2BAIi,b,d Bole surface fraction of dead boles inlayer im2 m?2BAIi,b,l Bole surface fraction of live boles inlayer im2 m?2BC British ColumbiaC CarbonCF Correction factor used in the spectralcorrectiondimensionlessCH2O CarbohydrateCO2 Carbon dioxidexxviiAcronymsDBH Diameter at breast height mEBC Energy balance closure % or percentage points(pp)EC Eddy covarianceEP EcophysiologicalGEP Gross ecosystem photosynthesis ?mol m?2 s?1GPP Gross primary productivity ?mol m?2 s?1H2O Water vapourHF Humidity factorHFP Soil heat flux plateIRGA Infrared gas analyzerLAD Leaf area density m2 m?3LAI Leaf area index m2 m?2LAIi,br Leaf area index of broadleaf vegeta-tion in layer im2 m?2LAIi,co Leaf area index of coniferous vegeta-tion in layer im2 m?2LiDAR Light detection and rangingLL Net ecosystem productivity partition-ing method using a linear regressionfitted to low-light level daytime dataMFLNRO BC Ministry of Forests, Lands andNatural Resource OperationsMOS Monin-Obukhov similarityMPB Mountain pine beetleN2 NitrogenNEE Net ecosystem exchange ?mol m?2 s?1NEEz Net CO2 exchange below the height z ?mol m?2 s?1NEP Net ecosystem productivity ?mol m?2 s?1NEPz Net ecosystem productivity belowheight z?mol m?2 s?1NFI National forest inventoryNPP Net primary productivity ?mol m?2 s?1NRHF Non-rectangular hyperbolic functionnRMSE Normalized root mean square errorNSERC Natural Sciences and Engineering Re-search Council of CanadaNT Net ecosystem production partition-ing method using nighttime dataO2 OxygenxxviiiRoman symbolsPAR Photosynthetically active radiation ?mol m?2 s?1PARtop Photosynthetically active radiation atthe tower top?mol m?2 s?1PARz Photosynthetically active radiation atheight z?mol m?2 s?1PST Pacific Standard TimeRH Relative humidity %RMSD Root mean square deviation(=RMSE)RMSE Root mean square error (=RMSD)RMSEspatial RMSE for all ground pyranometer lo-cations together weighted by the areaof the forest, of which they were con-sidered representativeSTD Standard deviationTFexwx Experimental transfer function usedin the spectral correction of thecospectrum of the vertical wind andvariable xdimensionlessTFfitwx Theoretical transfer function used inthe spectral correction of the cospec-trum of the vertical wind and variablexdimensionlessUTC Coordinated Universal TimeVEC Three-dimensional vector wind veloc-itym s?1WD Wind direction ?WDtop Wind direction at tower top ?WUE Water use efficiency g C kg?1 H2OWUEi Inherent water use efficiency(WUE/D)g C kg?1 H2O kPa?1Roman symbolsSymbol Description Unitsa Area covered by chamber m2xxixRoman symbolsA Leaf net assimilation ?mol m?2 s?1A1 tree disc area of an average tree at thebottom of a layermA2 tree disc area of an average tree at thetop of a layermAbr Leaf-level net assimilation rates ofbroadleaf vegetation?mol m?2 s?1Aco Leaf-level net assimilation rates ofconiferous vegetation?mol m?2 s?1Al Surface area of an average tree withina layerm2c Mole fraction of CO2 ?mol mol?1 wet aircp Specific heat of dry air J kg?1 K?1cp,m Specific heat of moist air J kg?1 K?1C1 tree circumference of an average treeat the bottom of a layermC2 tree circumference of an average treeat the top of a layermCa Heat capacity of air J m?3 s?1CG Heat capacity of the soil J m?3 s?1Cw Heat capacity of wood J m?3 K?1Cwa The reference cospectrum of the verti-cal wind and the acoustic temperatureCwx The cospectrum of the vertical windand variable xd Zero-plane displacement height mdt Estimated tree diameter mdw Diameter of thermocouple wire mD Vapour pressure deficit kPaE Evapotranspiration rate kg m?2 s?1fo,s Half-power frequency HzFc CO2 flux density ?mol m?2 s?1Fs Flux density of a scalar sg Acceleration due to gravity m s?2h Canopy height mha Thermal transfer coefficient W m?2 K?1hb Breast height (1.3 m) mH Tree height mk Van-Ka?rma?n constant (=0.40) dimensionlesska Thermal conductivity of the air W m?1 K?1xxxRoman symbolskl Lower limit for the kurtosis of a vari-able to be considered for the analysisku Upper limit for the kurtosis of a vari-able to be considered for the analysisK Eddy diffusivity m2 s?1KC Eddy diffusivity for CO2 m2 s?1KE Eddy diffusivity for latent heat m2 s?1KH Eddy diffusivity for sensible heat m2 s?1KM Eddy diffusivity for momentum orshear stressm2 s?1Ks Eddy diffusivity of a scalar s m2 s?1l Layer thickness mls Mixing length of turbulent transportof a scalar smL Obukhov length mLin Incoming longwave radiation flux den-sityW m?2Lout Outgoing longwave radiation flux den-sityW m?2Lw Length of thermocouple wire mmc CO2 molar mixing ratio ?mol mol?1 dry airmq Water vapour molar mixing ratio mmol mol?1 dry airms Molar mixing ratio of the scalar s mmol mol?1M Momentum flux density N m?2Mc Molar mass of CO2 kg mol?1Md Molar mass of dry air kg mol?1Mq Molar mass of H2O kg mol?1n Number of measurement locations in-cluded in analysis of the spatial vari-ability of shortwave irradiancedimensionlessNa Normalization factor of the referencecospectrum of the vertical wind andthe acoustic temperaturedimensionlessNd Number of days included in analysisof the spatial variability of shortwaveirradiancedimensionlessNt Number of trees contributing to alayerha?1 or m?2Nu Nusselt number dimensionlessxxxiRoman symbolsNx Normalization factor of the cospec-trum of the vertical wind and variablexdimensionlessp Air pressure kPaP Gross photosynthetic flux density be-low height z?mol m?2 s?1q Mole fraction of water vapour mmol mol?1 wet airQ? Net radiation flux density W m?2Q10 Temperature sensitivity of bole respi-ration (relative increase in respirationfor a 10 ? C increase in temperature)dimensionlessQE Latent heat flux density W m?2QG Soil heat flux density W m?2QH Sensible heat flux density W m?2QS Rate of change of energy storage W m?2ri,1 Inner radius of bole ring used in thecalculation of average bole tempera-turemri,2 Outer radius of bole ring used in thecalculation of average bole tempera-turemrl Lower limit of a variable to be consid-ered for the analysisru Upper limit of a variable to be consid-ered for the analysisR Respiratory flux density below theheight z?mol m?2 s?1Rb,d Bole respiration rate of dead boles ?mol m?2 s?1Rb,l Bole respiration rate of live boles ?mol m?2 s?1Re Ecosystem respiration ?mol m?2 s?1Re Reynolds number dimensionlessRf Foliage respiration ?mol m?2 s?1Rd Gas constant of dry air J kg?1 K?1Rs Soil respiration ?mol m?2 s?1Ru Universal gas constant J kg?1 K?1skl Lower limit for the skewness of a vari-able to be considered for the analysissku Upper limit for the skewness deviationof a variable to be considered for theanalysisxxxiiRoman symbolsstdu Upper limit for the standard deviationof a variable to be considered for theanalysisSc CO2 source/sink strength ?mol m?3 s?1Sd,i Average incoming shortwave flux den-sity for day d and pyranometer iW m?2Sd,spatial Spatially-averaged incoming short-wave flux density for day dW m?2Sin,top Shortwave incoming shortwave fluxdensity at tower topW m?2Sin Incoming shortwave radiation fluxdensityW m?2Sout Outgoing shortwave radiation fluxdensityW m?2Sspatial Spatially-averaged incoming short-wave flux densityW m?2t Time sTa Air temperature ?C or KTac Acoustic air temperature ?C or KTB Average bole temperature ?C or KTB,d Average bole temperature of deadtrees?C or KTB,l Average bole temperature of live trees ?C or KTc Thermocouple temperature ?C or KTi,n Bole temperature for a ring i mea-sured on the north side of the tree?C or KTi,s Bole temperature for a ring i mea-sured on the south side of the tree?C or KTpanel Panel temperature ?C or KTs Soil temperature ?C or KTv Virtual temperature ?C or KTw Temperature of the thermocouplewire?C or Ku Longitudinal (streamwise) wind veloc-itym s?1u? Friction velocity m s?1u?,top Friction velocity (4?(u?w?)2 + (v?w?)2)at tower topm s?1u?,z4?(u?w?)2 + (v?w?)2 at height z m s?1xxxiiiGreek symbolsuj Wind velocity component in j direc-tionm s?1v Lateral wind velocity m s?1V Chamber headspace volume m3VB Battery voltage VVl Bole volume of an average tree withinone layerm3w Vertical wind velocity m s?1wi Geospatial-weighting factor dimensionlessx Cartesian coordinate in the meanwind directionmxj Distance in j direction my Cartesian coordinate perpendicular tomean windmz Height above ground; mVertical Cartesian coordinate mz0 Roughness length mzasl Elevation above sea level mzinfl Inflection point height mzm Measurement height mzs Scaling height mzt Height just below the height, wherethe second derivative of the mean hor-izontal wind profile drops below zeromze Effective height mGreek symbolsSymbol Description Units? Albedo fraction or %?w Albedo of thermocouple wire %? Bowen ratio dimensionless? Curvature factor of the inflectionpoint of the non-rectangular hyper-bolic functiondimensionless? Dry adiabatic lapse rate 0.01 K m?1xxxivGreek symbols? Light saturated net photosynthesis innon-rectangular hyperbolic function?mol m?2 s?1?mc Error of molar mixing ratio of CO2due to pressure uncertainties?mol mol?1 dry air?mq Error of molar mixing ratio of watervapour due to pressure uncertaintiesmmol mol?1 dry air?p Pressure error kPa?Fs Rate of change of CO2 storage in theair?mol m?2 s?1?NEEi CO2 exchange within the vegetationlayer i?mol m?3 s?1?QS,B Rate of change of sensible heat in treebolesW m?3?QS,C Energy storage change due to CO2 as-similation or respirationW m?3?QS,E Rate of change of latent heat in theairW m?3?QS,H Rate of change of sensible heat in theairW m?3?z Layer thickness m? Dimensionless height (stability pa-rameter)dimensionless? Fitting parameter in Eq. 3.14 kPa?1? Potential temperature ?C or K?d Volume fraction of dead trees m3 m?3?l Volume fraction of live trees m3 m?3?s Volumetric soil water content m3 m?3 or %?tree Volume fraction occupied by trees m3 m?3? Latent heat of vaporization J kg?1? Canopy area index m2 m?2? Fraction of molar mass of dry air overmolar mass of waterdimensionless? Viscosity of air mm2 s?1?c Molecular diffusivity of CO2 ?mol m2 s?1? Density of moist air (?a + ?q) kg m?3?a Dry air density kg m?3 or mmol m?3?c CO2 density in air kg m?3 or mmol m?3?q Water vapour density in air kg m?3 or mmol m?3?s Density of the scalar s?stand Stand density stems m?2 or stems ha?1xxxvGreek symbols? Ratio of water vapour density in theair to dry air density (?q/?a)dimensionless?w Standard deviation of the verticalwind velocitym s?1?w,top Standard deviation of the verticalwind velocity at the top of the towerm s?1?w,z Standard deviation of the verticalwind at height zm s?1? Reynolds stress (shear stress = ?M) N m?2?top Reynolds stress at the top of the tower N m?2? Initial slope of non-rectangular hyper-bolic functiondimensionless? Stability function dimensionless?C Stability function for CO2 flux density dimensionless?E Stability function for latent heat fluxdensity or water vapour flux densitydimensionless?H Stability function for sensible heatflux densitydimensionless?M Stability function for momentum fluxdensity or shear stressdimensionless?a Heat of CO2 assimilation J kg?1? Inclination of the wind from the hori-zontal plane?xxxviAcknowledgementsI owe my deepest gratitude to all those people who have made thisdissertation possible.Foremost, I would like to express my sincerest appreciation to mysupervisor Dr. Andreas Christen for the continuous support during myPhD study and research and for his quick and helpful feedback. I would liketo thank him for sharing his immense knowledge as well as his programmingand visualisation skills with me. I learned a lot from him. His guidancehelped me throughout my research and writing of research papers and thisdissertation. I could not have imagined having a better supervisor andmentor for my PhD study.I am deeply grateful to Prof. T. Andy Black for his dedication insupporting me like a co-supervisor, for sharing his enormous knowledge, hispatience during our many fruitful discussions and the careful reading of allmy manuscripts. I am very thankful for this.I would like to thank the rest of my thesis committee: Dr. ChristianReuten, Prof. Ian McKendry and Prof. Jolie Meyer-Smith for theirencouragement, insightful comments, and support.I would like to offer my special thanks to Eugenie Paul-Limoges for herhelp, the fun we had in the field and during the campaign preparations aswell as the good discussions we had.I am indebted to Rick Ketler and Zoran Nesic for their extensive tech-nical support before, during and after the measurement campaign. I thankRebecca Bowler for her part in the measurement campaign and logisticalhelp in Prince George, and Prof. Art Fredeen, for providing lab space atUNBC. I very much appreciated the help from Ben Crawford, Eli Heymanand Dominic Lessard during the set-up and take-down of the field campaign.xxxviiAcknowledgementsI thank my fellow labmates in the Micromet lab, especially ScottKrayenhoff, Ben Crawford, Mike van der Laan, Chris Adderley and JoeyLee for all the fun we have had in the last four years and the gooddiscussions as part of the reading group or in the lab. Thanks also to allmembers of the Biomet lab. I always felt like I had a second home there.I have greatly benefited from TerreWEB and all its members throughthe training in communications. Special thanks to Les Lavkulich, JuliaDordel, Julie Wilson and Suzanne Simard.I thoroughly enjoyed working in the Geography department. I amgrateful for all the friendly faces in the hallways and the extraordinar-ily helpful staff, especially Sandy Lapsky, Julie Ranada and Eric Leinberger.Thanks also to all professors and instructors that taught me in variouscourses or whom I had the pleasure to work with as a TA.Thanks to Rebecca Bowler for making leaf-level CO2 assimilationmeasurements and providing species-specific leaf area indices, to Dr.Thomas Hilker and Dr. Nicholas Coops for proving LiDAR-derived leafarea index data and to Dr. Tony Trofymow for providing NFI data.Last but not least, I would like to thank my family and in-laws for theirsupport in all matters.xxxviiiDedicationI dedicate this dissertation to my dear husband Jakob for his incrediblesupport, patience and love.xxxixChapter 1IntroductionThe western part of North America is the native habitat of the mountainpine beetle (MPB, Dendroctonus ponderosae). Large outbreaks of thebeetle are common events, but the current outbreak in British Columbia(BC), which started in the late 1990s, is the largest ever registered inNorth America (Safranyik and Wilson, 2006). The BC Ministry of Forests,Lands and Natural Resource Operations (MFLNRO) reported that, as of2011, cumulative recorded outbreak areas totaled 181,000 km2 (MFLNRO,2012). Rising air temperatures due to climate change allow more beetlesto survive through the winter (Safranyik and Wilson, 2006). Furthermore,due to fire suppression, there is a vast area of even-aged mature pine trees,which is a favorable habitat for the MPB (Taylor and Carroll, 2004). It ispredicted that by 2017 the MPB will have killed 57% of the mature pinevolume in BC (Walton, 2013). Even though the MPB infestation in BCpeaked in 2005 and has slowed considerably since then (MFLNRO, 2012),the total outbreak area is still increasing and there are large areas of killedforest remaining. Worldwide, there are many other species of bark beetlescausing substantial tree loss, making this not only a regional but a globalproblem.Three different management responses to the outbreak of MPB exist: (i)non-invasive (no treatment), (ii) removal of only the affected trees (partialharvesting) and (iii) complete removal of the affected stand (clearcutharvesting). At the same time, the relative contributions of different forestcomponents (ground vegetation, secondary structure, crowns of healthyand dead trees) to the stand carbon (C) balance are unknown. Brown et al.(2012a) have shown that even in an apparently dead stand the CO2 sinkscan exceed the sources during the summer. They spectulated that theexisting secondary structure (mainly immature trees of different speciesnot killed by the beetle) and understory were largely responsible for theobserved net ecosystem uptake.1Chapter 1. IntroductionMPB outbreaks have a large impact not only on the logging industrybut also on ecosystems, climate, microclimate and the carbon dioxide (CO2)and water budgets in affected forests. Maness et al. (2012) have foundthat sensible, latent and radiative heat fluxes have changed significantly inBC due to the MPB and have resulted in increased surface temperatures.In this research project, I focused on the micrometerology and CO2exchange, which is directly connected to turbulent transport in and abovethe attacked forest canopy. However, turbulent exchange processes withinforest canopies, especially sparse canopies like the one studied here, arenot well understood. Thus, it is important to expand our knowledge andimprove the representation of turbulence in canopy models in order toprovide projections of future growth conditions in attacked forest stands.Studies of CO2, water vapour (H2O), energy (i.e., radiation, sensible andlatent heat) and momentum exchange and turbulent transport withinaffected canopies have helped to improve the understanding of these sourceand sink distributions, but further knowledge is necessary to improve themodels? ability to represent turbulence in a sparse canopy and to predict theeffects of MPB infestations on stand microclimate and growth conditions.This PhD research project was part of an NSERC Strategic Grant thatbrought together biometeorologists, micrometeorologists, ecophysiologists,and forest scientists from BC Universities, the Canadian Forest Service, andMFLNRO to assess the impact of different forest management strategiesfollowing MPB outbreaks on C emissions and sequestration, the forest wa-ter balance and microclimate. The open-canopy structure resulting fromthe MPB attack furthermore gave a unique opportunity to study turbu-lent transport in a sparse canopy. This dissertation addresses the impact ofcanopy structure and the influence of the MPB on the CO2, H2O, momen-tum and energy exchange within the canopy in a non-invasively managedlodgepole pine stand affected by MPB and in particular addresses the fol-lowing three research questions:1. What are the characteristics of the canopy microclimate after the MPBattack and the resulting reduction in canopy density?2. How is the available energy partitioned and how well is the energybalance closed within and above this MPB-attacked stand?3. How are the sources and sinks of CO2, water vapour and sensible heatvertically distributed throughout the canopy?21.1. Background and state of knowledgeTo address those questions, two micrometeorological approaches (eddycovariance and flux-gradient) and an ecophysiogical approach wereemployed in this dissertation.This dissertation is structured in five chapters, beginning with asection about background and current state of knowledge (Section 1.1)that includes a discussion of the storage and exchange of C, the MPB,turbulent exchange in and above canopies and the main measurementtechnique (the eddy-covariance technique) employed in this dissertation.This is followed by three major research chapters examining the verticaldistribution of radiation and energy balance partitioning (Chapter 2),the vertical distribution of CO2 sources and sinks (Chapter 3) andflux-gradient relationships within and above the canopy (Chapter 4).Chapter 5 summarizes the most important findings and conclusions of thisdissertation, presents possible technical improvements and potential futurework. Several appendices were added that show photographs of the fieldsite and instrumentation as well as discuss technical aspects of the dataprocessing and methodology in greater detail.1.1 Background and state of knowledge1.1.1 Carbon and carbon dioxideForests are important for the storage of C. The largest fraction of terrestrialecosystem C is stored in forests (Sabine et al., 2004). In BC?s conifer-dominated forests, the amount of stored C is especially high in the oldeststands (Black et al., 2008). On different time scales, forests either act as netsources of or as net sinks for CO2. Through the process of photosynthesis,trees convert CO2 from the atmosphere and H2O from the soil into oxygen(O2) and carbohydrates, whereby C (CH2O) is stored in the plant tissue.This process is restricted to the daytime, since photosynthetically activeradiation (PAR) is required. Higher temperatures, elevated atmosphericCO2 concentrations and atmospheric nitrogen deposition may enhance aforest?s ability to act as a CO2 sinks (Canadell et al., 2007; Denman et al.,2007). In general, given adequate water supply, there is a positiverelationship between mean annual temperature and annual C storage ratessince high temperatures extend the growing season period and consequentlyincrease the annual net ecosystem production (NEP), thereby increasing31.1. Background and state of knowledgethe uptake of CO2 by the plants (Baldocchi et al., 2005; Black et al., 2005).Respiration releases CO2 from soil and plants. During autotrophicrespiration CO2 is released directly by living leaves, boles and roots, whileduring heterotrophic respiration CO2 is released due to decomposition bymicroorganisms and fungi (Monteith and Unsworth, 2008). These processesoccur during both daytime and nighttime, but are dependent on moistureavailability and soil temperatures amongst others (Luo and Zhou, 2010).The uptake and release of CO2 varies depending to a number of factorsincluding the species composition of the stand, the stand developmentalstage, the growing season length, precipitation, temperature and solarradiation (Black et al., 2008). Higher temperatures lead to an increase inphotosynthesis, but at the same time the release of CO2 by respirationincreases, usually in an exponential manner (Law et al., 2002; Curtis et al.,2005). On the other hand, Barford et al. (2001) showed in a hardwood forestthat droughts increased annual C sequestration by suppressing respirationdue to the dry conditions . Similarly, Krishnan et al. (2006) found in aboreal aspen stand in the first year of a three-year long drought that respira-tion was suppressed while gross ecosystem photosynthesis actually increaseddue to the aspen tree roots being able to access water deep in the soil profile.Investigations showed that during the 1980s and the 1990s the netprimary productivity (NPP) of global terrestrial ecosystems, thus thenet CO2 uptake by autotrophs, increased globally by 6% as a result ofglobal warming (Nemani et al., 2003). When looking at a smaller scalethe sources exceed the sinks in young stands. Fredeen et al. (2007) foundthat it took approximately eight years after clearcut harvesting in a wetsub-boreal interior spruce and subalpine stand east of Prince George, BCto return to being a C sink. For very young stands, photosynthesis usuallydoes not balance the higher CO2 loss resulting from respiration in the soiland decomposition of residual material (e.g., logging residue) on the ground.Insects such as the MPB also have an impact on NEP, but this has oftenbeen ignored in large-scale C budget modelling studies (McGuire et al.,2001; Myneni et al., 2001). Kurz et al. (2008) conducted a regional-scalestudy, where they used a forest ecosystem model to determine the impactof the MPB, forest fires and harvesting on forest productivity and the Cbalance. They concluded that the impact of the MPB is substantial andit should be accounted for in large-scale modelling analyses. The results41.1. Background and state of knowledgeof this dissertation may provide information necessary to include insectinfestations in future C budget modelling at the stand, regional and globalscale.1.1.2 Mountain pine beetleThe mountain pine beetle (Dendroctonus ponderosae) is an insect nativeto the pine forests of western North America with a population thatperiodically erupts into large-scale outbreaks (Amman and Cole, 1983;Safranyik et al., 1974; Taylor and Carroll, 2004). These huge outbreaksare responsible for increased mortality and reduced growth of millions oftrees over extensive areas (Mattson and Addy, 1975). The MPB typicallyinhabits pines, particularly ponderosa pine (Pinus ponderosa), lodgepolepine (Pinus contorta), whitebark pine (Pinus albicaulis), scots pine (Pinussylvestris) and limber pine (Pinus flexilis).The MPB targets tall, old trees with an average diameter at breastheight (DBH) of 20 cm or greater (Amman et al., 1977; Cole and Amman,1969; Hopping and Beall, 1948; McGregor et al., 1981; Safranyik et al.,1974). It attacks the trees by boring holes in the bark in order to lay itslarvae. The MPB infests the trees with the blue stain fungus (Grosmanniaclavigera), which blocks the trees? resin output and thereby disables itsonly self-defence mechanism against the MPB. This makes it easier foradditional beetles to attack the vulnerable tree, and after a period of afew weeks, the large number of holes inhibit the transport of nutrients andwater within the tree. Within one year after the outbreak, the foliage ofthe trees turns red. After another year, the trees become grey in colour,indicating that they are dead. Further information on the MPB and itsmethods of attack can be found in Safranyik and Wilson (2006).By killing large numbers of trees, the MPB results in major ecologicaland social impacts (Volney and Fleming, 2000). It affects the loggingindustry and leads to harvesting losses as well as unemployment. At thesame time, it impacts the microclimate of stands and the mesoclimateof attacked regions. It influences the forest CO2 budget, particularlyby affecting older trees, which have a major role in C sequestration(Black et al., 2008) and reducing CO2 uptake and increasing heterotrophicrespiration (Kurz et al., 2008). Brown et al. (2010) showed that theexistence of secondary structure comprising tree seedlings, saplings,51.1. Background and state of knowledgesub-canopy and canopy trees of different species that survived the beetleattack might have a major influence on whether the forest is a net CO2sink or source. Furthermore, remote sensing data indicated that the MPBwas responsible for a substantial decrease in evapotranspiration ratesand an significant increase in radiative and sensible heat fluxes. Thiscorresponded to a comparable temperature increase (1 ?C) as observedfor other types of disturbance like for example wildfire (Maness et al., 2012).BC is currently experiencing the largest recorded MPB outbreak inNorth America. As mentioned above, this outbreak is one order of magni-tude greater than previous recorded outbreaks because of the increased areaof susceptible host trees and favourable climate (Safranyik and Wilson,2006). By the end of 2011, the cumulative outbreak area was 181, 000 km2(MFLNRO, 2012) with the effect ranging from single trees to total stands(Westfall, 2007). Models suggest that with increasing MPB attacks, forestsin BC are being converted from a net sink to a net source of CO2 andeven with decreasing MPB attacks, returning to pre-outbreak levels couldtake decades (Kurz et al., 2008). The maximum annual impact of theMPB attack on the forest C balance in BC is suggested to be on the sameorder as all of the direct forest fire emissions in Canada from 1959 to 1999(Kurz et al., 2008). Therefore, the MPB is suggested to have a positivefeedback on the global climate system by increased CO2 emissions leadingto increased warming which results in more beetles surviving the winterand also more beetle kill.Climate change influences insect distribution and abundance, eitherdirectly via effects on their life cycles or indirectly via host-plant de-fense, abundance of natural enemies or interactions with competitors(Ayres and Lombardero, 2000). Higher temperatures during summer andespecially during winter as well as reduced precipitation in summer has ledto an expansion of outbreaks in areas further north and higher in elevationthan recorded before (Safranyik and Wilson, 2006; Williams and Liebhold,2002; Logan and Powell, 2001).In response to the MPB attacks, three different management strategieshave been used as described in Black et al. (2008):? Clearcut harvesting: This strategy involves the complete removal ofthe pine canopy and the secondary structure causing the MPB to lose61.1. Background and state of knowledgeits host. However, this method may create concerns related to wildlife,thermal and escape cover and watershed protection (McGregor et al.,1987) and it has been shown by Brown et al. (2012a) that clearcut sitestake much longer to return to be C sinks compared to unharvestedattacked sites.? Partial harvesting: It involves selective removal of MPB-affected treeswith varying degrees of secondary structure retention. Only affectedtrees or trees with a certain diameter are removed, while the remainingtrees and secondary structure are left as undisturbed as possible. Themain goal of this strategy is to remove the MPB?s host and improveventilation within the canopy (McGregor et al., 1987). The increasedventilation and higher light transmission through the canopy may in-crease the photosynthesis rates of the living vegetation. Partial cuttingoffers the potential for reducing stand susceptibility to MPB and is alsocompatible with management of other resources as well. Mathys et al.(2013) found that an MPB affected stand returned to being a growingseason C sink two years after MPB infestation and partial harvesting.? No treatment: This is a completely non-invasive strategy where notrees are removed and the secondary structure can grow undisturbedin a mostly dead stand. This is the management strategy applied inthe forest stand that was studied in this dissertation. Brown et al.(2012a) have shown that unharvested stands can return to C sinksmuch faster than clearcut sites.Selection of an appropriate response must balance the concern for po-tential future economic viability of components of the secondary structure,the desire to preserve habitat and ecosystem biodiversity, and the need tominimize the disturbance of local and regional energy, carbon and waterbalances.1.1.3 Energy balance in canopiesForest canopies gain their energy from intercepted short and long-wave radiation and their radiation budget can be expressed as(Monteith and Unsworth, 2008):Q? = Sin ? Sout + Lin ? Lout, (1.1)where Q? is the net radiation, Sin and Sout are the incoming and outgo-ing shortwave radiation and Lin and Lout are the incoming and outgoing71.1. Background and state of knowledgelongwave radiation, respectively. This energy then causes air, tree or soiltemperatures to change (i.e., as stored sensible heat), is stored as latent heatby transformation of H2O between its states or is stored as chemical energythrough photosynthesis. The energy that is not stored is transported as tur-bulent or advective sensible or latent heat fluxes in and out of the canopy.Under ideal conditions (homogeneous stand, flat terrain, daytime) the ad-vective fluxes can be assumed to be negligible (Aubinet et al., 2012) and theenergy balance can be written as (Baldocchi et al., 2000):Q? = QH +QE +QG +QS , (1.2)where QH is the sensible heat flux, QE is the latent heat flux, QG is the soilheat flux and QS is the rate of change of energy storage. These fluxes givenot only information about the transport of energy but also about the avail-ability of energy. This energy could be used in C exchange processes; e.g.,when QG is high, there is a large amount of energy stored in the soil (result-ing in increased soil temperature) which may not only enhance plant growththrough increased photosynthesis, but also ecosystem respiration. The ver-tical distribution of energy balance partitioning in the canopy are affectedby stand density and canopy architecture or structure (leaf distribution andorientation, clumping), radiation extinction coefficient (i.e., how direct anddiffuse radiation are transmitted down through the canopy), water avail-ability and photosynthetic activity. In closed-canopy forests, a substantialfraction of the irradiance is intercepted in upper parts of the canopy and lessradiation reaches the ground during daytime than in open-canopy forests.1.1.4 Turbulent exchange in and above canopiesThe wind profile in a canopy layer, or roughness sublayer (Raupach et al.,1991), differs substantially from the typical profile in a boundary layer.The main difference between flow in and above a canopy and flow in aboundary layer is that momentum is absorbed from the air stream throughaerodynamic drag on the foliage over an extended vertical region ratherthan at the surface plane (Finnigan, 2000). In addition to skin (viscous)drag, there is also form (pressure) drag in a canopy. Form drag is causedby pressure differences between front and back of canopy elements1.Therefore it has been proposed that the canopy sublayer is more similar toa plane mixing layer (Raupach, 1989a; Raupach et al., 1996). The planemixing layer is usually formed when two airstreams of different velocities1AMS Glossary, http://glossary.ametsoc.org/wiki/Form drag81.1. Background and state of knowledgemerge downstream in a wind tunnel. It is characterized by an inflectedmean velocity profile, which is known to be inviscidly unstable to smallperturbations (Drazin and Reid, 1981).Similar to the plane mixing layer, the mean wind velocity within thecanopy increases roughly exponentially with height with a characteristicinflection point instability at the upper limit of the canopy (Fig 1.1a) wherethe shear is maximal (Finnigan, 2000). This inflected profile in the canopyis largely caused by the drag on the foliage. However, above the roughnesssublayer the typical logarithmic profile of a boundary layer can be found.In addition to the mean wind profile, the energy and momentum fluxes(Fig 1.1b) also differ from the boundary layer since they decrease rapidlywith depth inside the canopy. Another major difference, as Finnigan (2000)stated, is that especially large coherent structures control the turbulencedynamics. These have been shown to be responsible for a large fractionof mass, momentum and energy transport across the canopy-atmosphereinterface (e.g., Gao et al., 1989; Katul et al., 1998; Finnigan and Shaw,2000; Thomas and Foken, 2007). These large eddies can be seen as aresult of the inviscid instability of the inflected mean wind profile. Theytypically consist of a pair of counter-rotating stream-wise vortices wherethe downdraft between the vortex pair generates a sweep. Analyses withthe quadrant-hole technique has shown that sweeps rather than ejectionsdominate the eddy fluxes within the canopy (Finnigan, 2000). The largereddies and much of the turbulent kinetic energy (TKE) are produced abovethe canopy and are transported down into the canopy sublayer by sweeps.The geometric features and formation mechanisms of these coherentstructures are a function of canopy vegetation density (Novak et al., 2000;Poggi et al., 2004a; Dupont and Brunet, 2008).These coherent structures are also one reason why Monin-Obukhovsimilarity (MOS) theory is questonable within the canopy. MOS theoryis a relationship describing the vertical behavior of nondimensionalizedmean flow and turbulence properties within the atmospheric surface layer2.Gradient diffusion theory (K-theory) is based on MOS theory and workswell above the roughness sublayer, i.e., in the inertial sublayer. It assumesthat turbulent fluxes of a scalar are directed down the local gradient of that2AMS glossary: http://glossary.ametsoc.org/wiki/Monin-obukhov similarity theory,29 December 201391.1. Background and state of knowledge0.0 0.5 1.0 1.5 2.0u/u(h)0.00.51.01.52.0z/h0.0 0.2 0.4 0.6 0.8 1.0 1.2? u?w?/u*2Pine, LAI = 4.0 (Raupach et al., 1996)Eucalypt, LAI=1.0 (Denmead and Bradley, 1987)Spruce, LAI = 10.0 (Amiro, 1990)Aspen, LAI = 4.0 (Amiro, 1990)Pine, LAI = 2.0 (Amiro, 1990)Pine, LAI = 1.4 (Christen et al., 2008)(a) (b)Figure 1.1: Normalized wind speed (a) and momentum flux (b) reportedfrom different measurement studies in forest canopies under mainly neutralor unstable conditions. The wind profile shows a typical inflection point atthe top of the canopy. The momentum flux decreases rapidly with depthinto the canopy and stays approximately constant above. Details about thestudies are given in Table 4.2 in Chapter 4. LAI is the leaf area index.101.1. Background and state of knowledgescalar?s concentration, analogous to molecular diffusion3. Several studieshave shown that, at least in relatively dense canopies, counter-gradientfluxes can occur (e.g., Denmead and Bradley, 1987), which contradictsK-theory and therefore also MOS theory. However, it has also been debatedthat K-theory might be applicable under limited conditions in some opencanopies, for example in crop canopies (Bache, 1986). According to Corrsin(1974), K-theory can only be applied if the length scale of the transportprocess is much smaller than the length required for significant changes inthe mean gradient.Smaller eddies can also be found in the canopy. The drag on thefoliage is the cause for the wake mechanism that removes energy fromlarge eddies and passes it on to smaller scales. Additionally, wavingof the foliage is responsible for the splitting up of larger eddies intosmaller eddies. This result is known as the spectral short cut (Finnigan,2000). Kolmogorov (1941) assumed that there are no processes adding orsubtracting TKE from eddies within the inertial subrange so that energyis only transferred between wave numbers following the eddy cascade.Furthermore, he assumed that the inertial subrange is sufficiently distantfrom the anisotropic energy-containing eddies. However, these assumptionsare not always true within a canopy. The aformentioned mechanisms maylead to a second peak in the energy spectrum or to a deformation of thetypical -5/3 slope of the inertial subrange (Baldocchi and Meyers, 1988a).These eddy characteristics are valid in homogeneous and sufficientlydense canopies. For cases with a low vegetation density, turbulence appearsto resemble a rough-wall boundary layer [e.g. Poggi et al. (2004a)]. Thetransition from resembling a rough-wall boundary layer to being moresimilar to a mixing layer seems to depend on canopy density (Huang et al.,2009).To convert between temporal resolution and spatial resolution, ithas to be assumed that Taylor?s hypothesis can be used. However, thisassumption cannot always be made in highly turbulent canopy flows(Kaimal and Finnigan, 1994). Another problem is that turbulent transportby horizontal advection is often neglected and it is assumed that exchangesare only in the vertical dimension. This assumption might be reasonable3AMS glossary: http://glossary.ametsoc.org/wiki/Gradient transport theory, 29 De-cember 2013111.1. Background and state of knowledgeduring the day over a flat terrain, but at night, it often leads to anunderestimation of fluxes (Baldocchi, 2003).An MPB attack may also have an impact on the turbulence charac-teristics and the wind profile within a canopy. As a consequence of MPBoutbreaks, affected stands change structure and decrease in density. First,the outbreaks result in a loss of needles and smaller branches, making thetrees simpler in structure. This may lead to a reduction in roughness andwaving. Over time, stand density decreases, either because of the naturalfalling and decomposition of affected trees or because of the active removalof trees due to one of the invasive management strategies. The particularmanagement strategy chosen influences the time scale of this thinning effect.The degree of thinning is dependent on the existence of secondary structureand growth conditions in the particular forest and region. This effect againinfluences the effectiveness of scalar transport and hence the stand mi-croclimate as a main driver for regeneration and secondary structure growth.1.1.5 Eddy-covariance techniqueThe main measurement technique used in this dissertation is the eddy-covariance (EC) technique and is therefore described here in more detail.It is a statistical method used in micrometeorology and related fieldsand is possibly one of the most commonly used approaches to determinemomentum, sensible heat, water vapour and atmospheric gas (e.g., CO2)fluxes. It is based on the analysis of high-frequency wind and scalar timeseries.As early as the 19th century, Sir Osborne Reynolds developed theunderlying theory of the EC technique (Reynolds, 1895). Even thoughsome applications were made in the 1950s, the lack of adequate equip-ment postponed the establishment of the EC technique until the 1980s(Baldocchi, 2003). Since the early 1990s (Wofsy et al., 1993) it has beenused for year-round long-term monitoring above canopies.The EC technique measures the velocities of upward and downward mov-ing eddies and also measures fluctuations in the concentrations of scalars(e.g., CO2) (Baldocchi, 2003). The mean flux density is the rate at which121.1. Background and state of knowledgeany physical quantity is transported across a plane of unit area4 and canbe calculated by determining the covariance between fluctuations of verticalwind velocity (w?) and the mixing ratio of a constituent (m?s) (Baldocchi,2003):F = ?aw?m?s, (1.3)where ?a is the dry air density, the overbar denotes the mean of a quantityand the prime indicates the deviation of this mean.The measurements at one height represent the vertically integratedflux for a so-called ?footprint?, which is the surface area that contributesto the measured flux (Fig. 1.2). The dimensions and orientation of theflux footprint depend on the height of the measurement, surface roughnesslength, wind speed and direction as well as atmospheric stability (Schmid,2002). Different approaches exist to analytically assess the dimensions ofthe footprint in the surface layer (e.g. Schuepp et al., 1990; Horst and Weil,1994; Kormann and Meixner, 2001; Schmid, 2002), but the analysis of thefootprint within a forest canopy is very challenging.The typical equipment used for this technique includes high frequencysonic anemometers and, depending on the flux of interest, additionalinstruments such as high frequency open-path or closed-path infrared gasanalyzers (Fig. 1.3) and thermocouples. This equipment is responsiblefor measuring three-dimensional wind, temperature, and mixing ratios ofdifferent gases.Measurement frequencies between 1 Hz and 20 Hz have been establishedin the past. The choice of an appropriate frequency has to be done withcare and by considering the covariance spectrum (Finnigan et al., 2003).Too high of a frequency may lead to challenges during the recording of thedata, whereas too low of a frequency can be responsible for flux losses andaliasing effects.The averaging time period is also a crucial factor. Typical periods are onthe order of anywhere from minutes to a few hours. Finnigan et al. (2003)indicated that averaging times much longer than 15 minutes are necessaryto capture all eddy sizes involved. At the same time, Kidston et al. (2010)have shown that in their studies longer time periods did not improve the4AMS glossary,http://amsglossary.allenpress.com/glossary/search?id=flux-density1, 29 December 2013131.1. Background and state of knowledge(a)  Side view(b)  Plan viewSensorSensorzmWindWindfoot printfootprint isopleths60%50%90%80%70%Figure 1.2: Side view (a) and plan view (b) of the footprint [modified withpermission after Oke et al. (in prep.)].Ultrasonic anemometerIRGAThermocoupleFigure 1.3: Photograph of an EC system showing an ultrasonic anemometerCSAT3, an open-path gas infrared analyzer (IRGA) LI-7500 and a thermo-couple (photograph taken by Andreas Christen).141.1. Background and state of knowledgeresults, but rather led to concerns about the assumption of stationarityfor such long time periods. This is a prerequisite for the Reynoldsdecomposition to be applied.The EC technique is a well established technique to measure eddy fluxesabove a forest but less often used within the canopy space. In the followingchapters, the appropriateness of EC measurements within the canopy areaddressed.15Chapter 2Vertical distribution ofradiation and energy balancepartitioning2.1 IntroductionThe native habitat of the mountain pine beetle (MPB, Dendroctonusponderosae) is in the western part of North America. Large outbreaks arecommon events in the area but the current outbreak in British Columbia(BC), Canada, which started in the late 1990s, is the largest ever registeredin North America (Safranyik and Wilson, 2006). By 2011, 710 millionm3 of merchantable pine volume (Walton, 2012) in a total outbreak areaof 181, 000 km2 (MFLNRO, 2012) had been killed since the start of thisoutbreak. Management responses to the outbreak of MPB range fromcompletely non-invasive treatment to partial harvesting of only affectedtrees and complete removal of the affected stand (clearcut harvesting).Alterations of the forests due to MPB infestation and managementmay have a major impact on the microclimate within these forests andconsequently affect the growth conditions of living secondary structure,which comprises seedlings, saplings and sub-canopy trees. (Maness et al.,2012) found based on remote sensing data that the MPB was responsiblefor a substantial decrease in evapotranspiration rates and a significantincrease in radiative and sensible heat fluxes corresponding to a 1 ?Csurface temperature increase.It is expected that insect attacks turn forests from carbon sinks(gross primary productivity GPP > ecosystem respiration Re) to carbonsources (GPP < Re) (Kurz et al., 2008). Partial harvesting (i.e., selectiveremoval of MPB-affected trees with varying degrees of secondary structureretention) and non-invasive strategies (i.e., where secondary structure cangrow undisturbed in a decaying stand) will likely not prevent Re from162.1. Introductionbecoming larger, but will retain some of the GPP due to secondary structurein comparison to clearcut harvesting. Studies have shown that there is apotential for partial harvesting and non-invasive strategies to improve CO2uptake (Kurz et al., 2008; Edburg et al., 2011; Brown et al., 2012a) andharvest yields (Nishio, 2009). These partially harvested and non-invasivelymanaged forests are of a particular interest since Coates et al. (2006) haveshown that 20-30 % of MPB stands in central and northern BC havesufficient secondary structure to expect a midterm harvest even if simplyleft unharvested, and approximately 40-50 % could be restocked withoutfurther silvicultural intervention. In this study a non-invasively managedforest was studied. The study was part of a project aimed at assessing theimpact of different forest management strategies following MPB outbreakson carbon exchange, water balance and microclimate.In order to predict the future microclimate and growth conditionsin attacked stands where dead trees are not removed, it is necessary tounderstand how radiative and turbulent energy fluxes vary with heightin the canopy. The objectives therefore are, (i) to determine the verticaldistribution of net radiation within an MPB-attacked forest canopy, (ii)to quantify the vertical differences in the energy balance partitioning andenergy balance closure, and (iii) to determine the vertical distribution ofsources and sinks of sensible and latent heat.Turbulent fluxes are typically investigated using the eddy-covariance(EC) technique (Baldocchi, 2003). Since counter-gradient fluxes can occurwithin forest canopies and similarity theory is not applicable within thecanopy (Denmead and Bradley, 1985; Raupach, 1988; Finnigan, 2000),flux-gradient approaches were not used in this chapter. However, whenusing the EC technique in the canopy with the usual one-dimensionalapproach, advection and dispersive fluxes are neglected. Studies haveshown that in sparse canopies dispersive fluxes can become significant(Poggi et al., 2004b; Poggi and Katul, 2008) and that their effect islarger in the lower canopy than at the top of the canopy (Bohm et al.,2000). Aubinet et al. (2012) summarizes the typical problems with ECmeasurements at night, including significant advection under low turbulenceconditions and non-stationarity.In the past 20 years there have been many studies involving the mea-surements of fluxes within or below a forest canopy (e.g., Amiro, 1990b;Lee and Black, 1993a,b; Baldocchi and Vogel, 1996; Blanken et al., 1997;172.2. MethodologySaugier et al., 1997; Wilson et al., 2000; Roupsard et al., 2006; Jarosz et al.,2008; Zhang et al., 2010; Staudt et al., 2011). In this study the verticalchanges in energy balance partitioning within and above a canopy and re-lated energy flux sources and sinks to vegetation layers were assessed. Thereduced stand density due to the MPB attack provided a unique opportunityto study microclimate and turbulent transport in a sparse canopy.2.2 Methodology2.2.1 Conceptual frameworkDue to the horizontal homogeneity of the stand (see Sect. 2.2.2), a one-dimensional approach was used (Aubinet et al., 2012); a level was definedas a measurement height, while a layer was defined as a stratum between twolevels (see Fig. 2.1). For the lowest layer, the stratum was confined by theground and the lowest measurement level. The layer midpoint heights givenin Fig. 2.1 were defined as the centre points between two adjacent levels.The energy balance for levels was expressed as a flux density (W m?2) andfor layers as a flux-density divergence (W m?3).Energy balance at the levelsThe energy balance can be calculated at any level, as is commonly done forwhole-canopy volumes. The energy balance of the volume between the level(zm) and the soil surface can be expressed as:0 = Q? +QH +QE +QG +QS, (2.1)where Q? is the net radiation-flux density, QH is the sensible heat-flux den-sity, QE is the latent heat-flux density, QG is the soil heat-flux density andQS is the rate of change of energy storage in the volume between the groundsurface (z = 0) and the level (zm) per unit ground area. The storage term(Eq. 2.2) includes the rate of change of sensible heat in the air (?QS,H),the rate of change of latent heat in the air (?QS,E), the rate of change ofsensible heat in the tree boles (?QS,B) and the energy storage change dueto CO2 assimilation and respiration (?QS,C),QS =? zm0?QS,H dz +? zm0?QS,E dz +? zm0?QS,B dz +? zm0?QS,C dz.(2.2)182.2. MethodologyFigure 2.1: Schematic of levels and layers. A level is a measurement height,while a layer is a stratum between two measurement heights. Level, layermidpoint and canopy heights as well as stand structure [understory (0 ? 1m), secondary structure (1 ? 8 m) and overstory (8 ? 20 m)] height areindicated.192.2. MethodologyEquation 2.1 assumes horizontal homogeneity and that horizontalmean advection and horizontal turbulent flux density-divergence (?Q/?x)are negligible. It also assumes no mean vertical wind (w = 0). Theseassumptions are likely met in this stand based on the homogeneity of thestand structure and flat topography (see Sect. 2.3.1 below).The terms Q? and QG were measured with net radiometers and soilheat-flux plates, respectively, and QH and QE with EC systems andcalculated with Eqs. 2.12 and 2.13, respectively. In this chapter, the samesign convention as Rosenberg et al. (1983) was used, where a positive signdenotes an input into the control volume and a negative sign denotes anoutput from the control volume. This implies that during daytime Q? istypically positive, while QH , QE and QG are typically negative. At night,the opposite is usually the case. The storage terms were determined byintegrating over all layers between the ground and the given measurementheight zm (Eq. 2.2). A negative value of a storage term indicates thatenergy is stored below the level (i.e., a sink; typical daytime situation)and a positive storage term implies that energy is released (i.e., a source;typical nighttime situation). This sign convention was used to ensure aconsistent handling of energy fluxes because all terms that are positivedefine an energy source and those that are negative define an energy sinkfor the volume under consideration.The residual was calculated half-hourly as the contribution that cannotbe explained by the sum of Q?, QH , QE, QS and QG:Residual = Q? +QH +QE +QG +QS , (2.3)and it is the energy-flux density required to balance the energy input, out-put and storage change. Energy balance closure (EBC, in %) is defined as(Wilson et al., 2002; Barr et al., 2006):EBC = ? QH +QEQ? +QG +QS. (2.4)Energy balance of the layersIn order to determine the sources and sinks of the energy in the forest canopythe energy balance of the layers needs to be defined. It is assumed that thehorizontally homogeneous structure of the forest permits a one-dimensionaltreatment (i.e., no horizontal advection and no horizontal turbulent fluxdivergence). The energy balance of a layer can be expressed as:202.2. Methodology0 =?Q??z+?QH?z+?QE?z+?QG?z+?QS,H +?QS,E +?QS,B +?QS,C , (2.5)where the first four terms on the right-hand side are the vertical (zincreasing upward) flux-density divergences for Q?, QH , QE and QG. Theywere calculated as the difference between the fluxes measured at adjacentlevels divided by layer thickness. In the case of ?QG/?z, it is zero forall layers except the lowest one in which case it is QG/(1.2 m); ?Q?/?z,?QH/?z and ?QE/?z for the lowest layer are calculated as the measuredflux at the 1.2-m level divided by ?z =1.2 m, i.e., Q?, QH and QE wereassumed to be zero just below the soil surface. These three divergencescombine the flux divergence for the layer and the flux at the soil surface.To be consistent with the sign convention used above, a positive numberfor all terms in Eq. 2.5 implies that the layer is an energy sink (i.e., thelayer gains energy) and a negative number that it is an energy source (i.e.,the layer loses energy).The last four terms in Eq. 5 are the rates of change of sensible and latentheat in the air, the sensible heat and biochemical energy in the biomass,respectively. They were calculated as follows:? sensible heat storage change in the layer due to air temperature (Ta inK) change in the air volume:?QS,H = ?(1? ?tree)Ca?Ta?t, (2.6)where ?tree denotes the volumetric fraction occupied by trees(m3 m?3), Ca is the heat capacity of air (J m?3 K?1) and t is time(s);? latent heat storage change in the layer due to water vapour density(?q in kg m?3) change in the air in the tree-free volume:?QS,E = ?(1? ?tree)???q?t, (2.7)where ? is the latent heat of vaporization (J kg?1);212.2. Methodology? sensible heat storage change in the layer due to bole temperature (TB)change:?QS,B = ??treeCw?TB?t, (2.8)where Cw is the volumetric heat capacity of wood [approximate heatcapacity of solid wood at 20 ?C and 10 % moisture content: 1.5MJ m?3 K?1, USDA (2007)];? energy storage change in the layer due to CO2 assimilation and respi-ration only including the air volume:?QS,C =(?FC?z+ (1? ?tree)??c?t)?a, (2.9)where ?c is the CO2 density in the air (kg m?3) and ?a is the heatof CO2 assimilation [1.17? 107 J kg?1, Oke (1988)]. The first term isthe vertical CO2 flux (FC , see Eq. 3.1) divergence (kg m?3 s?1) andthe second term is the CO2 concentration change over time in the air(kg m?3 s?1). When FC is positive it is an upward flux and when it isnegative it is a downward flux. During the process of photosynthesisenergy is stored, while it is released during respiration. For the lowestlayer, an average constant soil respiration (1.2 ?mol m?2 s?1) was usedfor FC at the lower boundary. Due to low soil moisture, soil respirationwas approximately constant during the field campaign.The overbar in the equations represents a 30-min average. Whencalculating ?tree an estimated average tree diameter dt (m) and anestimated average stand density ?stand (stems m?2) in each layer wasused: ?tree = pi(d/2)2?stand. ?c, ?q and Ta for the layers in the storageequations were calculated by averaging the concentration and temperature,respectively, for the levels at the top and bottom of the layer. For thelowest layer, the concentrations and temperatures at only the upper levelwere used. The temperature and concentration changes for each 30-minperiod were defined by the change in average temperature or concentration,respectively between the 30-min period before and after the 30-min periodconcerned.In theory an additional factor accounting for the air volume change withheight between levels due to different volumes taken up by the solid canopyelements (boles, branches and needles) would need to be included in theequations of flux divergence. The air volume change with height in a forest,however, is small (Raupach and Shaw, 1982) and is neglected here.222.2. Methodology2.2.2 Field campaignMeasurement siteFigure 2.2: Photograph of the mountain-pine-beetle-attacked stand adjacentto the Crooked River Regional Park. This photograph was taken on 12 July2010 from the top of the measurement tower (30 m) in a south-west direction.An extensive field campaign was conducted in July and August2010 in an MPB-attacked lodgepole pine (Pinus contorta var. latifolia)stand (Fig. 2.2) adjacent to Crooked River Provincial Park (MPB-03:54?28?24.8??N, 122?42?48.4??W), 70 km north of Prince George in interiorBritish Columbia, Canada. The stand is about 1.5 km ? 1.5 km in size andis located at 710 m a.s.l. within the sub-boreal spruce sub-zone (SBSmk1,Meidinger and Pojar (1991)). It is characterized by a flat terrain (< 0.5 ?slope) and a homogeneous fetch > 0.4 km in all directions around theobservation tower.The stand was first attacked by MPB in 2003, and experienced almost100 % mortality of the mature lodgepole pine trees by 2007. In 2010, thestand had an approximate height (h) of 20 m, a leaf area index (LAI) of0.55 m2 m?2 and a stand density (?stand) of approximately 2520 stemsha?1 (see Table 2.3, understory shrubs not included). There were no LAImeasurements from before the MPB attack available. However, four years232.2. Methodologyafter the attack (2007) LAI was substantially higher (LAI = 0.9 m2 m?2,Brown et al. (2010)) than in 2010.The stand had a relatively well-developed secondary structure com-prising sub-canopy lodgepole pine, subalpine fir (Albies lasiocarpa), hybridspruce (Picea glauca ? engelmannii) and a few Douglas fir (Pseudotsugamenziesii var. glauca) trees and saplings. The secondary structure reacheda height of up to 12 m, but was most abundant in the lowest 8 m of thestand. The nutrient-poor, coarse-textured and well-drained gravelly soil ofglacio-fluvial origin was almost completely covered with mosses, lichens,broadleaf shrubs and herbaceous species. The most dominant speciesin the understory were Vaccinium species, ground cedar (Lycopodiumcomplanatum) and kinnikinnick (Arctostraphylos uva-ursi). More detailedinformation about the stand characteristics can be found in Brown et al.(2010) and Bowler et al. (2012). Photographs of the measurement site andthe instrumentation are shown in Appendix A.InstrumentationThe measurements were made on a scaffold tower (2.1 m long, 1.5 m wideand 32 m tall), on a roving tripod (1 m tall) and in the ground. An array ofseven EC systems was installed on the tower above and within the canopyat heights from 1.2 to 26.8 m (see Fig. 2.1), including a long-term ECsystem, which measures above-canopy fluxes through the year. All systemsfaced westward and consisted of one ultra-sonic anemometer (CSAT3,Campbell Scientific Inc. (CSI), Logan, Utah) measuring three-dimensionalwind (u, v, w) and acoustic temperature (Tac), one open-path infrared gasanalyzer (IRGA, LI-7500, LI-COR Inc., Lincoln, Nebraska) measuring watervapour (H2O) and carbon dioxide (CO2) molar densities and atmosphericpressure (p), and one fast-response fine wire (25.4 ?m) chromel-constantanthermocouple measuring air temperature (Tc). All EC data at the highestmeasurement level (26 m) were recorded with a frequency of 5 Hz and allothers with a frequency of 10 Hz on two synchronized CR-3000 (CSI) dataloggers.242.2.MethodologyTable 2.1: Instrumentation installed on the scaffold towerLevel Measurement Normalized Model Manufacturer Instrument Measurement Outputheight height a No. frequency frequency b(m) (Hz)7 30.5 1.53 CNR-1 K&Z Net radiometer 0.5 1/30 min26.8 1.34 CSAT3 CS Ultra sonic anemometer 60 5 Hz26.8 1.34 LI-7500 LI-COR IRGA 5 5 Hz26.8 1.34 custom made Thermocouple 5 5 Hz6 21.0 1.05 CSAT3 CS Ultra sonic anemometer 60 10 Hz21.0 1.05 LI-7500 LI-COR IRGA 10 10 Hz21.0 1.05 custom made Thermocouple 10 10 Hz5 16.5 0.83 CSAT3 CS Ultra sonic anemometer 60 10 Hz16.5 0.83 LI-7500 LI-COR IRGA 10 10 Hz16.5 0.83 custom made Thermocouple 10 10 Hz16.5 0.83 NR Lite K&Z Net radiometer 0.2 1/min4 11.9 0.60 CSAT3 CS Ultra sonic anemometer 60 10 Hz11.9 0.60 LI-7500 LI-COR IRGA 10 10 Hz11.9 0.60 custom made Thermocouple 10 10 Hz11.9 0.60 NR Lite K&Z Net radiometer 0.2 1/min3 7.6 0.38 CSAT3 CS Ultra sonic anemometer 60 10 Hz7.6 0.38 LI-7500 LI-COR IRGA 10 10 Hz7.6 0.38 custom made Thermocouple 10 10 Hz7.6 0.38 NR Lite K&Z Net radiometer 0.2 1/min2 2.7 0.14 CSAT3 CS Ultra sonic anemometer 60 10 Hz2.7 0.14 LI-7500 LI-COR IRGA 10 10 Hz2.7 0.14 custom made Thermocouple 10 10 Hz2.7 0.14 NR Lite K&Z Net radiometer 0.2 1/min1 1.2 0.06 CSAT3 CS Ultra sonic anemometer 60 10 Hz1.2 0.06 LI-7500 LI-COR IRGA 10 10 Hz1.2 0.06 custom made Thermocouple 10 10 Hz1.2 c 0.06 CNR-1 CS Net radiometer 0.2 1/minaMeasurement height is normalized to canopy height h = 20 m.bValues averaged over output period.cThis system was mounted on the roving tripod.252.2.MethodologyTable 2.2: Instrumentation installed in the ground.Instrument Model Manufacturer No. of Depth Measurement OutputNo. sensors frequency frequency(mm) (Hz) (min?1)Heat-flux plate CN3 Middleton Solar 3 50 0.2 1Thermocouple Fabricated in the lab 3 25 0.2 1Water content reflectometer CS-616 Campbell Scientific 3 100 0.2 1262.2. MethodologyNet radiation at the 2.7-m, 7.6-m, 11.9-m and 16.5-m heights wasmeasured with NRLite net radiometers (Kipp & Zonen B.V., Delft, TheNetherlands (K&Z)) and was recorded on a CR23X (CSI) data logger.For measurement frequency and output frequency see Table 2.1. Nearthe top of the scaffold tower (30.5 m) and on the roving tripod (1.2-mheight) incoming and outgoing shortwave and longwave radiation fluxeswere measured with two CNR-1 four-component net radiometers (K&Z)and net radiation was calculated from the four individually measuredcomponent fluxes. Even though the stand was relatively homogeneous andoverall had an open structure, there was a small variability in stand density(see Sect. 2.3.1 below). Therefore the roving tripod was moved to threedifferent locations with differing stand density (see Fig. 2.3 and Table2.5; position 1: 16 m south of tower (seven days, considered an area thatis more open than the average stand), position 2: 34 m west-south-westof tower (10 days, moderate) and position 3: 50 m west-north-west oftower (six days, relatively dense)) during the field campaign to improvethe representativeness of the measurements at this level. Moving the netradiometer horizontally at the other levels was not feasible and they werefixed for the entire campaign. The radiometer measurements on the tripodwere recorded on a CR1000 (CSI) data logger. All booms supporting theradiometers faced south of the tower. The measurement height, instrumentsand measurement frequencies of each level on the tower can be found inTable 2.1.Additional to the vertical radiometer array, shortwave irradiance wasmeasured at nine locations on the ground using five CM5 pyranometers(K&Z) and four precision spectral pyranometers (PSP, Eppley Laboratories,Newport, Rhode Island, USA). Measurements were taken simultaneouslyin three areas of the stand with differing vegetation density [P1 (A, B,C): open, P2 (A, B, C): moderate, P3 (A, B, C): dense]. In each of thethree areas, three of the nine pyranometers were located within a radiusof 9 m and measurements were recorded on three CR10X (CSI) data loggers.Soil temperature (three copper-constantan thermocouples at the 25-mmdepth), soil heat flux (three CN3 heat-flux plates, Middleton Solar, Victoria,Australia at 50 mm depth) and volumetric soil water content (three CS-616water content reflectometer, CSI, at 100 mm depth) were measured inthree plots [P1, P2 and P3; recorded on three CR10X (CSI) data loggers].At each plot one sensor for each variable (soil temperature, soil heat flux,soil moisture) was inserted into the ground. All soil measurements are272.2. Methodologysummarized in Table 2.2.Five chromel-constantan thermocouples were installed along a cross-section from south to north just below the bark, at 1/4 diameter and halfdiameter. The thermocouples were installed in a representative dead pinetree at breast height (diameter at breast height (DBH) = 0.15 m), in arepresentative living sub-alpine fir at breast height (DBH = 0.14 m) and atthe base (z = 0.1 m) of the same tree. For each thermocouple a small holewas drilled into the tree to the required depth and sealed with silicon afterthe thermocouple was placed in the right position. These thermocoupleswere recorded on the CR23X data logger. Based on the temperaturemeasurements at the same depth (Ti,n for temperature of a certain ring ion the north side, and Ti,s for temperature of the same ring on the southside, e.g. 1/4 diameter depth at the north and south sides of the tree),the average temperature for a ring at this depth was calculated. Thistemperature was weighted by the area of the ring to which the temperaturecorresponded (pi (r2i,1? r2i,2), where ri,1 and ri,2 are the inner and outer radiiof the corresponding ring, respectively). The average bole temperature(TB) at the given height was then computed by adding the weighted ringtemperatures and dividing them by the total stem cross-sectional area.Soil respiration was measured at 18 locations, where soil collars (collardiameter = 107 mm) were installed distributed throughout the stand.For these measurements a portable chamber system including an LI-800closed-path IRGA (LI-COR Inc.) and an opaque chamber (chambervolume = 0.00162 m3) were used. Measurements were taken on nine daysat different times of the day (from early morning to the evening, a totalof 135 measurements). The flux was calculated from the rate of change ofCO2 concentration measured in the chamber.Leaf area index was measured during the field campaign for the canopyabove the 1.2-m height along a 100-m east-west transect (one measurementevery 10 m) representative of the stand using a plant canopy analyzerLAI-2000, LI-COR Inc. Additional LAI measurements were also derivedfrom airborne light detection and ranging (LiDAR) measurements from2007. LAI data were based on cumulative foliage profiles, which weredetermined according to Coops et al. (2007).Hemispherical photographs were taken at each of the ground pyra-nometer locations and at the three tripod positions using a Coolpix E4300282.2. Methodologycamera (Nikon Inc., Melville, New York, USA) with a fisheye lens (FC-E8,Nikon Inc.) during the 2010 field campaign. A hemispherical photographtaken in 2007 with the same camera set-up below the measurement towerwas also available. The hemispherical photographs were processed usingdigital imaging techniques to separate pixels representing the sky vs. pixelsrepresenting the ground or trees. A relative canopy coverage was definedas the number of ground and tree pixels relative to all pixels within thehemisphere. Hence it is a relative measure of the fractional coverage ofcanopy structure that is blocking the sky at the given location.Average stand density (stems ha?1) and tree volume fraction (?tree,m3 m?3) were estimated based on forest inventory assessments conductedin 2006, when three ground plots (47 m north-east, 85 m south-westand 70 m west of the tower) were established and measured followingCanada?s National Forest Inventory (NFI) ground-plot protocols (NFI,2004). Vertical tree volume fraction profiles were calculated separatelyfor dead (?d) and live trees (?l). Since these NFI data were from 2006,and the mortality rate of mature pine trees increased afterwards to almost100 % (Bowler et al., 2012), it was assumed that all pine trees thatwere taller than 11.9 m and alive in 2006, were dead by 2010. For eachlayer, the number of trees ending in this layer, their average height andtheir average DBH were determined (see Table 2.3). Ormerod?s taperfunction (Ormerod, 1973) was used to determine the diameter at the topand bottom heights and Smalian?s volume relation (Fonseca, 2005) wasused to calculate the tree volume for each layer to which an average treecontributed. A tree contributed to a layer if it ended within or abovethis layer. If the tree ended within the layer but below the top of thelayer, only the length of the bole part that was within the layer wasconsidered. ?tree was then determined by multiplying the volume by thestand density and dividing by the layer thickness and then summing overthe two tree classes (small: H > 1.3 m and DBH < 90 mm; large: H >1.3 m and DBH > 90 mm). Seedlings, saplings and understory broadleafplants were not included in this calculation because of their very small vol-ume. More details on how ?tree was determined can be found in Appendix E.292.2.MethodologyTable 2.3: Stand density, average tree height (H) and average diameter at breast height (DBH) of trees that endin each layer separated into dead and living, small and large trees. These numbers do not account for seedlings,saplings and understory broadleaf plants.Dead LiveLayer height Tree class Stand density H DBH Stand density H DBH(m) (stems ha?1) (m) (mm) (stems ha?1) (m) (mm)1.2 - 2.7 Small 260 1.7 17 1260 1.9 12Large 7.5 2.6 115 0 n.a. n.a.2.7 - 7.6 Small 60 4.5 23 400 4.2 38Large 25 7.1 105 25 6.6 1037.6 - 11.9 Large 82.5 10.6 131 32.5 9.2 10711.9 - 16.5 Large 167.5 14.2 161 17.5 13.1 15116.5 - 21.0 Large 175 18.5 208 0 n.a. n.a.21.0 - 26.8 Large 7.5 21.5 282 0 n.a. n.a.302.2. MethodologyStand density and measured bole temperatures of dead and living treeswere used to calculate ?QS,B accounting for different tree properties inliving and dead trees (i.e., modifying Eq. 2.8 as follows):?QS,B = ?Cw(?d?TB,d?t+ ?l?TB,l?t), (2.10)where TB,d and TB,l are bole temperatures of dead and live trees, respec-tively.2.2.3 Quality control and data analysisThe time period used in this study was from 13 July 2010, 16:00 to 3 August2010, 15:30 PST for which the complete system was continuously in oper-ation. All times herein are given in Pacific Standard Time (PST = UTC -8 h). For the energy balance and radiation analysis all missing data wereinterpolated linearly for maximum time spans of 2 h. If gaps were longerthan 2 h, they were not filled. A particular 30-min period was only acceptedfor analysis if all variables at all levels were available after gap filling.Instrument CalibrationMost instruments were calibrated shortly before or after the field campaign.All radiometers were compared in a field comparison to standard sensors(pyranometers and pyrgeometers) that were previously calibrated byEnvironment Canada in 2008. Based on this comparison, new calibrationfactors were derived and applied to the measurements. All IRGAs werecalibrated using a CO2 span gas (390 ppm CO2 in dry air) and purenitrogen (N2) as a zero gas following the procedure described in LI-COR(2004). In a 3-week field intercomparison in June 2009, six of the sonicanemometers (with the exception of the longterm unit at the 26.8-mheight) were mounted 2.5 m above a grass field (Liss et al., 2009). Overthe intercomparison period, the mean wind speed and air temperature were2.4 m s?1 and 15.0 ?C, respectively. The standard deviation of the 30-mindifferences in u , v , w and T (acoustic) between each anemometer and astandard CSI CSAT sonic anemometer were approximately 0.05, 0.04 and0.02 m s?1 and 0.07 K, respectively. No adjustment in the calibrationsof the sonic anemometer was made. The heat-flux plates together with areference heat-flux plate (HFT-3, CSI; always kept in the laboratory) wereplaced in a soil heat-flux plate calibration box containing a 60-mm thickdry sand layer and a 0.55 m ? 0.55 m heater plate capable of generating312.2. Methodology100 W m?2. All heat-flux plates were positioned parallel to the heaterplate and all 20 mm from the heater plate. Calibration coefficients werederived from the regression between the three soil heat-flux plates and thereference based on the cooling curves. More information on the calibrationof the heat flux plates can be found in Appendix C.Turbulent flux calculationsAs a threshold check, the standard deviation, skewness and excess kurtosisof all turbulence data were examined to ensure their values were within arealistic range (see Table 2.4). At least 98.5 % of the high-frequency data ina 30-min interval had to be acceptable within these intervals to be used inthe analysis. Furthermore the data were iteratively despiked (Aubinet et al.,2012). Data had to fulfill the following requirement to be accepted:x? tx?x < x < x+ tx?x, (2.11)where x is the variable, x is the 30-min average of this variable, tx is thethreshold multiplier set for this variable and ?x is the standard deviationof the variable. tx = 6 for the horizontal wind components (u, v) and p, tx= 8 for the vertical wind component (w), Tac and Tc and tx = 10 for themolar water vapour (q) and molar CO2 density (c). The thresholds weredetermined empirically to ensure that no realistic data were removed. Thedespiking for each variable was repeated 10 times.Wind measurements were filtered for flow distortion by the sonicanemometer head. Flow distortion by the sensor head was assumed to besevere when the wind direction was between 263 and 277?, which was in-formed by wind-tunnel tests of typical CSAT3 instruments (Christen et al.,2001). Data for which the flow was from these directions were excludedfrom the calculations of the statistics. In order to compensate for themisalignment of sensors, a planar fit based on the full measurement periodwas applied to all wind measurements following Foken (2008). In AppendixB, the planar fit was compared to the single and the double rotation usingthe data of this study. Both, the planar fit and the single rotation werefound to be appropriate in this stand, while the double rotation resulted insome spikes but was generally comparable to the other two approaches.322.2.MethodologyTable 2.4: Thresholds for threshold check of turbulence data.Variable u v w Tac q c Tc p(m s?1) (m s?1) (m s?1) (?C) (mmol m?3) (mmol m?3) (?C) (Pa)Lower range, rl ?30 ?30 ?5 ?20 100 12 ?20 0Upper range, ru 30 30 5 40 1500 50 40 1100Upper stddev, stdu 4 4 1.5 2 ?a ?a ?a ?aLower skewness, skl ?3 ?3 ?2 ?2.5 ?5 ?5 ?2.5 ?aUpper skewness, sku 3 3 2 2.5 5 5 2.5 ?aLower kurtosis, kl ?2 ?2 ?2 ?2 ?2 ?2 ?2 ?aUpper kurtosis, ku 5 5 15 15 15 15 15 ?aaNot constrained.332.2. MethodologyH2O and CO2 densities were converted to instantaneous mass mixingratios mq = ?q/?d (kg kg?1) and mc = ?c/?d (kg kg?1), respectively, where?d is the density of dry air (kg m?3). For each half-hour, the covariancesobtained by 30-min block averaging, w?T ?a, w?m?q and w?m?c, were calcu-lated. The overbar denotes half-hourly averaging and the primes indicatefluctuations from the average. The acoustic temperature was used for airtemperature and no detrending was applied. The flux densities were thencalculated as follows:QH = ?Ca w?T ?a, (2.12)QE = ?? ?d w?m?q, (2.13)FC = ?d w?m?c, (2.14)where QH and QE are in units of W m?2 and FC in kg CO2 s?1 m?2.The Schotanus correction (Schotanus et al., 1983) was applied to QH .Since mixing ratios were used for the calculations of QE and FC insteadof densities, a density correction is not necessary (Webb et al., 1980). InAppendix D the flux densities based on mixing ratios were compared toflux densities based on H2O and CO2 densities that were density correctedfollowing Webb et al. (1980). The two approaches showed generally goodagreement.A spectral correction was applied to w?m?q and w?m?c to correct for sensorseparation similar to the experimental approach described in Aubinet et al.(2012). The power spectra of w? and u? and cospectra of w?T ?ac, w?m?qand w?m?c (with 60 frequency bands) were determined for each 30-min pe-riod. Only 30-min periods that fulfilled the following criteria were includedto eliminate time periods with very little turbulent transport: |w?T ?ac| >0.04 K m s?1 (approximately 50 W m?2), |w?q?| > 0.2 mmol m s?1 and|w?c?| > 0.003 mmol m s?1. The lower frequency limit of the inertial sub-range (fa) was determined visually in the median power spectra of u and was the point where the spectra start to show two parallel lines with straightslopes (on a log-log diagram) and fa was determined to be 0.03 Hz. Further-more the highest frequency in the inertial subrange that was not affectedby sensor separation was determined visually and termed the highest unaf-fected frequency (fb), which was determined to be 0.25 Hz. The cospectrumof w?T ?ac (Cwa) was used as a reference since both w and Tac were measured342.2. Methodologyby the same instrument and therefore the covariance was not affected bysensor separation. The integral intensity in the unaffected inertial subrangewas used to calculate a normalization factor for each cospectrum,Nx =? fbfaCwx(f)df, (2.15)Na =? fbfaCwa(f)df. (2.16)Nx is the normalization factor for the cospectrum that is to be corrected(Cwx), where x is either mq or mc and Na is the normalization factor forthe reference cospectrum of w?T ?ac and f is the frequency. An experimentaltransfer function TFexwx was calculated according to Aubinet et al. (2012),TFexwx(f) =NaCwx(f)NxCwa(f). (2.17)A theoretical transfer function TFfitwx was fitted through TFexwx (first proposedby De Ligne et al., 2010):TFfitwx = exp[?ln(2)(ffo,s)n]. (2.18)The parameters that are determined with this fitting are the half-powerfrequency fo,s and the exponent n. The correction factor (CF) was thencalculated using:CF =? fbfaCwx(f) df? fbfaTF fitwx (f) Cwx(f) df. (2.19)Aubinet et al. (2012) reported a wind-speed dependency, however it was notfound in our analysis. Therefore the median correction factor for each levelwas applied to all data for the same level. The correction factors were allvery small (less than 0.25 %).352.2. MethodologySoil heat-flux calculationsA storage correction was applied to QG to account for energy storage in thesoil layer between the heat-flux plate and the surface of the soil accordingto Foken (2008),QG(0) = QG(zs) +CG zs(Ts(t2)? Ts(t1))t2 ? t1, (2.20)where QG(0) is the soil heat-flux at the soil surface, zs is the soil depthat which the soil heat-flux plates were installed (zs = 50 mm), CG is thevolumetric heat capacity of the soil (using a porosity of 0.71 m3 m?3 and avolumetric fraction of mineral soil of 0.29 m3 m?3) and Ts(t1) and Ts(t2) arethe 30-min averaged soil temperatures (measured at zs = 25 mm) betweenthe surface and the heat-flux plate for the 30 min before and after the 30-minperiod concerned, so that t2 ? t1 is 60 min.Calculations of net radiationCNR-1 sensors have in the past been shown to be inaccurate when notventilated (Michel et al., 2008), especially when dewfall occurs. Thereforeall cases with dewfall were eliminated. The criterion for eliminating dewfallcases was when the case temperature of the CNR-1 (Tcase, ?C) was lessthan 5 % above the dewpoint temperature of the air (Tdp, ?C) at thesame measurement height (calculated as 100% ? (Tcase ? Tdp)/Tcase).Furthermore, longwave irradiance (Lin) was corrected for shortwaveirradiance (Sin) dependency by subtracting 1.5% of Sin from Lin assuggested by Michel et al. (2008) for our unventillated instruments. Thesecorrections were only conducted for the CNR-1 sensors since they areinstrument specific. Ensemble-averaged diurnal cycles of all radiationcomponents at z/h = 1.53 and at z/h = 0.06, and the net radiation at allheights with Q? measurements, were calculated by first binning the valuesinto hourly blocks and then averaging the hourly blocks.362.3. Results and discussion2.3 Results and discussion2.3.1 Spatial variability of canopy structure and radiationCanopy coverage was calculated for all measurement locations and issummarized in Table 2.5. Plot locations P1 and P2 had similar canopycoverage of ? 60 %, while P3 had a higher canopy coverage of 75 %.Coverage at the three tripod locations varied from 56 % (open) to 67 %(dense).Using the LiDAR-derived LAI data, the spatial variability of the standwas analyzed. First, a 200 m ? 200 m domain centered around the tower,split into 25 40 m ? 40 m cells, was defined. The cell size correspondsapproximately to twice the canopy height. Figure 2.3 shows LAI aroundthe tower, the grid and the locations of the tower, the pyranometer plotsand the tripod positions. The white contour lines show the averageabove-canopy, 24-h footprint of the turbulent fluxes during the fieldcampaign. The footprint was calculated following Kormann and Meixner(2001). The wind rose at bottom left shows the 24-h wind-directiondistribution measured at tower top (26.8 m); the flow was predominantlyfrom 135? (south-east) to 270? (west) and from ? 335? (north-north-west).Approximately 50 % of the 24-h footprint (and 60 % of the daytimefootprint; not shown) was located inside the domain.The average LAI for each cell was calculated. Although these LAImeasurements were taken in 2007, it can be assumed that the decreasein LAI (approximately 0.1 m2 m?2 yr?1; Brown et al., 2010) in all areaswas proportional to the previous LAI. We are here interested in therelative variability of the stand. Average values of LAI for the cellscontaining P1, P2 and P3 were 0.51, 0.59 and 0.76 m2 m?2, respectively(Table 2.5). Grid cells with LAI < 0.55 m2 m?2 were consideredP1-like, with 0.55 ? LAI ? 0.70 m2 m?2 were considered P2-like,and with LAI > 0.70 m2 m?2 P3-like. Eighteen of the 25 cells withinthe domain were P2-like, while only four were P3-like and three were P1-like.The spatially averaged Sin (Sspatial, W m?2) at ground level wascalculated for each minute based on the simultaneous measurements of thenine ground pyranometers in the three plots (tripod measurements werenot considered for the average since the tripod supported measurementsat the 1-m height). For the spatial average, geospatial-weighting factors372.3. Results and discussionFigure 2.3: Map of a 200 m ? 200 m domain (black grid with 40 m ?40 m cells) centered on the flux tower showing canopy LAI (colours) witha 5-m resolution, the 24-h above-canopy cumulative flux footprint (whitecontour lines), the three plots where ground-level Sin was measured and thethree positions of the roving tripod. The wind rose at bottom left shows theaverage 24-h wind-direction distribution above the canopy during the fieldcampaign.382.3. Results and discussionfor the three measurement locations were defined based on the above LAIanalysis (P1: 3/25, P2: 18/25, P3: 4/25, Table 2.5) to scale measurementswith the area of the forest, of which they are considered representative.The average values of Sin at each ground pyranometer location andtripod location and Sspatial were then calculated for each day for whicha full dataset was available (17 days). Then the root-mean-square error(RMSE) and the RMSE normalized by the ensemble-averaged 24-h valueof Sspatial (149 W m?2) (nRMSE) for each measurement location was de-termined (Table 2.5). Also RMSE for all ground pyranometer locations to-gether (RMSEspatial) weighted by the area of the forest, of which they wereconsidered representative, was calculated. The same geospatial-weightingfactors (wi) as for Sspatial were used,RMSEspatial =??i,dwi(Sd,i ? Sd,spatial)2nNd?iwi, (2.21)where Sd,i is the averaged Sin for day d and pyranometer i, Sd,spatial is thespatially averaged Sin for day d, n is the number of measurement locationsand Nd is the number of days included.The value of RMSEspatial for the entire 200 m ? 200 m domain was 18W m?2, which corresponds to 12 % of the ensemble-averaged Sspatial givingan indication of the spatial variability of Sin at ground level. Even thoughthe tripod measurements were made at 1-m height, the measurementswere very similar to the ground-level measurements. The values of RMSEat the three tripod locations (T1, T2 and T3) were 7, 11 and 4 W m?2,corresponding to the relatively small values of nRMSE of 5, 7 and 3 %,respectively. The RMSE of all tripod positions together was 8 W m?2(nRMSE = 5 %). The tower was located in an area with an averagecumulative LAI of 0.62 m2 m?2, which is comparable to LAI at tripodlocations T1 and T2 (0.62 and 0.61 m2 m?2, respectively) and P2 (0.59m2 m?2). In these three areas RMSE was determined to be between 7 and19 W m?2 (nRMSE between 5 and 13 %). The RMSE of all the three P2pyranometers together was 14 W m?2 (nRMSE of 10 %).If a constant ground albedo (? = 0.15, at z/h = 0.06, see Sect. 2.3.2) isassumed, the RMSE of S? at the ground would be ? 0.85 times the RMSE ofSin (between 6 and 16 W m?2). Regarding daily totals, S? is the dominantcontributor to Q?. These results show that if we average over longer time392.3. Results and discussionTable 2.5: Average cell LAI, RMSE and nRMSE in comparison to Sspatialfor each measurement site. For the plot sites weighting factors are given,which are used in the calculation of Sspatial.Site Cell LAIa Canopy coverage Weighting factor RMSE nRMSEb(%) (W m?2) (%)P1A 0.51 57.33/2515.3 10.3P1B 0.51 61.4 8.8 5.9P1C 0.51 60.2 21.3 14.3P2A 0.59 61.018/2519.0 12.8P2B 0.59 58.7 14.6 9.8P2C 0.59 56.2 7.0 4.7P3A 0.76 74.74/2548.0 32.2P3B 0.76 75.5 64.9 43.6P3C 0.76 74.7 68.8 46.2T1 0.62 56.2 n/a 7.3 4.9T2 0.61 59.0 n/a 10.9 7.3T3 0.64 66.7 n/a 4.2 2.8TOWER 0.62 65.8a n/a < 19.0c < 12.8caMeasured in 2007.bNormalized by ensemble-averaged all-day Sspatial.c Estimated using P2, T1 and T2.scales, the point measurements at the three tripod positions and the towercaptured the shortwave irradiance within the canopy well within ?11 %.Furthermore, since shading by trees decreased with height in the canopy,it can be assumed that the spatial variability of radiation decreased withheight in the canopy.2.3.2 Radiative exchangeShortwave radiation exchangeShortwave radiation fluxes on the flux tower at z/h = 0.06 and z/h = 1.53,as well as Sspatial and extraterrestrial shortwave irradiance (Sext), areshown in Fig. 2.4a. Sunrise and sunset occurred at approximately 04:00and 21:00 PST, respectively. The dip in Sin above the canopy aroundnoon was due to convective clouds, which were regularly observed in theearly afternoon. On average, 58 % of the daily total Sin above the canopyreached the 1-m height (z/h = 0.06), with especially high values of 87 %around 12:00 PST. In the morning and evening, however, larger shortwaveabsorption rates were observed due to the longer path length of direct402.3. Results and discussion(d)(c)(b)(a)06:00 12:00 18:00 24:0000:00Time (PST)510152025T (?C)0.060.140.380.600.831.051.34Bole20040060080010001200S (W m?2) SextSspatial 0100200300400500Q* (W m?2)0.060.140.380.600.831.53300400500L (W m?2) z/h z/hLoutLin 0.06 1.53z/hSoutSin 0.06 1.53z/hFigure 2.4: Averagediurnal cycles of ra-diation fluxes and airtemperature for theperiod from 13 July2010, 16:00 PST to3 August 2010, 15:30PST: a) Sin and Soutat the 1-m height andabove the canopy,Sspatial at the groundand extraterrestrialshortwave irradiance(Sext), b) Lin and Loutat the 1-m height andabove the canopy, c)net radiation at alllevels with radiationmeasurements and d)air temperature atall levels and just-below-the-bark boletemperature for adead tree at 1.3-mheight.412.3. Results and discussionradiation through the canopy at lower solar altitudes. The average dailytotals of Sin at z/h = 0.06 and 1.53 were 13.3 and 22.8 MJ m?2 day?1,respectively. The average daily total of Sspatial on the ground was 12.6MJ m?2 day?1 corresponding to 57 % of the daily total Sin above thecanopy.While Sin was substantially lower in the lower canopy than above, out-going shortwave radiation (Sout) at z/h = 0.06 (average daily total 1.9MJ m?2 day?1) and z/h = 1.53 (average daily total 1.8 MJ m?2 day?1)were very similar. A higher average albedo of ? = 0.15 in the field-of-viewof the down-facing pyranometer at z/h = 0.06 (corresponding to the ground)compared to an average albedo ? = 0.08 at z/h = 1.53 (corresponding tothe stand as a whole) compensates for the lower available Sin that can bereflected. The albedo was calculated based on the average daily totals ofSin and Sout. As a result Sout at z/h = 0.06 even exceeded Sout above thecanopy slightly between 07:00 and 12:00 PST.Longwave radiation exchangeLongwave radiation fluxes are shown in Fig. 2.4b. Outgoing longwaveradiation (Lout) was generally larger than Lin. During the daytime Loutwas larger in the lower canopy than above the canopy, while at night theopposite was the case. Since longwave radiation is a function of the surfacetemperature of objects emitting the radiation, it is important to considerair and bole temperatures (Fig. 2.4d). The bole temperature shown isthe average temperature just below the bark of a dead mature lodgepolepine tree at approximately 1.3 m above the ground (north and south sidesaveraged).Air temperature during the daytime increased with depth into thecanopy and average below-bark temperature was up to 4 K aboveair temperature at z/h = 0.06. At night, a temperature inversionextended all the way to the ground and below-bark temperatures wereapproximately 1 K above air temperatures at the 1.2-m height. Tem-perature differences between the top of the canopy and the lowest levelwere approximately 5 K at night and approximately 3 K during the daytime.In a dense canopy, air temperature usually decreases with depth into thecanopy during the daytime (e.g., Monteith, 1975) and at night it decreaseswith depth only in the upper part of the canopy and remains constant or422.3. Results and discussionslightly increases towards the ground (Huisman and Attenborough, 1991).However, the fact that the forest in this study is very open with LAI =0.55 m2 m?2 leads to a temperature inversion extending to the ground atnight and a relatively constant temperature increase with depth from thetop of the canopy to the ground during the daytime.Even though there was no bole temperature measurement in the uppercanopy available, the measurement at the 1.3-m height corresponded wellto the air temperature slightly above this height at night. Therefore, onecan assume that the bole surface temperature in the upper canopy was alsoclose to the air temperature during this time of the day. In view of this, Loutat z/h = 1.53 at night is expected to be higher than Lout at z/h = 0.06.This is because the lower down-facing pyrgeometer?s field-of-view coveredonly the colder lower parts of the trees and the ground, while the higherdown-facing pyrgeometer?s field-of-view included the warmer tree tops.During the day the opposite was the case, where the lower canopy waswarmer than the upper canopy and therefore Lout at z/h = 0.06 was largerthan Lout at z/h = 1.53.On the other hand, Lin at the top of the canopy originates solely from thesky, which is always colder than the trees; together the sky and trees are thesource of Lin at z/h = 0.06. For this reason Lin was always less than Lout atboth levels. The average daily total Lin at z/h = 0.06 and z/h = 1.53 was30.3 and 27.5 MJ m?2 day?1, respectively. The average daily total Lout was35.1 MJ m?2 day?1 at z/h = 0.06 and 34.8 MJ m?2 day?1 at z/h = 1.53.Net radiationQ? for all six levels that were equipped with either four-componentradiometers or net radiometers are shown in Fig. 2.4c. The average diurnalcycles between z/h = 0.38 and z/h = 1.53 show a relative smooth pattern,with the exception of the time around noon. This corresponds to theSin dip due to the convective cloud cover previously discussed. Betweenz/h = 0.06 and z/h = 0.14, a similar pattern as in Sin can be seen inthe morning and evening at z/h = 0.06, indicating that this was causedby a shading effect due to low solar altitude combined with increased treedensity in the lower canopy.From 05:00 to 19:30 PST, Q? increased with height from the bottomto the top of the canopy; however, above the canopy (z/h = 1.53) Q? was432.3. Results and discussionTable 2.6: Number of cases with unstable, neutral and stable conditions thatwere used in the daytime (Sin above the canopy > 5 W m?2), nighttime (Sinabove the canopy = 0) and 24-h analysis.Daytime Nighttime 24-hourTotal 567 246 842Unstable (z/L ? ?0.1) 413 21 436Neutral (?0.1 < z/L < 0.1) 112 88 215Stable (z/L ? 0.1) 31 137 179Stability not available 11 0 12slightly smaller than in the upper canopy (z/h = 0.82) except between 05:00and 08:00 PST. At night (from 19:00 to 05:00 PST) Q? decreased with heightwithin and above the canopy. At all levels Q? stayed relatively constant overthe course of the night. During the daytime, the decrease in Q? was larger inthe lower canopy below z/h = 0.38, which corresponded to the denser canopypart of the secondary structure. The decrease of Q? from the canopy top tothe ground was mainly caused by incoming shortwave radiation interceptedby the trees. At the top of the canopy there were very few trees that shadedthe specific location of the tower; yet there were trees at the horizon thatcontributed to an increase in Lin. However, a difference in the field-of-viewof the radiative source areas of the down-facing radiometer might also havehad an impact on these results.2.3.3 Energy balance partitioningThis section discusses the diurnal courses of QH , QE and QS +QG, the en-ergy balance partitioning at the levels, the flux divergence and contributionof the storage components in the layers. The diurnal courses, the daytime,nighttime and 24-h profiles represent ensemble averages. The diurnal courseswere calculated using the same procedure as for the diurnal course analysisfor the radiation explained above. Table 2.6 presents the number of stable,neutral and unstable cases determined that were included in the daytime,nighttime and 24-h analyses. Stability was determined using the stabilityparameter (z/L), where L is the Obukhov length (Kaimal and Finnigan,1994).442.3. Results and discussionDiurnal courses of QH , QE and QS +QGFigure 2.5 shows the diurnal cycles of QH , QE and QS +QG at the lowest(z/h = 0.06) and the highest (z/h = 1.34) level. Fluxes during the night-time (between 19:00 and 06:00 PST) were very small and several orders ofmagnitude smaller than during daytime (between 06:00 and 19:00 PST).During daytime all fluxes were negative and therefore fluxes were directedout of the control volume. At both levels QH showed the largest negativefluxes during daytime, while at night QS +QG showed the largest positivevalues. The difference between QS + QG at z/h = 0.06 and z/h = 1.34was small in the afternoon (11:00 to 18:00 PST); however, from 17:00 to04:00 PST, QS + QG differed more between the two levels, which was dueto a larger energy storage change in the air and boles, and moisture contentchange in the air for the higher level. At z/h = 0.06, QH and QE wereclose to zero at night while at z/h = 1.34, QH was slightly positive duringnighttime and QE was negative in the late evening (20:00 to 22:00 PST) andclose to zero for the rest of the night.DaytimeDaytime was defined as the time of the day when Sin above the canopy was> 5 W m?2. Figure 2.6 shows the ensemble-averaged daytime profile of theenergy balance. The values in the flux density profile (Fig. 2.6) give therelative contribution of each flux density at this level compared to the totalinput at the same level in %. For the second highest level (z/h = 1.05), Q?was linearly interpolated between the level above (z/h = 1.53) and below(z/h = 0.83) since no radiation measurements were available for this level.Even though this level was slightly above the given canopy height, a fewtaller trees and the changing radiative source area when moving upwardmight have influenced Q? at this level. For the highest EC measurementheight (z/h = 1.34) Q? was assumed to be equal to Q? at z/h = 1.53.During the daytime, all energy input was due to Q?, which increasedwith height from the bottom to the top of the canopy. A large fraction ofQ? was partitioned into QH (42 to 69 %), followed by QE (18 to 34 %)and QS +QG (6 to 9 %). QH varied only slightly in the upper canopy andabove (z/h ? 0.60, ?171 to ?187 W m?2), but the magnitude decreasedfrom the upper canopy to the ground (?171 to ?71 W m?2). Therelative contribution of QH was the lowest with 42 % and 52 % between0.13 ? z/h ? 0.38 where the secondary structure was most abundant, and452.3. Results and discussion00:00 06:00 12:00 18:00 24:00Time (PST)?500?400?300?200?100  1000Flux density (W m?2)QHQEQS + QG0.06 1.34z/hFigure 2.5: Ensemble-averaged diurnal courses of QH , QE and QS +QG atz/h = 0.06 and z/h = 1.34 for the time period from 13 July 2010, 16:00PST to 3 August 2010, 15:30 PST. The diurnal courses of Q? at the twoheights are shown in Fig. 2.4.462.3. Results and discussionFigure 2.6: Ensemble-averaged daytime flux densities of all energy balanceterms for the time period from 13 July 2010, 16:00 PST to 3 August 2010,15:30 PST. Numbers in the bars are the relative contribution of each compo-nent to the energy balance of the given level in %. The residual is calculatedas Q? +QH +QE +QS +QG.472.3. Results and discussion?50 0 50 100 150Flux divergence(W m?3)00.20.40.60.811.21.4?0.4?0.6 ?0.2 0 0.2Storage change rate(W m?3)(a) (b) ?QS,H?QS,E?QS,B?QS,C?QH/?z?QE/?z?Q*/?zz/hEnergy sinkEnergy sourceEnergy sinkEnergy sourceFigure 2.7: Ensemble-averaged daytime divergences of net radiation and theturbulent fluxes (a) and rates of change of storage (b) for the time periodfrom 13 July 2010, 16:00 PST to 3 August 2010, 15:30 PST. ?QG/?z was?7.72 W m?3 in the lowest layer.482.3. Results and discussionwas the highest above the canopy (69 %). QE showed a large relativecontribution at the lowest level (34 % at z/h = 0.06) when compared withthe levels above, but in absolute terms it varied very little throughout thecanopy and above (?40 to ?54 W m?2). QS +QG was relatively small forall levels in and above the canopy, accounting for only ?11 to ?19 W m?2(between 6 and 8 %), while QG (?9 W m?2) dominated this term.Energy balance closure was high in the upper canopy and above(z/h ? 0.60) with values ranging from 89 to 95 %, which was close toor higher than findings in other studies in forest ecosystems during thesummer (e.g., Aubinet et al., 2001; Wilson et al., 2002; Arain et al., 2003;Amiro et al., 2006; Barr et al., 2006) and was excellent near the groundwith 99 %. However, where secondary structure was most developed,EBC was only 66 ? 77 %. The reduced EBC in the lower canopy butabove the lowest measurement level, might have been due to a differencebetween the radiometer?s field-of-view and the EC sensor flux footprint.The net radiometers within the canopy have a conical field-of-view aroundthe sensor, 90 % of which has a diameter ? six times the measurementheight, whereas the EC system takes integral measurements with a varyingfootprint over time and dependent on measurement height, stability andwind direction and speed. Q? at the lowest level was measured using theroving tripod at three different locations T1 to T3 (see Fig. 2.3). Energybalance closure at this level was very good and may indicate that theQ? measurements at the tripod locations provided more representativesampling than on the tower in the lower canopy. However, in Appendix F,it can be seen that the good closure at z/h = 0.06 was at least partly dueto averaging of widely scattered data. Advective fluxes (Moderow et al.,2007) may have also contributed to the lack of energy balance closure.A closure test was conducted, where the dependency of EBC on frictionvelocity (u? = (u?w?2+ v?w?2)1/4; Stull (1988)) above the canopy was tested(not shown). u? thresholds that were used for the test were 0.1, 0.2 and0.3 m s?1. This test, however, showed that introducing these thresholdsdid not improve energy balance closure substantially during the daytime(< 1 percentage point (pp)). With a u? threshold of 0.4 m s?1 insufficientrecords were left to conduct a meaningful analysis.During the daytime, ?Q?/?z was positive and therefore an energy sourcefor the layers throughout most of the canopy; however, it was only slightlypositive above z/h = 0.38. For almost the entire canopy, ?QH/?z was nega-492.3. Results and discussiontive, i.e., the upward flux of sensible heat increased with height. ?QE/?z islargest in the lowest layer while for the remaining layers, ?QE/?z was small.Contributions by the different vegetation layers (ground layer, secondarystructure, overstory and above the canopy) to the total flux at the topof the tower were calculated by multiplying the flux-density divergenceof each measurement layer by its thickness and adding all measurementlayers that were part of the same vegetation layer. This sum was thendivided by the flux density measured above the canopy. The vegetationlayers are defined as follows: ground layer: z/h = 0 to 0.06, secondarystructure: z/h = 0.06 to 0.60, overstory: z/h = 0.60 to 1.05 and abovecanopy: z/h = 1.05 to 1.34. Similar proportions of Q? above the canopywere absorbed in the layers of the secondary structure (55 %) and theground layer (48 %), i.e. resulting in energy sources for these layers. For?QH/?z, three main contributing layers can be identified: the ground layer(38 % of the flux above the canopy), the secondary structure layer (53 %of the flux above the canopy), the overstory layer with some secondarystructure but mainly dead trees, where ?QH/?z decreased steadily (7% of the flux above the canopy) until it approached zero at the top ofthe canopy and above (z/h > 1). During this relatively dry period inthis stand with a dead overstory, most of QE originated in the groundlayer (z/h < 0.06, ?34 W m?3; Fig. 2.7a) making up 87 % of the totalQE measured above the canopy. This high proportion contrasts with theresults of several other studies that employed the EC method to measurefluxes from the understory in healthy forests. Lee and Black (1993b)found that approximately 30 % of the latent heat flux and approximately20 % of the sensible heat flux came from the understory and groundin an extensively thinned 28-year old Douglas-fir stand. Blanken et al.(2001) determined that 30 to 35 % of the latent heat flux came fromthe hazelnut understory and ground in a 70-year old boreal aspen stand.Staudt et al. (2011) found that 10 % of the forest?s evapotranspirationoriginated from close to the ground in a 54-year old Norway spruce stand.On the other hand, in a maritime pine forest during a drought period,Jarosz et al. (2008) found that the overstory pine followed a drought-avoiding strategy in contrast to the grassy understory, resulting in theunderstory accounting for as much as 45 % of the overall evapotranspiration.Figure 2.7b shows the vertical distribution of the rates of change of en-ergy storage in the forest. Energy storage due to the change of sensible heatin the air (?QS,H) was negative (i.e., air temperature increased) and made502.3. Results and discussionup the largest part of the energy storage in the upper canopy (z/h ? 0.60).It was almost constant throughout and above the canopy. All other terms,namely ?QS,E, ?QS,B and ?QS,C were also negative and therefore alsoaccounted for energy storage in the lower canopy where living vegetationwas abundant. In the lower canopy (z/h < 0.38), ?QS,B exceeded ?QS,Hand in the lowest layer ?QS,C was the largest contributor to energy stor-age. Above z/h = 0.14, ?QS,B decreased with height due to decreasing treevolume fraction. As described in Section 2.2.2, ?QS,B was estimated basedon TB measurements close to the ground and at 1.3 m above the ground.?QS,C was an energy source in the upper canopy because of respirationof the dead trees in the upper canopy. The magnitude of ?QS,E steadilydecreased with height throughout the canopy. Figure 2.7b shows that en-ergy storage change is negligible compared to ?QH/?z and ?QE/?z duringdaytime, i.e., as a good approximation (above the ground layer),?Q??z+?QH?z+?QE?z? 0. (2.22)Figure 2.8 shows the average Bowen ratio (? = QH/QE) profile atfour different times of the day (08:00, 11:00, 14:00, 17:00 PST) and theensemble-averaged daytime ?. The average daytime ? was calculated basedon the average daytime total QH and QE . At all times and all levels,? > 1, except in the morning at the lowest 2 levels. In the morning, ?increased with height from the ground to the upper canopy (z/h = 0.83 toz/h = 1.05) and then stayed relatively constant. During the rest of the day? increased again with height from the ground to the upper canopy butdecreased above. The dominance of QH generally increased over the courseof the day. Close to the ground, however, it decreased again in the evening.On average, ? during the day increased from 1.9 at the ground to 4.3at z/h = 0.83 and decreased slightly to 3.9 at the highest level (z/h =1.34). This reflected the strong source of sensible heat throughout the wholecanopy, while there was almost no latent heat added above the lowest layer.At the same time, relative QE contributions to the energy balance werelarger near the ground than above. QE > QH only in the early morning nearthe ground surface due to the evaporation of dewfall and soil moisture, andto transpiration of plants with high stomatal conductance in the morning.512.3. Results and discussion0 21 3 4 5?00.20.40.60.811.21.4z/h  08:00  11:00  14:00  17:00  AverageFigure 2.8: Average Bowen ratio (?) at 08:00, 11:00, 14:00 and 17:00PST and ensemble-averaged daytime Bowen ratio i.e., (daytime totalQH)/(daytime total QE).522.3. Results and discussionNighttimeNighttime was defined as the period when Sin = 0 above the canopy. Q?decreased from ?22 W m?2 at z/h = 0.06 to ?56 W m?2 at z/h = 1.34and much of this energy loss, especially in the upper canopy and above isaccounted for by QS + QG (33 to 44 % of the energy output) (Fig. 2.9).The second largest source of energy balancing the radiative loss was QH .However, with contributions of 9 % in the lower canopy to 33 % in theupper canopy, its relative contribution was smaller than during the day.The value of QH varied between 2 W m?2 at z/h = 0.06 and 16 W m?2 atz/h = 0.83. QE was small at all levels (magnitude less than 4 W m?2 and6 %). At night the residual was substantial and larger than 50 % in thelower canopy.Similar to the flux densities, the flux-density divergences were alsosmaller at night compared to the daytime (Fig. 2.10a). ?Q?/?z wasrelatively large in the layers below z/h = 0.14 and small in the layersabove. Both ?QE/?z and ?QH/?z were small throughout the canopy,but increased slightly in the lowest layer (z/h < 0.06). The significantincrease in ?QH/?z close to the the top of the secondary structure(0.38 < z/h < 0.60) largely balanced the increase in the magnitude of netradiative divergence at this height.At night, sensible heat storage change in the air and in the boles wereenergy sources (i.e., ?QS,H > 0 and ?QS,B > 0) for the net radiativeloss, about twice the magnitude of the sink they were during the daytimeand they decreased slightly with height (Fig. 2.10b). ?QS,C however,was close to zero in the upper layer, while the graph shows a small sinkof energy below z/h < 0.38, indicating the occurrence of advection andproblems with turbulent flux measurements at night in the lower canopysince photosynthesis does not occur at night.Values of EBC at night were lower than during the daytime, and variedbetween 13 % in the lower canopy to 58 % in the upper canopy (Fig. 2.9).The closure problem during the nighttime has been identified previously(e.g., Baldocchi and Meyers, 1988a; Berbigier et al., 2001; Wilson et al.,2002) and is usually attributed to stable stratification, low turbulence andpossible dominance of large-scale horizontal advection (e.g., Leuning et al.,2008) or dispersive fluxes (Poggi and Katul, 2008). As stated above,dispersive fluxes can become significant in a sparse canopy (Poggi et al.,532.3. Results and discussionFigure 2.9: Same as Fig. 2.6 but for nighttime.542.3. Results and discussion?20 ?15 ?10 ?5 0 5 1000.20.40.60.811.21.4z/hFlux divergence(W m?3)Storage change rate(W m?3)(a) (b) ?QS,H?QS,E?QS,B?QS,C?QH/?z?QE/?z?Q*/?zEnergy sinkEnergy sourceEnergy sinkEnergy source?0.5 0 0.5 1.0 1.5Figure 2.10: Same as Fig. 2.7 but for nighttime. ?QG/?z was 6.22 W m?3in the lowest layer.552.3. Results and discussionTable 2.7: Energy balance closure (EBC, in %) during nighttime at all sevenlevels (z/h) when using no threshold and when using different u? thresholds.The number of records (N) included in the analysis for each threshold is alsoshown.z/h no threshold u? > 0.1 m s?1 u? > 0.2 m s?1 u? > 0.3 m s?10.06 17.4 18.2 24.2 30.00.14 13.0 14.0 16.3 19.30.38 31.0 33.0 39.0 50.90.60 52.7 53.7 54.4 64.70.83 58.0 58.8 62.7 62.51.05 48.9 50.0 57.0 68.71.34 31.9 32.6 34.1 37.4N 249 225 144 732004b; Christen and Vogt, 2004) and their effect is larger in the lowercanopy than at the top of the canopy (Bohm et al., 2000). Furthermore,even though the stand in this study has an adequate and homogeneousfetch, absolute homogeneity and perfectly steady-state conditions are rarelyfound and can therefore lead to significant horizontal advective fluxes whenturbulent fluxes are small (Aubinet et al., 2012). In 55 % of the casesthat were used in our nighttime profile analysis were dynamically stable(z/L ? 0.1 at the top of the tower; Table 2.6). Observations in averageshowed stable stratification with a well-developed inversion extended allthe way to the ground. Energy balance closure tests for nighttime wereconducted using several u? thresholds (Table 2.7). For u? thresholds of0.2 m s?1 and 0.3 m s?1, EBC was improved by several pp at all levelsincreasing closure by up to 20 pp for z/h = 0.38. Appendix F shows a moredetailed analysis of turbulence thresholds in the context of EBC.24-h totalsFigure 2.11 shows the average 24-h flux densities of the energy balancecomponents and Fig. 2.12 shows the average 24-h flux-density divergencesand storage term components for all levels and layers, respectively. The24-h profiles in Figs. 2.11 and 2.12 were dominated by the daytimebehaviour and therefore were very similar to the daytime distribution inFigs. 2.6 and 2.7, respectively. This is because turbulent energy exchangeduring the daytime was almost an order of magnitude larger than at night562.3. Results and discussionand daytime took up approximately 17 h of the day during the campaign.Relative QH dominance was even larger than in the daytime analysis,while the storage contribution was smaller and closure was greater at alllevels. The ratio of QE to the incoming radiation at each level was alsoslightly larger than during daytime. Q? varied from approximately 77W m?2 or 6.6 MJ m?2 day?1 close to the ground to 169 W m?2 or 14.6MJ m?2 day?1 at the top of the canopy. Above the canopy, daily total Q?decreased again similarly to the daytime profile.The daily total flux-density divergences of Q?, QH and QE shown inFig. 2.12a were also dominated by the daytime and showed the strongestnegative ?QH/?z values (?39 W m?2 or ?3.4 MJ m?3 day?1) and?QE/?z values (?23 W m?2 or ?2.0 MJ m?3 day?1) close to the ground,near-zero values of ?QE/?z for all above layers and reduced but relativelystrong values of ?QH/?z (between ?5 and ?7 W m?3 or ?0.4 and ?0.6MJ m?3 day?1) where there was the secondary structure. ?Q?/?z was astrong energy source in the lower canopy (between 31 and 64 W m?3 or 2.7and 5.5 MJ m?3 day?1 at z/h < 0.14), an energy source for layers between0.14 < z/h < 0.60 (about 5 W m?3 or 0.4 MJ m?3 day?1) and close tozero above.Overall, 85 % of the total QE measured at the top of the tower originatedfrom the ground and 19 % from the layers with secondary structure, whilethe overstory composed of primarily dead pine trees appeared to be a weaksink (8 %) but this might be partly due to error in measuring the smalllatent heat fluxes since the dead trees would not be expected to absorbmuch water vapour. In the case of QH , 39 % of that measured at towertop originated from the ground, while 53 % and 8 % originated from thesecondary structure and the dead overstory layers, respectively. The groundlayer and the layers with secondary structure were similar sized sinks for Q?,i.e., 48 % and 55 %, respectively. The overstory was a very small sink for Q?.In the case of energy storage, daytime and nighttime ?QS,B compen-sated each other as expected and the boles overall neither stored nor re-leased substantial amounts of energy over the duration of the campaign.Also ?QS,H and ?QS,E were negligibly small in all layers on a 24-h ba-sis. ?QS,C was a relatively strong energy sink where the active secondarystructure and the ground vegetation was most abundant (?0.2 W m?3 or?0.01 MJ m?3 day?1 at 0.06 < z/h < 0.14) compared to the other stor-age terms (up to ?0.6 W m?3 or ?0.05 MJ m?3 day?1), while it was a572.3. Results and discussionFigure 2.11: Same as Fig. 2.6 but showing averaged 24-h profiles. Averageddaily total flux densities (MJ m?2 day?1) are also indicated on the x-axisat the top.582.3. Results and discussion?0.3?0.6 0?50 00 3 0?0.04 ?0.02?3 650 10000.20.40.60.811.21.4z/hEnergy sink Energy source Energy sink Energy source (a) (b)?QS,H?QS,E?QS,B?QS,C?QH/?z?QE/?z?Q*/?zFlux divergence(W m?3)Storage change rate(W m?3)Flux divergence(MJ m-3 day-1)Storage change rate(MJ m-3 day-1)Figure 2.12: Same as Fig. 2.7 but showing averaged 24-h profiles. Av-eraged daily total flux-density divergences (MJ m?3 day?1) are also indi-cated on a secondary x-axis at the top. ?QG/?z was ?3 W m?3 or ?0.26MJ m?3 day?1 in the lowest layer.592.4. Summary and conclusionssource above z/h = 0.38. ?QG/?z was an energy sink of ?3.0 W m?3 or?0.26 MJ m?3 day?1 in the lowest layer (not shown). This chemical energystorage is of longer duration (seasonal), and hence it is not surprising that?QS,C is the only term that over a 24-h period is not negligible.2.4 Summary and conclusionsThe open-stand structure resulting from the MPB attack allowed 60 % ofshortwave irradiance to reach the forest floor resulting in ground-level dailytotal net radiation being almost 50 % of that above the stand. The upperpart of the canopy was a strong source of sensible heat, a weak source oflatent heat with the Bowen ratio (?) reaching 4. The lower part of thecanopy with the understory and shrubs was a source of latent heat evenunder these dry conditions with ? being as low as 2.During the daytime, canopy energy storage was small with sensibleheat storage in the air being most important in the upper canopy, whileenergy storage in the lower canopy was mainly due to biomass heat storageand photosynthesis. At night the decrease in sensible heat storage in thebiomass and air accounted for up to 40 % of net radiative loss. Over 24hours, the changes in canopy energy storage and ground heat flux werenegligible.Energy balance closure was relatively high during the daytime, whenthe open-stand structure resulted in relatively strong coupling throughthe canopy and sub-canopy. However, in the layers where secondarystructure was most abundant, the residuals were as high as 30 %.Nighttime EBC residuals approached 60 % and therefore nighttime fluxmeasurements remain a concern inside the canopy and generally for theentire forest-atmosphere interface.While measurements at the tower appeared to be relatively representa-tive of the stand, improved spatial coverage with additional radiometer mea-surements, not only at ground level but also throughout the canopy space,would be strongly recommended for such a study and could contribute toobtaining improved closure. The penetration of shortwave radiation in thisopen stand and reduced within-canopy wind speed (see Chapter 4), resultingin a favorable ground-level microclimate, help explain the surprisingly rapid602.4. Summary and conclusionsrecovery of the stand following the beetle attack as reported by Brown et al.(2012a).61Chapter 3Vertical distribution ofcarbon dioxide sources andsinks3.1 IntroductionForests are important for the storage of carbon (C). About 2.2 times theatmospheric C, and the largest fraction of terrestrial ecosystem C is storedin forests (Sabine et al., 2004). Carbon is stored through photosynthesisin plant tissues, while heterotrophic and autotrophic respiration releaseC from the soil and plants to the atmosphere in the form of carbondioxide (CO2). In many healthy forests, C uptake exceeds the releasemaking them an overall sink for C (Baldocchi, 2008). Disturbances likeforest fires, harvesting and insect infestations, however, can turn forestecosystems into C sources (e.g., Kurz et al., 2008). Insects such as themountain pine beetle (MPB, Dendroctonus ponderosae) have an impacton the net primary production (NPP) of forests, but this has generallybeen ignored in large-scale carbon modelling studies (McGuire et al., 2001;Myneni et al., 2001). The native habitat of the MPB is in the western partof North America. Large outbreaks are common events in the region butthe current outbreak in British Columbia (BC), Canada, which startedin the late 1990s, is the largest outbreak ever recorded in North America(Safranyik and Wilson, 2006). By 2011, 710 million m3 of merchantablepine volume (Walton, 2012) in a total outbreak area of 181, 000 km2(MFLNRO, 2012) had been killed since the start of this outbreak.There are three different management responses to the outbreak ofMPB: (i) non-invasive (no treatment), (ii) removal of only the affectedtrees (partial harvesting) and (iii) complete removal of the affected stand(clearcut harvesting). Brown et al. (2012a) found that two MPB-attackedstands in the interior of British Columbia that received no treatment623.1. Introductionrecovered to C neutrality in three and five years, respectively, after beetleattack. At the same time, nearby clearcut sites remained C sources for upto 10 years after harvesting. They speculated that the growth responseof the secondary structure (trees and understory not killed by the beetle)following the attack was responsible for the fast recovery. In Chapter 2, itwas found that in the MPB-attacked stand discussed in this thesis 60 % ofabove-canopy shortwave irradiance reached the ground and that latent heat(and therefore water (H2O) vapour) originated mainly from the understorylayer underlining the important effect of the understory on the overall standmicroclimate. Given the high level of irradiance reaching the secondarystructure but small H2O flux originating from the secondary structurelayer, the vertical variation of water use efficiency (WUE), the ratio ofC uptake to H2O loss, is of interest. During photosynthesis, stomatalopenings (and thereby stomatal conductance) can be regulated. Whenstomatal conductance is high, more CO2 can be stored in plant tissuesthan when it is low, but at the same time more H2O will be transpiredand lost to the atmosphere. This trade-off between CO2 uptake and H2Oloss varies, however, between plant species and climatic conditions (e.g.,Marshall and Waring, 1984) and is described by WUE, which links the Cassimilated to the H2O loss by transpiration. Cowan and Farquhar (1977)proposed that plants control stomata to optimally satisfy the trade-offbetween the amount of C assimilated and the amount of H2O transpired.Studies have shown that there is a potential for partial harvestingand non-invasive strategies to improve CO2 uptake (Kurz et al., 2008;Edburg et al., 2011; Brown et al., 2012a; Mathys et al., 2013) and harvestyields (Nishio, 2009). Partially harvested and non-invasively managedforests are of a particular interest since Coates et al. (2006) have shown that20-30 % of MPB stands in central and northern BC have sufficient secondarystructure to expect a midterm harvest even if left unharvested, and approxi-mately 40-50 % could be restocked without further silvicultural intervention.In this thesis, a non-invasively managed MPB-affected lodgepole pinedominated stand in the interior of BC was studied. Brown et al. (2012a)identified that over the growing season this stand was a weak C sinkand hypothesized that the secondary structure was responsible for theuptake. This study aimed to validate this hypothesis by quantifying howmuch different layers of the canopy contributed to the stand?s overallrespiration, photosynthesis and transpiration. Knowing the processes on alayer-by-layer basis is necessary to develop models that project the course633.2. Methodologyof the recovery of non-invasively managed MPB-impacted lodgepole pinestands. The specific objectives of the paper are: (i) to determine thevertical distribution of CO2 sources and sinks within and above the canopyof this MPB-attacked pine stand, (ii) to determine the average vertical CO2flux profiles, and source and sink strengths in the three vegetation layers(understory, secondary structure and overstory) for different times of theday, (iii) to partition fluxes into respiration and photosynthesis componentsin the different layers, and (iv) to determine the WUE of the differentvegetation layers.Two independent approaches are used to answer these questions,namely the eddy-covariance approach (EC) (Baldocchi, 2003) and anecophysiological approach (EP) which scales photosynthesis and respirationmeasurements to the entire ecosystem using chamber measurements of CO2exchange on foliage and boles, climatic measurements and stand structureinformation (Pypker and Fredeen, 2002a,b).There have been a number of studies measuring turbulent fluxesusing the EC approach within or below a forest canopy to partitionsub-canopy contributions (e.g., Lee and Black, 1993b; Baldocchi and Vogel,1996; Blanken et al., 1997; Saugier et al., 1997; Wilson et al., 2000;Blanken et al., 2001; Blanken and Black, 2004; Roupsard et al., 2006;Jarosz et al., 2008), where usually one EC system was installed above thecanopy and one within the canopy. Only few studies (e.g., Staudt et al.,2011; Zhang et al., 2010) have used a larger number of systems to determinethe vertical structure of turbulent exchange and to the authors? knowledgethis is the first study that uses a high vertical resolution to partitioncanopy-layer contributions to the net ecosystem exchange (NEE). Otherstudies have used an inverse-Lagrangian approach to determine scalarsources and sinks within a canopy from a measured vertical scalar concentra-tion profile (e.g., Katul et al., 1997; Juang et al., 2006; Brown et al., 2012b).3.2 Methodology3.2.1 Measurement siteThe study site was located in a lodgepole pine dominated stand adjacent toCrooked River Provincial Park (70 km north of Prince George, BC, Canada54?28?24.8??N, 122?42?48.4??W). The stand was first attacked by MPB in643.2. Methodology2003, experienced almost 100 % mortality of the mature pine trees by 2007and was non-invasively managed after the MPB attack. The stand wascharacterized by a rich secondary structure consisting of living sub-canopylodgepole pine, subalpine fir (Albies lasiocarpa), hybrid spruce (Picea glauca? engelmannii) and a few Douglas-fir (Pseudotsuga menziesii var. glauca)trees and saplings, while the dead overstory consisted almost entirely oflodgepole pine (Fig. 3.1). The secondary structure had a maximum heightof 12 m, but most (> 90 %) of the secondary structure was smaller than4 m tall. The ground was widely covered with mosses, lichens, Vacciniumspecies, ground cedar (Lycopodium complanatum) and kinnikinnick (Arc-tostraphylos uva-ursi), which were between a few cm and 1 m tall. Thestand height (h) was 20 m and the canopy above the 1.3-m height had anaverage leaf area index (LAI) of 0.55 m2 m?2 in 2010. Fig. 3.2 shows thevertical LiDAR-derived leaf area density (LAD) distribution above the 3-mheight in 2006 (pers. comm. T. Hilker) and the estimated LAD of living veg-etation in three vegetation layers as used in calculations (see Section 3.2.3).The stand had a relatively homogeneous fetch > 0.4 km in all directionsaround the tower and the terrain was flat (< 0.5 ? slope). A full descriptionof the stand can be found in Brown et al. (2010) and Bowler et al. (2012).The stand density variability and its effect on radiation transmission andenergy balance partitioning was discussed in Chapter 2. Photographs of themeasurement site and the instrumentation are shown in Appendix A.3.2.2 InstrumentationAn intensive field campaign was conducted during July and August of 2010.A 30-m tall scaffold tower was used as the main platform of measurements,while some instruments were installed on a roving tripod, in the soil or inboles. All times given in the following text are Pacific Standard Time (PST= UTC ? 8h). In the following, a level was defined as a measurement height,while a layer was defined as a stratum between two levels.ClimateIncoming photosynthetically active radiation (PAR, ?mol m?2 s?1) wasmeasured at six heights (Table 3.1) on the tower and a roving tripod (onlythe lowest measurement level) using six upward-facing quantum sensors(two quantum sensors SQ-110, Apogee Instruments Inc., Logan, Utah atthe 1.2- and 16.8-m heights; two line quantum sensors LI-191SA, LI-CORInc., Lincoln, Nebraska at the 7.6- and 11.9-m heights; two quantum653.2. MethodologyFigure 3.1: Photograph of the forest structure in the MPB-attacked stand:dead mature pine trees, sparse living secondary structure and widespreadground coverage in the understory. This photograph was taken on 9 July2010 just before the start of the field campaign close to the tower.663.2. Methodology0 0.01 0.02 0.03 0.04 0.05 1.14LAD (m2 m?3)0 0.5 1 1.5 z/hFigure 3.2: Average profile of LiDAR-derived leaf area density (LAD) (blue)in 2006 and assumed LAD of living vegetation in 2010 as used in the eco-physiological approach based on on-ground destructive LAI measurements(green). Below the 3-m height (z/h = 0.15) LAD based on LiDAR datacannot be determined since the signal cannot be separated from groundreturns.673.2. MethodologyTable 3.1: Selected instrumentation installed on the scaffold towerh z/ha Fc PAR ?c, ?q26.80 1.34 CSAT3, LI-7500 LI-190b LI-840 gas multiplexer, LI-750021.00 1.05 CSAT3, LI-7500 - LI-840 gas multiplexer, LI-750016.50 0.83 CSAT3, LI-7500 SQ-110 LI-840 gas multiplexer, LI-750011.90 0.60 CSAT3, LI-7500 LI-191SA LI-840 gas multiplexer, LI-75007.60 0.38 CSAT3, LI-7500 LI-191SA LI-840 gas multiplexer, LI-75002.70 0.14 CSAT3, LI-7500 LI-190 LI-840 gas multiplexer, LI-75001.20 0.06 CSAT3, LI-7500 SQ-110c LI-840 gas multiplexer, LI-7500aMeasurement height is normalized to canopy height h = 20 m.bThis measurement was made at the 30-m heightcThis system was mounted on the roving tripod.sensors LI-190, LI-COR at the 2.7- and 30.0-m heights). The position of theroving tripod was changed three times over the course of the campaign tocapture the small stand density variability (see Chapter 2). A comparablespatial sampling was not possible for the higher measurement levels. Afour-component net radiometer (CNR-1, Kipp & Zonen B.V., Delft, TheNetherlands) was installed above the canopy at the 30-m height measuringincoming and outgoing short and longwave radiation. For all radiometersat the 2.7- and 30-m heights, 30-min averages were recorded, while for allother levels 1-min averaged radiometer measurements were recorded.Air temperature (Ta) and relative humidity (RH) were measured at the6-m height using a temperature and relative humidity probe (HMP45C,Vaisala Oyj, Helsinki, Finland) and precipitation was measured with atipping bucket rain gauge (TE525M, Campbell Scientific (CSI), Logan,Utah) at the 25-m height. For all these measurements, 30-min averageswere recorded.Bole temperature (TB) of a living subalpine fir (diameter at breastheight (DBH): 14 cm) and a dead lodgepole pine (DBH: 15 cm) wasmeasured with 8 thermocouples (custom-made, Type T) at 1.3-m height andrecorded using a solid-state multiplexer (AM25-T, CSI). The thermocoupleswere placed just below the bark on the north and south sides of each tree.Soil temperature (Ts; at 0.025-m depth) and soil moisture content (?s; at0.1-m depth) were measured using thermocouples (custom-made, Type T)and water content reflectometers (CS-616, CSI), respectively in three plots(P1, P2 and P3) around the tower with slightly differing stand density (seeChapter 2). A temperature correction was applied to the CS-616 data as683.2. Methodologydescribed in Campbell Scientific (2012). For all bole and soil measurements1-min averages were recorded.Eddy-covariance measurementsSeven eddy-covariance systems were installed on the tower at the 1.2-, 2.7-,7.6-, 11.9-, 16.5-, 21.0- and 26.8-m heights (Table 3.1) . Each comprisedan ultrasonic anemometer (CSAT3, CSI) measuring three-dimensional windspeed (u, v and w) and acoustic temperature, an open-path infrared gasanalyzer (IRGA; LI-7500, LI-COR) capable of measuring CO2 and H2Omolar densities (?c and ?q, respectively) and pressure (p) and a fast-responsefine-wire thermocouple (25.4 ?m, Type E, custom-made). The measurementfrequency for all these instruments was 10 Hz at all heights except the 26-mheight level where the measurement frequency was 5 Hz.Soil and bole respirationSoil and bole respiration (Rs and Rb, respectively) was determined witha manual portable chamber system, which is described in Jassal et al.(2007). The system was equipped with a closed-path IRGA (LI-800,LI-COR) and a temperature and relative humidity probe (HMP35CF,CSI). Measurements were conducted with an opaque, cylindric PVCchamber (volume = 0.0163 m3, inside diameter = 0.107 m). The pumpdrew air from the chamber at 2.5 l min?1 through the sampling tubediverting 0.8 dm3 min?1 to the IRGA. CO2 mole fraction, temperatureand relative humidity were recorded at a frequency of 1 Hz. Measurementswere taken in six plots (B1 to B6, of which two were always close toeach soil measurement plot P1, P2 and P3) covering areas with varyingstand density (see Chapter 2). Within each of the chamber measurementplots (B1 to B6), PVC collars were attached to three trees (one collaron each tree, DBH between 0.114 and 0.286 m) with galvanized wireand sealed with silicone caulk and three collars were installed in the soil.Soil temperature and water content were measured with a hand-heldthermocouple and a hand-held volumetric soil water content measurementsystem (Hydrosense, CSI), which were inserted into the soil close to thecollars at the time of the chamber measurements and sampled the top 0.1 mof the soil. Chamber measurements were made on nine days between 07:00and 18:30, including three diurnal runs on a subset of the sampling locations.693.2. MethodologyLeaf net assimilationLeaf net assimilation (A) was measured using a portable photosynthesissystem (LI-6400, LI-COR). Measurements were made on 39 understoryand secondary structure plants on nine days simultaneously with the ECmeasurements between 08:00 and 19:00. These measurements includedone diurnal run on a subset of seven plants and full runs on seven days,where 27 assigned plants were measured once a day (different times of theday). Vapour pressure deficit (D) and Ta in the chamber were recordedas well as PAR outside the chamber. The same procedure as Bowler et al.(2012) was followed, where measurements were made in unshaded locationsin the stand and needles younger than one year were excluded from themeasurements. Shoots were clipped from conifer trees and measured within5 min after clipping while understory broadleaf species were measuredin situ unless they were located too close to ground. Each measurementwas repeated three times and the average of the three measurements wascomputed to capture any short-term variability in environmental variablesaffecting gas exchange. The hemi-surface leaf area of the measured brancheswas determined destructively as described in Bowler et al. (2012).Vertical CO2 concentration profileAccurate CO2 mole fractions (c, ?mol mol?1 moist air) were measured alongthe tower using a closed-path IRGA (LI-840, LI-COR, measurement fre-quency 1 Hz). The IRGA was connected to seven tubes (Synflex 1300, 4.0mm inner diameter, Saint-Gobain Performance Plastics, Wayne, NJ, USA)to sample air from each of the seven EC levels. The system sampled se-quentially for 3 min 25 s per level though the seven levels from bottom totop using a gas multiplexer with solenoid valves. The flow rate through theSynflex tubes was 5 l min?1 , while only 0.6 l min?1 were fed into the IRGA.All Synflex tubes had the same length to avoid pressure differences. Thesystem was calibrated every 1 h to 3 h by running consecutively nitrogen(N2) as a zero gas and a CO2 span gas (CO2 in dry air) into the air samplingintake at the bottom level. Intake of ambient air during the calibration wasavoided by keeping the calibration gas flow higher than 5 l min?1. Eachcalibration gas was measured for 3 min at the end of the half hour. Duringthe 30-min periods without calibration, the lowest level was measured foran additional 6 min at the end of the half hour.703.2. Methodology3.2.3 Analysis and correctionsCO2 exchange was determined for three canopy layers, which were definedas follows: the understory layer: 0 - 1.2 m (z/h = 0 to 0.06), the secondarystructure layer: 1.2 - 11.9 m (z/h = 0.06 to 0.60), and the overstory layer:11.9 - 20 m (z/h = 0.60 to 1.00). The data included in this study wereobtained between 14 July and 3 August 2010. The two following weekswere included to establish light response curves and to calibrate the LI-840IRGA. All instruments (except the EC system at the 26.8-m height) werecalibrated or intercompared before, during or after the field campaign.Eddy-covariance approachIn the EC approach, ?c (?mol m?3) was converted to the instantaneousmolar mixing ratio mc = ?c/?a (?mol mol?1), where ?a is the molar densityof dry air (mol m?3). For each half hour, the 30-min averaged covariancew?m?c was calculated, where w is the vertical wind speed (m s?1). Theoverbar denotes half-hourly averaging and the primes indicate fluctuationsfrom the average. The molar flux density (Fc, ?mol m?2 s?1) was thencomputed as (Webb et al., 1980):Fc = ?a w?m?c (3.1)Positive values of Fc are upward fluxes and negative values are downwardfluxes. The same corrections and quality control procedures as presentedin Chapter 2 were applied to the EC data: despiking, spectral correction,planar fit, and removal of data that were affected by anemometer and towerflow distortion. The data was inspected visually for unrealistic data, whichwere then excluded from the analysis. In this subjective approach, datafrom each level was compared to the other levels and each half hour wascompared to the half hours before and after.Fc is the directly measured flux; however, a correction for the rate ofchange in CO2 storage in the air column beneath the flux measurementlevel must be applied as follows in order to determine the net CO2 exchange(NEEz, ?mol m?2 s?1) below each level:NEEz = Fc +?Fs, (3.2)The rate-of-storage change (?Fs) is defined as?Fs =? z0??c?tdz, (3.3)713.2. Methodologywhere z is the measurement height (m) and t is the time (s). To calculatethe rate of storage change, differences in open-path IRGA (i.e., LI-7500)molar concentrations between the 30-min periods before and after the30-min period concerned were determined. For this the open-path IRGAmeasurements were calibrated against the closed path (i.e., LI-840)measurements. For the top level above the canopy NEEz is equivalent tothe total net ecosystem exchange.The CO2 source/sink strength (Sc, ?mol m?3 s?1) was then determinedusing the conservation equation of a scalar (Stull, 1988):??c?t+uj??c?xj=?c?2?c?x2j+ Sc ??(u?j??c)?xj, (3.4)where t is the time, uj is the wind velocity component in the j direction, xjis the distance in the j direction and ?c is the molecular diffusivity of CO2. Ifit is assumed horizontal homogeneity (?/?x = 0, ?/?y = 0), no subsidence(w = 0) and that diffusion is negligibly small, then the second and thirdterm (advection by mean wind and molecular diffusion, respectively) arezero and in the fifth term (divergence of the turbulent flux) only the verticalflux divergence remains, which when solving for Sc gives:Sc =??c?t+?(w???c)?z, (3.5)where a positive value of Sc indicates a source and a negative value indicatesa sink. Since ?c = mc?a and given Eqs. 3.2 and 3.5:Sc =dNEEzdz, (3.6)In discrete form, Sc for a layer between z1 and z2 can be written as:Sc,z1?z2 =NEEz2 ?NEEz1z2 ? z1. (3.7)The soil respiration determined with the portable chamber system was usedas the lower boundary of the lowest layer, so thatSc,0 m?z1 =NEEz1 ?Rsz1. (3.8)723.2. MethodologyPartitioning NEEz between gross ecosystem photosynthesis andrespirationThree approaches were used to partition NEEz, which is ?net ecosystemproduction below the height z (NEPz), into gross ecosystem photosynthesisand respiration rates below the height z (P and R, respectively), whereNEPz = P ?R. The first approach was to determine R at each level byfitting a non-rectangular hyperbolic function (NRHF approach) to daytimeNEP vs. PAR (Gilmanov et al., 2003), where daytime is defined as PAR> 5 ?mol m?2 s?1.NEPz =?PAR + ? ??(?PAR + ?)2 ? 4???PAR2??R, (3.9)where ? is the initial slope of the function, ? is the light-saturated netphotosynthesis and ? is the curvature factor for the inflection point.Several other studies have had success with this approach applied to theentire ecosystem in which they used a rectangular hyperbolic function(Lee et al., 1999; Suyker and Verma, 2001; Griffis et al., 2004). The secondapproach was to determine R by fitting a linear regression to low-light level(5 < PAR < 200?mol m?2 s?1) daytime NEPz data following Jassal et al.(2007) (LL approach). The two approaches were applied once using PARmeasured at each level and once using PAR measured above the canopy.The third approach was to use nighttime NEPz (PAR = 0, NT approach)(e.g., Stoy et al., 2006). Since no clear temperature dependence usingnighttime data was found, R in this case was determined as the averagenighttime NEPz over the three week period.Water use efficiencyWater use efficiency (WUE) is defined as the mass of C (g) assimilated perunit mass of water loss (kg) by transpiration (Cowan and Farquhar, 1977).In order to calculate WUE, evapotranspiration rates (E) were determinedusing H2O flux and profile concentration measurements:E = ?aw?m?q +? z0??q?tdz, (3.10)wheremq is the H2O molar mixing ratio. The rate-of-change-in-storage termand w?m?q were calculated with open-path IRGA (i.e., LI-7500) data. WUEwas then determined as WUE = P/E and the inherent WUE was calculatedas WUEi = WUE?D (Beer et al., 2009).733.2. MethodologyEcophysiological approachUsing the EP approach NEE was calculated using:NEE =3?i=1?NEEi +Rs, (3.11)where i is the vegetation layer index (understory (i = 1), secondary structure(i = 2) and overstory (i = 3)) and ?NEEi (?mol m?2ground s?1) is the CO2exchange within the vegetation layer i, which was calculated using:?NEEi = AbrLAIi,br +AcoLAIi,co +Rb,dBAIi,b,d +Rb,lBAIi,b,l, (3.12)where A is the leaf-level net assimilation rate (?mol m?2 leaf s?1) of livingleaves, LAIi (m2 leaf/m2 ground) is the vegetation-specific leaf area indexin layer i. The subscripts br and co stand for broadleaf and coniferousvegetation, respectively. Rb,d and Rb,l are the bole respiration rates(?mol m?2 bole s?1) and BAIi,b,d and BAIi,b,l are the surface fractions (m2bole surface/m2 ground) within layer i of dead and living boles, respectively.Dead needle respiration was neglected, as measurements showed that theirrespiration rates were very small and less than measurement resolution ofthe LI-6400 and the chamber system.In a first step, light response curves for A were established for broadleafand coniferous leaves separately. The non-rectangular hyperbolic functionin Eq. 3.9 that was used at a layer level previously was here combined witha humidity factor (HF) and fitted to the data (Gilmanov et al., 2013) on aleaf level:A =?PAR + ? ??(?PAR + ?)2 ? 4???PAR2?HF?Rf , (3.13)where Rf is the foliage respiration rate and HF depends on D as follows(McCallum et al., 2013):HF = exp(??D), (3.14)where ? (kPa?1) is a fitting parameter.The vegetation-specific LAI for each of the three layers was based onthe species-specific LAI from Bowler et al. (2012), which was determined in743.2. Methodology2008 and 2009 and assumed to also be applicable in 2010. Broadleaf vegeta-tion belonged entirely to the ground coverage and small bushes. Small treeswere typically 2 to 3 m tall. Therefore, all LAI associated with broadleafplants, conifer seedlings and saplings, and a third of the small-tree LAI wasassumed to belong to the understory layer (LAIunderstory,br = 1.088 m2 m?2,LAIunderstory,co = 0.077 m2 m?2), while the remaining two thirds of thesmall-tree and all tall-tree LAI was assumed to belong to the secondarystructure layer (LAIsecondary,co = 0.400 m2 m?2). It was assumed thatthere were no living leaves in the overstory layer (i.e., LAIoverstory = 0).More information on how these LAI values were determined can be foundin Appendix G. Total LAD of each layer is shown in Fig. 3.2.In order to calculate net assimilation for the entire campaign, D wascalculated from mq measured by the open-path IRGAs at all measurementlevels. For times when mq data were not available, D was calculatedusing the HMP RH measurements. The values of PAR and D at 1-mheight were used for the understory layer and the average of PAR andD at 2.7, 7.6 and 11.9-m height were used for the secondary structurelayer. Net assimilation was calculated at a 1-min resolution and thenaveraged over 30 min; however, for D only 30-min averages were available,and D was assumed constant for the entire half hour. For the broadleafvegetation a spherical-leaf-angle distribution was assumed and interceptedlight was calculated according to (Eq. 15.6 in Campbell and Norman, 1998).In a second step, bole and soil respiration rates (i.e., Rb and Rs) weredetermined from the rate of change in the CO2 molar mixing ratio, mc, in thechamber headspace after placement of the chamber on the collar followingGaumont-Guay et al. (2006):Rb and Rs =?aVadmcdt, (3.15)where V and a are the chamber headspace volume and the area covered bythe chamber, respectively. The dependence of Rb on TB was then establishedby fitting the following Q10 relationship (Gaumont-Guay et al., 2006) to theRb data from all boles.Rb = R10QTB?101010 (3.16)where TB is in ?C, R10 is Rb at TB = 10 ?C and Q10 is the temperaturesensitivity of Rb (i.e., the relative increase in Rb for a 10 K increase in753.3. Results and discussionTB). The average just-below-bark temperature (north and south sidemeasurements of a living subalpine fir tree and a dead lodgepole pine treeaveraged) measured at the same time as the chamber measurement wasused as TB to establish this relationship and later to calculate the exchangerates for the entire campaign. A logarithmic transformation together witha linear regression was employed for Rb,l as described by Morgenstern et al.(2004), since a non-linear ordinary least squares fit assumes homogeneousvariance in the data (Tabachnick and Fidell, 2001), which was not observedfor Rb,l. The root mean square error (RMSE) was calculated based on thelogarithmic transformation. For Rs as in the case of nighttime R mentionedabove, no clear Ts dependence was found and therefore, the average Rsover all soil collars and days was used as Rs for the entire campaign.The bole surface area of living and dead boles in each layer per unitground area was determined from layer-specific bole volume fractions fromChapter 2. The resulting BAI values were: BAIunderstory,b,l = 3.01 ? 10?2,BAIsecondary,b,l = 2.20 ? 10?2, BAIoverstory,b,l = 0, BAIunderstory,b,d =3.61 ? 10?2, BAIsecondary,b,d = 17.63 ? 10?2, BAIoverstory,b,d = 2.35 ? 10?2.Branches were neglected. Details on how BAI of the different layers wasdetermined can be found in Appendix E. Using the EP approach, Sc ineach vegetation layer was then determined by dividing ?NEEi by thevegetation layer thickness.3.3 Results and discussion3.3.1 Climatic conditionsThe weather at the site varied over the course of the campaign from moderateconditions towards the beginning of the campaign to warm and very dryconditions towards the end (Fig. 3.3). Ta, D and Ts increased and ?sdecreased over the course of the campaign. Only on four days (21, 22, 30and 31 July) were small amounts (< 1 mm day?1) of precipitation recorded,while only on 22 July did the precipitation result in an increase in soilmoisture content. July and August of 2010 were particularly dry comparedto previous years and relatively warm (Brown et al., 2013). The evaporativefraction (QE/(QE +QH); Barr et al., 2006) measured above the canopy wasgenerally low (< 0.4) corresponding to high Bowen ratios (? = QH/QE)(> 2). The evaporative fraction had a decreasing trend over the course of thecampaign. The conditions were generally sunny with some convective cloudsin the afternoon. Only on 22 July was the radiation substantially reduced763.3. Results and discussionover the entire day. Very little reduction of PAR compared to above canopyvalues (PARtop) (Fig. 3.4) was found in the upper canopy where LAD wassmall (Fig. 3.2). The decrease of PAR increased with depth into the canopywhere LAD was larger. The penetration of PAR through the canopy waslargest around midday, when up to 70 % of PARtop was recorded at the 1-mheight. At the same time, vertical PAR gradients were largest close to theground but were smallest in the upper part of the canopy compared to theother times of the day. When the solar altitude was low, PAR gradientswere small close to the ground, while they were larger above. On average,almost 60 % of the daily PARtop reached the 1-m height, which is the sameas the value for S reported in Chapter 2.3.3.2 CO2 fluxes over the course of the campaignThe air-column-storage-corrected CO2 flux density below z/h = 0.06, 0.6and 1.34 corresponding to the levels just above the understory, secondarystructure and above the canopy, respectively, is shown in Fig. 3.5. Substan-tial downward fluxes (NEEz < 0) were recorded above the canopy duringthe daytime, implying that the ecosystem was taking up CO2. NEEz wasalso negative at the two other levels during daytime. During nighttime thefluxes were upward (NEEz > 0) but in magnitude mostly smaller than thedaytime flux. While the magnitude of NEEz increased substantially fromthe top of the understory (z/h = 0.06) to the top of the secondary structure(z/h = 0.6), on some days it stayed nearly constant and even decreasedslightly during daytime between z/h = 0.6 and z/h = 1.34. The magnitudeof the afternoon NEEz at all levels and in particular NEEz of the under-story (z/h = 0.06) decreased over the course of the campaign, indicatingthat the extended dry period affected the CO2 uptake by the plants. Theextended dry period has a larger effect on understory broadleaves than onthe coniferous secondary structure in this canopy.3.3.3 Diurnal cycle and flux profilesThe ensemble-averaged diurnal cycle of c (determined from LI-840 mea-surements), the standard deviation of vertical wind (?w), the rate of CO2storage change in the air (?Fs; determined from LI-7500 measurements),and NEEz at all seven levels are shown in Fig. 3.6. Between shortly beforesunset (19:00) and shortly after sunrise (5:00), c increased almost linearlyby 60 to 80 ?mol mol?1 and the increase was the largest close to theground compared to the other levels. At the same time, ?w being used here773.3. Results and discussion201514 252116 262217 272318 282419 29 3130 01 02AugustJuly030500100015002000PAR(?mol m?2 s?1)0102030T a  (?C)0123D (kPa)5101520T s  (?C)3.54.04.55.0  s  (%)?00.250.500.75Precipitation(mm/day)0.10.20.30.4QE / [QE + QH ]942.31.5?30?min average Daily averagePrecipitation?s(a)(b)(c)(d)(e)(f)Figure 3.3: (a) Half-hourly averages of above-canopy photosynthetically ac-tive radiation (PAR), (b) half-hourly averages and daily average air tem-perature Ta at the 6-m height determined from HMP measurements, (c)half-hourly averages of vapour pressure deficit (D) at the 6-m height deter-mined from HMP measurements, (d) half-hourly averages of soil tempera-ture (Ts) at the 0.025-m depth, (e) half-hourly averages of volumetric soilwater content (?s) at the 0.1-m depth and daily total precipitation, and (f)daily (24-h) average evaporative fraction (QE/(QE +QH)) and Bowen ratio(?) above the stand for the three-week period of the campaign in 2010.783.3. Results and discussion   00 20 40 60 80 1000.20.40.60.81.01.21.41.6z/h05:0008:0011:0014:0017:0020:00PAR/PARtop (%)Figure 3.4: Ensemble-averaged half-hourly profiles of incoming photosyn-thetically active radiation (PAR) normalized by PAR above the canopy(PARtop) at 05:00 (105 ?mol m?2 s?1, 9.3 ? solar altitude), 08:00 (847?mol m?2 s?1, 34.9 ?), 11:00 (1483 ?mol m?2 s?1, 53.7 ?), 14:00 (1350?mol m?2 s?1, 47.3 ?), 17:00 (729 ?mol m?2 s?1, 23.4 ?) and 20:00 (40?mol m?2 s?1, ?0.9 ?). Ensemble-averaged PARtop and solar altitude val-ues are given in parentheses. Sketches if trees and bushes indicate wherethe understory, secondary structure and overstory layers where located.793.3. Results and discussion?20 ?10 0 10 ?20 ?10 0 10 ?20 ?10 0 10 NEEZ (?mol m?2 s?1)(a) z/h = 1.34(b) z/h = 0.60(c) z/h = 0.06201514 252116 262217 272318 282419 29 3130 01 02AugustJuly03Figure 3.5: Half-hourly averages of NEEz over the course of the campaignin 2010 just above the understory (z/h = 0.06), at the top of the secondarystructure (z/h = 0.6) and above the canopy (z/h = 1.34).as a measure of turbulence, was relatively low at all levels and was highlycorrelated with the friction velocity (u? =?u?w?2+ v?w?2). While otherstudies have reported cases of intermittency occuring during nighttime(e.g., van Gorsel et al., 2007), there was only an indication of intermittencyduring one night (18 July, at the top two levels). At 6:00, one hour aftersunrise and at the same time as ?w increased, c at all levels droppedremarkably until it stayed almost constant from 11:00 to 19:00. Two hoursafter the turbulence increased, the atmosphere became well mixed and theconcentrations were almost constant throughout the canopy and above.The measured flux (Fc) was generally upward at nighttime and therewas a sharp increase in Fc around 6:00, the same time when c startedto decrease. This increase, however, vanished when taking the rate ofCO2 storage change (Fig. 3.6d) into account, i.e., NEEz was close tozero, implying that the measured flux was related to an early morningflushing of CO2 similar to that described by Yang et al. (1999) for aboreal aspen stand. During the study period, the steady increase in cover night and the flushings in the morning were regularly observed (on803.3. Results and discussion0.060.140.600.380.831.05 1.34SunriseSunset0 12 18 246Time (PST)?6 ?4 ?2 0 2 4 NEEZ (?mol m?2 s?1)?4 ?2 0 2 4   (?mol m?2 s?1)?4 ?2 0 2 4 F C (?mol m?2 s?1)380 400 420 440 460 480 c  (?mol mol?1)0.2 0.4 0.6 0.8 1 w ( m s?1)?(a)(b)(c)(d)(e)?FSFigure 3.6: Ensemble-averaged diurnalcycle of (a) CO2mole fraction (c,measured with LI-840 and expressed as?mol mol?1 moist air),(b) standard deviationof the vertical windvelocity (?w), (c) mea-sured CO2 flux density(Fc), (d) rate of CO2storage change (?Fs)below each level and(e) air-column-storagecorrected CO2 fluxdensity (NEEz) at theseven levels.813.3. Results and discussionat least 11 days). Similar findings have been reported by Grace et al.(1995, 1996) in tropical forests and are evident in the measurementsreported by Goulden et al. (2006). After 6:00, Fc and NEEz weregenerally negative and therefore directed downward during the daytime,with the magnitude of downward NEEz being largest between 7:00 and10:00, implying that net photosynthesis was strongest at this time of the day.As can also be seen in Fig. 3.7a, during daytime, NEEz decreased withheight from the ground to z/h = 0.38 and then increased only slightlywith height. The downward flux was strongest in the early morning (6:00)when D was lowest and ?s was highest during the day. When usingaverage soil chamber measurements as the lower boundary condition forthe lowest layer, the strongest CO2 uptake during daytime was found inthe lowest layer (z/h < 0.06, Sc = ?2.5?mol m?3 s?1), where all theunderstory vegetation was found (Fig. 3.7 b). The secondary structurelayer (0.06 < z/h < 0.60) was also a relatively strong CO2 sink of up to0.5 ?mol m?3 s?1. The overstory showed small positive Sc, indicatingthat respiration dominated over photosynthesis in this layer. However,also above the canopy Sc was slightly positive, which could be causedwhen the turbulent source area was larger than the fetch, e.g. duringrelatively stable conditions. At nighttime, NEEz also decreased with heightbelow z/h = 0.14, resulting in an unrealistic CO2 sink, which indicatesthe possible occurrence of advection since photosynthesis is not possibleat night. Large scale advection or dispersive fluxes might have playeda role here. Dispersive fluxes are typically larger lower in the canopythan at the top (Bohm et al., 2000; Aubinet et al., 2012) and can besignificant in sparse canopies (Christen and Vogt, 2004; Poggi et al., 2004b;Poggi and Katul, 2008). Above z/h = 0.14, NEEz increased with heightresulting in an almost equally strong CO2 source throughout the rest of thecanopy and above the canopy.Fig. 3.8a shows the average soil respiration determined with the soilchamber system (spatially and temporally averaged) and the ensemble-averaged daytime NEEz partitioned into R and P using the differentmethods described in Sec. 3.2.3 (more details on the partitioning analysisand a robustness test can be found in Appendix H). All partitioningmethods show relatively similar results, with only the method based onnighttime NEEz resulting in larger P and R values in the upper canopy andabove. Fig 3.8b shows the photosynthetic and respiratory flux divergences(?P/?z and ?R/?z, respectively) based on the partitioning method using823.4. Comparison of eddy-covariance and ecophysiological approachesthe relationship between low-light level daytime fluxes and PAR abovethe canopy. Soil respiration was used as the lower boundary condition forcalculating ?R/?z in the lowest layer. The lower boundary condition forcalculating ?P/?z in the lowest layer was zero since no photosynthesisoccurs in the ground.R decreased close to the ground and increased with height above, re-sulting in a negative ?R/?z in the lowest two layers and slowly decreasingpositive ?R/?z with height above. A negative ?R/?z means that theflux of R decreases with height. This is physically not possible but ratherindicates measurement difficulties due to changing source areas or becauseof advection and a changing contribution of dispersive fluxes. Furthermorethe lower boundary condition of the lowest layer, i.e. Rs was assumedconstant in time and space for the entire campaign and was determinedwith an independent approach, which could have led to discrepancies. Forz/h ? 0.38, ?R/?z was positive and decreased slowly with height. Thiscorresponded to the distribution of tree boles and needles in the canopy,with considerable vegetation in the lower canopy while there was less andonly dead vegetation in the upper canopy. P increased relatively stronglywith height in the understory and secondary structure layers (belowz/h = 0.6) and stayed approximately constant above. This resulted in thestrongest photosynthetic activity being where the understory was located(approximately 1.0 ?mol m?3 s?1) and substantial photosynthetic activityof up to 0.4 ?mol m?3 s?1 in the secondary structure layer, while in theoverstory layer ?P/?z was < 0.1 ?mol m?3 s?1.3.4 Comparison of eddy-covariance andecophysiological approaches3.4.1 Ecophysiological resultsFor the ecophysiological approach, light response curves for leaf-level CO2assimilation of coniferous and broadleaved components were optimized anddependence of respiration components on temperature were established(Fig. 3.9a and b). Assimilation rates were strongly influenced by D. Theparameters for A in Eq. 3.13 were ? = 0.056, ? = 34.933 ?mol m?2 s?1,? = 2.995 ? 10?5, Rf = 0.366 ?mol m?2 s?1, ? = 0.834 kPa?1 for conifersand ? = 0.061, ? = 24.223 ?mol m?2 s?1, ? = 8.931 ? 10?6, Rf = 0833.4. Comparison of eddy-covariance and ecophysiological approaches?6 ?4 ?2 0 2 40.00.20.40.60.81.01.21.4z/h?1?1.5 ?0.5 0 0.5DaytimeNighttimeNEEZ (?mol m?2 s?1) SC (?mol m?3 s?1)00:0004:0008:0012:0016:0020:00RS(a) (b)Figure 3.7: (a) Ensemble-averaged air-column storage corrected flux profilesat different times of the day: 00:00, 04:00, 08:00, 12:00, 16:00, 20:00 PST.The red hexagon shows the spatially and temporally averaged soil respira-tion measured with the portable chamber system, which was used as thelower boundary condition for CO2 source strength calculations of the lowestlayer. (b) Ensemble-averaged daytime and nighttime profiles of CO2 sourcestrength. All profiles were determined from EC measurements.843.4. Comparison of eddy-covariance and ecophysiological approachesLL, PARzLL, PARtopNRHF, PARzNRHF, PARtopNTRs?R/?z ?P/?zR  P10 2 4 5 6 730.00.20.40.60.81.01.21.4z/h?0.5 0 0.5 1.51P and R (?mol m?2 s?1)   P/  z and    R/  z (?mol m?3 s?1)? ? ? ?(a) (b)Figure 3.8: (a) Ensemble-averaged daytime gross photosynthetic (P ) andrespiratory (R) flux density (cumulative P or R for ecosystem below z/h)using the following partitioning methods: linear fit to low-light level daytimedata (LL) using PAR at each level (PARz) and using PAR above the canopy(PARtop), fitting a non-rectangular hyperbolic function (NRHF) using PARzand PARtop, and partitioning based on average nighttime (NT) data. Thered hexagon shows the spatially and temporally averaged soil respirationmeasured with the portable chamber system, which was used as the lowerboundary condition for respiratory flux divergence calculations for the lowestlayer. (b) Flux divergence of P and R based on LL using PARz. All profileswere determined from EC measurements.853.4. Comparison of eddy-covariance and ecophysiological approachesPAR  (?mol m?2 s?1)TB (?C)A br (?mol m?2 s?1)R b,l (?mol m?2 s?1)A co (?mol m?2 s?1)?202460 500 1000 1500 200005101520D < 1 kP1 kPa < D < 2 kP2 kPa < D < 3 kP3 kPa < D < 4 kP4 kPa < D < 5 kP15 20 25 3010.25(a)(b)(c)Figure 3.9: Measured(symbols) and fitted(solid lines) lightresponse relationshipsfor foliar net assimila-tion rate of (a) conifertrees (Aco) and (b)understory broadleafvegetation (Abr).Solid lines are thefitted light responsecurves for D = 0.5(black), 1.5 (purple),2.5 (red), 3.5 (yellow)and 4.5 kPa (green).(c) Dependence oflive bole respiration(Rb,l) on bole tem-perature (TB). Thesolid line is a linearfit using a logarithmictransformation.863.4. Comparison of eddy-covariance and ecophysiological approaches?mol m?2 s?1, ? = 0.353 kPa?1 for broadleaf vegetation.A strong temperature dependence was found for Rb,l (Fig. 3.9c)using the Q10 function (Eq. 3.16) resulting in R10 = 0.952 ?mol m?2 s?1and Q10 = 1.836 (RMSE = 0.55 ?mol m?2 s?1). However, as indicatedearlier, no clear dependence of Rs on soil temperature was found. Thiscan be explained by the fact that the soil moisture levels were very low(?s < 5%). Jassal et al. (2008) found in a temperate Douglas-fir stand thatfor ?s < 11%, Rs becomes decoupled from soil temperature. An averagevalue of Rs (averaged over all collars and all days, number of samples =170) of 1.36 ?mol m?2 s?1 (standard deviation = 0.61 ?mol m?2 s?1) wasused for the entire campaign.Measured Rb,d were very low and varied between ?0.10 and 0.32?mol m?2 s?1. The fluctuations of CO2 molar mixing ratios in themeasurement chamber (due to noise and measurement error) were largecompared to mc increases due to bole respiration during the 1 to 2 minmeasurement period. Furthermore, cracks in dead boles below the barkcould have led to air leakage into or out of the chamber. In the case ofdead-bole respiration, there was no clear dependence on TB. The medianRb,d of 0.05 ?mol m?2 s?1 (25 percentile: ?0.03 ?mol m?2 s?1 and 75percentile: 0.23 ?mol m?2 s?1) was used for the entire campaign.3.4.2 ComparisonIn this section, NEE and the contributions of the three vegetation layersto the overall NEE (?NEEz) based on the EP and EC approaches arecompared. The average value of Rs mentioned above (1.36 ?mol m?2 s?1)was used in both approaches. Fig. 3.10 shows half-hourly ?NEEz andNEE, and Fig. 3.11 shows the ensemble averaged diurnal cycle of ?NEEzfor the three vegetation layers and the two approaches.In the understory layer, the two approaches showed comparable ?NEEzduring the nighttime, which were close to zero. During the daytime,EP downward flux contributions were usually much larger. Only onsome days with low PAR and sometimes with high D, fluxes of the twoapproaches were comparable. The impact of the distribution of small treeLAI to the different layers on the vertical EP flux distribution was tested.Variation of understory small tree LAI contributions between 0 % and 66 %(corresponding to small tree contributions to the secondary structure layer873.4. Comparison of eddy-covariance and ecophysiological approaches?NEE (?mol m?2 s?1)NEE (?mol m?2 s?1)?10 0 10 ?10 0 10 ?10 0 10 ?10 0 10 EPEC2015 252116 262217 272318 282419 29 3130 01 02AugustJuly03(a) Overstory(b) Secondary structure(c) Understory(d) Entire standFigure 3.10: Half-hourly NEE contributions (?NEEz) over the course ofthe campaign in 2010 of the three vegetation layers ((a) understory, (b)secondary structure and (c) overstory) determined using the eddy-covariance(EC) and ecophysiological (EP) approaches and (d) NEE determined usingthe two approaches. Some individual values of measured Fc that were largerthan 10 ?mol m?2 s?1 and smaller than -15 ?mol m?2 s?1 are not shown.Two days at the bginning of the campaign were not used for the comparisonbecause of missing bole temperatures.883.4. Comparison of eddy-covariance and ecophysiological approaches0 6 12 18 24?10 ?5 0 5 ?5 0 5 ?10 ?5 0 5 ?5 0 5 EPEC?NEE (?mol m?2 s?1)NEE (?mol m?2 s?1)Time (PST)(d) Entire stand(a) Overstory(b) Secondary structure(c) UnderstoryFigure 3.11: Ensemble-averaged diurnal cycle of the NEE contributions(?NEEz) of the three vegetation layers ((a) understory, (b) secondary struc-ture and (c) overstory) determined using the eddy-covariance (EC) andecophysiological (EP) approaches and (d) NEE determined using the twoapproaches for the period 15 July to 15 August 2010.893.4. Comparison of eddy-covariance and ecophysiological approachesof 100 % and 33 %, respectively) resulted in daytime flux differences of< ? 5 % in the understory and < ? 15 % secondary structure layer. Bothapproaches indicated that the daytime flux magnitudes decreased towardsthe end of the campaign. For the secondary structure, ?NEEz of the twoapproaches was very similar. EC measurements, however, showed slightlylarger variations over the course of the day. In the overstory layer duringdaytime, the EC approach showed mainly positive values of ?NEEz withrelatively large variations. At night, however, ?NEEz was close to zero(0.0001 ?mol m?2 s?1). The EP approach resulted in a constant positiveflux close to zero (0.0017 ?mol m?2 s?1).Overall, the EP approach resulted in larger magnitude of NEE, morethan twice that of the EC-determined NEE during some hours of the daymainly due to the substantial flux contribution of the understory layer. Onaverage the daytime Sc of the understory determined with the EP approach(see Table 3.2 and Fig. 3.12) was ?3.20 ?mol m?3 s?1, which is almost2.6 times the magnitude of that determined using the EC approach (?1.24?mol m?3 s?1). However, in both approaches, the understory was thelargest CO2 sink compared to the other layers. For the secondary structurelayer, both approaches determined almost the same ensemble-averageddaytime sink strength of Sc,EP = ?0.17 ?mol m?3 s?1 and Sc,EC = ?0.18?mol m?3 s?1, while for the overstory the EP approach resulted in a sourcestrength close to zero and the EC approach a small source strength of0.02 ?mol m?3 s?1. Even with a small layer thickness, the understorywas the largest contributor to the overall NEE with the EP approach(ensemble-averaged ?NEEz = ?3.82 ?mol m?2 s?1 compared to ?1.72 and0.00 ?mol m?2 s?1 for the secondary structure and overstory, respectively).With the EC approach, the magnitude of the ensemble-averaged ?NEEzof the secondary structure layer was slightly larger (?1.82 ?mol m?2 s?1)than of the understory (?1.49 ?mol m?2 s?1), while that of the overstorywas 0.18 ?mol m?2 s?1.903.4.Comparisonofeddy-covarianceandecophysiologicalapproachesEddy covariance?3.0 ?2.0 ?1.0 0.0Sc, mol m? 3 s? 10.20.40.60.81.01.2?21.0 m11.9 m1.2 m(a) (b)z/hEcophysiological approach?3.0 ?2.0 ?1.0 0.0Sc, mol m? 3 s? 10.20.40.60.81.01.2?21.0 m11.9 m1.2 mz/hFigure 3.12: Ensemble-averaged vertical distribution of CO2 sources and sinks (Sc) summarized for the threevegetation layers based on (a) the eddy covariance approach and (b) the ecophysiological approach.913.4. Comparison of eddy-covariance and ecophysiological approachesThere are several possible explanations for the differences in the un-derstory layer. On one hand, there are many uncertainties involved in themodelling of EP fluxes. An overestimation of LAI in this layer is possibleas well as an overestimation of assimilation rates since leaf clumping wasnot considered in this analysis. Several other biases using photosynthesismeasurement systems have been discussed in the literature, like difficultiesto capture high natural variability in photosynthesis (Baldocchi, 2003),acclimatization of leaf photosynthesis to sunny conditions and verticalgradients in photosynthetic capacity (Ellsworth and Reich, 1993). Biaseswhen using the respiration chamber include disturbance of local wind,which in this canopy with low wind speed are small and alteration ofthe heat and water balances (Livingston and Hutchinson, 1995) of thesoil or boles. High CO2 concentrations from the operators breath couldhave an effect if the seal between the chamber and collar is not perfect.Furthermore, uncertainties in LAI and BAI and their relative attributionto layers are added when scaling up to canopy scale.On the other hand, EC measurements close to the ground are challengingbecause essential assumptions can fail in the canopy. Even though energybalance closure (EBC) seemed to be relatively high close to the ground(Chapter 2), a closer analysis showed that the high values were mainly dueto averaging of relatively large variations. During daytime when steadyatmospheric conditions are prevalent and since the site has a flat terrainand homogeneous fetch, NEE determined with the EC approach above thecanopy can be assumed to be reliable (Baldocchi, 2003). Since under theseconditions above the canopy the EP approach showed substantially largerdownward fluxes than the EC approach, there is an indication that the EPapproach might have overestimated the CO2 assimilation in the understoryor underestimated the respiration of the dead boles. A study at the samesite conducted in 2007, 2008 and 2009, where gross ecosystem photosynthesis(GEP) above the canopy determined by the EC approach was compared toEP photosynthesis measurements also resulted in a similar discrepancy asin our study (Bowler et al., 2012). Since LAI in our study was based onthe LAI in Bowler et al. (2012) and both studies showed larged understoryEP photosynthesis rates, an overestimation in LAI of the understory wouldbe possible. At nighttime, however, EC results must be interpreted withcaution since EBC closure was poor (Chapter 2) and advection of CO2could possibly have occured.923.5. Water use efficiencyTable 3.2: Source/sink strength in the three vegetation layers (understory,secondary structure and overstory) determined using the eddy-covariance(EC) and the ecophysiological approaches (EP), and photosynthetic andrespiratory flux divergence determined using the EC measurements and theLL methodVegetation layer Sc,EP Sc,EC ?PEC/?z ?REC/?z?mol m?3 s?1 ?mol m?3 s?1 ?mol m?3 s?1 ?mol m?3 s?1Understory -3.20 -1.24 1.18 -0.06Secondary structure -0.17 -0.18 0.27 0.09Overstory 0.00 0.02 0.05 0.073.5 Water use efficiencyThe sinks of CO2 during daytime in our stand were distributed throughoutthe understory and secondary structure layer (see Section 3.3.3), whilelatent heat and therefore water vapour originated mainly from the ground(Chapter 2). The dissimilarity in CO2 sinks and H2O sources implieschanging WUE with height in this canopy during daytime.To determine the ensemble-averaged daytime WUE (Fig. 3.13b),the ensemble-averaged daytime water vapour mass flux density and thephotosynthetic contribution to the CO2 mass flux density were determined(Fig. 3.13a). While P increased with height for z/h < 0.60, where mostof the living vegetation was located, E varied only slightly with heightthroughout the entire canopy. Above z/h = 0.60, P stayed roughlyconstant. The ensemble-averaged daytime WUE increased with height forz/h < 0.38, which indicated that foliage higher in the canopy had a greaterWUE than lower in the canopy. WUE stayed approximately constant inthe upper part of the canopy (z/h > 0.38). Mkhabela et al. (2009) studiedWUE at several forest sites disturbed by fire and harvesting and foundthat recently disturbed sites tend to use water less efficiently. In theirstudy, very open sites had WUE < 2 g C kg?1 H2O, while full canopy sitesranged between 2 and 2.6 g C kg?1 H2O. In our study, ensemble-averageddaytime WUE varied with height between approximately 2.3 and 6.5g C kg?1 H2O. Even though the stand was a disturbed site with a sparsecanopy, WUE was relatively high in the upper canopy, especially due tothe rapid increase in P relative to E for 0.14 < z/h < 0.4. There was little933.5. Water use efficiencyP and E contributed by the upper canopy. WUE specific to the understoryand secondary structure layer was also determined as WUE = ?P/?E.WUE of the understory and the secondary structure layers were 2.26 and18.08 g C kg?1 H2O, respectively. These findings fit well with the factthat the flux contributions of the understory were more affected by the dryconditions than the secondary structure. The ensemble-averaged verticalprofile of the daytime inherent water use efficiency (WUEi) showed asimilar pattern as WUE but values were roughly 20 % larger.Ensemble-averaged daytime WUE and WUEi for the first (14 to 20July), second (21 to 27 July) and third weeks (28 July to 3 August) of thecampaign were determined (Fig. 3.13c) to assess the canopy?s behaviour asconditions became drier. Between the first and second weeks, the changesin WUE were small. During the third week, when drought effects becamemore pronounced, WUE values in and just above the understory layer(z/h < 0.14) were similar to the previous weeks but increased by roughly20 % in the upper canopy. WUEi showed a significant increase from thefirst to the second week and even higher values in the third week forz/h ? 0.38 reaching values of up to 10.9 g C kPa kg?1 H2O. In comparison,Vickers et al. (2012) found WUEi values of about 6 g C kPa kg?1 H2Oabove a young ponderosa pine stand during seasonal drought conditions. Inthe lower canopy (z/h < 0.14), WUEi changed only from the second to thethird week and changes were smaller than above. WUEi is an indicationfor how well plants adjust to climatic conditions (Beer et al., 2009). Inthis forest, the secondary structure layer consisting only of conifers wasclearly more able to adjust to the extended dry period than the broadleafunderstory.943.5.Wateruseefficiency0 3.5?10?5 7?10?5 1.05?10?4 1.4?10?4 0 2 4 6 8 0 2 4 6 8 10 1210 2 3 414-20 July21-27 July28 July-3 AugWU E WU E i  WU EWU E i0.00.20.40.60.81.01.21.4z/hP (g C m?2 s?1)E (kg H2O m?2 s?1)PEP (?mol C m?2 s?1)WUE (g C/kg H2O)WUEi (g C kPa/kg H2O)   WUE (g C/kg H2O)WUEi (g C kPa/kg H2O)   (a) (b) (c)Figure 3.13: Ensemble-averaged daytime (a) P and E and (b) WUE and WUEi over the entire campaign. (c)Ensemble-averaged daytime WUE and WUEi for the first (14 to 20 July), second (21 to 27 July) and third week(28 July to 3 August) of the campaign.953.6. Summary and conclusions3.6 Summary and conclusionsIn this study, two independent approaches were assessed to determinethe vertical distribution of CO2 sources and sinks within and above thecanopy of a lodgepole pine stand that had been attacked by mountainpine beetle. The first, the eddy-covariance (EC) approach, used ECmeasurements of CO2 flux at seven heights in and above the stand,while the second, the ecophysiological (EP) approach, used chamber CO2exchange measurements on foliage and boles weighted by leaf and bolesurface area. Both approaches were consistent in the vertical distributionof sources and sinks for three different layers of vegetation - understorydominated by broadleaf shrubs, secondary structure consisting of conifertrees (dead and live) and overstory with only dead pine trees; however, themagnitudes varied between the approaches.Strong CO2 flushing was regularly observed in the morning and mea-surement of air-column CO2 storage change was important to determine theactual CO2 exchange of the vegetation layers by means of EC. CombiningCO2 storage changes and eddy fluxes made it possible to determine CO2flux contributions during the daytime; however, during the nighttimelimited mixing made it difficult to reliably determine fluxes.Relatively good agreement was found between rectangular hyperbolicand linear light response methods of partitioning NEEz between R andP as a function of height in the canopy, while using the respirationrelationship obtained from nighttime NEE measurements tended tosomewhat overestimate R and therefore P .Over the entire campaign, EC measurements indicated that the standwas a sink for CO2. Photosynthesis of the living vegetation exceeded therespiration of the living and dead vegetation and soil within the standduring daytime. The secondary structure and especially the understorylayers were CO2 sinks, implying that the secondary structure and especiallyground coverage were responsible for this MPB-attacked stand being a CO2sink. The EC approach also indicated that the dead boles were weak CO2sources, while the soil was a strong CO2 source.The water use efficiency (?P/?E) of the secondary structure layer waseight times higher than that of the understory layer. Cumulative WUE(i.e., sum P/sum E up to height z) increased from the ground to the top963.6. Summary and conclusionsof the secondary structure and varied between 2.3 and 6.5 g C kg?1 H2O.Inherent water use efficiency (WUEi) of the secondary structure in-creased substantially over the course of the campaign, while understoryWUEi changed little. This implies that the secondary structure consist-ing only of conifers clearly exhibited adjustment to the extended dry period.These measurements showed that the secondary structure was re-sponsible for a large portion of the CO2 uptake as was postulated byBrown et al. (2012a); however, the understory was a similarly large or evenlarger contributor to the uptake. Very likely, the open-stand structure withas much as 60 % of of the daily above-canopy photosynthetically activeradiation reaching the 1-m height and wind protection by standing deadtrees were responsible for a favorable microclimate supporting the growthof and the CO2 uptake by the immature vegetation.97Chapter 4Flux-gradient relationshipswithin and above the canopy4.1 IntroductionA common method to determine fluxes (?flux? will be used but flux densityis implied) in the surface layer is the flux-gradient method which is basedon scalar gradients and empirical relationships (Monteith and Unsworth,2008). The eddy diffusivity (K) needs to be known to determine the fluxwhen the corresponding scalar gradient is known. The eddy diffusivity, alsocalled the turbulent transfer coefficient, is a constant of proportionality,which relates a scalar gradient to its flux densities and is based on gradientdiffusion theory (also called K-theory) and has the units of m2 s?1. Thereare several approaches to calculate K, all of which are based on theMonin-Obukhov similarity (MOS) theory. MOS theory uses dimensionalsimilarity to determine transport in the surface layer, which is the layerclose to the surface in which the fluxes vary vertically by less than 10 %and is therefore also called the constant-flux layer (Stull, 1988).The flux-gradient method is relatively reliable in the upper partof the surface layer, the inertial sublayer, in which the structure ofturbulence depends only on scales such as the friction velocity andheight (Monteith and Unsworth, 2008). However, in the layer below,the roughness sublayer, the flux-gradient method may result in incorrectestimation of fluxes. The roughness sublayer is defined as the layer inwhich the flow is strongly influenced by the individual roughness elementsand is therefore not spatially homogeneous (Cheng and Castro, 2002).Furthermore, Denmead and Bradley (1987) showed that counter-gradientfluxes can be found within canopies, which are located inside the roughnesssublayer. Finnigan (1985) stated that flux-gradient relationships only workwhen the scale of the mechanism that produces the flux is much smallerthan the scale of the gradients. Several studies (e.g. Thom, 1975) found984.1. Introductionthat the wind profile did not follow the logarithmic profile as usually seenin the surface layer. They observed an exponential decay of windspeedwithin the plant canopy. Raupach et al. (1996) showed that the behaviorinside the canopy resembled the behavior of a mixing layer, with aninflection point at the top of the canopy. The inflection point might triggerKelvin-Helmholz instabilities, which generate coherent structures and causeintermittency making the use of K-theory problematic (Raupach et al.,1996). I acknowledge the results from various studies that K-theory is notgenerally applicable within a forest canopy; however, these studies weremainly conducted in relatively dense or closed canopies. Studies have foundthat K-theory might be applicable in certain conditions in some canopiese.g., in crop canopies (Bache, 1986).In this study, turbulent exchange in an open-canopy forest stand witha leaf area index (LAI) of 0.55 m2 m?2 is examined. In Chapter 3, it wasfound that this canopy behaves relatively differently from dense canopiesand that nighttime intermittency typically found in denser forest canopieswas not observed. The complexity of turbulent transport in forest canopiesusually require higher order closure models (e.g., Wilson and Shaw, 1977),but if K-theory is applicable in this sparse and open-canopy forest, simplermodels (one-and-a-half-order closure) could be used.Given that previous results in this study differed from those obtained instudies of denser canopies, the objective of this chapter was to determinewhether K-theory can be used in such an open-canopy stand. In order tomeet this objective the following questions were addressed:(i) Is there a well-defined relationship between fluxes and gradients? Arethere times when counter-gradient fluxes occur?(ii) During times when gradient diffusion occurs, does the exchange matchpredictions using MOS theory? How does the eddy diffusivity change withheight within and above the canopy?(iii) Can scalar similarity between momentum, sensible heat, latent heat andcarbon dioxide (CO2) be observed in this open-canopy stand?994.2. Theory4.2 TheoryThe flux-gradient method builds on the transfer equation for turbulent trans-port (Monteith and Unsworth, 2008):Fs = ??awls?ms?z, (4.1)where Fs is the flux of a scalar s, ?a is the density of dry air, w is the meanvelocity (in our case the vertical mean wind velocity), ls is the mixinglength for turbulent transport of s, ms is the mixing ratio of s and z isthe height above ground. The bar stands for the temporal average. Theaveraging period must be chosen to be longer than time scales of eddiesthat are responsible for transporting the flux. An averaging period of 30min is typically used.The quantity wls can be summarized as the turbulent transfer coefficientor eddy diffusivity Ks, so that Eq. 4.1:Fs = ??aKs?ms?z. (4.2)In the case of the momentum flux (M), Eq. 4.2 becomes:M = ??KM?u?z, (4.3)whereKM is the eddy diffusivity for momentum and u is the mean horizontalwindspeed. Since the shear stress (?) is defined as ? = ?M , it can beexpressed as:? = ?KM?u?z. (4.4)Analogous to the above, the flux-gradient equations for the sensible heatflux density (QH in W m?2), the latent heat flux (QE in W m?2) and theCO2 flux density (Fc in ?mol m?2 s?1) can be written as:QH = ?KH?acp???z, (4.5)QE = ?KE???q?z, (4.6)FC = ?KC??c?z, (4.7)1004.2. Theorywhere KH , KE and KC are the eddy diffusivities for sensible heat, latentheat and CO2, respectively, ? is the potential temperature, ?q is thewater vapour (H2O) molar density, ?c is the CO2 molar density, ? isthe total air density, cp is the specific heat of air, and ? is the latentheat of evaporation. Under neutral conditions KM = KH = KE = KC(Monteith and Unsworth, 2008). Webb et al. (1980) found that the mix-ing ratio gradient must be used for minor constituents such as H2O and CO2.In the surface layer under neutral conditions, the u can be describedusing the logarithmic wind profile equation:u =u?kln(zsz0) (4.8)and the gradient of u can then be written as:?u?z=u?kzs, (4.9)where k is the von-Ka?rma?n constant (0.40 Foken, 2008), u? is the frictionvelocity (u? =??? in m s?1), zs is a scaling height (m) and z0 is theroughness length (m), which can also be described as the height at which uis zero. It is important to note that u is not actually zero at this height, but itis the height at which the extrapolated inertial-sublayer wind profile is zero.For unstable conditions u above z0 is smaller and for stable conditions it islarger than for the neutral case. Therefore the gradient of u is smaller underunstable and larger under stable conditions than under neutral conditions.Knowing this, Eq. 4.9 can be expanded for any stability conditions bymultiplying it by a dimensionless stability factor, the stability function (?Min the case of momentum flux or shear stress) as follows:?u?z=u?kzs?M , (4.10)where ?M = 1 for neutral conditions, ?M > 1 for stable conditions and ?M <1 for unstable conditions. Rearranging Eq. 4.10 the following expression for?M is obtained:?M =kzsu??u?z(4.11)Similarly, the stability functions for sensible heat (?H), latent heat (?E) andCO2 (?C) flux can be written as:?H =kzsT????z, (4.12)1014.2. Theory?E =kzsq???q?z, (4.13)?C =kzsc???c?z, (4.14)whereT? =QH?cp1u?, (4.15)q? =QE?1u?, (4.16)c? =Fcu?. (4.17)Combining Eqs. 4.10 and 4.4 and using the surface layer predictions for?M , KM can also be predicted for the surface layer:KM =kzsu??M. (4.18)Analogous, KH , KE and KC can be predicted:KH =kzsu??H, (4.19)KE =kzsu??E, (4.20)KC =kzsu??C. (4.21)Businger et al. (1971) determined stability functions for the surfacelayer empirically during the Kansas experiment in 1968. Dyer (1974) andHo?gstro?m (1988) later recalculated them based on the same field data (seeFig. 4.1), which resulted in (Kaimal and Finnigan, 1994):?M ={(1? 16?)?1/4 if ? 2 ? ? ? 01 + 5? if 0 < ? < 1(4.22)?H ={(1? 16?)?1/2 if ? 2 ? ? ? 01 + 5? if 0 < ? < 1(4.23)1024.2. Theorywhere ? is the dimensionless height, which is a stability parameter. ?E and?C are expected to behave the same way as ?H (Monteith and Unsworth,2008). ? is calculated as:? = zs/L, (4.24)where L is the Obukhov length, which is defined as follows (Foken, 2008):L = ? u3?k gTvQH?cp, (4.25)where g is the acceleration due to gravity and Tv is the virtual temperature(in K), which can however be approximated with the air temperature (Ta).To be precise, it would be needed to use the buoyancy flux to calculateL, but within the measurement accuracy there is no significant differenceto using the sensible heat flux instead (Foken, 2008).The stability regimesare generally defined as stable if ? > 0, neutral if ? = 0 and unstable if ? < 0.?0.01?0.1?1?100.11.010.0?0.01 0.10 1.00??1?H,E,C?MFigure 4.1: Predictions of the stability functions (?) for the surface layer.The stability functions for sensible heat (?H), latent heat (?E) and CO2 (?C)are expected to behave the same way. The stability function predictions formomentum (?M ) differ under unstable conditions from ?H , ?E and ?C ,while they are all the same for stable conditions.In the inertial sublayer, the flux measurements at one height can be usedto calculate ? and K at any height and for any stability, which will be calledthe global scaling. Regarding the roughness sublayer, one possibility wouldbe to also use the global scaling by using measurements above the canopy and1034.3. Methodologyapply them to the entire canopy. Another possibility would be to use localscaling, which uses local fluxes (measured at height z) to determine ? andK.There are also different possible scaling heights that can be considered for zs.One would be the height z above the surface. In this case, Eqs. 4.18 - 4.21predict that K changes linearly with height from the ground under neutralconditions. In the case of vegetation canopies, the zero-plane displacementheight (d) is usually considered (Monteith and Unsworth, 2008), so thatzs = z ? d in all equations above. The zero-plane displacement height isdefined as the height d. It can be regarded as the height at which themean drag on the surface appears to act (Jackson, 1981) However, insidethe canopy, using z? d causes problems because z? d is negative for z ? d.Therefore, it is proposed here to use an effective height ze for zs, which isdefined as:ze =?????z ? d if z ? 2d,d if d ? z < 2d,z if z < d.(4.26)The choice of ze was informed by the characteristic profiles of K discussedlater in this chapter. Fig. 4.2 shows the four possible combinations (I - IV)of the two scaling types and the two scaling heights.4.3 Methodology4.3.1 Measurement siteExperimental field work was carried out on a 30-m tall scaffold tower in anopen-canopy lodgepole pine (Pinus contorta var. latifolia) stand adjacentto Crooked River Provincial Park (MPB-03: 55?06?42.8?N, 122?50?28.5?W)in the interior of British Columbia, Canada. The pine trees in the standhad been attacked by the mountain pine beetle (MPB, see Chapters 2 and3) in 2003, which resulted in almost 100 % of the mature pine trees beingkilled by 2007 and a low LAI of 0.55 m2 m?2 in 2010. The MPB attack andthe following reduction in canopy density of the previously already relativelysparse stand (465 stems ha?1 of dead standing pine and 75 stems ha?1 ofliving trees of different species taller than 1.3 m and with a diameter atbreast height > 90 mm in 2006) provided a unique opportunity to studyturbulent exchange in a sparse and open canopy. The canopy height (h)was 20 m. The stand had a relatively rich secondary structure of immaturetrees, bushes and ground vegetation < 12 m. The homogeneous fetch was> 0.6 km in all directions around the tower and featured a flat surface. More1044.3. Methodologyglobal localI IIIII IVScalingscaling height zs = zzs = zzs = dzs = z - dFigure 4.2: The four combinations of scaling types (global and local) andscaling height types.information on the field site can be found in Chapters 2 and 3. Photographsof the measurement site and the instrumentation are shown in Appendix A.4.3.2 InstrumentationHigh-frequency measurements of 3-dimensional wind velocity (u, v andw), CO2 and H2O molar density (?c and ?q, respectively), and airtemperature (Ta) were made at seven levels on the scaffold tower at the1.2-, 2.7-, 7.6-, 11.9-, 16.5-, 21.0- and 26.8-m heights (Table 4.1). Windand acoustic air temperature (Tac) measurements were made with sevenultrasonic anemometers (CSAT3, Campbell Scientific (CSI), Logan, Utah).Air temperature was also measured with seven fine-wire, fast-responsethermocouples (welded 25 ?m bare factory-welded Chr-Con thermocouples(Type E) were soldered on to TT-E-30-SLE duplex (30 gauge) 3-cm longsupporting Chr-Con wires, which were connected via Omega connectorsto non-shielded Chr-Con extension wire pair (EXPP-E-24S-SLE) whichwere connected directly into the data logger wiring panel). Even thoughshielding and aspiration would have been desirable for temperature gradientmeasurements, this was not possible due to power restrictions. Wind and1054.3. Methodologytemperature were measured at 5 Hz at the top level and 10 Hz at all otherlevels.Measurements of ?c and ?q were made by employing a combinationof seven open-path infrared gas analyzer (IRGA) (LI-7500, LI-COR Inc.,Lincoln, Nebraska) and one closed-path IRGA (LI-840, LI-COR). Theseven LI-7500 IRGAs were installed at the seven measurement levels andmeasured continuously at a frequency of 5 Hz at the top level and 10Hz at all other levels. The LI-840 IRGA was connected to seven synflextubes (4-mm inner diameter), through which air was sampled from eachof the seven levels sequentially. The LI-840 IRGA output CO2 and H2Omole fractions (c and q, respectively). All synflex tubes had the samelength to avoid pressure differences. During every half hour, the systemsampled sequentially for 3 min 25 s per level for each of the seven levelsfrom bottom to top using a gas multiplexer with solenoid valves. The flowrate through the tubing was 5 l min?1, and the flow rate into the IRGAwas approximately 0.6 l min?1 while the surplus gas was bypassed. Thepump used was a micro diaphragm pump (Model NMP850KNDCB, KNFNeuberger, Oxfordshire, Great Britain). Due to power limitations, it wasnot possible to employ seven LI-840 systems measuring at all levels continu-ously. The LI-7500 IRGAs also measured air pressure (p) at the seven levels.Except LI-840 measurements, all measurements at the lowest 3 levelswere recorded on a CR3000 datalogger (CSI), while all but the LI-840 mea-surements at the 11.9-, 16.5- and 21.0-m height and the thermocouple mea-surements at the 26.8-m height were recorded on a separate CR3000 dat-alogger. Both dataloggers were kept in the same white, sealed dataloggerbox and protected from the sun. All other measurements but the LI-840measurements at the 26.8-m height were recorded on a CR1000 datalogger(CSI), which was kept in a separate white and sealed datalogger box. LI-840measurements were recorded on a separate CR1000 datalogger which wasplaced inside a white sealed box together with the LI-840 system. More de-tails on the instrumentation used in this chapter can be found in Chapters2 and 3.1064.3.MethodologyTable 4.1: Instrumentation and measurements conducted at each of the seven levels (1.2-, 2.7-, 7.6-, 11.9-, 16.5-,21.0- and 26.8-m heights). One instrument of each type was installed at each level except the LI-840 IRGA wherethere was only one instrument installed at the bottom of the tower, which sampled air sequentially from each levelthrough synflex tubing.Instrument Model Manufacturer Measured MeasurementVariables FrequencyUltrasonic anemometer/thermometer CSAT3 Campbell Scientific Inc. u, v, w, Tac 10 Hz aThermocouple Type E, 0.0254 mm custom made Ta 10 HzaOpen-path infrared gas analyzer LI-7500 LI-COR Inc. ?c, ?q, p 10 HzClosed-path infrared gas analyzer LI-840 Campbell Scientific Inc. c, q 1 HzaExcept at the 26.8-m height, where the measurement frequency was 5 Hz.1074.3. Methodology4.3.3 CalibrationWind, shear stress and sensible heat fluxSix of the seven ultrasonic anemometers employed in this study (lowest sixlevels on the tower) were intercompared in the field between 27 May and 15June 2009 (Liss et al., 2009). The sensors were all installed side-by-side (ap-proximately 1.6-m separation) at 2.5-m height above a flat unmanaged grasscovered terrain (average grass height during intercomparison was 1.3 m) onWestham Island, Delta, BC (123.1768?W, 49.0863?N). Half-hour averages ofthe three-dimensional vector wind speed (VEC =?u2 + v2 + w2), the kine-matic shear stress (u?w?) and kinematic heat flux (w?T ?) were determined.The overbar denotes half-hourly averaging and the primes indicate fluctua-tions from the average. The average VEC during the intercomparison was2.46 m s?1. Since the vertical wind contributed only very little to the overallwind speed (on average < 0.02 m s?1) this can be treated as the horizontalvector wind (i.e., the mean horizontal wind speed). A half hour was onlyconsidered for the intercomparison if 90 % of the high-frequency wind mea-surements were coming from within ?45 ? of the front of the sensor array toavoid flow distortion by sonic head and mounting structure. One sensor wasused as the reference sensor and calibration coefficients (slopes and offsets)for VEC, u?w? and w?T ? compared to the reference sensor were determined.These calibration coefficients were later applied to the horizontal mean wind(u), u?w? and w?T ? measured at MPB-03 in this study.Thermocouple temperatureFine-wire thermocouples are fast-response and high-precision sensors. Theyare accurate for 2 reasons: 1) a particular thermocouple has a predictableand repeatable relationship between temperature and voltage (electric po-tential) (Seebeck effect) and 2) the datalogger being used is high quality(very good microvoltmeter) and is maintained in an isothermal condition(very well insulated enclosure).Therefore, Ta measurements made with theseven thermocouples were not calibrated. All thermocouple were measuredusing one of two CR3000 data loggers.Air pressurePressure was measured by each of the LI-7500 IRGAs separately. Largepressure differences of up to 1.1 kPa (see Fig. I.1 in Appendix I) betweenthe levels were detected, which could not be attributed to the height1084.3. Methodologydifferences between the levels. The manual of the LI-7500 IRGA gives thepressure measurements uncertainty as ?1.5 % (LI-COR, 2004). Therefore,pressure measurements at the top level (z/h = 1.34) were used as referencemeasurements to calibrate all sensors and then adjusted for their height.The pressure sensor at the lowest level (z/h = 0.06) failed for the entirefield campaign. As further described below, measurements of the levelabove where adjusted for height differences and then used for the lowestlevel. Data from 11 July 2010 16:00 to 23 August 2010 16:00 PST wereused for this calibration.Each level was plotted against the pressure at z/h = 1.34 and a linearregression was fitted to the data (Fig. I.2 in Appendix I). The resultingcalibration coefficients are given in Table I.1 in Appendix I.Since there is a pressure difference expected due to the heightdifference of the levels, a height correction was added to the offset.The height correction was calculated based on the barometic equation(Liljequist and Cehak, 1994) and using average temperature at the sevenlevels and average pressure above the canopy (92.71 kPa). The resultingheight corrections and the total calibration offset (offset from linear fit +height correction) are given in Table I.2 in Appendix I. Fig. 4.3 showsthe resulting pressures at all seven levels after the calibration coefficientsincluding height correction were applied. To compensate for the lack ofpressure measurements at z/h = 0.06, pressure measurements at z/h = 0.14were used for this level using the linear fit coefficients at the same level butusing the height correction that corresponds to z/h = 0.06.Because one level was picked arbitrarily as the reference level, the finalpressure might still differ from the real atmospheric pressure, but differencesare expected to correspond to a smaller error when used to calculate mixingratios or concentration differences. As shown in Appendix J, the mixingratio error due to a pressure error of 1.1 kPa resulted in an mq errorof 0.14% and and mc error of 0.0012 %.CO2 and H2O molar densityAll LI-7500 IRGAs were calibrated before the field campaign and alsochecked after the field campaign in the laboratory using a dew pointgenerator (LI-610, LI-COR Inc.), a zero gas (N2) and a CO2 span gas(420.94 ppm before and 390.11 ppm after the field campaign). The1094.3. Methodology12 Jul 17 Jul 22 Jul 27 Jul 01 Aug 06 Aug 11 Aug 16 Aug9192939495p (kPa)Figure 4.3: Pressure at the six levels after the calibration coefficients includ-ing the height offsets were applied. Red: z/h = 0.06, orange: z/h = 0.14,light green: z/h = 0.38, dark green: z/h = 0.60, turquoise: z/h = 0.83,blue: z/h = 1.05 , black: z/h = 1.34.calibration gas cylinders were calibrated in the laboratory using standardsprovided by the Canadian Greenhouse Gases Measurement Laboratory,Meteorological Service of Canada, Downsview, Ont. LI-7500 IRGAs areknown to capture high-frequency variations in the concentrations well butare less reliable when measuring absolute atmospheric concentrations dueto temperature and pressure related drifts. An LI-840 IRGA was usedto calibrate the seven LI-7500 sensors on a half-hourly basis. The LI-840IRGA itself was calibrated regularly.The system was calibrated every 1 to 3 h by injecting consecutivelynitrogen (N2) as a zero gas and a CO2 in dry air span gas into the airsampling intake at the bottom level at the end of the half-hour. Differentspan gases were used over the course of the campaign (until 30 Jul: 404.08?mol CO2 mol?1 dry air, 31 Jul - 2 Aug: 451.28 ?mol CO2 mol?1 dryair, 4 - 8 Aug: 498.48 ?mol CO2 mol?1 dry air). Intake of ambient airduring the calibration was avoided by keeping the calibration gas flow ratehigher than 5 l min?1. The surplus gas was released to the atmosphere.Each calibration gas was measured for 3 min at the end of the halfhour. During the 30-min periods without calibration, the lowest level wasmeasured for an additional 6 min at the end of the half hour. A subset1104.3. Methodologyof data (between 2 min and 15 s before the end of the sequence at eachlevel) was used to calculate 105-s averages, one for each level and eachcalibration gas (if the calibration gases were used) for each half hour. Thesesubsets were chosen to make sure that tubing flushing and pressure vari-ations due to opening and closing of the solenoids did not affect the analysis.Air temperature (Ta) and pressure (p) were measured at each level withfine-wire thermocouples and the LI-7500 IRGAs, respectively. Since LI-7500pressure measurements have a relatively high uncertainty (?1.5 %, LI-COR,2004), a pressure correction was conducted, which is described above.LI-840 IRGA calibration: It was found that cell pressure variations andtemperature variations had a significant effect on LI-840 IRGA measure-ments. These cell pressure variations were caused by variations in pumpflow. Battery voltage was dependent on solar radiation causing the pumpflow variations. Appendix K describes my procedure for correcting for bat-tery voltage dependency. Fig. 4.4 shows the mc measurements of the CO2span gas made with the LI-840 IRGA before and after correcting for batteryvoltage dependence.22 Jul 24 Jul 26 Jul 28 Jul 30 Jul 01 Aug 03 Aug400420440460480500520mc (?mol mol-1)LI?840, uncalibratedLI?840, calibratedCO2 span gas concentrationFigure 4.4: LI-840 IRGA mc measurements of the CO2 span gas before andafter the calibration and actual CO2 span gas concentrations. CO2 span gasconcentrations varied over the course of the campaign.LI-7500 IRGA calibration: Using the calibrated 105-s averages mea-sured by the LI-840 IRGA, continuous LI-7500 IRGA measurements at each1114.3. Methodologylevel were corrected. The LI-840 IRGA mole fractions were therefore con-verted to molar densities by using the atmospheric thermocouple Ta and pat the level from which the air was sampled. The lag between the LI-840IRGA and the LI-7500 IRGA was determined by correlating the traces ofthe two sensors and it was typically 20 s ? 2 s. For each level and everyhalf hour, the LI-7500 IRGA measurements during the 105-s long LI-840IRGA averaging period shifted forward by 20 s was averaged. For every halfhour that LI-7500 IRGA and LI-840 IRGA measurements were available, thedifference between the LI-840 IRGA and LI-7500 IRGA averages was deter-mined. To correct the LI-7500 IRGA measurements of a half hour, the offsetwas then linearly interpolated between the periods when the LI-840 IRGAmeasured simultaneously. Depending on when the LI-840 IRGA measure-ment was conducted during a half hour, the offset was either interpolatedbetween the half hour before and the half hour concerned or between thehalf hour concerned and the next half hour. The determined interpolatedoffset was then applied to the half-hourly averaged LI-7500 IRGA ?c or ?qfor the half hour concerned.4.3.4 UncertaintiesIn order to set limits on the ability to determine the flux-gradient exchange,the uncertainties were determined.Horizontal wind speedDuring the above described sonic anemometer field intercomparison (Sec-tion 4.3.3), the standard deviation (STD) of VEC ? VECref for each sensorincluded in the intercomparison was determined. The subscript ref standsfor the reference sensors. STD was between 0.039 and 0.057 m s?1 for thedifferent sensors. The latter was used as the uncertainty of u in this chapter.Air temperatureThe thermocouple error is the sum of the errors in the reference temper-ature measurement, the temperature-to-voltage polynomial fit error, thethermocouple-voltage measurement accuracy (Campbell Scientific, 2013),and a radiative error. To reduce the error due to wire properties thewire for all thermocouples was taken from the same spool. As explainedabove, the thermocouples were connected to the datalogger via 36-gaugesupport wires and unshielded chromel-constantan extension leads. Both1124.3. Methodologyloggers were kept in the same white, sealed box. Voltage measurement(?0.04 %) and temperature conversion errors were expected to be very small.Thermocouple measurements of the lowest three levels were recordedon one logger and the top four levels were recorded on another logger,which was kept in the same logger box. All levels were affected bysmall variations in reference junction measurements due to temperaturegradients across the logger wiring panel and the fact that the loggermeasured the reference temperature at only one spot on the wiring panel.Lee and Barr (1998) estimated the panel temperature (Tpanel) error dueto temperature variations across the reference temperature block to be0.0028 K. The layer at 0.38 < z/h < 0.60 was additionally affected by theTpanel measurement accuracy as the temperature measurements for thislayer were recorded on two different loggers. Campbell Scientific (2013)gives the Tpanel accuracy as 0.3 K. In the worst case the inaccuraciesof the two logger could add up to 0.6 K. This, however, is not verylikely. It was observed that for these two dataloggers during timeswith constant vertical potential temperature (?) gradients, measured ?and therefore Ta disagreed by < 0.06 ?C between z/h = 0.38 and z/h = 0.60.Another contributor to the temperature gradient error was the radiativeerror caused by variations in shading throughout the canopy. FollowingTanner and Thurtell (1969) the radiation error can be calculated bydetermining the energy balance of the thermocouple wire. See Appendix Lfor the complete energy balance of the thermocouple wire.Using the 24-h averaged u (2.04 m s?1) and the ensemble-averagedS between 10:00 and 14:00 PST (663.21 W m?2) at z/h = 1.34, thethermocouple temperature error (Tw?Ta, where Tw is the wire temperatureand Ta is the air temperature) is 0.08 K. When using the 24-h averaged u(0.22 m s?1) and the ensemble-averaged S between 10:00 and 14:00 PST(463.16 W m?2) at z/h = 0.06, Tw ? Ta is 0.12 K. These temperatureerrors would only directly translate into temperature gradient errorsif two thermocouples were measuring under the same wind conditionsand one thermocouple was totally exposed to the sun while the otherthermocouple was entirely protected from short-wave radiation. Given acertain compensation of radiation and wind speed effect, that half-hourlyaverages of the temperature are used, and that the gradients are calculatedfor layers thinner than 6 m, the radiation related error can be assumedto be at least half of the difference between Tw ? Ta at the top and at1134.3. Methodologythe bottom level. Therefore, an error of < 0.02 K is assumed. Since allother errors can be assumed to be much smaller, the sum of the radiationerror and the error due to Tpanel accuracy (0.08 K) was used as the totaltemperature error for temperature gradient calculations for the layer at0.38 < z/h < 0.60 and the radiation error (0.02 K) only was used for allother layers.CO2 and H2O densityThe reduction of measurement errors of CO2 and H2O concentrations dueto calibration was discussed in Section 4.3.3. In summary, the determineduncertainties that were further used in this chapter were 17.1 ?mol m?3 for?c and 1.03 mmol m?3 for ?q.Momentum and sensible heat flux densityIn the above described ultrasonic anemometer field intercomparison(Section 4.3.3), STD of u?w? ? u?w?ref and STD of T ?w? ? T ?w?ref were de-termined for the sensors that were part of the intercomparison. STD rangedbetween 0.00517 and 0.01291 m2 s?2 and between 0.00409 and 0.00676K m s?1 for u?w? ? u?w?refand T ?w? ? T ?w?ref , respectively. The max-imum STDs were used as the uncertainties for u?w? and T ?w? in this chapter.CO2 flux densityWesely and Hart (1985) determined the precision of Fc to be within 10to 20 % due to the natural geophysical variability. Nesic et al. (2007)conducted a six-day field intercomparison where Fc was measured witha closed-path infrared gas analyzer (IRGA) and an open-path IRGA(LI-7500) over a raised bog surface in July 2004. In both cases the same3-D sonic anemometer (R3, Gill Instruments Ltd., Lymington, UK) wasemployed to measure the vertical wind. Both systems compared very well(close to the 1:1 line) and the root mean square error (RMSE) of the datacompared to the linear fit was 0.405 ?mol m?2 s?1, which was used in thischapter as the Fc uncertainty.1144.3. MethodologyH2O flux densityNo intercomparison data were available in this case to determine the sensorrelated uncertainty of latent heat flux measurements. Dyer and Hicks (1972)determined the run-to-run uncertainty due to the natural variability of latentheat flux to be at least 10 % under ideal environmental conditions. Thedetection limit of the latent heat flux density, was determined based onlong-term latent flux measurements conducted with an LI-7500 IRGA and aCSAT3 sonic anemometer over a hybrid poplar plantation in Albert, Canada(HP09). During the wintertime when latent heat fluxes were very small,fluxes < 1 W m?2 (= 0.023 mmol m?2 s?1) could clearly be detected, whichwas used as the latent heat flux uncertainty in this chapter.4.3.5 AnalysisCO2 and H2O molar mixing ratioCO2 and H2O molar mixing ratios (mc andmq, respectively) were calculatedas:mq = ?qMd?a(4.27)mc = ?cMd?a, (4.28)where Md is the molar mass of dry air (0.028964 kg mol?1) and ?a wascalculated as p/RuTa ? ?q, where Ru is the universal gas constant.Potential temperatureThe potential temperature (?) was calculated as:? = Ta + ?(z + zasl), (4.29)where ? is the dry adiabatic lapse rate (0.01 K m?1), z is the measurementheight above ground and zasl is the elevation of the site above sea level.Flux densities and shear stressFor each half-hour, the covariances obtained by 30-min block averaging,w?T ?ac, w?m?q and w?m?c, were calculated. Sensible heat flux density (QH),1154.3. Methodologylatent heat flux density (QE) and CO2 flux density (Fc) were calculatedaccording to Eqs. 4.30, 4.31, 4.32, respectively.QH = ?cp w?T ?ac, (4.30)QE = ? ?a w?m?q, (4.31)Fc = ?a w?m?c, (4.32)QH and QE are positive when their flux direction is upward5. Fc is alsopositive when the flux is upward.The Reynolds shear stress (?) was calculated as? = ??u?w?, (4.33)where ? is the air density. As shown in Appendix M, even though strongdirectional wind shear exists in this canopy, the absolute contribution ofv?w? to the overall shear stress was small and Eq. 4.33 is sufficient to use.According to Eq. 4.33, ? is positive when the shear is directed downward.The same corrections and quality control were applied as in Chapters 2 and3.Eddy diffusivities and stability functionsGiven that eddy flux and scalar measurements were made at seven discreteheights (levels), the eddy diffusivities was calculated based on the measure-ment of fluxes by EC (? , QH , QE and Fc) and the corresponding gradients(?u/?z, ??/?z, ??q/?z, ??c/?z) for six layers, which were confined bythe seven levels:KM =???u?z, (4.34)KH = ?QH?cp???z, (4.35)KE = ?QE???q?z, (4.36)5In contrast to Chapter 2 where the focus was on energy balance partitioning, thebiometeorological sign convention is used here.1164.3. MethodologyKC = ?Fc??c?z, (4.37)where ? stands for the difference between two measurement heights.By using eddy fluxes averaged between two adjacent levels, the eddydiffusivities for the six layers between the levels were calculated for every30-min period.The stability functions were then calculated as:?H =kzsT????z, (4.38)?E =kzsq???amq?z, (4.39)?C =kzsc???amc?z, (4.40)?M =kzs??u?w??u?z. (4.41)Using the eddy fluxes, T? = T ?w?/??u?w?, q? = ?am?qw?/??u?w?, c? =?am?cw?/??u?w?. The layer midpoint height was used when calculating zs.K and ? were determined according to all scaling combinations.Zero-plane displacement heightThe zero-plane displacement height (d) was determined iteratively similarto Simpson (1996). First, the average wind speed at the 26.8-m height(z/h = 13.8) was determined for neutral stability, which was for this purposedefined as |?| < 0.02, where ? = (z ? d)/L. As a starting point d was set to2/3h (Foken, 2008). Second, d was then determined as:d =z1 + 0.19 ekuu?(4.42)This equation assumes that z0/d = 0.19. Steps one and two were thenrepeated iteratively until d did not change significantly.1174.4. Results and discussionInflection point in the wind speed profileThe inflection point for each 30-min interval was determined using the fol-lowing six steps:i. A cubic spline was fit to u to increase the vertical resolution to 1 m.ii. A running mean (5-m window) was applied to the spline fit to reducethe slightly exaggerated curvature of the fit.iii. The second derivative (SD) of the spline fit was determined numerically.iv. The height zt was determined as the height below and closest to theheight where the SD became zero, so that SD(zt)> 0 (wind profilebending right coming from below) and SD(zt + 1 m)< 0 (wind profilebending left coming from below).v. If several heights matched iv, the height was chosen where SD(zt) ?SD(zt + 1 m) was largest implying the strongest change in curvature.vi. The height was then interpolated linearly between zt and zt+1m tolocate the inflection point (zinfl)4.4 Results and discussion4.4.1 Zero-plane displacement height and roughness lengthThe zero-plane displacement height d can usually be roughly estimated asd = 0.67h (Foken, 2008). In our case, however, the analysis of d resultedin d = 8.0 m including a total of 96 half hours with neutral conditions,which corresponds to d/h = 0.40. If z0/d = 0.19 as assumed in theanalysis of d, z0 = 1.46 m (z0/h = 0.07), which is in the typical rangefor coniferous forests. Monteith and Unsworth (2008) give a characteristicvalue for z0 of a coniferous forest as 1.0 m and Foken (2008) listed atypical z0 of 1-2 m for forests. Raupach (1994) derived relationshipsbetween the canopy area index (?), d and z0. If branches and leaves areneglegted, it can be assumed that ? in our canopy is equal to the total bolesurface area (0.28 m2 m?2, see Chapter 2). For this ?, Raupach?s relation-ships predict d/h ? 0.4 and z0/h ? 0.1, which fit very well with our findings.1184.4. Results and discussion4.4.2 Profiles of scalars and corresponding fluxesEnsemble averaged profiles of the mean horizontal wind speed (u), the po-tential temperature (?), the H2O molar mixing ratio (mq), and the CO2mixing ratio (mc) and their corresponding flux densities (? , QH , QE andFc, respectively) were determined separately for three-hour periods of theday and for four stability regimes (stable: ? > 0.1, neutral: ?0.1 < ? < 0.1,unstable: ?1.0 < ? < ?0.1 and free convection: ? < ?1.0). A half hour wasonly considered if both the variable of interest and the corresponding fluxwere available at all levels. Stability was determined at z/h = 1.34. In thecase of u and ? , the profiles were normalized by the values at canopy heightand z/h = 1.34, respectively, to compare them to profiles from several otherstudies under neutral conditions, which are listed in Table 4.2.Table 4.2: Properties of six canopies of which the horizontal mean wind andshear stress profiles are shown in Fig. 4.5Canopy Site h (m) LAI (m2 m?2) ReferenceEucalypt Moga 12 1.0 Raupach et al. (1996)Pine MPB-06 16 1.4 Christen et al. (2008)Pine Whiteshell 15, 20 2.0 Amiro (1990b)Pine Uriarra 16, 20 4.0 Denmead and Bradley (1987)Aspen Whiteshell 10 4.0 Amiro (1990b)Spruce Whiteshell 12 10.0 Amiro (1990b)Horizontal wind speed and shear stressThe u profile decreased first rapidly and then slowly into the canopy (Fig4.5). During nighttime and under stable conditions, our measurementscompared well with other measurements conducted in different kinds ofcanopies mainly under near-neutral conditions. However, during daytime,under neutral and unstable conditions, the rapid decrease of u at thetop of the canopy was slightly less pronounced but continued furtherdown into the canopy. When looking at the inflection point height (Fig.4.6), it can be seen that zinfl was higher during nighttime than duringdaytime. The median zinfl/h ranged between 0.76 during nighttime and0.63 during daytime. Stable conditions resulted in a higher zinfl thanneutral conditions; however, unstable conditions resulted in very similarmedian zinfl as neutral conditions. Generally, zinfl was lower than in all1194.4. Results and discussionother studies it was compared to, where it was usually located at the topof the canopy, i.e., z/h = 1 (Finnigan, 2000). Poggi et al. (2004b) foundin a flume experiment that even though the shear in wind decreased withcanopy density, the inflection point was always located close to the canopytop.Several studies have described secondary maxima of u (e.g., Shaw, 1977;Raupach and Thom, 1981; Baldocchi and Meyers, 1988b; Amiro, 1990b).In this study, there was only a very small increase in wind speed withdepth close to the ground (from z/h = 0.14 to 0.06) between 0 and 6 PST.Between 0 and 3 PST, ? was also slightly negative at z/h = 0.14. Shaw(1977) stated that the secondary wind speed maxima happened in canopieswith a relatively open structure close to the ground compared to above. Inthis stand however, the canopy structure did not decrease down into thecanopy (see Fig. 3.2) resulting in no clear secondary maximum.The shear stress decreased rapidly with depth into the canopy. However,this decrease was more pronounced during nighttime than during daytime.During nighttime and for stable conditions the shear stress stayed almostconstant for z/h ? 0.38, lower than in profiles found in the other studies.During daytime, however, the decrease continued all the way to the ground.Above the canopy, ? was approximately constant as expected in the surfacelayer; however, it stayed also almost constant in the upper canopy and ?/?topwas larger in the upper canopy than in the other studies. Stable conditionsbehaved very similarly to nighttime profiles, while neutral and unstableconditions showed a gradually slower decrease with decreasing height in?/?top in the upper canopy. Overall, the ensemble averaged ? directionwas consistent with u gradients and therefore with gradient diffusion theory.Potential temperature and sensible heat fluxDuring nighttime, there was a clear temperature inversion extending allthe way to the ground (Fig. 4.7) and at the same time QH was negativeimplying a downward sensible heat flux. The magnitude of QH increasedwith height but it was still small throughout the canopy. In denser forests,the lowest temperatures at night are usually found in the center or upperpart of the canopy with temperatures higher at the ground while it isthe opposite during daytime (e.g., Denmead and Bradley, 1985). Theensemble-averaged stable profile had the same shape as the nighttime1204.4. Results and discussionprofiles. At transition times, (6 - 9 and 18 - 21 PST) when the profilesshow very little ? variation with height, QH was positive. From 9 to 18PST, ? was largest at the ground and decreased with height. During thistime, QH was positive and in the direction of gradient diffusion and itwas large compared to other times of the day. QH increased with heightfor z/h ? 0.8 and stayed approximately constant above. It was alreadyshown in Chapter 2 that most of the available energy was partitioned intoQH during daytime. The ensemble-averaged unstable profile resembled thedaytime profiles. Under neutral conditions, there was on average a smallinversion; however, QH was directed upward, indicating counter gradientdiffusion. Temperature varied especially close to the ground over the courseof the day. Except for neutral cases, ensemble averaged profiles of ? andthe direction of QH were consistent with gradient diffusion theory.H2O mixing ratios and latent heat fluxesDuring nighttime (21 - 3 PST) and under stable conditions, mq increasedwith height (Fig. 4.8) likely due to condensation at the ground, while QEwas close to zero i.e., not confirming a downward flux of water vapour.Dew was observed on many days at the ground in the early morning sincetemperatures decreased substantially over night. Between 3 and 6 PST, theprofile became approximately constant and later slightly decreased withheight. Between 0 and 6 PST, QE also started to become positive and thenincreased substantially over the course of the day. Especially, between 9 and15 PST, QE increased with height below z/h = 0.60, implying that there isa source of H2O in the lower canopy as discussed in Chapter 2. Unstableensemble-averaged profiles again resembled daytime profiles. Under neutralconditions, however, the ensemble averaged mq was still slightly smallerat z/h ? 0.38 than above while the direction of QE was upward; e.g., theneutral ensemble-averaged mq profile (showing a weak inversion) and thecorresponding fluxes were not consistent with gradient diffusion theory.CO2 mixing ratios and CO2 fluxesIn the case of CO2 mixing ratios, the largest gradients were found duringnighttime (between 18 and 6 PST) near the ground (Fig. 4.9), when mcdecreased with height below z/h < 0.38 and stayed approximately constantabove. At the same time, Fc was also positive. The Fc profile between 01214.4. Results and discussionand 3 PST however, showed that flux measurements during nighttime wereproblematic. As already discussed in Chapter 3, the decrease in Fc withheight below z/h = 0.14 suggested a sink of CO2. Photosynthesis was notpossible at this time and the sink must have been caused by advection ormeasurement error. Between 6 and 18 PST, the ensemble averaged mcprofiles were almost constant with height and Fc was downward (Fc < 0)throughout the canopy. Only between 12 and 15 PST above the canopy(z/h = 1.34) was Fc positive. The magnitude of the downward flux ofCO2 was largest in the center part of the canopy and values were smallerabove and below. As discussed in Chapter 3, this means that there is asink of CO2 below z/h = 0.38 and a source of CO2 above correspondingto the layers of living and dead vegetation, respectively. The flux profilesindicated the largest CO2 uptake in the lower canopy occurred in themorning, while the QE profiles also showed the largest source of latent heatfor z/h = 0.60 occurred between 9 and 12 PST. CO2 fluxes were generallyconsistent with gradient diffusion theory. However, the ensemble averagedprofile for neutral conditions shows that there was a small positive gradientof mc, where mc was largest at the ground and Fc was slightly positivethroughout the canopy even though it was of relatively small magnitude.Under unstable conditions, the ensemble-averaged profiles resembled thedaytime profiles in shape. Under strongly unstable conditions, it is evidentthat the magnitude of Fc was larger than under stable, neutral or weaklyunstable conditions.1224.4.Resultsanddiscussion0 ? 3 PST (110)0.0 0.5 1.0 1.50.00.20.40.60.81.01.21.4z/h3 ? 6 PST (105)0.0 0.5 1.0 1.56 ? 9 PST (113)0.0 0.5 1.0 1.59 ? 12 PST (113)0.0 0.5 1.0 1.512 ? 15 PST (115)0.0 0.5 1.0 1.5?u / ?u(h)15 ? 18 PST (117)0.0 0.5 1.0 1.518 ? 21 PST (113)0.0 0.5 1.0 1.521 ? 24 PST (110)0.0 0.5 1.0 1.5Stability dependent0.0 0.5 1.0 1.50.0 0.5 1.0 1.50.00.20.40.60.81.01.21.4z/h0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5?/? top0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 ? > 0.1 (168)?0.1 <? < 0.1 (308)?1.0 <? < ?0.1. (367)? < ?1.0 (53)0.99 m/s 1.20 1.53 1.97 2.14 2.30 1.90 1.211.351.492.011.300.05 N m-20.05 0.24 0.41 0.47 0.49 0.29 0.08 0.080.200.410.22Pine, LAI = 4.0 (Raupach et al., 1996)Eucalypt, LAI=1.0 (Denmead and Bradley, 1987)Spruce, LAI = 10.0 (Amiro, 1990)Aspen, LAI = 4.0 (Amiro, 1990)Pine, LAI = 2.0 (Amiro, 1990)Pine, LAI = 1.4 (Christen et al., 2008)3-hour averagesThis study: Pine, LAI = 0.55Figure 4.5: Ensemble averaged profiles of the horizontal mean wind speed (u) normalized by the wind speed atcanopy height (u(h)) and ensemble averaged profiles of shear stress (?) normalized by ? at z/h = 1.34 (?top)for 3-h periods of the day and four stability regimes. The normalization values are given in coloured numbers.Numbers in brackets are number of half hours included in the statistics of each profile. The grey lines are profilesdetermined in other studies, which were not separated by time, but were mainly measurements under unstable orneutral conditions.1234.4. Results and discussion 110 105 113  113  115  117  113 1100 5 10 15 20hour, PST0.00.20.40.60.81.0z infl/h 168 308  367 530.1< ? ?0.1< ?<0.1 ?1.0< ?<?0. 1 ?< ?1.00.00.20.40.60.81.0z infl/h(a)(b)25 %75 %Median10 %90 %MeanFigure 4.6: Ensemble averaged height of inflection point (zinfl) normalizedby the canopy height (h) for 3-h periods (a) and for different stability con-ditions (b). Numbers below bars give the number of half-hours included inthe calculations of the boxplot.1244.4.Resultsanddiscussion0 ? 3 PST (99)15 200.00.20.40.60.81.01.21.4z/h3 ? 6 PST (90)15 206 ? 9 PST (109)15 20 259 ? 12 PST (110)20 25 3012 ? 15 PST (114)25 30 35? 15 ? 18 PST (116)25 30 3518 ? 21 PST (113)25 30 3521 ? 24 PST (100)20 25Stability dependent20 25?100 0 1000.00.20.40.60.81.01.21.4z/h?100 0 100 ?100 0 100 200 100 200 300 400 100 200 300 400QH (W m ?2 )0 100 200 300 ?100 0 100 ?100 0 100 0 100 200 ? > 0.1 (153)?0.1 < ? < 0.1 (287)?1.0 < ? < ?0.1. (359)? < ?1.0 (52 )3-hour averages(?C)?Figure 4.7: Ensemble averaged profiles of the potential temperature (?) and sensible heat flux (QH) for 3-h periodsof the day and different stability regimes. Numbers in brackets are number of half hours included in the statisticsof each profile.1254.4.Resultsanddiscussion0 ? 3 PST (33)10 11 12 130.00.20.40.60.81.01.21.4z/h3 ? 6 PST (12)10 11 126 ? 9 PST (24)10 11 12 139 ? 12 PST (55)10 11 1212 ? 15 PST (60)9 10 11mq (mmol mol-1)15 ? 18 PST (45)9 10 1118 ? 21 PST (71)9 10 11 1221 ? 24 PST (70)11 12 13Stability dependent10 11 12?40?20 0 20 400.00.20.40.60.81.01.21.4z/h?40?20 0 20 40 0 20 40 60 40 60 80 100 40 60 80 100 QE (W m-2) 20 40 60 80 ?40?20 0 20 40 ?40?20 0 20 40 0 20 40 60 ? > 0.1 (61)?0.1 <? < 0.1 (129)?1.0 <? < ?0.1. (159)? < ?1.0 (21)3-hour averagesFigure 4.8: Ensemble averaged profiles of the H2O mixing ratio (mq) and latent heat flux (QE) for 3-h periods ofthe day and different stability regimes. Numbers in brackets are number of half hours included in the statistics ofeach profile.1264.4.Resultsanddiscussion0 ? 3 PST (28)425 4500.00.20.40.60.81.01.21.4z/h3 ? 6 PST (12)425 450 4756 ? 9 PST (24)400 4259 ? 12 PST (54)375 40012 ? 15 PST (60)375 400mc (?mol mol-1)15 ? 18 PST (42)375 40018 ? 21 PST (68)375 40021 ? 24 PST (68)375 400 425Stability dependent400 4250 30.00.20.40.60.81.01.21.4z/h0 3 ?3 0 ?3 0 ?3 0Fc (?mol m-2 s-1)?3 0 ?3 0 3 0 3 ?3 0 ? > 0.1 (59)?0.1 <? < 0.1 (123)?1.0 <? < ?0.1. (154)? < ?1.0 (20)3-hour averagesFigure 4.9: Ensemble averaged profiles of the CO2 mixing ratio (mc) and CO2 flux (Fc) for 3-h periods of the dayand different stability regimes. Numbers in brackets are number of half hours included in the statistics of eachprofile.1274.4. Results and discussion4.4.3 Gradient and counter-gradient transportSo far, it was examined whether the ensemble-averaged profiles (3-hperiods) of ? , QH , QE and Fc behave as predicted by gradient-diffusiontheory. Due to the averaging, however, it is not possible to tell whetherthere were single half hours when counter-gradient fluxes occurred.In this section, the frequency of occurrence of counter-gradient fluxesover the course of the day and whether counter-gradient fluxes oc-curred only for small flux magnitudes will be examined. In the rest ofthe chapter, heights of layers will be referred to using layer midpoint heights.Temporal distributionFigs. 4.10, 4.11, 4.12 and 4.13 show the relative frequency of occurrence ofgradient and counter-gradient diffusion of momentum, sensible heat, H2Oand CO2, respectively as a function of time of day. Due to measurementuncertainty, when the scalar gradient or the flux was smaller than theuncertainties discussed in Section 4.3.4, it could not be determined whetherfluxes followed gradient or counter-gradient diffusion theory and thosesituations are shown in white.Fig. 4.10 shows that there are very few half hours when shear stresswas countergradient. At all levels, the overall frequency of counter-gradienttransport was < 0.7 %. However, with increasing depth into the canopy,the frequency of half hours when ? or u gradients were smaller thanthe measurement uncertainties became larger. At z/h = 0.10, gradienttransport could be identified in only 17.7 % of the half-hours, whilecounter-gradient transport could be identified in only 0.1 % of the halfhours. Given the larger wind speed and shear stress above the canopyduring daytime, conformity to gradient diffusion theory could be examinedfor more half hours than during nighttime.The sensible heat flux direction mainly conformed to gradient dif-fusion theory at all levels (Fig. 4.11). At night, however, QH was toosmall in the lower canopy in many cases to determine conformity togradient-diffusion theory. In the upper canopy, small gradients madea relatively large number of cases undeterminable. Counter-gradientfluxes were frequently observed in the early morning or in the eveningat all levels. For example, approximately 55 % of the cases at 7 PST at1284.4. Results and discussionz/h = 0.10 and 90 % at 10 PST at z/h = 1.20 were counter gradient.Above the canopy (z/h = 1.20), counter-gradient transport was the mostfrequent with an overall (24-h) relative frequency of occurrence of 19.9%, while in the other layers the overall frequency of occurrence was < 6.7 %.In the case of H2O vapour transport (and therefore latent heat) counter-gradient transport contributed overall with 20.6 % at z/h = 0.10, whilein 41.8 % of the cases, transport direction conformed to gradient-diffusiontheory (Fig. 4.12). Interestingly, the case of water vapour counter-gradientfluxes occurred most commonly during daytime, where they accounted forup to 50 % of the cases during some hours of the day. In the layers above,counter-gradient fluxes occurred less often, but they occurred throughoutthe entire day. Gradient-diffusion transport of water vapour was dominantat z/h = 0.26. Even though the frequency of gradient-diffusion transportwas larger than the frequency of counter-gradient fluxes in all layers, therewere many half hours, when gradient-diffusion conformity could not bedetermined for z/h ? 0.49 due to too small H2O gradients or QE.Similar to H2O, the occurrence of counter-gradient CO2 fluxes wasdistributed over the entire day. Even though the overall relative frequencyof counter-gradient fluxes in the lowest layer was the largest, there was alsono clear pattern that counter-gradient fluxes occurred more often in thelower canopy than above. At those levels where counter-gradient fluxesoccurred less frequently, flux direction conformity to gradient diffusiontheory was also detected less frequently and there were more half hourswhen uncertainties were larger than measured CO2 gradients or Fc.1294.4.Resultsanddiscussionz/h = 0.10020406080100Rel. frequency (%)z/h = 0.26 z/h = 0.49z/h = 0.710 6 12 18Time (PST)020406080100Rel. frequency (%)z/h = 0.940 6 12 18Time (PST)z/h = 1.200 6 12 18Time (PST)17.7 0.145.7 0.560.8 0.268.4 0.271.8 0.374.9 0.7Figure 4.10: Ensemble-averaged relative frequencies of occurrence of shear stress corresponding to counter-gradient(red) and gradient diffusion (blue) for each hour of the day and the six layers. White areas show the relativefrequency of half hours when either the flux or the wind gradient was smaller than the uncertainties and gradientdiffusion conformity could not be determined reliably. Red and blue numbers give the ensemble-averaged 24-hrelative frequency (in %) of occurrence of counter-gradient and gradient fluxes, respectively.1304.4.Resultsanddiscussionz/h = 0.10020406080100Rel. frequency (%)z/h = 0.26 z/h = 0.49z/h = 0.710 6 12 18Time (PST)020406080100Rel. frequency (%)z/h = 0.940 6 12 18Time (PST)z/h = 1.200 6 12 18Time (PST)47.0 3.851.2 6.767.5 4.770.7 2.348.319.959.1 4.5Figure 4.11: Same as Fig. 4.10 but for sensible heat flux.1314.4.Resultsanddiscussionz/h = 0.10020406080100Rel. frequency, (%)z/h = 0.26 z/h = 0.49z/h = 0.710 6 12 18Time (PST)020406080100Rel. frequency, (%)z/h = 0.940 6 12 18Time (PST)z/h = 1.200 6 12 18Time (PST)41.820.672.2 4.447.7 6.140.8 7.633.8 7.430.414.2Figure 4.12: Same as Fig. 4.10 but for H2O flux.1324.4.Resultsanddiscussionz/h = 0.10020406080100Rel. frequency (%)z/h = 0.26 z/h = 0.49z/h = 0.710 6 12 18Time (PST)020406080100Rel. frequency (%)z/h = 0.940 6 12 18Time (PST)z/h = 1.200 6 12 18Time (PST)44.020.537.116.2 44.0 9.335.716.721.8 8.932.912.5Figure 4.13: Same as Fig. 4.10 but for CO2 flux.1334.4. Results and discussionRelationships between fluxes and gradientsIn the following, the relationships between the fluxes and their correspond-ing scalar gradients will be examined (Figs. 4.14, 4.15, 4.16 and 4.17).Eqs. 4.34, 4.35, 4.36 and 4.37 show that the proportionality factor betweenthe two is the eddy diffusivity. Since the eddy diffusivity is expected tochange with stability, it was distinguished between different local stabilityconditions, where the stability regimes are defined as in Section 4.4.2. InFigs. 4.14, 4.15, 4.16 and 4.17, if a point is lying in the upper left or thelower right quadrant, counter-gradient transport is implied. Otherwise, theflux direction conforms with gradient-diffusion theory.In the case of shear stress, most half hours have a positive horizontalmean wind speed gradient and very often also ?/? > 0 (Fig. 4.14). Onlyin the lowest layer (z/h = 0.10), negative ?/? occurred relatively often (35% of the time), while in all other layers the occurrence of ?/? < 0 wasnegligible. In all layers ?/? and ?u/?z are strongly correlated. KM (theslope of the relationship between ?/? and ?u/?z) increased with height inthe canopy, while the increase was less pronounced between z/h = 0.49 and0.71. The slope was clearly less steep for stable cases than for neutral casesand therefore KM was most of the time much smaller for the stable thanfor the neutral cases. However, the slope did not change much when goingfrom neutral to weakly or strongly unstable conditions. The relationshipbetween stability and slope was not very clear for z/h ? 0.49. This isbecause the stability regimes were determined by the stability above thecanopy since it is difficult to determine stability in the canopy. However,the stability in the lower canopy likely did not vary much.The kinematic heat flux and ???/?z were clearly related (Fig. 4.15).Counter-gradient fluxes occurred more often than for shear stress; however,their frequency of occurrence was still relatively low (< 24 %) in all layers.Furthermore, in many counter-gradient cases the flux was smaller thanthe flux uncertainty. The slopes show that KH also clearly increased withheight. There was again little difference between neutral and unstablecases. It is difficult to infer information about KH in the upper layers forstable cases since the gradients and the fluxes were very small.Flux-gradient relationships were not as clear at z/h = 0.10 for H2O asfor the shear stress and sensible heat (Figs. 4.16 and 4.17, respectively).For all layers above, there was a strong relationship between QE/? and1344.4. Results and discussion???q/?z. Counter gradient fluxes occurred more often than in the case of? and QH ; however, QE/? or ???q/?z was small when counter-gradientfluxes occurred, except at z/h = 0.10. If counter-gradient fluxes occurred,QE was typically upward and ?q gradients were positive.As for water vapour, the relationship between Fc and ??c/?z wasquite scattered for the z/h = 0.10 but showed a clear relationship in thelayers above (Fig. 4.13). Also counter-gradient transport occurred morefrequently than for ? and QE; however, a large number of the measurementswere located within the uncertainty range of the ?c measurements. Neutraland unstable conditions resulted in similar slopes, while the relationshipbetween Fc and ???c/?z was less clear for stable conditions due to largerscatter.1354.4.Resultsanddiscussionz/h = 0.100.00.40.81.2? /?  (m2 s?2)z/h = 0.26 z/h = 0.49z/h = 0.710.0 0.1 0.2 0.3?u/?z (s-1)0.00.40.81.2z/h = 0.940.0 0.1 0.2 0.3z/h = 1.200.0 0.1 0.2 0.34998114617164819142472699182180735209849208678522179 ? > 0.1 ?0.1 < ? < 0.1 ?1.0 < ? < ?0.1 ? < ?1.0 Figure 4.14: Kinematic shear stress (?/?) vs. horizontal mean wind speed gradient (?u/?z) for the six layers anddifferent stability conditions. Each point represents one 30-min average. Counter-gradient transport occurred whenpoints lie in the top left or the bottom right quadrant. Grey bands around the zero lines are uncertainty bands.The four numbers in the corners show how many 30-min values lie in each quadrant including the uncertaintybands.1364.4.Resultsanddiscussionz/h = 0.100.00.20.40.6z/h = 0.26 z/h = 0.49z/h = 0.71?0.8 ?0.4 0.0 0.40.00.20.40.6QH/(? cp) (K m s?1)z/h = 0.94?0.8 ?0.4 0.0 0.4?/ z (K m? 1)z/h = 1.20?0.8 ?0.4 0.0 0.44094116428339210159306411171183184451882326496755825434826174285? ? ? > 0.1 ?0.1 < ? < 0.1 ?1.0 < ? < ?0.1 ? < ?1.0 Figure 4.15: Same as Fig. 4.14 but for kinetic sensible heat flux (QH/(?cp)) and mean potential temperaturegradients (???/?z).1374.4.Resultsanddiscussionz/h = 0.10?101234z/h = 0.26 z/h = 0.49z/h = 0.71?15 ?10 ?5 0 5 10? / z (mmol m? 4)?101234QE/?  (mmol m?2 s?1)z/h = 0.94?15 ?10 ?5 0 5 10z/h = 1.20?15 ?10 ?5 0 5 1021327169149321293689285226189224239196247368975213549652??q ? > 0.1 ?0.1 < ? < 0.1 ?1.0 < ? < ?0.1 ? < ?1.0 Figure 4.16: Same as Fig. 4.14 but for water vapour flux (QE/?) and mean H2O density gradients (???q/?z).1384.4.Resultsanddiscussionz/h = 0.10?6?303z/h = 0.26 z/h = 0.49z/h = 0.71?40 0 40 80?6?303Fc (?mol m?2 s?1)z/h = 0.94?40 0 40 80z/h = 1.20?40 0 40 802101219315119120816140175127352222002142111115911510318617784103156? / z (?mol m? 4)??c ? > 0.1 ?0.1 < ? < 0.1 ?1.0 < ? < ?0.1 ? < ?1.0 Figure 4.17: Same as Fig. 4.14 but for CO2 flux (Fc) and mean CO2 density gradients (???c/?z).1394.5. Comparison to surface-layer predictions4.5 Comparison to surface-layer predictions4.5.1 Stability functionsSo far, it was determined whether fluxes were counter to or in the samedirection as gradient diffusion. However, during times of gradient diffusion,fluxes might have been larger or smaller than predicted by gradient diffusiontheory. The stability functions for momentum, sensible heat, latent heatand CO2 determined in this study were compared to the surface-layerpredictions (see Eqs. 4.22 and 4.23). For this purpose, bin averages of themeasurements were determined. Only half hours when K > 0 and ? > 0were included. The stability that was used in the stability functions wasdetermined at each level using the effective height as the scaling height(zs = ze).Under these conditions, the bin-averaged measurements of ?M matchedthe predictions quite well (Fig. 4.18). For z/h = 0.49 and 0.71, ??1M wasslightly overestimated and therefore ?M slightly underestimated, while atz/h = 0.10, ??1M was underestimated and therefore ?M overestimated bythe predictions. For z/h = 0.10, there were not enough measurements leftafter excluding measurements smaller than the measurement uncertaintyfor ? > 0 to compare them to the predictions.In the case of sensible heat fluxes, stability function predictions andmeasurements agreed relatively well under stable and neutral conditions(Fig. 4.19). Except for z/h = 0.49, however, the predictions clearlyunderestimated ??1H , i.e., ?H was overestimated, under unstable conditions.The agreement of the predictions for the stability functions and themeasurements was better for latent heat flux (Fig. 4.20) than for for sensibleheat flux. Due to few data points, however, there was some scatter of thebin-averages. In the lowest two layers, ??1E appeared to be larger underweakly stable conditions (?1.0 < ? < ?0.1) than predicted. Enhancementin ??1H and ?1E corresponding to enhanced turbulent transport compared toMOS theory predictions, were also observed by Shuttleworth et al. (1989)under neutral and unstable conditions above a temperate forest of Scotspine and above a dense, tropical rain forest.The measured stability functions (?C) for CO2 flux were larger (??1Cwas smaller) in most cases than the predictions (Fig. 4.21). Under stable1404.5. Comparison to surface-layer predictionsconditions, only in the layers z/h = 0.10, 0.94 and 1.20, did predictions andmeasurements compare well.According to Foken (2008), it is well known that the surface-layer uni-versal functions underestimate the turbulent exchange under strongly stableconditions. In our case, the bin averages indicate that the stability functionslevel out for ? & 0.5. Handorf et al. (1999) proposed a constant universalfunction ?M = 4 for ? > 0.6, which corresponds to ??1M = 0.25. This valueis, however, smaller than our measurements (??1M ? 0.5).1414.5.Comparisontosurface-layerpredictions0.010.11.010.050.0?0.1?10.00.010.11.010.050.0? M?10.1 5.0 ?0.1?10.0 0.1 5.0 ?0.1?10.0 0.1 5.0z/h = 0.10 z/h = 0.26z/h = 0.71 z/h = 0.94 z/h = 1.20z/h = 0.49?Figure 4.18: Stability functions for shear stress, where red crosses are 30-min averaged results from this study,while black dots are bin averaged results from this study and the black line is the surface-layer prediction.1424.5.Comparisontosurface-layerpredictions0.010.11.010.050.0?0.1?10.00.010.11.010.050.0? H?10.1 5.0 ?0.1?10.0 0.1 5.0 ?0.1?10.0 0.1 5.0z/h = 0.10 z/h = 0.26 z/h = 0.49z/h = 0.71 z/h = 0.94 z/h = 1.20?Figure 4.19: Same as Fig. 4.18 but for sensible heat flux.1434.5.Comparisontosurface-layerpredictions0.010.11.010.050.0?0.1?10.00.010.11.010.050.0? E?10.1 5.0 ?0.1?10.0 0.1 5.0 ?0.1?10.0 0.1 5.0z/h = 0.10 z/h = 0.26 z/h = 0.49z/h = 0.71 z/h = 0.94 z/h = 1.20?Figure 4.20: Same as Fig. 4.18 but for H2O flux.1444.5.Comparisontosurface-layerpredictions0.010.11.010.050.0?0.1?10.00.010.11.010.050.0? C?10.1 5.0 ?0.1?10.0 0.1 5.0 ?0.1?10.0 0.1 5.0z/h = 0.10 z/h = 0.26 z/h = 0.49z/h = 0.71 z/h = 0.94 z/h = 1.20?Figure 4.21: Same as Fig. 4.18 but for CO2 flux .1454.5. Comparison to surface-layer predictions4.5.2 Eddy diffusivityUsing the predicted stability functions (?) and measured u?w?, the eddydiffusivity (K) was predicted for each level. As previously discussed, thereare two types of scaling (global and local) and two types of scaling heights(z or ze) that can be used in the prediction of ?, giving four different scalingcombinations: I: zs = z and global scaling, II: zs = z and local scaling, III:zs = ze and global scaling and IV: z = ze and local scaling. Figs. 4.22,4.23 and 4.25, 4.24 compare measured and predicted profiles of K usingcombination IV. Profiles using combination I to III are shown in AppendixN. The RMSE values of the K predictions from the measurements usingeach combination (Tables 4.3, 4.4, 4.5 and 4.6) were also examined. In thissection, only cases when K > 0 were included.The profiles using combination IV show that the measured KM , KH ,KE and KC generally increased in a exponential manner with heightthroughout the canopy (with the exception of KC in unstable conditions -see below). As predicted, KM , KH , KE and KC increased with decreasingstability above the canopy. All four eddy diffusivities, KM , KH , KE andKC , were close to zero in the lowest layer (z/h = 0.1). Maximum valueswere usually reached above the canopy at z/h = 1.20. Median valuesof measured KM above the canopy were about 1.5, 5.5 and 7.0 m2 s?1under stable, neutral and unstable conditions, respectively. Measured KHreached median values of 1 and 11 m2 s?1 above the canopy under stableand neutral conditions, respectively. Under neutral conditions the largestmedian value of measured KH was determined at z/h = 0.94, which wasapproximately 2 m2 s?1. Median values of measured KE were about 0.5, 1.5and 4 m2 s?1 under stable, neutral and unstable conditions, respectively atz/h = 1.20. Measured KC increased with height under stable and neutralconditions (median at z/h = 0.94: approximately 0.5 and 1.0 m2 s?1,respectively). However, under unstable conditions, KC increased only upto z/h = 0.71 (median at this height: about 1.5 m2 s?1) and was slightlylarger than at z/h = 0.94 and 1.20.For z/h = 0.10, 0.94 and 1.20 the predictions were slightly smaller thanmeasured KM and for z/h = 0.26 and 0.49 they were slightly larger thanmeasured KM but the differences were relatively small. The predictions alsoagreed with the measurements of KH relatively well in most cases. Abovethe canopy under unstable conditions, predicted values of KH were about 25% less than measured values. KE was in most cases slightly overestimated1464.5. Comparison to surface-layer predictionsby the predictions, but again the differences were small. Similarly, pre-dicted KC was slightly smaller under neutral and unstable conditions thanmeasured KC . However, under unstable conditions KC was substantiallyoverestimated by a factor of up to 5.5. These discrepancies were likely dueto the distribution of CO2 sources and sinks and were largest during daytimeunder sunny conditions, which also resulted in the most unstable conditions.Using the scaling and height combination IV was, together withcombination III, the one that resulted in the smallest RMSE values (seeTables 4.3, 4.4, 4.5 and 4.6). Using either global or local scaling madeonly little difference, sometimes improving but sometimes worseningthe predictions. Introducing the effective height ze, on the other hand,improved the predictions substantially. The changes were small in thelower canopy, since both approaches assume zs = z for z ? d, but weresignificant above. The improvement was especially evident under unstableconditions. The RMSE of KE at z/h = 0.94 under unstable conditionswas for example improved by a factor of 3.5 when using combination IVcompared to combination II.Fig. 4.26 shows the median values of all eddy diffusivities under stable,neutral and unstable conditions in the six layers. Under stable conditionsKM , KH , KE and KC were very similar at z/h ? 0.26. Above, KMgenerally increased faster with height than the other diffusivities. Abovez/h = 0.49, values of KH were between those of KE and KM , while valuesof KE and KC were similar to each other throughout the canopy. Underneutral conditions KH and KE were comparable in magnitude, while KMwas approximately twice the magnitude of KH and KE . In the uppercanopy and above KC was smaller than all other diffusivities, while in thelower canopy it was comparable to KH and KE . Under unstable conditions,KC was the smallest eddy diffusivity above z/h = 0.26, while KE andKM were very similar except above the canopy. KH was the largest eddydiffusivity under unstable conditions above z/h = 0.10. Because of thepreferential upward transport of heat, KH is also expected to be largerthan KM (Monteith and Unsworth, 2008). Measurements reviewed byDyer (1974) suggested that KM = KE = KC , under unstable conditions,which was however not found in the current study.1474.5. Comparison to surface-layer predictions?top < ?0.1 (233)4 100.00.20.40.60.81.01.21.4z/h?0.1 <  ?top < 0.1 (128)KM (m2  s?1)?top >  0.1 (15)0 2 6 8 4 100 2 6 8 4 100 2 6 825 % 75 %Median10 % 90 %MeanFigure 4.22: Measured (red) and predicted (grey) eddy diffusivities for shearstress (KM ) for three stability regimes. The prediction uses the local scalingand the adjusted zs (combination IV). The numbers in brackets are thenumber of half hours included in the analysis.1484.5. Comparison to surface-layer predictions0.00.20.40.60.81.01.21.4z/h?top < ?0.1 (18) ?0.1 <  ?top < 0.1 (58) ?top >  0.1 (39)4 10KH  (m2  s?1)0 2 6 8 12 4 100 2 6 8 12 4 100 2 6 8 1225 % 75 %Median10 % 90 %MeanFigure 4.23: Same as Fig. 4.22 but for KH .1494.5. Comparison to surface-layer predictions0 2 4 6 8 100.00.20.40.60.81.01.21.4z/h0 2 4 6 8 10 0 2 4 6 8 10?top < ?0.1 (11) ?0.1 <  ?top < 0.1 (23) ?top >  0.1 (8)KE  (m2  s?1)25 % 75 %Median10 % 90 %MeanFigure 4.24: Same as Fig. 4.22 but for KE .1504.5. Comparison to surface-layer predictions0 2 4 6 80.00.20.40.60.81.01.21.4z/h0 2 4 6 8 0 2 4 6 8?top < ?0.1 (9) ?0.1 <  ?top < 0.1 (17) ?top >  0.1 (11)KC  (m2  s?1)25 % 75 %Median10 % 90 %MeanFigure 4.25: Same as Fig. 4.22 but for KC .1514.5. Comparison to surface-layer predictions2 4 100.00.20.40.60.81.01.21.4z/h1 4 5K (m 2 s?1)0.2 0.4 0.6 0.8 1.0?top < ?0.1 ?0.1 <  ?top < 0.1 ?top >  0.1 6 8 2 3KCKEKHKM0 00Figure 4.26: Median values of KM , KH , KE andKC under unstable, neutraland stable conditions for the six layers. Note that different scales are usedon the x-axis1524.5.Comparisontosurface-layerpredictionsTable 4.3: Root mean square error (in m2 s?1) of measured KM compared to predicted KM for the four scalingcombinations described in Fig. 4.2 for three stability regimes.? < ?0.1 ?0.1 ? ? < 0.1 0.1 ? ? < 1.0z/h I II III IV I II III IV I II III IV0.10 0.76 0.78 0.77 0.78 0.50 0.52 0.51 0.51 0.06 0.05 0.05 0.050.26 0.30 0.28 0.28 0.28 0.24 0.24 0.25 0.25 0.12 0.11 0.11 0.100.49 1.70 1.47 0.94 0.87 0.90 1.01 0.47 0.59 0.22 0.17 0.22 0.140.71 3.12 2.68 1.67 1.74 1.76 1.81 1.27 1.38 0.24 0.40 0.44 0.320.94 3.39 3.02 1.54 1.54 1.75 1.78 1.19 1.23 0.42 0.37 0.68 0.471.20 3.55 3.37 2.81 2.84 2.28 2.33 2.52 2.59 1.16 1.20 1.34 1.34Table 4.4: Same as Table 4.3 but for KH .? < ?0.1 ?0.1 ? ? < 0.1 0.1 ? ? < 1.0z/h I II III IV I II III IV I II III IV0.10 0.11 0.09 0.11 0.12 0.05 0.07 0.05 0.07 0.02 0.03 0.02 0.030.26 1.01 1.08 1.26 1.15 0.35 0.38 0.38 0.38 0.03 0.13 0.04 0.120.49 2.22 1.89 1.64 1.23 0.71 1.63 0.46 1.09 0.21 0.26 0.20 0.230.71 4.80 4.11 2.12 2.10 1.22 2.45 0.79 1.08 0.28 0.40 0.21 0.250.94 6.86 6.93 2.22 1.67 1.99 2.48 1.85 2.06 1.33 0.80 1.51 1.271.20 5.25 5.22 3.72 3.82 1.60 1.76 2.50 2.86 0.64 0.47 0.70 0.551534.5.Comparisontosurface-layerpredictionsTable 4.5: Same as Table 4.3 but for KE.? < ?0.1 ?0.1 ? ? < 0.1 0.1 ? ? < 1.0z/h I II III IV I II III IV I II III IV0.10 0.91 0.96 0.94 0.96 0.04 0.05 0.05 0.05 0.10 0.12 0.10 0.120.26 0.66 0.43 0.51 0.43 0.29 0.35 0.26 0.35 0.05 0.07 0.07 0.070.49 2.36 1.28 1.19 0.62 0.98 1.02 0.72 0.71 0.23 0.27 0.23 0.240.71 4.75 3.89 1.57 1.43 1.64 1.56 0.75 0.78 0.98 0.49 1.06 0.320.94 6.61 6.86 2.11 1.98 1.72 1.54 1.41 1.51 0.68 0.53 0.62 0.401.20 8.88 8.88 4.77 4.77 3.22 3.34 2.16 2.16 1.72 2.02 1.73 2.03Table 4.6: Same as Table 4.3 but for KC .? < ?0.1 ?0.1 ? ? < 0.1 0.1 ? ? < 1.0z/h I II III IV I II III IV I II III IV0.10 0.32 0.41 0.26 0.41 0.03 0.03 0.03 0.03 0.01 0.02 0.01 0.020.26 1.05 1.73 0.87 1.73 0.17 0.11 0.17 0.11 0.05 0.20 0.06 0.190.49 4.17 5.45 2.68 3.90 0.53 0.41 0.43 0.34 0.25 0.31 0.24 0.260.71 6.84 8.39 2.80 3.21 1.50 1.64 1.46 1.67 0.44 0.64 0.25 0.380.94 10.13 10.81 4.53 4.53 0.81 0.79 0.87 0.71 0.97 0.58 1.00 0.301.20 13.90 13.90 7.41 7.41 2.95 3.25 2.91 3.32 0.53 0.49 0.36 0.331544.6. Summary and conclusions4.6 Summary and conclusionsThe mountain pine beetle attack at the studied stand resulted in anopen-canopy structure. The turbulent exchange within and above thissparse canopy was studied to determine the applicability of gradientdiffusion theory within a sparse canopy, which would ease the modeling ofcanopy exchange. The relationships between horizontal wind speed (u),potential temperature (?), H2O mixing ratio (mq) and CO2 mixing ratio(mc) and their corresponding fluxes were examined and the frequencyof the occurrence of counter-gradient fluxes was quantified. There wasa clear relationship between the gradients of u, ?, mq and mc and theircorresponding fluxes at most heights.Overall, shear stress (?) and sensible heat flux (QH) were mostly in thedirection of gradient diffusion throughout the canopy. Counter-gradientfluxes were more common for QH than for ? , and counter-gradient fluxesfor QH were mainly detected in the morning and the evening. In the case oflatent heat flux (QE) and CO2 flux (Fc), counter-gradient fluxes occurredthroughout the day, but were less frequent than gradient diffusion.During times of gradient diffusion, momentum exchange agreed wellwith the predictions using Monin-Obukhov similarity (MOS) theory oftransport in the surface-layer (K-theory). Sensible and latent heat exchangewere also predicted relatively well under stable and neutral condition;however, under unstable conditions predictions overestimated the fluxes atmost heights. The stability functions for CO2 were mostly underestimatedby the MOS predictions, resulting in overestimates of the fluxes.The eddy diffusivities obtained from gradient and flux measurements in-creased approximately exponentially with height. Under stable and neutralconditions, the eddy diffusivity for momentum (KM ) was generally sub-stantially larger than the other eddy diffusivities. This is expected sincemomentum experiences in addition to skin drag also form drag due to pres-sure differences. Under unstable conditions the eddy diffusivity for sensibleheat flux (KH) was the largest. Under the latter conditions, KE and KMwere very similar to each other in the canopy, which was expected. Underneutral conditions, the eddy diffusivities of sensible and latent heat (KE)were very similar. Under unstable and neutral conditions, the eddy diffusiv-ity for CO2 (KC) was smaller than the other eddy diffusivities except closeto the ground likely due to the source/sink distribution of CO2.1554.6. Summary and conclusionsThe use of a local or a global scaling caused little differences in thepredictions of the eddy diffusivities, but the effective height (ze) resulted ina substantial improvement of the predictions compared to using the heightabove ground as the scaling height.During times of gradient diffusion, K-theory using MOS theory predic-tions for the surface layer could be used to determine momentum, sensibleheat and latent heat transport within this open-canopy stand and above.However, the use of K-theory to determine CO2 transport within and abovethe canopy is problematic under unstable conditions. Resulting from this,the use of 1.5 order models can only be used to model the transport of mo-mentum in this stand. For sensible heat, latent heat and CO2 higher orderclosure models would be required.156Chapter 5ConclusionsThis chapter summarizes the main conclusions and implications of this dis-sertation in a lodgepole pine forest with non-invasive management followinga mountain pine beetle (MPB) attack and answers the three research ques-tions posed in the Introduction. Furthermore, it discusses possible technicalimprovements and potential future work.5.1 ConclusionsThe overall conclusions of this dissertation are:1. Radiative transmission through the canopy was high after thereduction in canopy density due to the beetle attack.The attack resulted in an open and sparse canopy (leaf area index of0.55 m2 m?2) with a dead overstory, an intact secondary structure (amix of mostly immature trees of different species) and a rich under-story (bushes, seedlings, saplings and ground vegetation less than 1 mhigh). This open-canopy structure allowed 60 % of the above-canopyshortwave and photosynthetically active radiation to reach the forestfloor, which contributed to a high (50 %, ensemble-averaged over theentire three week period) daily-total ground-level net radiation com-pared to that above the stand.2. The open-canopy structure resulted in a strong coupling be-tween all canopy layers and the atmosphere above.In contrast to denser canopies, where there are substantial periodswhen the lower canopy is decoupled from the upper canopy and theatmosphere above (e.g., Thomas et al., 2013), in this open canopy, alllayers and the atmosphere above were strongly coupled. This was seenin the temperature and the wind profiles. Temperature inversions ex-tending to the ground at night and a relatively constant temperatureincrease with depth from the top of the canopy to the ground during1575.1. Conclusionsdaytime were measured regularly in this canopy. In denser canopies,air temperature usually decreases with depth into the canopy duringdaytime (e.g., Monteith, 1975) and at night it decreases with depthonly in the upper part of the canopy and remains constant or slightlyincreases towards the ground (Huisman and Attenborough, 1991). Inthis stand, wind speed increased continuously from the ground toabove the canopy, while in denser canopies secondary wind maximaare common (e.g., Oliver, 1971; Shaw, 1977; Raupach and Thom, 1981;Baldocchi and Meyers, 1988b; Amiro, 1990b). The strong coupling isalso evident in the relatively small gradients through the canopy.3. The aerodynamic characteristics of this stand differed fromthose with denser canopies.Wind profiles showed that there was a good ventilation in the canopyduring the daytime. The inflection point was located lower (z/h ? 0.7)in the canopy than found in other studies (Finnigan, 2000). Thecanopy structure also resulted in a relatively low zero-plane displace-ment height (at z/h = 0.40), which agrees with predictions for acanopy of this density (Raupach, 1994). Related to this, the shearstress profile showed that shear stress was not only approximatelyconstant above, but also in the upper part of the canopy, which isdifferent than in denser canopies (Finnigan, 2000). The normalizedshear stress (normalized by the shear stress above the canopy) wasalso generally larger within this sparse canopy than in denser canopiesunder unstable and neutral conditions.4. A large portion of the available energy was partitioned intosensible heat during the daytime resulting in a Bowen ratiogreater than two throughout the canopy.Water vapour and therefore latent heat, originated mainly from thelowest 5 % of the canopy. The sources of sensible heat were distributedthroughout the entire canopy. As a result of the different vertical dis-tributions of the sources of sensible and latent heat and the dominanceof sensible over latent heat flux, the Bowen ratio varied between twonear the ground and four at the top of the canopy.5. Energy-balance closure was relatively high throughout thecanopy during the daytime. During the daytime, when the open-canopy structure resulted in relatively strong coupling of the canopyand sub-canopy, high energy-balance closure values were observed.However, residuals of up to 30 % where found in the layers in which sec-1585.1. Conclusionsondary structure was most abundant. During the nighttime, energy-balance closure residuals approached 60 % and therefore nighttime fluxmeasurements remain a concern for inside the canopy and generallyfor the entire forest-atmosphere interface.6. The understory and the secondary structure were mainly re-sponsible for CO2 uptake while the overstory was a weak CO2source.The largest downward flux of CO2 was found in the center part ofthe canopy with lower fluxes below and above. This distinct shape ofthe CO2 flux profile implied that the secondary structure was a rela-tively strong CO2 sink, which confirms the postulation by Brown et al.(2012a). The understory, however, was a similarly large or even largercontributor to CO2 uptake. The mostly dead overstory was a weaksource of CO2 due to the slow decomposition of lodgepole pine bolesand branches.7. The secondary structure trees had a substantially higher wa-ter use efficiency (WUE) than the understory vegetation andexhibited better adjustment to the extended dry period.H2O release and CO2 uptake by plants are strongly related to stom-atal conductance and therefore sinks for CO2 and sources of H2O wereexpected to be similarly distributed. However, even though the CO2sinks were distributed throughout the lower two thirds of the canopy,the H2O sources were mainly located close to the ground. This dis-similarity in H2O sources and CO2 sinks resulted in vertical differ-ences of WUE (the ratio of the rate of CO2 uptake to the rate ofH2O release) showing differing capabilities of the coniferous secondarystructure trees and the mixed understory (broadleaves and conifers) toconserve water. Furthermore, the secondary structure trees adaptedbetter to the extended dry period during the field study than theunderstory vegetation. The secondary structure WUE increased muchfaster with increasing dryness than the understory WUE. Calculationsof the inherent water use efficiency (WUE/D, where D is the vapourpressure deficit) further confirmed these findings.8. K-theory appeared to work for shear stress when using theproposed effective height, but was problematic for all otherfluxes due to counter-gradient turbulent diffusion and com-plications in the predictions of the eddy diffusivity.K-theory is known to be problematic in canopies. This study shows1595.1. Conclusionsthat under the given conditions counter-gradient fluxes were seldomobserved for shear stress. Using an adjusted effective height in the cal-culations of the stability functions and the eddy diffusivities resultedin good agreement between the measurements and predictions of shearstress following Monin-Obukhov similarity (MOS) theory. The com-mon occurrence of counter gradient fluxes of sensible heat in the morn-ing and evening implies that K-theory could only be used between thelate morning and afternoon. During those times, MOS theory predic-tions were adequate when using the effective height. Counter-gradientfluxes occurred throughout the entire day in the case of latent heatand CO2 fluxes making the use of K-theory inadequate to determineturbulent exchange of those passive scalars in this canopy. Further-more, MOS theory for CO2 highly overestimated the eddy diffusivityin unstable conditions.9. The eddy covariance (EC) technique was found to be an ef-fective approach to determining the turbulent fluxes as wellas the distributions of the sources and/or sinks of sensibleheat, latent heat, CO2 and momentum in this sparse canopy.The locations of the CO2 sources and sinks determined using the ECapproach agreed with the results from the ecophysiological approach,even though they differed in magnitude. Furthermore, the canopywas generally well coupled with the atmosphere above and during halfhours when gradient diffusion occurred, eddy-diffusivity predictionsand calculations based on EC measurements often agreed well. This,together with the high energy-balance closure, implied that the ECtechnique proved to be a sound approach in the study of turbulent ex-change as well as the distribution of the sources and sinks in such anopen-canopy stand during daytime. However, in denser canopies withmarkedly reduced vertical mixing and where advection likely plays animportant role in the transport of CO2, the approach would likely beproblematic and would need to be tested carefully. An advantage ofthe EC method was that it provided continuous flux measurements incontrast to the ecophysiological method that was also used to deter-mine CO2 exchange. The ecophysiological method was time intensiveand adequate temporal and spatial upscaling of chamber measure-ments was challenging. This method, however, gave species specificinformation, which was not available when using the EC approach.1605.2. Implications5.2 ImplicationsGiven the large area of MPB-affected forest in British Columbia andneighbouring regions (e.g., Alberta, Yukon and Colorado), and comparableforest kills in other parts of the world due to insect attacks (e.g., sprucebudworm in eastern Canada and the US), the results of this study are notonly of local interest. This study shows that non-invasive managementafter insect attacks in a forest can be an adequate response from acarbon balance perspective. Due to reduced canopy density (due initiallyto the marked reduction in LAI and later the falling of killed trees),the large amounts of radiation transmitted through the canopy andthe wind protection by the standing dead trees favour the growth ofsmaller vegetation and therefore the recovery of the stand. As shown byBrown et al. (2012a), the stand returned to being a carbon sink within arelatively short time (approximately five years) after the MPB attack, muchfaster than clearcut-harvested sites. Furthermore, the study showed thatthis MPB-attacked stand had a significantly different microclimate thandenser and healthy stands. This needs to be considered in future carbonand water budget modeling of open-canopy and insect-infested stands.5.3 Technical improvements and potential futureworkIn this section, possible technical improvements and potential future workare discussed. The following suggestions could be considered if parts of thestudy were to be repeated in the same or a different stand:In this study, point measurements of radiation were made within thecanopy. However, a spatial average of radiation measurements wouldbe preferable, e.g., using line sensors or automatically operating trams(e.g., Lee and Black, 1993a; Baldocchi and Vogel, 1996) to capture thehigh spatial variability of radiation in a canopy. To determine the spatialvariability in radiation at all levels well, several canopy-access towerscould be required. In this case, it would be very important to make surethat these structures would not obstruct and influence the turbulent fluxmeasurements in the canopy. Furthermore, diffuse radiation measurementscould be made to obtain information on the impact of diffuse and directradiation on photosynthesis.1615.3. Technical improvements and potential future workNet photosynthesis measurements on the leaves could be improved byvarying the light levels manually between total darkness and maximumambient light conditions. This can be done using spectrally-neutral shadecloth of various weave densities. Bole respiration could be determined witha higher accuracy, if measurements were conducted for longer time periods(e.g., 15 min). However, very long time periods would need to be avoideddue to possible drifting of the concentration measurements.During parts of the day, the presence or absence of gradient diffusioncould not be determined due to the accuracy of gradient and/or fluxmeasurements being too low for this purpose. If these measurements wereto be repeated, CO2 and H2O gradient measurements could be improved byemploying a higher quality IRGA (e.g., an LI-7000) in the existing systemor a closed-path IRGA for each level measuring concentrations continuouslyat all level (similar to the system used by Leitch, 2010). Therefore flow rateshave to be high and the same for all levels. A manifolded system like thatused by Yang et al. (1999) would be an option. Power limitations, however,need to be considered if working at a remote location. Furthermore, CO2and H2O measurements could be improved by keeping the voltage appliedto the suction pump constant and by maintaining a constant temperaturein the box containing the closed-path infrared gas analyzer. Temperatureuncertainties could be reduced by connecting all thermocouples to the samedatalogger and in the case of a Campbell Scientific Inc. datalogger choosingchannels close to the location of reference temperature measurement on thedatalogger panel.We have shown that even at this reasonably homogenous and very flatstand, advection and/or dispersive fluxes may play a role, especially duringnighttime. Including measurements of these fluxes (which, of course, arecurrently major challenges in micrometeorology) in future work would berecommended to fully capture the scalar transport in this canopy.Every study raises new interesting questions. The following topics couldbe investigated in future studies:Given the rich dataset from this study and the limited information onturbulence in sparse canopies, it would be of great interest to further studyturbulent exchange and the role of coherent flow structures in this sparsecanopy. Coherent structures are responsible for a large part of the turbulentexchange (Finnigan, 2000) and these structures are not well studied insparse canopies (Bailey and Stoll, 2013). Correlation coefficients could be1625.3. Technical improvements and potential future workdetermined to compare the exchange efficiencies of the different scalars andfurther study could be conducted on the similarity between them similarto the work of Roth and Oke (1995), who studied the exchange efficiencyof heat, mass and momentum over in urban environment. This datasetcould also be used to test Lagrangian models developed to account forcounter-gradient diffusion in forest canopies, e.g., the localized near-fieldtheory of Raupach (1989b). These data provide an important test casewhere the far-field component likely dominates the near-field componentfor much of the time. Such information is necessary to predict turbulentexchange accurately on a regional scale using computer models rather thanat a local scale when using the EC measurement approach.A length-scale analysis could show if the overestimation of the eddydiffusivity of CO2 is due to the fact that changes in vertical concentrationgradients are too small compared to the turbulent length scales. Manymodeling approaches are based on K-theory and if the previous statementis true, the use of K-theory based models would be inadequate in thisstand.The EC and the ecophysiological approach both showed that the deadstanding boles were a sources of CO2, although their results differedconsiderably in magnitude. Commonly, studies only consider respirationof fallen dead trees. Given that trees can remain standing for severalyears after dying (e.g., Mitchell and Preisler, 1998) and there are largeareas of dead standing trees, it would be very worthwhile to further studytheir respiration rate and biological reasons for their respiration, e.g., ratesof decay of the bole after MPB attack and the effect of the blue stainfungus. It would also be important to determine how the respiration rateschange after the trees fall, i.e., what is the effect of moisture and microbialpopulations moving into the fallen trees. This would likely help explain arespiration pulse if it occurs.All measurements used in this dissertation were made during the sum-mertime at the peak of the growing season. Due to warmer temperatures andhigh light levels, photosynthesis, respiration and evapotranspiration ratescan be expected to be higher than during the wintertime. Therefore, verti-cal differences in CO2 sources and sinks can be expected to be larger duringthe summer than the wintertime. Under favorable light and moisture condi-tions the exchange rates of CO2 and H2O could be higher during late springand early fall than during the extended dry period in the summer of 2010;1635.3. Technical improvements and potential future workhowever, generally lower exchange rates are expected during spring and fallthan during summer. 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If not otherwise mentioned all photographs were taken during the 2010field campaign by Carmen Emmel, Eugenie Paul-Limoges or Rick Ketler.Figure A.1: Photographs of the three vegetation layers: (a) understory veg-etation, (b) secondary structure and (c) overstory vegetation.184AppendixA.PhotographsofthefieldsiteandinstrumentationFigure A.2: Panorama view (360 ?) of the MPB-attacked lodgepole pine stand adjacent to Crooked River ProvincialPark (MPB-03) taken from the top of the flux tower (30 m). Photograph provided by Dr. Thomas Hilker.185Appendix A. Photographs of the field site and instrumentationFigure A.3: Photograph of MPB-attacked lodgepole pine stand adjacent toCrooked River Provincial Park (MPB-03) taken from the top of the fluxtower (30 m) on 12 July 2010 in a west direction.186Appendix A. Photographs of the field site and instrumentationFigure A.4: Photograph of the measurement tower with the seven measure-ment levels equipped with eddy-covariance systems, inlets for the closed-path infrared gas analyzer and radiometers. In the center part of the towerthe rain gauge (TE525M, Campbell Scientific (CSI), Logan, Utah) can beseen. Just below the top of the tower, a propeller-vane anemometer (model05103 R.M. Young Inc., Traverse City, MI) was installed. Photograph wastaken from south of the tower.187Appendix A. Photographs of the field site and instrumentationFigure A.5: Eddy-covariance systems atthe seven levels look-ing from the tower to-wards the west.188Appendix A. Photographs of the field site and instrumentationFigure A.6: Box containing the closed-path infrared gas analyzer (LI-840)and a CR1000 datalogger.189Appendix A. Photographs of the field site and instrumentationFigure A.7: Photograph of the eddy-covariance system at the z = 1.2-m height showing the open-path infrared gas analyzer (LI-7500, LI-CORInc., Lincoln, Nebraska), the ultrasonic anemometer (CSAT3, CSI) and thethermocouple. The funnel of inlet for the closed-path (LI-840, LI-COR)infrared gas analyzer and the solenoids connection for the supply of thecalibration gas.190Appendix A. Photographs of the field site and instrumentationFigure A.8: A sample of the radiometer used in the field campaign: (a) four-component net radiometer (CNR-1, Kipp & Zonen B.V., Delft, The Nether-lands (K&Z)) and quantum sensors (SQ-110, Apogee Instruments Inc., Lo-gan, Utah) installed on tripod, (b) two four-component net radiometers(CNR-1) during the in-field radiometer intercomparison at the beginning ofthe field campaign (one was later installed on the tripod, while the otherone stayed at the tower top) and one quantum sensor (LI-190, LI-COR),which was continuously installed at the tower top, (c) net radiometer (NRLite, K&Z) installed at the 2.7-m height and (d) pyranometer (CM5, K&Z)installed on the ground.191Appendix A. Photographs of the field site and instrumentationFigure A.9: Hemispherical photographs taken at the ground pyranometerlocations (P1A to P3C), the tripod locations (T1 to T3) and the tower. Thetower photograph was taken in the summer of 2007 by Mathew Brown. Allother photographs were taken in July 2010.192Appendix A. Photographs of the field site and instrumentationFigure A.10: (a) Manual portable chamber system equipped with a closed-path infrared gas analyzer (LI-800, LI-COR) and a temperature and relativehumidity probe (HMP35CF, CSI) using an opaquely covered chamber whilemeasuring bole respiration. (b) The clear chamber while measuring at a soillocation. The quantum sensor attached to the system can also be seen inthis photograph.193Appendix A. Photographs of the field site and instrumentationFigure A.11: All trees on which bole respiration measurements were per-formed. The numbers refer to the tree codes given in Table A.1.194Appendix A. Photographs of the field site and instrumentationTable A.1: ID, tree species, status and bole circumference at breast heightfor all trees on which bole respiration measurements were performed.ID Species Status circumference at breast height (m)I-1 lodgepole pine live 0.38I-2 lodgepole pine live 0.36I-3 lodgepole pine dead 0.90II-1 lodgepole pine live 0.36II-2 lodgepole pine dead 0.52II-3 subalpine fir live 0.43III-1 lodgepole pine dead 0.66III-2 subalpine fir live 0.50III-3 lodgepole pine live 0.37IV-1 subalpine fir dead 0.51IV-2 lodgepole pine live 0.82IV-3 subalpine fir live 0.39V-1 subalpine fir live 0.41V-2 lodgepole pine live 0.41V-3 lodgepole pine dead 0.69VI-1 subalpine fir live 0.48VI-2 subalpine fir live 0.45VI-3 lodgepole pine dead 0.55195Appendix A. Photographs of the field site and instrumentationFigure A.12: All soil locations where soil respiration measurements wereperformed. The numbers refer to the soil collar ID, where the roman numberindicates to which of the six plots the collar belongs. Photographs of I-1,I-2 and III-3 were taken at the end, while all other photographs were takenat the beginning of the field campaign.196Appendix A. Photographs of the field site and instrumentationFigure A.13: (a) The portable photosynthesis system (LI-6400, LI-COR)and (b) the attached transparent cuvette and quantum sensor.Figure A.14: Location of bole temperature measurements. Green tape cov-ers the entry holes for the bole thermocouples. All thermocouples wereconnected to a multiplexer located in the white box.197Appendix BAppropriateness of singlerotation, double rotation andplanar fitIn the analysis in this dissertation, a combination of a single rotationand a planar fit (called planar fit henceforth) was used to rotate thecoordinate system so that average of the u-component of the wind wasalways pointing into the mean wind. Explanations of all rotation typesused here can be found in Aubinet et al. (2012). A single rotation is definedas a rotation of the coordinate system so that the half-hourly averageof the u-component of the wind is always positive and the half-hourlyaveraged perpendicular horizontal v-component is zero. Another commonrotation approach is the double rotation where the half hourly averageof the vertical wind component (w) would also be zero. When usingthe planar fit, however the average of w over the entire campaign iszero while half hourly individual w is not forced to be zero. Thisapproach can be used to correct for tilt of the anemometer or to adjustto tilted terrain (Wilczak et al., 2001). Furthermore a triple rotation ispossible, where after doing the double rotation a third rotation is added toensure that v?w? is zero. All rotations are described in Aubinet et al. (2012).Micrometeorologists are reluctant to apply a double rotation within thecanopy since vertical winds different from zero are possible in the canopy(Baldocchi and Hutchison, 1987). Also planar fits are not commonlyapplied within the canopy. Usually a single rotation is used within thecanopy while double rotations or planar fits are, however, commonly usedabove the canopy. Here, we test if the use of a planar fit is suitable in thecanopy of the current study.The reasoning behind using a planar fit in this study is that there is apossibility that the seven booms and mounting of the sonic anemometers198Appendix B. Appropriateness of single rotation, double rotation and planar fit(a)100 200 300?20?1001020(b)100 200 300?20?1001020?, ()(c)100 200 300?20?1001020(d)100 200 300WD ( )?20?1001020(e)100 200 300WD ( )?20?1001020(f)100 200 300WD ( )?20?1001020?, ()(g)100 200 300WD ( )?20?1001020? ? ????Figure B.1: Wind inclination (?) vs. wind direction (WD) at the sevenlevels (a: 1.2 m, b: 2.7 m, c: 7.6 m, d: 11.9 m, e: 16.5 m, f: 21.0 m andg: 26.8 m) before any rotation or planar fit was applied. Wind directionis direction relative to magnetic geographic North. Each dot is a 30-minaverage from 14 July to 3 August 2010.100 200 300?20?1001020100 200 300?20?1001020100 200 300?20?1001020100 200 300?20?1001020100 200 300?20?1001020100 200 300?20?1001020100 200 300?20?1001020(a) (b)?, ()(c) (d)WD ( )(e)WD ( )(f)WD ( )?, ()(g)WD ( )? ? ????Figure B.2: Same as Fig. B.1 but after planar fit was applied199Appendix B. Appropriateness of single rotation, double rotation and planar fitinstalled along the tower are slightly tilted. Figs. B.1 and B.2 show inclina-tion of the wind from the horizontal plane (?) (also sometimes called angleof attack) plotted against wind direction (WD) before and after the planarfit was applied, respectively. The inclination is calculated as:? = ?tan?1(wVEC), (B.1)where VEC is the vector wind calculated as:VEC =?u2 + v2. (B.2)The vertical wind is positive if it is an upward wind, while it is negativeif it is a downward wind. Therefore, wind from above will result in apositive ? and wind from below in a negative ?.Especially at the 7.6-m height, westerly winds had a substantial upwardcomponent before the planar fit was applied, while easterly winds have asimilarly substantial downward component. Note that for the planar fitonly a slope correction was applied, while the offset correction was omittedsince only the slope correction has an effect on turbulent fluxes. After theplanar fit was applied, ? was similarly distributed for all wind directionsat all levels. The rotation angles resulting from the planar fit are given inTab. B.1. The rotation angles around the x-axis and the y-axis are called? and ?, respectively. Rotation angles around the x and y-axis were lessthan 5 ? at all seven levels. At z = 7.6 m,the largest rotation around they-axis (? = 4.79 ?), while at z = 1.2 m the largest rotation angles aroundthe x-axis (? = 1.65 ?) were found.Table B.1: Rotation angles for planar fitz(m) ? (?) ? (?)1.2 1.65 0.052.7 0.65 0.257.6 1.56 4.7911.9 0.26 2.1716.5 0.51 0.4121.0 1.15 0.6926.8 1.58 0.91200Appendix B. Appropriateness of single rotation, double rotation and planar fitCertain wind inclination could result from flow distortion of vegetationclumps near the sensors. However, the vegetation around the tower wasrelatively homogeneous. The relatively large measured inclination atz = 7.6 m could partly be caused by the roof installed on the towerapproximately at this height above the data loggers (see Fig. B.3). Thiswould not be a natural effect caused by the canopy but would be introducedby the measurement set up.Figure B.3: Photograph of the lower half of the measurement tower showingthe wooden roof structure installed close to the level at the 7.6-m height. Thephotograph is taken from West of the tower looking East. The photographwas taken by the author.In the following, momentum flux calculated using three rotationmethods will be compared: half-hourly individual single rotation, planar fitand half-hourly individual double rotation. Note that in case of the planarfit and double rotation all quality checks as described in Chapter 2 wereconducted, while for the single rotation the only applied check that wasconducted was that only full half-hour datasets were considered. Figs B.4shows the half-hourly averaged kinematic shear stress (u?w?) on 24 July201Appendix B. Appropriateness of single rotation, double rotation and planar fit2013 (a representative day during the campaign) using the three rotationapproaches, and u at all seven levels.(a)06:00 12:00 18:00 00:00time (PST)?0.04?0.020.000.02(b)06:00 12:00 18:00 00:00time (PST)?0.050.000.05u?w? (m2  s?2 )(c)06:00 12:00 18:00 00:00time (PST)?0.3?0.2?0.10.0u?w? (m2  s?2 )(d)06:00 12:00 18:00 00:00time (PST)?0.6?0.5?0.4?0.3?0.2?0.10.0u?w? (m2  s?2 )(e)06:00 12:00 18:00 00:00time (PST)?1.0?0.8?0.6?0.4?0.20.0(f)06:00 12:00 18:00 00:00time (PST)?1.2?1.0?0.8?0.6?0.4?0.2u?w? (m2  s?2 )(g)06:00 12:00 18:00 00:00time (PST)?1.0?0.8?0.6?0.4?0.2u?w? (m2  s?2 )(h)06:00 12:00 18:00 00:00time (PST)1234u (m s?1 )u?w? (m2  s?2 )u?w? (m2  s?2 )Figure B.4: (a - g) Momentum flux (u?w?) based the three rotation ap-proaches (green: single rotation, red: double rotation and black: planar fit)at the seven levels (a: 1.2 m, b: 2.7 m, c: 7.6 m, d: 11.9 m, e: 16.5 m, f: 21.0m and g: 26.8 m) on 24 July 2010. (h) Half-hourly averaged horizontal wind(u) measured at the seven levels (red: 1.2 m, orange: 2.7 m, light green: 7.6m, green: 11.9 m, turquoise: 16.5 m, blue: 21.0 m and black: 26.8 m) onthe same day.The single rotation and the planar fit showed very similar resultsfor u?w?. The double rotation resulted most of the time in similarresults as well, however, during some half hours it showed some spiking.Fig. B.5 shows u?w? determined with double rotation vs. planar fitand u?w? determined with single rotation vs. planar fit. Table B.2gives the correlation coefficients (R2) and the linear fit parameters forthe the comparisons. The single rotation and the planar fit agree atall levels better (slope > 0.963, R2 > 0.909) than the double rotationand planar fit (slopes > 0.809, R2 > 0.664). The higher up in thecanopy the better the three rotation methods agreed. Especially the sin-gle rotation and planar fit had a very high correlation high up in the canopy.202Appendix B. Appropriateness of single rotation, double rotation and planar fitFigure B.5: (a - g) Kinematic momentum flux (u?w?) determined with doublerotation vs. planar fit (blue: linear fit) and u?w? determined with singlerotation vs. planar fit (red: linear fit) at the seven levels (a: 1.2 m, b: 2.7m, c: 7.6 m, d: 11.9 m, e: 16.5 m, f: 21.0 m and g: 26.8 m). Every dotstands for a 30-min period between 14 July and 3 August 2010. The linesare linear regressions fitted to the red and blue dots.203Appendix B. Appropriateness of single rotation, double rotation and planar fitTable B.2: Linear fit coefficients and correlation coefficients for u?w? of dou-ble rotation vs. planar fit and single rotation vs. planar fit.double vs. planar single vs. planarz(m) slope offset R2 slope offset R21.2 0.809 0.004 0.664 0.963 0.000 0.9092.7 0.976 0.004 0.821 0.978 0.000 0.9927.6 0.991 0.000 0.975 0.991 0.000 0.98211.9 0.936 0.007 0.984 0.973 0.000 0.99816.5 0.943 0.005 0.984 0.984 0.000 1.00021.0 0.914 0.000 0.981 0.964 0.000 0.99726.8 0.985 0.003 0.981 0.953 0.000 0.994204Appendix CHeat flux plateintercomparisonA soil heat flux plate (HFP) intercomparison was conducted from August 9to 15, 2012. Two CN3 heat flux plates (serial number (SN): F239 and F579,both Middleton Solar, Victoria, Australia) were compared to a referenceheat flux plate (SN: H063006, HFT-3, Campbell Scientific, Logan, UT,USA). The intercomparison procedure was based on an internal report onheat flux plate intercomparisons written by Trevor Baker (pers. com.).Figure C.1: Insulated sand chamber used to calibrate heat flux plates. Thechamber was heated by a central heater plate powered by an Anatek 50V/1Apower supply. Photograph taken by Trevor Baker.Soil heat flux plates were calibrated in an insulated sand chamber (seeFig. C.2), which was heated by a central heater plate powered by anAnatek 50V/1A power supply (Anatek, Amherst, New Hampshire). Forthe intercomparison, one side of the chamber (opposite the heater plateplugs) was excavated so that it was half-empty. The three HFPs (thereference HFP and the two other HFPs) were inserted into the chamber atequal distance from and parallel to the heater plate with their tops facing205Appendix C. Heat flux plate intercomparisontowards it. The reference HFP was located between the HFPs that wereto be calibrated. The chamber was slowly filled with sand, making surethat plates did not move and wires ran vertically upwards. The powersupply was attached to the heater plate turned on to maximum voltageand current (?29 V, 1 A). The chamber was heated for approximately22 h (until temperature did not change significantly anymore) to allowit to reach thermal equilibrium. When the chamber reached thermalequilibrium, the power supply was turned off and the chamber was left tocool for approximately 24 h. When the chamber had fully cooled down,the HFPs were flipped before repeating the above procedure. This allowedto calibrated the HFPs in both directions. Heat flux measured by the theHFPs was recorded on a CNR10X datalogger (Campbell Scientific, Logan,UT, USA). The maximum heat flux from the power supply was 75 W m?2.The reference HFP measurements were used to determine calibrationcoefficients, rather than using the calculated heat flux that could bedetermined with Power = voltage2/resistance. Furthermore only thecooling period and only when the reference sensor measured less then 40Wm?2 was considered for the calibration.The last calibration dated back to June 01, 1971 for F239 withcalibration coefficients of 37.4532 W m?2 mV?1 for F239in and 39.0625W m?2 mV?1 for F239out. The last calibrated for F579 dated back toApril 01, 1975 with calibration coefficients of 45.8716 W m?2 mV?1 forF579in and 47.3934 W m?2 mV?1 for F579out. The subscripts in and outmean that the top or the bottom of the HFP was facing the heater plate,respectively.New calibration coefficients were determined by plotting the referencemeasurements against the measurements from the HFPs that were to becalibrated. The new calibration coefficients for F239in was 53.967 W m?2mV?1 (Fig. 1), for F579in was 72.413 W m?2 mV?1 (Fig. 2), for F239outwas 59.979 W m?2 mV?1 (Fig. 3) and for F579out 61.142 W m?2 mV?1(Fig. 4). Table C.1 summarizes the new calibration factors. The calibrationfactors from the intercomparison period when the HFP tops were facingthe heat plate were used to correct the field campaign data. All otherHFPs used in this study were calibrated in a separate intercomparison butfollowing the same procedure.206Appendix C. Heat flux plate intercomparisonTable C.1: New calibration factors (in W m?2 mV?1).in outF239 53.967 59.979F579 72.413 61.142Figure C.2: Voltage measured by the each HFP plotted against the refer-ence HFP heat flux (QG,ref) for (a) F239in, (b) F239out, (c) F579in and (d)F579out. The equations of the linear regression and the correlation coeffi-cients (R2) are also shown.207Appendix DComparing the WPLcorrection to eddy fluxesbased on mixing ratiosWhen calculating the CO2 or H2O flux densities, a density correction iscrucial when using open-path IRGAs (Webb et al., 1980). However, if CO2or H2O mixing ratios are used in the calculations instead of densities, thisdensity correction is not required (Webb et al., 1980). For quality control,the two approaches to determine density corrected flux densities werecompared using the data in this thesis.First, latent (QE in W m?2) and CO2 flux densities (Fc in ?mol m?2s?1) were calculated based on instantaneous mixing ratios using Eqs. D.1and D.2, respectively.QE = ??aw?m?q (D.1)Fc = Mc?aw?m?c, (D.2)where Mc is the molar mass of CO2, mq is the H2O mixing ratio and mc isthe CO2 mixing ratio (both in g kg?1), w is the vertical wind speed (in ms?1), ?a is the density of dry air (in kg m?3) and ? denotes the latent heatof evaporation (2.45 ? 106 J kg?1). Overbars denote half-hourly averagesand primes are deviations from this average.H2O and CO2 densities were converted to instantaneous mixing ratiosusing Eqs. D.3 and D.4.mq =MqMdep? e (D.3)208Appendix D. Comparing the WPL correction to eddy fluxes based on mixing ratiosmc =?c?a(D.4)where Mq and Md are the molar mass of H2O and dry air (in kg mol?1),respectively. ?c is the CO2 density in kg m?3, p is the air pressure in kPa.The water vapour pressure (e in kPa) and density of dry air (?a in kg m?3)were calculated as:e = ?qRwTa, (D.5)?a =p? eRdTa, (D.6)where ?q is the H2O density in the air in kg m?3, Ta is the air temperaturein K and Rd is the gas constant of dry air.Second, the density correction according to Webb et al. (1980), hence-forth called the WPL correction, was applied to the 30-min averaged covari-ances to calculate the QE and Fc:QE = (1 + ??)(QE,raw + ??q?QHcp,m Ta), (D.7)FC = Fc,raw +?c?a? ?1 + ??E +?c?QHcp,mTa, (D.8)where ? = MdMq and ? =?q?a, ? is the total density of the air, QH is thesensible heat flux and cp,m is the specific heat of moist air. The uncorrectedlatent heat and CO2 flux densities (QE,raw and Fc,raw, respectively) werecalculated as:QE,raw = ?w???q, (D.9)Fc,raw = Mcw???c. (D.10)Both methods to calculate the density-corrected QE and Fc wereapplied to all data from 14 July to 3 August 2010. To assess the similarityof the results of both of the two methods were plotted against each other,for QE and Fc and each level separately. In the figures, the subscript WPLimplies that the method based on the WPL correction was used and thesubscript inst implies that the method based on instantaneous mixingratios was used. The comparison of QE is shown in Fig. D.1 and the209Appendix D. Comparing the WPL correction to eddy fluxes based on mixing ratiosgraphical comparison of Fc can be found in Fig. D.2. All figures also showthe 1:1 line, linear regression coefficients and Pearson correlation coefficients.In the case of QE the calculated fluxes using the two approaches weresimilar, which can be seen by the proximity of the plotted dots to the 1:1line. Furthermore, the regression slopes were always 1.01 and the correlationcoefficients (R2) were always 1.00. Also for Fc, both methods resulted insimilar fluxes for most levels but were more scattered than for QE. Atz = 1.2, R2 was 0.96 and the slope was 0.90. At all other levels R2 wasbetween 0.98 and 0.99 and the slopes were between 0.93 and 0.99.210AppendixD.ComparingtheWPLcorrectiontoeddyfluxesbasedonmixingratiosz = 1.2 m0 50 100 150050100150QE,WPL (W m?2)z = 2.7 m0 50 100 150050100150z = 7.6 m0 100 2000100200z = 11.9 m?500 50100150200250QE,inst (W m? 2)?50050100150200250z = 16.5 m?500 50100150200250QE,inst (W m? 2)?50050100150200250QE,WPL (W m?2)z = 21.0 m?500 50100150200QE,inst (W m? 2)?50050100150200z = 26.8 m?150 0 150 300QE,inst (W m? 2)?1500150300y =  1.01 x +  1.01R2 =  1.00y =  1.01 x +  1.01R2 =  1.00y =  1.01 x +  1.01R2 =  1.00y =  1.01 x +  1.01R2 =  1.00y =  1.01 x +  1.01R2 =  1.00y =  1.01 x +  1.01R2 =  1.00y =  1.01 x +  1.01R2 =  1.00Figure D.1: Comparison of the latent heat flux density based on instantaneous mixing ratio (QE,inst) and using theWPL correction (QE,WPL). Each dot stands for one half hour. The black lines show the 1:1 line. The equationsof the linear regressions and the Pearson correlation coefficients are also given.211AppendixD.ComparingtheWPLcorrectiontoeddyfluxesbasedonmixingratiosz = 1.2 m?6 ?4 ?2 0 2 4?6?4?2024Fc,WPL (?mol m?2 s?1)z = 2.7 m?5 0 5 10?50510z = 7.6 m?10 0 10 20 30?100102030z = 11.9 m?10 0 10 20Fc,inst (?mol m? 2 s? 1)?1001020z = 16.5 m?10 0 10 20 30Fc,inst (?mol m? 2 s? 1)?100102030Fc,WPL (?mol m?2 s?1)z = 21.0 m?20?100 10 20 30 40Fc,inst (?mol m? 2 s? 1)?20?10010203040z = 26.8 m?20 0 20 40Fc,inst (?mol m? 2 s? 1)?2002040y =  0.90 x +  0.90R2 =  0.96y =  0.93 x +  0.93R2 =  0.98y =  0.93 x +  0.93R2 =  0.99y =  0.93 x +  0.93R2 =  0.99y =  0.96 x +  0.96R2 =  0.99y =  0.97 x +  0.97R2 =  0.99y =  0.98 x +  0.98R2 =  0.99Figure D.2: Comparison of the CO2 flux density based on instantaneous mixing ratio (Fc,inst) and using the WPLcorrection (Fc,WPL). Each dot stands for one half hour. The black lines show the 1:1 line. The equations of thelinear regressions and the Pearson correlation coefficients are also given.212Appendix EVertical profile of treevolume and surfaceIn this appendix the vertical profile of average bole volume fractionand average bole surface fraction at the mountain pine beetle (MPB)infested lodgepole pine stand MPB-03 are determined. The results of thisappendix were used in the analysis of the vertical energy balance profile(Chapter 2)and the analysis of the vertical distribution of CO2 sourcesand sinks using an ecophysiological approach at the same stand (Chapter 3).This analysis was based on National Forest Inventory (NFI) data pro-vided by Dr. Tony Trofymow (Pacific Forestry Centre). Ground plots wereestablished and measured at MPB-03 adjacent to Crooked River ProvincialPark in 2006 following NFI guidelines (NFI 2004E). The NFI data includedtree height (H, in m), diameter at breast height (DBH, in cm) and tree sta-tus (live or dead), amongst others. Data was reported separately for smalland for large trees. Plot size for small tree counts was 0.005 ha and for largetree counts was 0.04 ha.E.1 Tree taperIn the following, the canopy is split into seven separate layers, where thelayers are defined as:Layer 1: 0.0 - 1.2 m,Layer 2: 1.2 - 2.7 m,Layer 3: 2.7 - 7.6 m,Layer 4: 7.6 - 11.9 m,Layer 5: 11.9 - 16.5 m,Layer 6: 16.5 - 21.0 m,Layer 7: 21.0 - 26.8 m.213E.1. Tree taperTable E.1: Number (Nt), average height and average DBH of dead trees bylayer they end in.End in layer Tree type Nt (ha?1) Average height (m) Average DBH (mm)2 small 260 1.70 16.82 large 7.5 2.60 115.03 small 60 4.50 23.03 large 25 7.13 105.34 large 82.5 10.59 130.85 large 167.5 14.22 160.76 large 175 18.51 207.67 large 7.5 21.5 282.0Table E.2: Number (Nt), average height and average DBH of live trees bylayer they end in.End in layer Tree type Nt (ha?1) Average height (m) Average DBH (mm)2 small 1260 1.90 12.43 small 400 4.20 38.03 large 25 6.58 103.34 large 32.5 9.15 107.35 large 17.5 13.05 150.5Vertical tree taper, volume and surface profiles were determinedseparately for dead and live trees. For each layer, the number of treesending in this layer, their average height and their average DBH wasdetermined (Tables E.1 and E.2). Small trees and large trees were in a firststep treated separately since they come from separate counts.Ormerods taper function (Ormerod, 1973) was used to determine thediameter of each average tree at the top and the bottom height of each layerit contributed to:dt(h)2 = DBH2(H ? hH ? hb)1.6(E.1)where h is the height above ground (h ? H), d(h) is the stem diameter atheight h and hb is the breast height (1.3 m).214E.2. Tree volume fractionE.2 Tree volume fractionFor the calculation of energy storage change in the boles, the vertical profileof bole volume is needed. Smalians volume formula was used to calculatethe volume (Vl, m3) of each average tree that contributed to a layer:Vl =A1 +A22l (E.2)where A1 (m2) is the tree disc area at the bottom of the layer, A2 (m2) isthe tree disc area at the top of the layer and l is the layer thickness (m).The tree disc area was calculated with the standard area formula for a circle:A = pi(dt/2)2. A tree contributed to a layer if it ended within or above thislayer. If the tree ended within the layer but below the top of the layer, onlythe length of the bole part that was within the layer (not the entire layerthickness) was used and A2 was the diameter at the top of the tree (which isbasically A2 = 0 m2, because the diameter becomes close to 0 m at the topof the tree). The average volume of a tree type (e.g. small tree, ending inlayer 2) per ha was then determined by multiplying the tree types volumeby the number of trees of this type per ha. Volume per ha ground was thenconverted to volume per m2 ground. The volume of all trees that had atleast parts of their boles within the layer were added to determine the totalwood volume per m2 ground and then the volume faction of a layer (?tree,m3 tree m?3 canopy) was calculated as:?tree =?i ViNt,i[m?2]l(E.3)Dead and live trees were kept separate because their tree temperaturesrates differed during the 2010 field campaign and separate tree bolemeasurements for live and dead trees were available. Table E.3 shows thebole volume fractions (?tree , m3 m?3) determined from this analysis.Since this NFI data is from 2006, and we know that the mortality rate ofmature pine trees increased afterwards to almost 100 % (Bowler et al., 2012),it was assumed that all pine trees that were larger than 16.5 m and alivein 2006, were dead by 2010. Therefore in the energy balance calculationsthe volume fraction of live and dead trees in layer 5 were 0 m3 m?3 and8.91 ? 10?5 m3 m?3, respectively.215E.3. Tree surface fractionTable E.3: Bole volume fractions (?tree, m3 m?3) for each layer and treestatus in 2006.Dead trees Live treesLayer 1 1.25?10?3 2.16?10?4Layer 2 1.04?10?3 1.06?10?4Layer 3 6.89?10?4 3.59?10?5Layer 4 3.01?10?4 5.27?10?6Layer 5 8.90?10?5a 9.51?10?8bLayer 6 6.94?10?6 0Layer 7 4.14?10?9 0aAssuming that all trees taller than 16.5 m were dead by 2010, 8.91 ? 10?5 m3 m?3was used in the calculations of the energy balance.bAssuming that all trees taller than 16.5 m were dead by 2010, 0 m3 m?3 was used inthe calculations of the energy balance.E.3 Tree surface fractionFor the ecophysiological analysis of CO2 source/sink distribution, the aver-age bole surface fraction was needed. The tree surface area for each averagetree contributing to a layer was then determined using a similar function asSmalians volume function, but for surface area:Al =C1 + C22l (E.4)where Al (m2) is the tree surface area of an average tree within the layerand C1 and C2 (m) are the tree circumferences at the top and the bottomof the layer, respectively. The tree circumference was calculated with thestandard circumference formula for a circle: C = 2pidt/2. The averagesurface area of a tree type (e.g. small tree, ending in layer 2) per ha wasthen determined by multiplying the tree types surface area by the numberof trees of this type per ha. We then converted surface area per ha groundto the surface area per m2 ground. The surface area of all trees that haveat least parts of their boles within the layer were added to determine thetotal surface area per m2 ground, which is the area fraction of a layer (BAI,m2 tree m?2 canopy). Dead and live trees were kept separate because theirCO2 exchange rates differed substantially during the MPB-03 2010 fieldcampaign and separate tree bole measurements for live and dead trees areavailable. Table E.4 shows the bole volume fractions determined in this216E.3. Tree surface fractionTable E.4: Bole surface area fractions (BAI, m2 m?2) for each layer and treestatus in 2006.Dead trees Live treesLayer 1 3.61?10?2 3.01?10?2Layer 2 3.81?10?2 1.15?10?2Layer 3 9.10?10?2 9.08?10?3Layer 4 4.72?10?2 1.45?10?3Layer 5 2.07?10?2a 7.41?10?5bLayer 6 2.69?10?3 0Layer 7 7.13?10?6 0aAssuming that all trees taller than 16.5 m were dead by 2010, 2.08 ? 10?2 m2 m?2was used in the calculations of the energy balance.bAssuming that all trees taller than 16.5 m were dead by 2010, 0 m2 m?2 was used inthe calculations of the energy balance.analysis.Since this NFI data is from 2006, and we know that the mortality rate ofmature pine trees increase afterwards to almost 100 % (Bowler et al., 2012),it was assumed that, as for the volume fraction, all pine trees that werelarger than 16.5 m and alive in 2006, were dead by 2010. Following thisassumption the surface area fraction of live and dead trees in layer 5 were 0m2 m?2 and 2.08?10?2 m2 m?2, respectively.217Appendix FEnergy balance closure andturbulence thresholdsUnder low turbulence conditions, the atmosphere above the canopy can bedecoupled from the canopy layers below resulting in a non-negligible advec-tion term. Under these conditions energy balance closure (EBC) decreasessubstantially. This is typically a problem during nighttime. Researchersuse turbulence thresholds to exclude those low turbulence periods. Tur-bulence dependency of EBC was examined for all seven levels that weremeasured during the 2010 MPB-03 field campaign. Details about the fieldsite and instrumentation are given in Chapter 2. Measurements were madeat seven measurements levels with heights normalized by the canopy heightof z/h = 0.06, 1.14, 0.38, 0.60, 0.83, 1.05 and 1.34. EBC was calculated forevery half hour and every level asEBC =QE +QHQ? ??QS ?QG, (F.1)where QE, QH , Q?, ?QS and QG are the latent heat flux density, sensibleheat flux density, net radiative flux density, rate of change in energy storagein the control volume and soil heat flux density (all in W m?2).Typical measures of turbulence used in this context are the frictionvelocity (u? =4?u?w?2+ u?v?2)(e.g., Barr et al., 2006) and the standarddeviation of the vertical wind velocity (?w =?w?2, where w is the verticalwind) (e.g., Launiainen et al., 2005).Energy balance closure was plotted against u? and ?w to determine,which u? and ?w thresholds were the most adequate to ensure a goodclosure but without losing too much data. Fig. F.1 shows EBC plottedagainst u? at the same level (u?,z), while Fig. F.2 shows EBC plottedagainst u? above the canopy (z/h = 1.34, u?,top) for the EBC range of 0to 1.5. u?,z and u?,top thresholds at each level, above which EBC did not218Appendix F. Energy balance closure and turbulence thresholdsimprove substantially were determined visually and are listed in Table 2.4.Table F.1: Visually determined u? thresholds when using u? at the samelevel (u?,z) and above the canopy (u?,top) for the seven measurement levels.z/h u?,z threshold (m s?1) u?,top threshold (m s?1)0.06 0.12 0.350.14 0.14 0.350.38 0.15 0.350.60 0.23 0.350.83 0.25 0.351.05 0.35 0.351.34 0.35 0.35Fig. F.3 shows EBC plotted against ?w at the same level (?w,z), whileFig. F.4 shows EBC plotted against ?w above the canopy (?w,top) for theEBC range of 0 to 1.5. ?w,z and ?w,top thresholds at each level, abovewhich EBC did not improve substantially were determined visually and arelisted in Table 2.4.Table F.2: Visually determined ?w thresholds when using ?w at the samelevel (?w,z) and above the canopy (?w,top).z/h ?w,z threshold (m s?1) ?w,top threshold (m s?1)1 0.15 0.502 0.20 0.503 0.35 0.504 0.40 0.505 0.50 0.506 0.50 0.507 0.50 0.50There was a more apparent change in slope when using u? as the tur-bulence criterion than when using ?w. Hence in this study, using u? is abetter criterion to exclude periods with low EBC due to low turbulence.The change in slope was similarly apparent when using u? and ?w above thecanopy as when using u? and ?w measured at the levels. It can also be seenthat the EBC at z/h = 0.06 determined in Chapter 2 was due to averaginga large spread of EBC values.219Appendix F. Energy balance closure and turbulence thresholdsz/h= 0.060.1 0.2 0.3 0.4 0.5u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.140.1 0.2 0.3 0.4 0.5u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.380.1 0.2 0.3 0.4 0.5u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.600.2 0.4 0.6u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.830.2 0.4 0.6 0.8 1.0u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.050.2 0.4 0.6 0.8 1.0 1.2u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.340.2 0.4 0.6 0.8 1.0 1.2 1.4u*,z (m s? 1)0.00.20.40.60.81.01.21.4EBCFigure F.1: Half-hourly energy bal-ance closure (EBC, black crosses) forall seven levels plotted against theequivalent of the friction velocity atthe same level (u?,z), showing clo-sure ranging from 0.5 to 1.5. Thered lines show the u?,z thresholds aslisted in Table F.1.220Appendix F. Energy balance closure and turbulence thresholdsz/h= 0.060.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top  (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.140.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top  (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.380.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top  (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.600.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.830.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top  (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.050.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top  (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.340.2 0.4 0.6 0.8 1.0 1.2 1.4u*,top  (m s? 1)0.00.20.40.60.81.01.21.4EBCFigure F.2: Half-hourly energy bal-ance closure (EBC, black crosses) forall seven levels plotted against thefriction velocity above the canopy(u?,top), showing closure rangingfrom 0.5 to 1.5. The red lines showthe u?,top thresholds as listed in Ta-ble F.1.221Appendix F. Energy balance closure and turbulence thresholdsz/h= 0.060.05 0.10 0.15 0.20 0.25 0.30 0.35?w,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.140.1 0.2 0.3 0.4?w,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.380.2 0.4 0.6?w,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.600.2 0.4 0.6 0.8 1.0?w,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.830.2 0.4 0.6 0.8 1.0?w,z (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.050.2 0.4 0.6 0.8 1.0 1.20.00.20.40.60.81.01.21.4?w,z (m s? 1)EBCz/h= 1.340.2 0.4 0.6 0.8 1.0 1.2?w,z (m s? 1)0.00.20.40.60.81.01.21.4EBCFigure F.3: Half-hourly energy bal-ance closure (EBC, black crosses) forall seven levels plotted against thestandard deviation of the verticalwind at the same level (?w,z), show-ing closure ranging from 0.5 to 1.5.The red lines show the ?w,z thresh-olds as listed in Table F.2.222Appendix F. Energy balance closure and turbulence thresholdsz/h= 0.060.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.140.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.380.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.600.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 0.830.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.050.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCz/h= 1.340.2 0.4 0.6 0.8 1.0 1.2?w,top (m s? 1)0.00.20.40.60.81.01.21.4EBCFigure F.4: Half-hourly energy bal-ance closure (EBC, black crosses)for all seven levels plotted againstthe standard deviation of the verti-cal wind above the canopy (?w,top),showing closure ranging from 0.5 to1.5. The red lines show the ?w,topthresholds as listed in Table F.2.223Appendix GSpecies-specific leaf areaindexThis appendix examines the vertical distribution of species specific leaf areaindex (LAI) at the mountain pine beetle (MPB) infested lodgepole pinestand MPB-03 (adjacent to Crooked River Provincial Park). The resultsof this appendix were used in the analysis of the vertical distribution ofCO2 sources and sink using an ecophysiological approach (see Chapter3). The data presented in this appendix is based on species-specific LAImeasurements (Table G.1) from Bowler et al. (2012). Only living trees areconsidered in this appendix. According to the National Forest Inventoryguidelines (NFI 2004E), large trees are defined as trees ? 1.3 m and with aDBH ? 9 cm and Small trees are trees that are taller than 1.3 m and havea DBH < 9 cm.The broadleaf vegetation was solely abundant below 1.2 m height andtherefore the broadleaf LAI (1.088 m2 m?2) belonged entirely to the under-story layer as defined in the CO2 source/sink analysis (Chapter 3). Smalltrees have an average height of 1.93 m for pine trees and 3.53 m for firtrees. It was assumed that one third of the leaves were located within theunderstory layer and two thirds belonged to the secondary structure layer.Therefore small trees contribute with 0.053 m2 m?2 to the understory layerand with 0.107 m2 m?2 to the secondary structure layer. Seedling andsaplings were assumed to belong entirely to the understory layer (0.024 m2m?2). Large trees were assumed to only contribute to the secondary struc-ture layer. Therefore, they contributed with 0.293 m2 m?2 to the LAI ofthe secondary structure layer. All conifers were assumed to have the samephotosynthesis rates and all understory broadleaf species were also assumedto have the same photosynthesis rates, so that LAI-contributions to thevegetation layers could be summarized as shown in Table G.2.224AppendixG.Species-specificleafareaindexTable G.1: Average species specific data from MPB-03: tree diameter at breast hight (DBH), plant density,foliage mass, specific leaf area (SLA) and leaf area index (LAI) (from Bowler et al., 2012). Numbers in bracketsare standard deviations.DBH Plant density Foliage mass SLA LAI(cm) (stems ha?1) (kg ha?1) (cm2 g?1) (m2 m?2 ground)Large tree Pine 11.35 37 118.8 52.8 (5.3) 0.063Fir 12.38 63 439.6 50.3 (7.5) 0.221Spruce 13.55 2 15.8 54.6 (6.4) 0.009Total 102 574.2 0.293Small tree Pine 1.75 650 146.3 52.8 (5.3) 0.077Fir 3.53 200 164.9 50.3 (7.5) 0.083Total 850 311.2 0.160Seedling/sapling Pine N/A 1100 24.41 52.8 (5.3) 0.013Fir N/A 450 19.1 50.3 (7.5) 0.010Spruce N/A 50 2.0 54.6 (6.4) 0.001Total 1600 45.7 0.024Broadleaf Shrub N/A N/A 178.9 173.8 (49.4) 0.311Herb N/A N/A 55.5 199.1 (59.7) 0.111Evergreen N/A N/A 396.9 104.7 (64.7) 0.416Lycopod N/A N/A 283.9 88.1 (37.4) 0.250Total 915.2 1.088225Appendix G. Species-specific leaf area indexTable G.2: Contributions of broadleaf and coniferous vegetation to the threevegetation layers.Layer Plant type LAI (m2 m?2)Understory Broadleaf 1.088Conifer 0.077Secondary structure Broadleaf 0Conifer 0.400Overstory Broadleaf 0Conifer 0226Appendix HNEP partitioningSeveral approaches exist to partition net ecosystem productivity(NEP = ?NEE, where NEE is net ecosystem exchange) into grossecosystem photosynthesis (GEP) and respiration (R). In this thesis, threedifferent approaches were used and compared: Non-rectangular hyperbolicfit through daytime NEP data following Gilmanov et al. (2003), linear fitthrough low-light-level daytime data following Jassal et al. (2007) and anighttime approach as explained in Stoy et al. (2006).Photosynthetically active radiation (PAR) was measured at all levels ex-cept the second highest level. For this level we interpolated linearly PARfrom the measurements above and below this level. The level heights (z)normalized by the canopy height (h) were z/h = 0.06, 0.14,0.38, 0.60, 0.83,1.05, 1.34. CO2 flux density (Fc) was measured with eddy-covariance in-strumentation at all seven levels (for details on instrumentation and fieldsite see Chapter 3) and storage-corrected CO2 flux density (NEEz in ?molm?2 s?1) was determined as:NEEz = Fc +? zo??c?tdz, (H.1)where the second term is the rate of storage change, ?c is the CO2 molardensity (in ?mol m?3) and t is the time (s). NEPz is by definition = ?NEEz.All NEPz and PAR values are 30-min averages. No turbulence thresholdswere used. To follow the NEP sign convention, positive values of NEPzmean the rate that C is taken up or stored by the ecosystem below levelz while negative values mean the rate C is being lost from the ecosystembelow level z.H.1 Non-rectangular hyperbolic fit usingdaytime NEPFollowing Gilmanov et al. (2003), NEPz was partitioned into cumulativephotosynthesis (P ) and respiration (R) rates below the level z. Thirty-min227H.2. Linear fit under low-light conditionsperiods were only included in this analysis if PAR > 5 ?mol m?2 s?1during the same half hour.A non-rectangular hyperbolic function (Gilmanov et al., 2003) was fittedto all 30-min averaged data from each level. The non-rectangular hyperbolicfunction used was:NEPz =?PAR + ? ??(?PAR + ?)2 ? 4???PAR2??R (H.2)where ? is the initial slope of the function, ? is the light-saturated netphotosynthesis, ? is the curvature factor for the inflection point and R isthe respiration rate of the ecosystem beneath level z. In the following, thisanalysis is done once using PAR at each level (PARz) and once using PARabove the canopy (PARtop).Figures H.1 and H.2 show NEPz plotted against PARz and PARtop,respectively and the fitted function for each level. The fitting parametersdetermined using the PARz and PARtop are given in Table H.1.H.2 Linear fit under low-light conditionsIn another approach to determine R, daytime NEPz measurements underlow light levels (PAR between 5 and 200 ?mol m?2s?1) were used. Usinga linear regression, R equals the negative value of the intercept value ofthe linear fit on the y-axis at PAR = 0. Figures H.3 and H.4 show themeasured data and the fitted lines for each level when using PAR measuredat each level (PARz) and PAR above the canopy (PARtop), respectively.The resulting fit parameters (slope and R = ?intercept) are given in TableH.2. If PARz was used, low light levels were defined as 5 < PARtop < 200?mol m?2s?1 and if PARtop was used they were defined as 5 < PARtop < 400?mol m?2s?1.228H.2. Linear fit under low-light conditionsz/h = 0.06500 1000 1500PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.14500 1000 1500PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.38500 1000 1500PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.60500 1000 1500PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.83500 1000 1500PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.05500 1000 1500PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.34500 1000 1500PARz ( ?mol m? 2 s? 1)?10?50510NEPz (?mol m?2  s?1 )0Figure H.1: Daytime NEPz plottedagainst PARz for all seven levels.Crosses are 30-min averaged dataand dashed lines are the correspond-ing fits for the 30-min averaged data.229H.2. Linear fit under low-light conditionsz/h = 0.06500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.14500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.38500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.60500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.83500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.05500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.34500 1000 1500PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0Figure H.2: Daytime NEPz plottedagainst PARtop for all seven levels.Crosses are 30-min averaged dataand dashed lines are the correspond-ing fits for the 30-min averaged data.230H.2. Linear fit under low-light conditionsz/h = 0.0650 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.1450 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.3850 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.6050 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.8350 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.0550 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.3450 100 150PARz ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0Figure H.3: Low-light level daytimeNEPz plotted against PARz for allseven levels. Crosses are 30-min av-eraged data and solid lines are thecorresponding linear fits for the 30-min averaged data.231H.2. Linear fit under low-light conditionsz/h = 0.0650 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.1450 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.3850 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.6050 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 0.8350 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.0550 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0z/h = 1.3450 100 150PARtop ( ? 2 s? 1)?10?50510NEPz (?2  s?1 )?mol m?mol m0Figure H.4: Low-light level daytimeNEPz plotted against PARtop for allseven levels. Crosses are 30-min av-eraged data and solid lines are thecorresponding linear fits for the 30-min averaged data.232H.3. Q10 model based on nighttime dataTable H.1: This table contains the fitting parameters of the non-rectangularhyperbolic functions for each level determined based on half-hourly averageddata using PARz and PARtop. It also gives the root mean square error(RMSE) of the data compared to the fitted lines.PARz z/h ? ? ? R RMSE(?mol m?2 s?1) ?mol m?2 s?1) (?mol m?2 s?1)0.06 0.009 1.66 0.9999 0.79 1.0970.14 0.006 1.83 0.9999 0.50 1.6970.38 0.012 4.96 0.9915 1.42 2.8150.60 0.014 5.67 0.9952 2.14 2.9200.83 0.012 5.07 0.9999 2.31 3.4381.05 0.011 5.17 0.9999 2.35 3.5741.34 0.009 4.80 0.9999 2.51 4.406PARtop z/h ? ? ? Rd RMSE(?mol m?2 s?1) ?mol m?2 s?1) (?mol m?2 s?1)0.06 0.003 1.57 0.9999 0.71 1.0930.14 0.003 1.88 0.9746 0.53 1.6910.38 0.006 5.06 0.9822 1.31 2.8250.60 0.009 5.61 0.9999 2.08 2.9030.83 0.010 4.98 0.9999 2.24 3.4521.05 0.010 5.19 0.9999 2.36 3.5771.34 0.009 4.80 0.9999 2.51 4.406H.3 Q10 model based on nighttime dataIn a third approach, R was estimated by applying the Q10 model to thenighttime NEPz data. Nighttime was defined as the time when short-wave irradiance above the canopy was equal to zero. The Q10 relationshipGaumont-Guay et al. (2006):R = R10 QTa?10 ?C10 ?C10 , (H.3)where Ta is the air temperature, R10 is the respiration at 10 ?C and Q10 isthe relative increase in R for a 10 ?C increase in Ta. As can be seen in Fig.H.5, the determined Q10-relationship was not reliable for some of the levels233H.4. ComparisonTable H.2: This table contains the fitting parameters (slope and R = -intercept) of the linear fit for each level determined based on 30-min averagedlow-light-level daytime data either using PAR at each level (PARz) or PARabove the canopy (PARtop). It also gives the root mean square error (RMSE)of the data compared to the fitted lines.PARz z/h R Slope RMSE(?mol m?2 s?1) (?mol m?2 s?1)0.06 0.77 0.008 1.5900.14 0.56 0.007 1.8180.38 1.29 0.010 3.2140.60 1.86 0.010 3.8000.83 2.07 0.011 5.6051.05 2.52 0.015 5.0721.34 2.78 0.015 5.328PARtop z/h R Slope RMSE(?mol m?2 s?1) (?mol m?2 s?1)0.06 0.64 0.002 1.3880.14 0.49 0.003 1.5620.38 1.42 0.007 3.2360.60 1.76 0.006 3.8810.83 2.12 0.010 4.0041.05 2.50 0.014 4.7571.34 2.78 0.015 5.328(decreasing R with temperature). Therefore, average nighttime respirationfor each level was determined and is given in Table H.3.H.4 ComparisonThe results of the above approaches are summarized in Fig. H.6, wherethe R profile determined based on 30-min averaged daytime data when fit-ting a non-rectangular hyperbolic function, based on low-light level daytimedata when fitting a linear regression and the average nighttime R valuesare shown. A bootstrapping analysis was conducted in order to determinethe robustness of the results. 100 subsamples of the data were determined(a random 90 % of the data) for each method and the same analysis was234H.4. Comparisonz/h = 0.065 10 15Ta (?15?10?50510NEPz (?2  s?1 )?C)?mol mz/h = 0.145 10 15Ta (?15?10?50510NEPz (?2  s?1 )?C)?mol mz/h = 0.385 10 15 20Ta (?15?10?50510NEPz (?2  s?1 )?C)?mol mz/h = 0.605 10 15 20Ta (?15?10?50510NEPz (?2  s?1 )?C)?mol mz/h = 0.835 10 15 20Ta (?15?10?50510NEPz (?2  s?1 )?C)?mol mz/h = 1.055 10 15 20Ta (?15?10?50510NEPz (?2  s?1 )?C)?mol mz/h = 1.3410 15 20Ta (?C)?15?10?50510NEPz (?2  s?1 )?mol mFigure H.5: Nighttime NEPz plot-ted against Ta for all seven levels.Crosses are 30-min averaged dataand solid lines are the correspond-ing Q10 fits for the 30-min averageddata.235H.4. ComparisonTable H.3: This table contains the mean and standard deviation (STD) ofnighttime NEPz.z/h Mean STD(?mol m?2 s?1) (?mol m?2 s?1)0.06 -0.84 1.150.14 -0.38 1.150.38 -1.22 1.400.60 -1.95 1.850.83 -2.33 2.931.05 -3.03 2.961.34 -3.48 2.56conducted on each of the subsamples. Standard deviations (STD) of these100 subsamples were calculated and are shown in Fig. H.6. All partitioningmethods resulted in similar profiles, with only the method based on night-time NEPz averages showing larger R values in the upper canopy and above.The method based on low-light level daytime data had the smallest STDsand was therefore the robustest. In this case, STDs were very similar if usingPARz or PARtop. Only at z/h = 0.06 and 0.38, STD was significantly largerwhen using PARz than when using PARtop. The largest STDs were foundfor the method fitting the non-rectangular hyperbolic function to daytimedata and using PARtop, which was therefore the least robust method.236H.4. Comparison(a)1 2 3R (?mol m ? 2 s? 1)0.00.20.40.60.81.01.21.4z/h(b)1 2 3R (?mol m? 2 s? 1)0.00.20.40.60.81.01.21.4z/h(c)1 2 3R (?mol m? 2 s? 1)0.00.20.40.60.81.01.21.4z/h(d)1 2 3R (?mol m? 2 s? 1)0.00.20.40.60.81.01.21.4z/h(e)1 2 3R (?mol m? 2 s? 1)0.00.20.40.60.81.01.21.4z/h(f)1 2 3R (?mol m? 2 s? 1)0.00.20.40.60.81.01.21.4z/hNTNRHF, PARzNRHF, PARtopLL, PARzLL, PARtop0 0 00 0 0Figure H.6: Respiratory (R) flux density profiles (cumulative R for ecosys-tem below z/h) based on 30-min averaged data determined with the fol-lowing partitioning methods: (a) partitioning based on average nighttime(NT) data, fitting a non-rectangular hyperbolic function (NRHF) using (b)PARz and (c) PARtop as well as linear fit to low-light-level daytime data(LL) using (d) PAR at each level (PARz) and (e) using PAR above thecanopy (PARtop). Error bars are standard deviations determined with thebootstrapping analysis. (f) shows all R profiles in one plot.237Appendix ISupporting figures and tablesfrom pressure calibrationThis Appendix shows figures and tables from the pressure calibration ofthe LI-7500 infrared gas analyzers. The pressure calibration is described inSection 4.3.3.12 Jul 17 Jul 22 Jul 27 Jul 01 Aug 06 Aug 11 Aug 16 Aug9192939495p (kPa)Figure I.1: Pressure (p) at the six levels before any calibration was applied.Orange: z/h = 0.14, light green: z/h = 0.38, dark green: z/h = 0.60,turquoise: z/h = 0.83, blue: z/h = 1.05 , black: z/h = 1.34.238Appendix I. Supporting figures and tables from pressure calibration92.092.593.093.5p z/h=0.14 (kPa)92.092.593.093.5p z/h=0.38(kPa)92.092.593.093.5p z/h=0.60 (kPa)92.092.593.093.5p z/h=0.83 (kPa)92.0 92.5 93.0 93.5pz/h=1.34 (kPa)92.092.593.093.5p z/h=1.05(kPa)Figure I.2: Correla-tion between the pres-sure at each level andthe pressure at z/h =1.34. Shown are half-hourly averages.239Appendix I. Supporting figures and tables from pressure calibrationz/h Slope Offset (kPa) R20.14 0.98419 1.35140 0.984070.38 0.97899 1.05508 0.978970.60 0.99298 0.11810 0.992850.83 0.99877 0.27767 0.998661.05 0.97940 1.77837 0.97942Table I.1: Slopes and offsets from linear regression and coefficients of de-termination for z/h = 0.14 to 1.05 compared to pressure at z/h = 1.34.z/h Height correction (kPa) Total offset (kPa)0.06 0.28100 1.632400.14 0.26415 1.615550.38 0.21039 1.265460.60 0.16331 0.282410.83 0.11330 0.390971.05 0.06324 1.84161Table I.2: Height corrections and the total calibration offset (offset fromlinear fit + height correction) for the pressure at each level240Appendix JMixing ratio uncertaintiesdue to propagation ofpressure uncertaintiesJ.1 IntroductionLatent heat and carbon dioxide (CO2) fluxes determined in this dissertationrequired measurements of CO2 and water vapour (H2O) mixing ratios(mc and mq, respectively). Open-path infrared gas analyzers (IRGA,model LI-7500, LI-COR Inc., Lincoln, Nebraska) used to measure molardensities of CO2 and H2O (?c and ?q, respectively) in mmol m?3.The open-path IRGAs also measured pressure (p) inside the control box,which were later on used to make density corrections to the calculated fluxes.The pressure measurements were used to convert ?c and ?q to mixingratios (in g kg?1). During the data analysis relatively large pressuredifferences (?p of up to 1.1 kPa) between the measurement levels wereobserved, which could not be explained by the height differences. Themeasurements of p were corrected by adjusting them to p at one arbitrarilyselected level (see Section 4.3.3), but there was still the possibility thatp was offset by the same amount at all level even though p differencesbetween the levels were expected to be correct. In order to understand theimpact of pressure inaccuracies, an error estimation is presented here.J.2 Uncertainty analysisJ.2.1 Water vapour mixing ratioWe assume that the actual p was lying within the range of measuredpressures at the different levels before p was calibrated. Therefore the241J.2. Uncertainty analysismaximum possible p error (?p) was assumed to be ?1.1 kPa.The mixing ratio for H2O (mq) was calculated as:mq = 0.611ep ? e , (J.1)where e is the water vapour pressure (kPa). Following the propagation ofuncertainties, the error of mq due to pressure uncertainties is:?mq = ?0.611e(p ? e)2 ?p (J.2)The average measured e and p at z/h = 0.38 were 1.12 kPa and 93.21 kPa,respectivelyThis resulted in an mq error of ?8.07 ? 10?3 g kg?1. With an averagemq of 7.43 g kg?1, the error corresponds to ?mq = ?1.1 %. More generally,the relative error of mq can also be written as,?mqmq= ? ?pp? e ? ??pp. (J.3)Therefore, the relative error in p translates almost directly into the relativeerror in mq.J.2.2 Carbon dioxide mixing ratioFor the estimation of mc, similar to Section J.2.1 a maximum pressure un-certainty of ?p = ?1.1 kPa was assumed. mc is calculated with the followingequation:mc =?c?a(J.4)where ?a is the dry air density (kg m?3). The dry air density can be calcu-lated as follows:?a =p? eRdTa, (J.5)where Rd is the gas constant of dry air (= 287.05 J kg?1 K?1) and Ta is theair temperature in K. Combining Eqs. J.4 and J.5, mc can be calculated as:mc =?c Rd Tap? e (J.6)242J.3. Summary and conclusionsFollowing the propagation of uncertainties the CO2 mixing ratio error (?mc)is:?mc = ??c Rd Ta(p ? e)2 ?p (J.7)The average ?c during the field campaign was ?c = 6.74 ? 10?4 kg m?3,while the average air temperature was Ta = 289 K. This resulted in ?mc =?7.25 ? 10?3 g kg?1, which is an error of ?mc = ?1.2% with an averageCO2 mixing ratio of mc = 0.607 g kg?1. More generally, the relative errorof mc can also be written as,?mcmc= ? ?pp? e ? ??pp. (J.8)Therefore, the relative error in p again translates almost directly into therelative error in mc.J.3 Summary and conclusionsDuring the MPB-03 field campaign in the summer of 2010 relatively largepressure differences between measurements at different heights were mea-sured, which could not be attributed to height differences between sensors.Even though the pressure differences between the levels were corrected byadjusting all levels to the measurements at one arbitrarily chosen level, itwas still possible that the pressure was offset at all levels. Maximum p dif-ferences between the levels before calibration were on the order of ?1.1 %,which we assumed to be the maximum pressure error. An uncertainty analy-sis was conducted in order to assess the uncertainties of mq and mc resultingfrom these pressure uncertainties. In both cases, the analysis showed thatthe maximum uncertainties due to pressure errors were very small (< ?1.1% for mq and < ?1.2 % for mc). Therefore, pressure errors of this mag-nitude are considered to have a negligible effect on measured mixing ratiogradients.243Appendix KLI-840 IRGA calibrationIn the summer of 2010, carbon dioxide (CO2) and water vapour (H2O)concentrations were measured at seven heights on a measurement tower ata mountain pine beetle (MPB) affected lodgepole pine stand (MPB-03) ininterior British Columbia (data used in this dissertation). To yield highaccuracy in the measurements of CO2 and H2O, the open-path infraredgas analyzer (IRGA) (model LI-840, LI-COR Inc., Lincoln, Nebraska) thatwas used to measure mole fractions at the seven levels sequentially, wascalibrated regularly. This Appendix explains the LI-840 calibration.The system was calibrated every 1 to 3 h by injecting consecutivelynitrogen (N2) as a zero gas and a CO2 in dry air span gas into the airsampling intake at the bottom level at the end of the half-hour. Differentspan gases were used over the course of the campaign (until 30 Jul: 404.08?mol CO2 mol?1 dry air, 31 Jul - 2 Aug: 451.28 ?mol CO2 mol?1 dry air,4 - 8 Aug: 498.48 ?mol CO2 mol?1 dry air). Intake of ambient air duringthe calibration was avoided by keeping the calibration gas flow rate higherthan 5 l min?1. The surplus gas was released to the atmosphere. Eachcalibration gas was measured for 3 min at the end of the half hour. Moreinformation about the instrumentation and the use of this data can befound in Chapter 4.First, CO2 signals from the LI-840 IRGA were adjusted based on thecalibration gas meaurements. Half hours, when both, the span and thezero gas were used were determined. Although LI-840 measurements aremole fractions, since both gases contained no water vapour, the mixingratio (mc) was equal to the mole fraction. A two-point calibration wasconducted for each of these half hours. The resulting slopes and offsetsshowed a small but clearly visible diurnal cycle with the slope and offset ata minimum value at about noon (Fig. K.1).LI-840 panel temperature (Tpanel) and cell pressure variations canaffect the mixing ratios measured by the LI-840 IRGA. The total drift in244Appendix K. LI-840 IRGA calibration22 Jul 26 Jul 30 Jul 03 Aug 07 Aug0.9940.9960.998Slope (?mol mol?1 V?122 Jul 26 Jul 30 Jul 03 Aug 07 Aug?0.8?0.6?0.4Offset ?1(?mol mol) ) Figure K.1: Slope (top) and offset (bottom) determined with two pointcalibrations for each half hour for CO2. Time is in PST and tickmarks areplaced at noon.22 Jul 26 Jul 30 Jul 03 Aug11.812.212.613.0V B (V)02004006008001000S in,top (W m-2)Figure K.2: Half-hourly averaged battery voltage (VB) and short wave irra-diance above the canopy (Sin,top). Time is in PST and tickmarks are placedat noon.245Appendix K. LI-840 IRGA calibration12.0 12.2 12.4 12.6 12.8VB  (V)0.9940.9960.998Slope (?mol mol-1 V-1)12.0 12.2 12.4 12.6 12.8?0.9?0.8?0.7?0.6?0.5?0.4Offset (?mol mol-1)VB  (V)Figure K.3: CO2 slope (left) and offset (right) from the two-point calibra-tions vs. the battery voltage (VB). The black lines are the fitted curvesdescribed by Eqs. K.1 and K.2, respectively.mole fraction without re-zeroing or re-spanning is given as < 0.4 ppm/Kpanel temperature for CO2 and < 0.009 ppt/K for H2O (LI-COR, 2003).Maximum Tpanel changes from one half hour to the next during the studyperiod was 3.8 K resulting in maximum drifts of 1.52 ppm for CO2 and0.03 ppt for H2O. Cell temperature is kept constant at 50 ?C in the LI-840IRGA and therefore does not add to the measurement uncertainties.Pump strength can influence the cell pressure of the LI-840 IRGA.The pump used in the calibration system to suck the air into the LI-840IRGA was powered by batteries, which were charged using solar panels.The battery voltage (see Fig. K.2) therefore followed the diurnal cycleof the incoming shortwave irradiance during daytime, while it furtherdecreased at night when there was no charging but battery usage continued.Half-hourly average battery voltage (VB) was recorded. Slopes and offsetswere related to VB measured by the calibration system data logger duringthe same half hour (see Fig. K.3) and the resulting relationships werelater used to correct LI-840 mixing ratios. Since the calibration gaseswere measured at the end of each half hour, VB of the half-hour con-cerned and the next half hour were averaged for use in the LI-840 calibration.246Appendix K. LI-840 IRGA calibrationThe relationship between the offsets and VB was rather linear albeit withsome scatter, while the relationship between the slopes and VB was betterrepresented by a logistic function. The equations for the fitted relationshipsare:slope =0.9969411 + e3.45179 (10.3171?VB ), (K.1)offset = ?6.53478 + 0.473847VB , (K.2)where the units of slope, offset and VB are ?mol mol?1 V?1, ?mol mol?1and V, respectively. Fig. 4.4 shows the CO2 span measurements before andafter the calibration and the concentrations of the calibration gases. Theoffsets of the measured concentrations were removed and the amplitudesof the diurnal variations was reduced substantially by the calibration.Before the calibration the standard deviation (STD) of the span gasmeasurements was 0.778 ?mol mol?1 (= 26.9 ?mol m?3) and decreasedto 0.434 ?mol mol?1 (= 15.0 ?mol m?3) after the calibration. The rootmean square error (RMSE) from the actual span gas concentrations was0.493 ?mol mol?1 (= 17.1 ?mol m?3) after the calibration. When applyingthe VB-based LI-840 calibration, as indicated above VB was interpolatedbetween the half hour before, the half hour of measurement and the halfhour after the LI-840 measurement was done based on the time during thehalf hour when the level or calibration gas was measured. Since VB wasclosely related to Sin, which again was closely related to the air temperaturethis calibration also compensated for temperature-related drifts. After thecalibration was applied no clear dependency of offsets and slopes on Tpanelwas found.The previously mentioned calibration gases were both H2O free and couldtherefore be used as H2O zero gases; however, no dewpoint generator wasemployed in the field. Therefore, only the measurement offset for H2O couldbe determined. For the slope, the same relationship as for CO2 was assumed.The same half hours as for the CO2 calibration were used for the H2Ocalibration.The offsets followed a diurnal cycle, which were attributed to the vari-ations in battery voltage and therefore in cell pressure. The relationshipbetween the offsets and VB is shown in Fig. K.4 and were approximated bythe logistic function:247Appendix K. LI-840 IRGA calibration12.0 12.2 12.4 12.6 12.8 VB (V)?0.15?0.10?0.05Offset (mmol mol-1)Figure K.4: H2O offset from the intercomparison of LI-840 IRGA H2O zerogas measurements with the battery voltage (VB). The black line is the fittedcurve described by Eq. K.3.22 Jul 24 Jul 26 Jul 28 Jul 30 Jul 01 Aug 03 Aug?0.050.000.050.100.15 LI?840, uncalibratedLI?840, calibratedH2O zero gas concentrationmq (?mol mol-1)Figure K.5: LI-840 IRGA mq measurements of the H2O zero gas before andafter the calibration was applied. The red line is the zero line.248Appendix K. LI-840 IRGA calibrationoffset =?0.13531 + e?3.6390 (12.1519?VB ), (K.3)where the units of offset and battery voltage are mmol mol?1 and V, re-spectively. Fig. K.5 shows the H2O zero measurements before and after thecalibration was applied. While there was still a wave-like behaviour visible,the STD of the LI-840 mq measurements decreased from 0.038 mmol mol?1(= 1.33 mmol m?3) to 0.030 mmol mol?1 (= 1.03 mmol m?3). RMSD ofthe calibrated mq from the zero line was 0.030 mmol mol?1 (= 1.03 mmolm?3).249Appendix LEnergy balance of thethermocouple wireFollowing Tanner and Thurtell (1969) the radiation error of a thermocouplecan be calculated by determining the energy balance of the thermocouplewire:Sin(1? ?w)dwLw = hadwpiLw(Tw ? Ta), (L.1)where Sin is the solar irradiance (in W m?2), ?w is the albedo of the wire (50%, Tanner and Thurtell, 1969), dw is the diameter of the wire (25.4 ? 10?6m), Lw is the length of the wire and ha is the thermal transfer coefficient(in W m?2 K?1). Solving for the temperature difference between the wiretemperature (Tw) and the air temperature (Ta), the temperature error dueto radiation (Tw ? Ta) can be calculated as:Tw ? Ta =Sin(1? ?w)hapi(L.2)Using the relationship between ha and Nusselt number (Nu), ha can becalculated as:ha =ka NuD, (L.3)where ka is the thermal conductivity of the air (0.0257 W m?1 K?1 at 20?C, Monteith and Unsworth, 2008). For the data studied in this dissertation,forced convection can be assumed, in which case Nu can be calculated as (forReynolds numbers between 10?1 to 103, Monteith and Unsworth, 2008):Nu = 0.32 + 0.51Re1/2, (L.4)where Re is the Reynolds number, which is defined as (Campbell and Norman,1998):Re =du?, (L.5)where u is the wind speed (in m s?1) and ? is the viscosity of air (15.4 mm2s?1 at 20 ?C, Campbell and Norman, 1998).250Appendix MThe effect of directional windshear on calculations ofReynolds stressIn a general form the Reynolds stress (?) is a tensor. In the specific case ofsurface layer horizontally homogeneous conditions it is (Stull, 1988):? =??u?u? u?v? u?w?v?u? v?v? v?w?w?u? w?v? w?w??? (M.1)On the horizontal plane, it is affected by u?w? and v?w? (see Fig. M.1).In most studies and books, the v?w? and u?v? components of the shear stressare neglected (e.g., Amiro, 1990a; Finnigan, 2000; Monteith and Unsworth,2008) and ? is calculated as:? = ??u?w?. (M.2)This however, is only true if the wind direction does not change withheight. The wind direction (WD) profile was determined using measure-ments at all seven levels on the flux tower. Fig. M.2 shows the ensemble-averaged difference between WD at each level and WD at z/h = 1.34(WDtop). Half hours were only included if WD was available at all lev-els. The profile shows that on average WD rotated counterclockwise (WD-WDtop < 0) from above the canopy down into the canopy. The rotationcompared to WDtop was on average smaller than 6 ? at all levels. The rangebetween which WD-WDtop varied, increased steadily with depth into thecanopy. While at canopy top (z/h = 1.05) in 80 % of the cases the windrotated by less than 6.31 ?, close to the ground in more than 50 % of thecases the rotation was either > 19.9 ? counterclockwise or > 10.6 ? clockwisecompared to WDtop and in 20 % of the cases the rotation was even > 38 ?(clockwise or counterclockwise) . This means that even though on averageWD rotation in the canopy compared to WDtop was relatively small, there251Appendix M. The effect of directional wind shear on calculations of Reynolds stressFigure M.1: Schematic showing how the two vertical shear components acton a horizontal plain.were many half hours when WD rotation was substantial. Such WD rota-tions have also been found in several other studies (e.g., Pinker and Holland,1988; Pyles et al., 2004; Su et al., 2008). Smith et al. (1972) and Su et al.(2008) found that rotation depends on canopy structure and meteorolog-ical conditions. WD rotation increases with vegetation area density andincreasing wind speed. Su et al. (2008) found that the rotation is small-est under neutral conditions and increases with increasing magnitude of thestability factor, i.e. when conditions become either more stable or moreunstable. They found that in an aspen dominated leafless canopy with avegetation area density of approximately 2 m2 m?2 the average rotation ofWD compared to WD above the canopy varied between 20 and 40 ? coun-terclockwise. Pyles et al. (2004) found a counterclockwise rotation of up to100 ? in a Douglas-fir and hemlock dominated 67-m tall canopy with a leaf252Appendix M. The effect of directional wind shear on calculations of Reynolds stressarea index of 11.4 m2 m?2.?40 ?20 0 20 40WD ?  WDtop (?)0.00.20.40.60.81.01.21.4z/h25 % 75 %Median10 % 90 %MeanFigure M.2: Rotation of wind direction (WD) expressed as the differencebetween WD at each level and WD at z/h = 1.34 (WDtop).We therefore hypothesize that the sometimes large WD rotations in thiscanopy indicated a shear stress that was not only affected by the gradientin mean horizontal wind speed (resulting in u?w? 6= 0) but also by the windrotation (resulting in v?w? 6= 0), especially below z/h = 0.38.According to Stull (1988), the magnitude of the kinematic shear stress(?/?) in a column with rotating WD with height can be calculated as:|?/?| =?u?w?2+ v?w?2(M.3)In order to determine the contributions of v?w? to ? , |u?w?| was plottedagainst the results of Eq. M.3 (Figs. M.3 and M.4). The measurementswere close to the 1 : 1 line implying that v?w? had a small absolutecontribution to the overall shear stress. When looking at the relative rootmean square deviation (RMSD) of u?w? from the results of Eq. M.3 (TableM.1) and Fig. M.3, the relative contribution of v?w? increased with depthinto the canopy resulting in almost 32 % RMSD close to the ground. Since,however, there is no simple method to calculate the directional shear stress253Appendix M. The effect of directional wind shear on calculations of Reynolds stress(in contrast to the magnitude of the shear stress) and absolute contributionsof v?w? were small, it was determined sufficient to use Eq. M.2 to calculate ? .z/h = 0.060.02 0.04 0.060.020.040.06z/h = 0.140.02 0.06 0.100.020.060.10z/h = 0.380.05 0.15 0.250.050.150.25z/h = 0.590.1 0.3 0.50.10.30.5z/h = 0.820.2 0.6 1.00.20.61.0|u?w?|z/h = 1.050.2 0.6 1.00.20.61.0z/h = 1.340.2 0.6 1.00.20.61.0|u?w?|?(u?w?2 + v?w? 2) ?(u?w?2 + v?w? 2) ?(u?w?2 + v?w? 2)?(u?w?2 + v?w? 2)Figure M.3: Magnitude of the kinematic shear stress without v?w? (|u?w?|)plotted against the same including v?w? (?u?w?2+ v?w?2) at the seven levels.Each dot represents a 30-min averaged measurement. The black line is the1:1 line.Table M.1: Absolute and relative root mean square deviation (RMSD) ofu?w? from results of Eq. M.3.z/h RMSD (m2 s?2) RMSD (%)0.06 0.0035 31.90.14 0.0055 31.10.38 0.0076 13.50.59 0.0089 6.20.82 0.0109 5.21.05 0.0125 5.71.34 0.0157 6.6254Appendix M. The effect of directional wind shear on calculations of Reynolds stress0.00.40.81.20.0 0.4 0.8 1.20.0 0.4 0.8 1.20.00.40.81.20.0 0.4 0.8 1.2 0.0 0.4 0.8 1.2z/h = 0.06 z/h = 0.14 z/h = 0.38 z/h = 0.59z/h = 0.82 z/h = 1.05 z/h = 1.34|u?w?||u?w?|?(u?w?2 + v?w? 2) ?(u?w?2 + v?w? 2) ?(u?w?2 + v?w? 2)?(u?w?2 + v?w? 2)Figure M.4: Same as Fig. M.3 but using the same scale for all levels.255Appendix NEddy diffusivity profilesusing different scalingcombinationsThere are two types of scaling (global and local) and two definitions ofscaling height (z or ze) that can be used in the prediction of ?, giving fourdifferent scaling combinations, which are explained in Chapter 4: I: zs = zand global scaling, II: zs = z and local scaling, III: zs = ze and global scalingand IV: z = ze and local scaling. Profiles of measured eddy diffusivities ofmomentum (KM ), sensible heat (KH), latent heat (KE) and CO2 (KC) andtheir predicted values are shown in this appendix and in Chapter 4. Fig.N.1 to N.12 show KM , KH , KE and KC for combination I to III. Profilesfor combination IV are shown in Chapter 4 (Fig. 4.22 to 4.25). There islittle difference between using local or global scaling. However, there is aclear benefit of using the effective height ze compared to using the heightabove the ground z as zs.256Appendix N. Eddy diffusivity profiles using different scaling combinations?top < ?0.1 (10)0 2 4 6 8KC (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (14)0 2 4 6 8KC (m2 s? 1)?top >  0.1 (23)0 2 4 6 8KC (m2 s? 1)Figure N.1: Measured (red) and predicted (grey) eddy diffusivities for windshear (KM ) using global scaling and zs = z (combination I). The numbersin brackets are the number of half hours included in the analysis.?top < ?0.1 (9)0 2 4 6 8KC (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (11)0 2 4 6 8KC (m2 s? 1)?top >  0.1 (16)0 2 4 6 8KC (m2 s? 1)Figure N.2: Same as Fig. N.1 using local scaling and zs = z (combinationII).257Appendix N. Eddy diffusivity profiles using different scaling combinations?top < ?0.1 (9)0 2 4 6 8KC (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (23)0 2 4 6 8KC (m2 s? 1)?top >  0.1 (16)0 2 4 6 8KC (m2 s? 1)Figure N.3: Same as Fig. N.1 using global scaling and zs = ze (combinationIII).?top < ?0.1 (13)0 2 4 6 8 10 12KE (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (19)0 2 4 6 8 10 12KE (m2 s? 1)?top >  0.1 (14)0 2 4 6 8 10 12KE (m2 s? 1)Figure N.4: Measured (red) and predicted (grey) eddy diffusivities for sensi-ble heat (KH) using global scaling and zs = z (combination I). The numbersin brackets are the number of half hours included in the analysis.258Appendix N. Eddy diffusivity profiles using different scaling combinations?top < ?0.1 (13)0 2 4 6 8 10 12KE (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (17)0 2 4 6 8 10 12KE (m2 s? 1)?top >  0.1 (11)0 2 4 6 8 10 12KE (m2 s? 1)Figure N.5: Same as Fig. N.4 using local scaling and zs = z (combinationII).?top < ?0.1 (11)0 2 4 6 8 10 12KE (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (24)0 2 4 6 8 10 12KE (m2 s? 1)?top >  0.1 (11)0 2 4 6 8 10 12KE (m2 s? 1)Figure N.6: Same as Fig. N.4 using global scaling and zs = ze (combinationIII).259Appendix N. Eddy diffusivity profiles using different scaling combinations?top < ?0.1 (24)0 2 4 6 8 10 12KH (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (48)0 2 4 6 8 10 12KH (m2 s? 1)?top >  0.1 (73)0 2 4 6 8 10 12KH (m2 s? 1)Figure N.7: Measured (red) and predicted (grey) eddy diffusivities for latentheat (KE) using global scaling and zs = z (combination I). The numbers inbrackets are the number of half hours included in the analysis.?top < ?0.1 (22)0 2 4 6 8 10 12KH (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (33)0 2 4 6 8 10 12KH (m2 s? 1)?top >  0.1 (53)0 2 4 6 8 10 12KH (m2 s? 1)Figure N.8: Same as Fig. N.7 using local scaling and zs = z (combinationII).260Appendix N. Eddy diffusivity profiles using different scaling combinations?top < ?0.1 (19)0 2 4 6 8 10 12KH (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (77)0 2 4 6 8 10 12KH (m2 s? 1)?top >  0.1 (55)0 2 4 6 8 10 12KH (m2 s? 1)Figure N.9: Same as Fig. N.7 using global scaling and zs = ze (combinationIII).?top < ?0.1 (280)0 2 4 6 8 10KM (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (94)0 2 4 6 8 10KM (m2 s? 1)?top >  0.1 (32)0 2 4 6 8 10KM (m2 s? 1)Figure N.10: Measured (red) and predicted (grey) eddy diffusivities for CO2(KC) using global scaling and zs = z (combination I). The numbers inbrackets are the number of half hours included in the analysis.261Appendix N. Eddy diffusivity profiles using different scaling combinations?top < ?0.1 (260)0 2 4 6 8 10KM (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (86)0 2 4 6 8 10KM (m2 s? 1)?top >  0.1 (23)0 2 4 6 8 10KM (m2 s? 1)Figure N.11: Same as Fig. N.10 using local scaling and zs = z (combinationII).?top < ?0.1 (249)0 2 4 6 8 10KM (m2 s? 1)0.00.20.40.60.81.01.21.4z/h?0.1 < ?top < 0.1 (138)0 2 4 6 8 10KM (m2 s? 1)?top >  0.1 (23)0 2 4 6 8 10KM (m2 s? 1)Figure N.12: Same as Fig. N.10 using global scaling and zs = ze (combina-tion III).262

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