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Energy balance closure in a boreal old-growth jack pine stand and clearcut, and implications for eddy… Kidston, Joe 2006

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Energy balance closure in a boreal old-growth jack pine stand and clearcut, and implications for eddy covariance C 0 2 flux measurements. By JOE KIDSTON B.Sc, Imperial College of Science, Technology, and Medicine, London, 2002 A THESIS SUBMITTED IN PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science In THE FACULTY OF GRADUATE STUDIES (Atmospheric Science) THE UNIVERSITY OF BRITISH COLUMBIA April 2006 © Joe Kidston,2006 A b s t r a c t The accuracy of the components of the surface energy balance were analysed, in an attempt to determine the cause of the imbalance that is commonly observed in energy balance closure studies when eddy covariance (EC) measurements of the sum of sensible (H) and latent (LE) heat fluxes, which we call the total surface layer heat flux (7), are compared with the net radiation (R„) minus the soil heat flux. We utilise data from a mature boreal jack pine forest, and a jack pine clearcut, both part of the boreal ecosystem research monitoring sites (BERMS) study area in central Saskatchewan, Canada, to elucidate differences in the cause of the imbalance when EC measurements are made over tall vegetation compared to when they are made close to a solid surface. We demonstrate that at the clearcut site (HJP02), a significant portion of the imbalance was caused by both the overestimation of R„ due to instrumentation issues and the inclusion of the tower in the field of view of the downward facing radiometers, and underestimation of LE due to attenuation of H2O variance in the sample tube of the closed-path infrared gas analyser. Loss of low-frequency covariance due to insufficient averaging time, and systematic advection of fluxes away from the EC tower, were discounted as significant issues; the latter through comparison of measurements from a second, roving EC system with the long term system. That the spatial and temporal distributions of T were well behaved, and furthermore that there was not similarity of the relative magnitudes of the turbulent fluxes during half-hours when different closure was achieved despite similar climatic conditions, implied that the variation in closure was not caused by micrometeorological processes that impacted all turbulent fluxes similarly, and therefore the turbulent fluxes should not be forced for closure. ii Conversely at the mature forest site (O JP), loss of low-frequency covariance when a 30-min. averaging time was used contributed significantly to the systematic imbalance. However, stationarity became a significant issue when longer averaging times were used; averaging times that were long enough to capture all of the low-frequency covariance were too long to resolve all of the high-frequency covariance. This, combined with analysis of the 30-min. flux data that showed similarity between T and net ecosystem-atmosphere exchange of CO2 (NEE), implied that where EC measurements are made over tall canopies, T should be forced for energy balance closure while retaining the measured Bowen ratio, and the same factor should be applied to NEE. iii T a b l e o f Contents Abstract ii Table of Contents -iv List of Tables vii List of Figures ix List of abbreviations xvi Acknowledgments xix 1 Introduction 1 1.2 Basic Considerations 3 2 Methods 7 2.1 Description of sites 7 2.2 Flux footprints at HJP02 10 2.3 Description of locations of the roving EC system 13 2.4 Instrumentation at HJP02 14 2.4.1 Long-term climate/EC system 14 2.4.2 Roving climate/EC system 15 iv 2.5 Data Analysis 16 2.5.1 Turbulent flux calculations 16 2.5.2 Data quality control 17 2.5.3 Methods of calculating C 18 2.5.4 Spectral analysis 18 2.5.5 Roving system calibration 18 3 Results and Discussion 20 3.1 Accuracy of the measurement of A 20 3.1.1 Accuracy of the measurement of Rn at H JP02 20 3.1.2 Diurnal variation of C: implications for the accuracy of the storage fluxes 24 3.2 Accuracy of the measurement of TEC 28 3.2.1 Underestimation of high-frequency LEEc 29 3.2.2 Loss of low-frequency covariance due to insufficient averaging time 39 3.3 Spatial and temporal variability of the SL fluxes at HJP02 -implications for the existence of venting 47 3.3.1 Similarity of C at different spatial locations - implications for the existence of systematic venting locations 47 3.3.2 Temporal and spatial variability of the SL fluxes at HJP02 -implications for the existence of random venting locations 50 3.4 Similarity between SL fluxes 54 v 4 Conclusions 61 References 64 Appendix 1: Further spectral analysis 69 Appendix 2: Nocturnal C at HJP02 76 Appendix 3: The relationship between C and wind direction 79 Appendix 4: The influence of u* on C at OJP 81 vi List of Tables Table 1. Footprint contributions for x (direction parallel to mean wind) and y (direction perpendicular to mean wind) calculated using a Lagrangian particle dispersion model (Kljun et al. 2002), provided by N. Kljun (pers. comm.). ry-rg are daytime scenarios, and rj is a nighttime scenario. The variables distinguishing scenarios o-r7 from rj are printed in bold. 80% and 90% subscripts indicate that, e.g., 80% of the contributions to the total flux are within a distance x < xso% from the tower. xmax is the distance from the tower that had the maximum effect on the flux 12 Table 2 . Summary of roving system data collection periods in 2004 14 Table 3. Regression parameters for fluxes measured by the roving and main eddy covariance (EC) systems during the calibration periods: sensible heat flux measured by EC instrumentation (HEC), latent heat flux measured by the EC instrumentation (LEEC), net shortwave radiation flux (Rsnet), net longwave radiation flux (Rmet), and soil heat flux measured by the soil heat flux plates (GT) 19 Table 4. Systematic errors in the measurement of R„ as given in the specifications for the CNR1 radiometer employed at HJP02. Column 3 gives the magnitude of the error during a typical midday situation"1", where the error has been assumed to have linear dependency 21 Table 5. Summary of the underestimation of LEEC due to high-frequency attenuation of H2O variance in the sample tube of the closed-path IRGA. Transfer functions (TFs) were calculated based on the data shown in Fig. 5 (HJP02) and Fig. 8 (OJP) for the low and high RH stratifications, and set to unity below frequencies //. Underestimation of LEEC was calculated as the difference from unity of the ratio of the integral of the w-TA cospectra over all frequencies with the appropriate TF applied, to the integral of the w-TA cospectra over all frequencies without the TF applied. The w-TA cospectra for the high and low u* stratifications are shown in Fig. 7 (HJP02) and Fig. 9 (OJP) 37 Table 6. Regression parameters for TEC computed using longer averaging period, against TEc computed using a 30-minute averaging period. The 30-minute fluxes were averaged over 2, 4, or 8 periods, for comparison with the 60, 120, and 240-minute fluxes, respectively, and the regressions included data for the entire diurnal cycle. Data were recorded during July 2004 at HJP02 and during July and August 2003 at OJP 41 Table 7. Regression parameters for T against A at OJP using different averaging periods for TEC- A was averaged over 2, 4, or 8 periods, for comparison with the 60, 120, and 240-minute fluxes, respectively. The data are for the same period as in Table 6. 46 Table 8. (a)-(c). Regression parameters of T against A for the main system and roving system 49 Table 9. Regression parameters for the spatial variation in A and the spatial variation in TEC at HJP02 (data shown in Fig. 13) 52 viii L i s t o f F igu res Fig. 1. Aerial photograph of HJP02 showing the layout of the site, some topography, windrows of logging slash, and the locations of roving eddy system 9 Fig. 2 Climate variables at HJP02 during 2004: (a) Daily total incident shortwave radiation flux (Rsd)- (b) Mean daily air temperature (Ta) at 2 m. (c) Mean daily wind speed (u) at 5 m. (d) Mean daily volumetric soil water content (VWC) at depth 0- 15 cm 10 Fig. 3. (a) Ensemble averages of R„ - G (available energy flux, A, solid line) and H + LE (total surface layer heat flux, T, dashed line). Data were recorded at HJP02 during June 2003, 2004, and 2005. (b) Mean of energy balance closure (Q for each half-hour, (MOR method, solid line) with error bars representing one standard deviation for each half-hour. Ratio of the mean of T to the mean of A (ROM method, dashed line) 26 Fig. 4. (a) Ensemble average of A (solid line) and T (dashed line). Data were recorded at OJP between day of year (DOY) 150-300, 2004 and 2005. (b) C using the MOR method (solid line) with error bars representing one standard deviation for each half-hour, and C using the ROM method (dashed line) 27 Fig. 5. Ratio of ensemble average vertical wind speed (w)-H20 mixing ratio cospectra to w-7/a cospectra, stratified by relative humidity (RH): RH< 30 (solid line), 50 < RH < 57 (dashed line), and 60% < RH (dotted line). Data were recorded during July 2004 at HJP02 when HEC > 100 W m"2, LEEC > 75 W m"2, and C0 2 flux measured by the EC instrumentation (Fc) > 0 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 22, 20, and 18 respectively, ix and the mean RH for the low, medium, and high RH stratifications was 26, 53, and 72% respectively 31 Fig. 6. Ratio of ensemble average W - H 2 O mixing ratio cospectra for the closed-path system to W - H 2 O mixing ratio cospectra for the open-path system, stratified by RH. Data were recorded at HJP02 during the same half-hours as the corresponding RH stratifications shown in Fig. 5 32 Fig. 7. Ensemble-average w-Ta cospectra stratified by friction velocity (w*): u* < 0.4 (dashed line), all u* (solid line), and u*> 0.7 m s"1 (dotted line). Data were recorded at HJP02 during the same half-hours as the data shown in Fig. 5, and the low-, all-, and high-w* stratifications contain 13, 153, and 18 half-hours, respectively 33 Fig. 8. Ratio of ensemble average W - H 2 O mixing ratio cospectra to w-7*a cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during July and August 2003 at OJP when HEC > 150 W m"2, LEEC > 100 W m"2, and FC < -5 umoim"2 s"1, The number of half-hours contained within the low, medium, and high RH stratifications was 21, 19, and 21 respectively, and the mean RH for the low, medium, and high RH stratifications was 35, 45, and 68% respectively 35 Fig. 9. Ensemble-average w-Ta cospectra stratified by u*: u* < 0.4 (dashed line), all-w* (solid line), and u* > 1.1 m s"1 (dotted line). Data were recorded at OJP during the same half-hours as the data shown in Fig. 8, and the low-, all-, and high-u* stratifications contain 10, 109, and 9 half-hours respectively 36 Fig. 10. C as a function of LEEC I E[Ec- Data were recorded at HJP02 between May and September, 2004 and 2005, when clear-sky Rsd (Rpoi) > 500 W m"2, and have been x bin averaged by LEEC I HEc- Also shown is the standard error in the mean for each bin 39 11. Ensemble average cospectra of w-TA (a) and W-H2O mixing ratio (b) for 30-min. averaging period (solid line) and 240-min. averaging period (dotted line). Data were recorded at OJP between 1000 and 1400 CST during July and August 2003 43 12. Ensemble average w-TA cospectra (a) and W-H2O mixing ratio cospectra (b) for 30-min. averaging period (solid line) and 240-min. averaging period (dotted line). Data were recorded at OJP between 0600 and 1000 CST during July and August 2003 46 13 (a) Regression of A measured by the roving system against A measured by the main system, (b) Regression of TEC measured by the roving system against TEc measured by the main system. See Table 9 for regression parameters. The data were recorded while the roving system was at Location 3 51 14. Diurnal variation of skewness: A (solid line), TEC (dashed line), and Rsd (dotted line) at OJP (a) and HJP02 (b). Skewness was calculated from the half-hourly flux values, for each hour of the day, i.e. fluxes were first binned by hour of the day, and then the skewness was calculated for the distribution of all the fluxes within a given hour. Data were recorded during daylight hours (Rpot > 0 W m"2) between May and October, 2004 and 2005 53 15. Fc as a function of downwelling photosynthetically active photon flux density (Q). Data were recorded at OJP during summer, 2004 and have been bin averaged, and stratified by C. C during the daytime (Q > 0) using the MOR method was 53%, xi 75%, and 102% for the low, medium, and high C stratifications respectively. Also shown is the standard error of the mean for each bin 55 16. Normalised fluxes plotted against C: A (dashed line), HEc (dot-dashed line), LEEc (solid line), and FC (dotted line), normalised by their respective means when 0.98 < C < 1.02. Data were recorded at OJP when (Q > 900 umol m"2 s"1, 8 < TA < 18°C and 0.07 < VWC < 0.2) during 2003, 2004, and 2005, and have been bin averaged, with 150 half-hours in each bin 57 17. Normalised fluxes plotted against C: A (dashed line), HEc (dot-dashed line), LEEC (solid line), and FC (dotted line), normalised by their respective means when 0.98 < C < 1.02. Data were recorded at HJP02 when (Q > 900 umol m"2 s"1, 8 < TA < 18 °C, and 0.07 < VWC < 0.16) during summer 2003, 2004, and 2005, and have been bin averaged, with 200 half-hours in each bin 60 Al 1. Ratio of ensemble average W - C O 2 mixing ratio cospectra to w-TA cospectra, stratified by RH: RH < 30 (solid line), 50 < RH < 57 (dashed line), and 60% < RH (dotted line). Data were recorded during July 2004 at HJP02 when H > 100 W m"2, LE > 75 W m"2, and FC > 0 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 22, 20, and 18 respectively, and the mean RH for the low, medium, and high RH stratifications was 26, 53, and 72% respectively 70 Al 2. Ratio of ensemble average \v-CO2 mixing ratio cospectra to w-TA cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during July and August 2003 at OJP when H > xii 150 W m"2, LE > 100 W m"2, and Fc < -5 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 21, 19, and 21 respectively, and the mean RH for the low, medium, and high RH stratifications was 35, 45, and 68% respectively 71 Al 3. Ratio of ensemble average W-H2O mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during July and August 2004 at OA when H> 150 W m"2, LE > 100 W m"2, and Fc < -5 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 21, 19, and 21 respectively, and the mean RH for the low, medium, and high RH stratifications was 35, 45, and 68% respectively 72 Al 4. Ratio of ensemble average W-CO2 mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during the same periods as the corresponding RH stratifications shown in Fig. Al 3 73 Al 5. Ensemble-average w-Ta cospectra stratified by u*\ u* < 0.42 (dashed line), all-w*(solid line), and u*> 1.1 m s"1 (dotted line). Data were recorded at OA during the same half-hours as the data shown in Fig. Al 3, and the low-, all-, and high-u* stratifications contain 13, 159, and 12 half-hours respectively 74 Al 6. Ensemble average cospectra of w-Ta (a) and w-H20 mixing ratio (b) for 30-min. averaging period (solid line) and 240-min. averaging period (dotted line). Data were recorded between 0600 and 1400 CST during July and August 2003 at OJP. 75 xiii Fig. A2 1. Nocturnal TEc as a function of u*. Half-hours following periods of low u* (u* < 0.08 m s"1, open circles). Half-hours following periods with high u* (u* > 0.15 m s"1, crosses). Data were recorded at HJP02 between May and September, 2003, 2004, and 2005, and have been bin averaged 77 Fig. A2 2. C as a function of u* during the nighttime (Rpo, < 0). Data were recorded at HJP02 between May and September, 2003, 2004, and 2005, and have been bin averaged with 200 half-hours in each bin. C was calculated using the ROM method, and error bars were calculated using dC2 -fee} ST2 + dC_ KdAj SA2 where §T and 8A are the standard deviations of T and A respectively 78 Fig. A3 1. C versus wind direction for HJP02 (solid line) and OJP (dashed line). Data were recorded during the summers of 2004 and 2005 when R p o t > 50 W m"2 80 Fig. A4 1. (a) ensemble average diurnal variation of u* for high-w* days (solid line) and low-w« days (dashed line), (b) ensemble average diurnal variation of C for high-w* days (solid line) and low-w» days (dashed line). Data were recorded at OJP between May and September, 2003, 2004, and 2005 82 Fig. A4 2. (a) Diurnal variation of u* on days when u* is relatively high in the afternoon compared to the morning (u*i„creaSi„g_u; solid line) and days when u* is relatively low in the afternoon compared to the morning (u*decreasing_u*, dashed line), (b) Diumal variation of C on days when u* is relatively high in the afternoon compared to the morning (Cmcreasing_u*, solid line) and days when u* is relatively low in the afternoon xiv compared to the morning (Cdecreasmg_u*, dashed line), (c) Ratio of TdeCreasing_u* to Tj„creasmg_u* (dashed line) and ratio of A decreasing^* to A i n c r e a s m g J I * (solid line). Data were recorded at OJP between May and September, 2003, 2004, and 2005 83 xv List of abbreviations Variable Units Description A Wrn 2 available energy flux, A = R N - G C % energy balance closure, C = T/A fi Hz Frequency below which it was assumed that there was no high-frequency attenuation H2O mixing ratio in the sample tube of the closed-path IRGA. Fc Limol m"2 s"1 turbulent flux of CO2 measured using eddy covariance GT Wm"2 soil heat flux measured below the soil surface using a soil heat flux plate Gbiomass Wm"2 rate of change of heat storage in above ground biomass H Wm - 2 surface-atmosphere sensible heat flux HEC Wm - 2 turbulent flux of sensible heat measured using eddy covariance. Hoiher Wm - 2 transport of sensible heat flux not measured by eddy covariance L m Monin-Obhukov scaling length LE Wm"2 surface-atmosphere latent heat flux LEEC Wm - 2 turbulent flux of latent heat measured using eddy covariance LE0ther Wm - 2 transport of latent heat flux not measured by eddy covariance xvi Q 2 1 umol m" s" downwelling photosynthetically active radiation Q Wm"2 Sources or sinks of energy below the eddy covariance height are not measured Ru Wm"2 downwelling longwave radiation flux Rldp Wm - 2 difference between RLd and longwave radiation flux emitted by the surface of the pyrgeometer. RLnet Wm"2 net longwave radtiation flux RLU Wm"2 upwelling longwave radiation flux Riup Wm"2 difference between RLu and longwave radiation flux emitted by the surface of the pyrgeometer Rn Wm"2 net radiation flux Rpot Wm"2 clear-sky Rsd Rsd Wm"2 downwelling shortwave radiation flux Rsu Wm"2 upwelling shortwave radiation flux Sc02 umol m"2 s"1 rate of change of C O 2 storage between the soil-surface and the eddy covariance measurement height Sc Wm"2 rate of change of heat storage between the soil-surface and the heat flux plate. SH Wm"2 rate of change of sensible heat storage between the soil-surface and the eddy covariance measurement height SLE Wm"2 rate of change of latent heat storage between the soil-surface and the eddy covariance measurement height xvii ST W m"2 rate of change of total heat storage between the soil-surface and the eddy covariance measurement height T W m'2 total surface layer heat flux TEC W nf2 total heat flux measured at the eddy covariance height Tother W m - 2 transport of total heat flux not measured by eddy covariance TA °C air temperature u m s'1 wind speed u* m s"1 friction velocity w m s_1 vertical wind speed x m distance z m height z0 m roughness length for momentum EC eddy covariance IRGA infrared gas analyser NEE L i m o l m"2 s"1 net ecosystem exchange of CO2 RH % relative humidity SL surface layer TF transfer function T Y M un-normalised transfer function VWC m3 m"3 volumetric soil water content xviii Acknowledgments The mentoring and guidance of Andy Black was instrumental in inspiring this study, and it also would not have been possible without the help and support of Kai Morgernstern. Further academic supervision provided by R. Stull and T. Oke was also much appreciated. Alan Barr was responsible for the meteorological (climate) measurements at the sites, and Harry McCaughey was responsible for the operation of the EC instrumentation at OJP during 2005. The technical assistance of Zoran Nesic, Andrew Sauter, Rick Ketler, Shawn O'Neill and Stephanie Thompson is sincerely acknowledged, as is the maintenance and quality assurance of meteorological measurements provided by Werner Bauer, Dell Bayne, Natasha Neumann, Erin Thompson, Steve Enns, Dave Wieder, and help provided by David Gaumont-Guay. Funding was provided by the Fluxnet Canada Research Network (through Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) and BIOCAP Canada), a NSERC operating grant to Andy Black, and also the Climate Research Branch of the Meteorological Service of Canada. xix 1 Introduction Fluxes of radiation, sensible heat, water vapour, CO2, and other trace gases between the Earth's surface and the atmosphere are a primary control on the state of the atmosphere. When these fluxes change, complex feedback processes come into effect until a new steady state is reached. The processes that control these fluxes therefore need to be well understood if we are to be able to predict the state of the atmosphere Eddy covariance (EC) is a powerful tool for measuring energy and CO2 fluxes at a scale of hundreds to thousands of m2 (Baldocchi; Schmid 1994; Wofsy et al. 1993) which when coupled with measurements of variables such as radiation, temperature, and moisture, can be used to better understand the processes controlling ecosystem-atmosphere exchange (Law et al. 2002). One measure used to quantify the accuracy of measured fluxes is energy balance closure, which utilises the fact that the energy flux into a system must equal the energy flux leaving the system, plus any energy storage change in the system. At the surface of the Earth this is expressed as Rn = H + LE + G + Q . (1) where R„ is the net radiation flux density, H is the sensible heat flux density, LE is the latent heat flux density, G is the heat flux density into the surface, and Q is the sum of fluxes from any other energy sinks or sources, including photosynthesis, which is usually assumed to be negligible. As is common in micrometeorology, flux will imply flux density, and so the word density in this context will be omitted. Energy balance closure (Q is often expressed as 1 C = (H + LE)/(R„-G) (2) where the sum of the fluxes in the denominator is then called the available energy flux (,4),Monteith 1981. We will call the sum of the fluxes in the numerator the total surface layer (SL) heat flux and use the symbol (J). The measurement of r i s independent of the measurement of A, and so C can be used to evaluate the relative accuracy of T versus A. Analysis of numerous data sets obtained over various surface types shows that T is often about 70-90% of A (Aubinet et al. 2000; Blanken et al. 1998; Twine et al. 2000 Barr et al. 2006; Wilson et al. 2002). Several explanations for this systematic imbalance have been hypothesized including: different source locations for T versus A, instrument offset, neglected energy sinks, loss of low or high-frequency contributions to the turbulent fluxes contained within T, and neglected transport processes of the SL fluxes, e.g. horizontal advection and subsequent venting of fluxes away from the EC tower , or vertical transport due to processes not measured by EC (Black et al. 1996; Mahrt 1998; Massman and Lee 2002; Twine et al. 2000; Wilson et al. 2002). Evidence is accumulating that suggests the systematic imbalance is due to the underestimation of T. Twine et al. (2000) demonstrated that the measurement of A: (a) is unlikely to be the cause of a systematic imbalance, and (b) given the stated accuracy of the measurement of its components, could not account for the magnitude of the imbalance. The authors argued that closure should be forced by increasing H and LE such that the measured Bowen ratio, i.e. H/LE, remains unchanged. Wilson et al. (2002) found that during the daytime, for a given level of incident photosynthetically active radiation (PAR), the magnitude of measured net ecosystem exchange of CO2 (NEE) was reduced during periods when C was low, and also that measured nocturnal NEE was reduced 2 when C was low. This is consistent with the hypothesis that variations in C are due to variations in how well measurements ofH + LE represent T, and that underestimation of exchange impacts the measurement of all three SL fluxes similarly. Finnigan et al. 2003 demonstrated that over tall canopy sites, loss of low-frequency covariance was a significant problem at tall canopy sites when 30-min. averaging times were used, and demonstrated similarity between T and NEE. The objectives of this study were to: (1) determine whether errors in the measurement of A are likely to cause a significant imbalance, (2) utilise spectral analysis to quantify the accuracy of the measurement of T, (3) assess the temporal and spatial behaviour of T to qualify and quantify the occurrence of venting of SL fluxes, and (4) elucidate the similarity between SL fluxes, to determine whether NEE is underestimated when T is underestimated. 1.2 Bas i c Cons ide ra t ions When conducting an energy balance study using EC, fluxes are not measured at the surface itself, but, for R„, H, and LE (and NEE), across a plane at height z above the surface, and for G the plane at depth d below the surface, and so to conduct a full energy balance, the rate of change of energy storage between these 2 planes must also be measured. In order to address the cause of the imbalance it is useful to define the measurements that make up the terms in Eq. (2). Net radiation can be expressed as R n = RSnet + RLne, (3) 3 where Rs„e, and Rmet are the net shortwave and longwave radiation fluxes at the E C height, and Rsne,=Rsd-Rsu (4) RLnel = Rld ~ RLu (5) where the subscripts d and u indicate downwel l ing and upwel l ing fluxes respectively. W e do not measure Ru and RLu directly, but rather the difference between RLd and RLu, and the longwave radiation emitted by the pyrgeometer's sensor surface, RLdP and RLup respectively. Because the bodies o f the downward and upward facing pyrgeometers are in thermal contact and so at the same temperature, RLnel = RLdp ~ RLup (6) In this study G is defined as G = GT +SR + Gh. (7) T G biomass V / where Gj is the conductive heat flux measured by a soi l heat flux plate placed below the soi l surface, SG is the rate o f heat storage change in the soi l between the heat flux plate and the surface, and Gbiomass is the rate o f heat storage change i n aboveground biomass. Implicit in the definition o f E q . (7) is the assumption that there is no non-conductive transfer o f heat across the plane o f the heat flux plate, and that a l l energy storage change between the plate and the surface is sensible (i.e. phase change is ignored) W e w i l l express the S L fluxes as H = HEC+SH+HOLHER (8) 4 LE = LEEC+SLE+LEolher (9) NEE = Fc + SC02 + F0lher (10) I II III IV Term (I) of Eqs. (8)-(10) is the surface-atmosphere exchange for the appropriate scalar quantities. On the right hand side (RHS), term (II) is the turbulent flux at height z, calculated from the covariance of the scalar with vertical wind speed (w), term (III) is the rate of storage change of the scalar between the surface and z, and term (IV) is the transport across the plane at height z due to any processes not measured by the EC instrumentation. Any divergence of upwelling longwave radiation between the surface and EC height (the only significant radiation divergence) would be included in the storage terms in Eqs (8) and (9), and although this may result in a small error in the magnitude of H and LE, it would not affect C. This form of estimating H and LE was used as it was the best estimate of the surface-values, and was also useful when discussing the similarity of SL fluxes. From the definition of T it follows that T = TEC+ST+Tolher (11) I II III IV Systematic underestimation of T could result from the underestimation of terms II or III of Eq (11), or if the term IV is > 0. Term II may be underestimated due to loss of high-frequency or low-frequency covariance resulting from sensor response or separation and averaging/coordinate rotation time respectively. High frequency loss can be corrected by applying a transfer function, which will depend on instrumentation (i.e. time constant, measurement frequency, path averaging, sensor separation and flow rate in the tube of a closed path IRGA), and the actual turbulent cospectra at the site in question (Massman 2000). It may be possible to deal with low-frequency loss by extending the averaging time over which fluxes are calculated, but this also raises the possibility of the averaging time becoming so long that high-frequency deviations of scalar concentrations from the mean become non-meaningful, thereby reducing covariance with w. Term IV may be significantly different from zero due to (a) systematic horizontal advection of fluxes away from points where EC towers are typically placed and (b) spatially homogenous vertical transport of SL fluxes due to processes that are not typically measured by EC, e.g. pressure flux (Massman and Lee, 2002). With regard to (a), Kanda et al. (2004) used large eddy simulation (LES) to show that under convective conditions the flux magnitude in the SL is spatially heterogeneous due to convection cells. Lee and Black (1993) and Lee (1998) proposed that poor closure during unstable conditions was due to non-zero w where the overbar represents a time average. McNaughton (2004) described Theodorsen ejection amplifier like (TEAL) structures, which vent scalars, and may form at preferential locations such as edges or obstacles which distort flow, and minor heterogeneities such as differing albedo or roughness length (McNaughton, pers-comm.). It is unclear whether these venting points would be at random or systematic locations, and what proportion of the excess transport at the vent would be due to mass flow transport (w > 0), which is not discernible by EC systems due to an inherent 2-D or 3-D nature (Finnigan 1999). In order to investigate whether the imbalance was caused by overestimation of A or underestimation of T, we first investigate the accuracy of A , then the accuracy of TEC, 6 before finally ut i l is ing the temporal and spatial behaviour o f T compared wi th A to draw conclusions on the l ike ly magnitude o f T0,her- W e use measurements from 2 long-term E C measurement sites wi th different characteristics (i.e., a clearcut and a forest), and also compare measurements from the long-term E C system in the clearcut wi th measurements from a second system that roved wi th in the clearcut. The a im was to place the roving system such that its footprint w o u l d lie wi th in the same spatially homogeneous area as the main system footprint, and therefore the true flux source strength for the 2 measurements w o u l d be equivalent. Furthermore, the roving system tower was to be placed away from the location o f the main system tower, and close to topographical features, to investigate whether these might result in preferential venting o f S L fluxes at these points. A t such a location, i f some o f the excess transport was turbulent, we expected to find that C consistently exceeded 100%. The advantage o f doing this at a site wi th a long-term tower present was that we could obtain 2 data sets for C simultaneously and so systematic variations in climatic conditions w o u l d not complicate the analysis o f the spatial variation in C. 2 Methods 2.1 Description of sites The O l d Jack Pine (OJP) and Harvested Jack Pine 2002 (HJP02) sites are part o f the B E R M S network, wh ich includes 4 jack pine sites as a chronosequence wi th in the harvest cycle. O J P , approximately 100 k m N E o f Prince Alber t , Saskatchewan, near Narrow H i l l s P rov inc ia l Park, is a 70-year-old jack pine stand that is ca. 15 m tall wi th a stand density o f ca. 1190 trees ha"1 (see Baldocchi et al . 1997; Griff is et al . 2003 for a 7 detailed site description). HJP02 is located ca. 4 km northeast of OJP (53.945 °N, 104.649 °W) at an elevation of 517 m above sea level. The site was logged in August 2000 and the surface scarified in spring 2002, and the ground cover was sparse grass and shrubs and slash left over from harvesting operations (http://berms.ccrp.ec.gc.ca/). Stand density before logging was likely similar to OJP, and post harvest stump height was ca. 0.15 m, with the diameter at this height ca. 0.15-0.20 m. The left over slash piles formed patterned rows (ca. 3 m wide with ca. 4-m wide gaps between the rows, Fig. 1) up to ca. 1 m high, which is characteristic of this type of harvesting operation. We therefore estimated the roughness length to be ca. 0.1 m (10% of the highest significant surface roughness elements), which was confirmed from the ratio of friction velocity (w») to wind speed («) in neutral conditions. The albedo of the site surface in the absence of snow cover was approximately 0.15 ± 0.01 depending on volumetric soil water content (VWC), which had an annual mean when the soil was not frozen of 0.12 mW 3 for the 0-15 cm layer (Fig. 2d). The soil is a sand, with organic matter visible only in the upper 10-20 cm. The leaf area index (LAI) was visually estimated to have increased from 0.2 ± 0.2 to 0.5 ± 0.2 during the growing seasons of 2003 to 2005, and was comprised primarily of grasses and jack pine seedlings. There was also some lichen, which covered most of the surface at OJP, but was largely removed at HJP02 during scarification. The mean Bowen ratio at the site during daytime hours with no snow cover in 2004 was 2.2, and varied from 4.9 during periods when VWC was in the lowest quintile, to 0.97 when VWC was in the highest quintile. During the roving EC experiment period (11/08-04/10, 2004) the mean daytime Bowen ratio was 1.3, and mean air temperature (Ta) at the site was 9.8 °C (Fig. 2b). The mean annual Ta for 2004 was -1.1 °C. Fig. 2 shows the temporal variation 8 o f key climatic variables at H J P 0 2 during 2004. Total dai ly RSJ (F ig . 2 (a))varied from ca. 0.1 to 30 M J day"1 m - 2 , and there were numerous cloudy ( low RSd) days throughout the summer, mean dai ly (24-hr) Ta (F ig . 2 (b)) varied from ca. —40 to 20 °C, mean daily u varied from <1 to >7 m s", and mean daily V W C was conservative, remaining at ca. 0.12 F i g . 1. A e r i a l photograph o f HJP02 showing the layout o f the site, some topography, windrows o f logging slash, and the locations o f roving eddy system. 9 E 30 T>, 20 S 10 S o w 20 0 • -20 -40 <" 5 E O o E 0.1 O I 0 If1 1 to 1 1 1 1 1 I I I I 1 i i i i i i I I i i i i i i i i ' l 1 1 1 1 1 1 1 1 T I 1 i i i i i v ^ ^ ^ ^ i i i i 1 1 1 1 1 1 Jan Mar May July Sep Nov Fig. 2 Climate variables at HJP02 during 2004: (a) Daily total incident shortwave radiation flux (Rsd)- (b) Mean daily air temperature (Ta) at 2 m. (c) Mean daily wind speed (u) at 5 m. (d) Mean daily volumetric soil water content (VWC) at depth 0 - 1 5 cm. 2.2 Flux footprints at HJP02 When doing an energy balance study it is important that the source footprints of the component fluxes lie within the same homogenous area (Baldocchi 2003). SL fluxes usually have a footprint approximately 1-2 orders of magnitude greater than that for A (Schmid 2002), so it was necessary to ensure that the site had adequate homogenous fetch to encompass the SL flux footprint. Table 1 summarizes the results of the footprint analysis for combinations of H, zo, u and stability. 10 For the daytime scenarios xpo% < 130 m, which as seen in Fig. 1, was less than the fetch in all directions for the main system location. For the nighttime scenario x9o% = 500 m, which was greater than the fetch in some directions, and implies that under very stable conditions there may be a small contribution to the flux from beyond the clearcut. However, the wind direction at night was rarely from the south (not shown), which was the direction of minimum fetch, and nocturnal turbulent fluxes did not depend on wind direction (not shown), so these wind directions were not excluded. 11 Table 1. Footprint contributions for x (direction parallel to mean wind) and y (direction perpendicular to mean wind) calculated using a Lagrangian particle dispersion model (Kljun et al. 2002), provided by N. Kl jun (pers. comm.). r\-r6 are daytime scenarios, and V7 is a nighttime scenario. The variables distinguishing scenarios r2-r7 from r/ are printed in bold. 80% and 90% subscripts indicate that, e.g., 80% of the contributions to the total flux are within a distance x < xso% from the tower. xmax is the distance from the tower that had the maximum effect on the flux. ri n rs re >7 / / ( W m - 2 ) 360 360 360 360 100 100 -30 Roughness 0.01 0.01 0.01 0.04 0.01 0.01 0.01 length, z0, (m) -Wind speed, u 4 2 6 4 4 6 2 (ms- 1 ) Stability -0.23 -1.16 -0.08 -0.09 -0.08 -0.03 0.20 parameter, z/L xso% (m) 65 55 62 40 70 80 195 Y80% (m) 25 15 15 17 20 20 35 Xgo% (m) 75 60 98 70 115 130 500 Y90% (m) 30 17 18 20 25 20 60 Xmax (m) 15 7 10 5 15 10 10 12 2.3 Description of locations of the roving EC system The 3 locations of the roving system are shown in Fig. 1. Location 1 was approximately 100 m west of the main tower. The slope that is indicated in Fig. 1 running from the northwest to the southeast across the site is gentle, such that the southwest portion of the site is ca. 2 m higher than the northeast portion, and this elevation change occurs over a horizontal distance of ca. 25 m. Location 1 was chosen because it was in the lee of the steepest part of this slope when the wind was from the prevailing direction (NW). The hypothesis was that the high pressure created in the lee (Kaimal and Finnigan 1994) might lead to a preferential updraft, and therefore induce venting. Location 2 was ca. 5 m from the edge at the south-eastern corner of the site, such that when the wind was from the prevailing direction air travelled across the clearcut before reaching the edge. Relatively dense ca. 15-year-old, 3-4 m high jack pine trees formed the edge in this vicinity, and it was chosen because the rest of the edge facing into the prevailing wind direction was either formed by a road or by less dense trees and bushes, which presented a less significant aerodynamic obstacle to the airflow. Location 3 was on one of the darkest and largest slash piles that form the windrows visible in Fig. 1. The albedo at this location was significantly lower than at the main tower during the same measurement period (0.11 compared to 0.15). It was hypothesized that increased net shortwave radiation might result in elevated surface temperature, leading to convectively driven venting. Table 2 details the roving system data collection periods. 13 Table 2 .. Summary of roving system data collection periods in 2004. Period of data collection (Day of Year) Number of half-hours Comparison 1 224.5 -230.4 (Aug 11-17) 281 Location 1 230.6 - 239.2 (Aug 17-26) 414 Location 2 239.6 - 245.4 (Aug 26-Sept 1) 280 Location 3 245.6-275.4 (Sept 1-Oct 1) 1433 Comparison 2 275.7 -278.5 (Oct 1-Oct 4) 143 2.4 Instrumentation at HJP02 2.4.1 Long-term climate/EC system The main tower was installed at the site in March 2003. At the EC instrument height of 2 m, a CSAT-3D (Campbell Scientific Inc. (CSI), Logan, Utah, U.S.A.) anemometer-thermometer with a sampling frequency of 20 Hz was used to measure high-frequency wind speed and air temperature fluctuations. An LI-7500 (LI-COR, Lincoln, Nebraska, U.S.A.) open-path infrared gas analyser (IRGA), used to measure high-frequency water vapour and CO2 density fluctuations, was installed in March 2003 and removed in November 2004. Calibration was performed in the laboratory prior to deployment. In November 2003 an LI-7000 (LI-COR) closed-path IRGA was installed. A temperature-controlled housing maintained the temperature of the closed-path IRGA at 37 ± 0.5 °C, and a flow rate of 8 L min"1 ensured turbulent flow along the 2-m length of the sampling tube, which had an internal diameter of 4 mm. The IRGA was calibrated 14 daily by saturating the air at the intake (which was within 20 cm of the sonic array) with first a dry N 2 (zero CO2/H2O) gas and then a gas of known CO2 mixing ratio (with roughly atmospheric-CO"2 concentration). A n HMP45C (Vaisala Oy, Helsinki, Finland) temperature and relative humidity (RH) probe placed 1 m above the soil surface provided measurements used to calculate SH and SLE- R-L.net and Rs„et were measured 2 m above the surface using a CNR1 (Kipp & Zonen, Delft, Netherlands) four-way radiometer. GT was measured using 4 soil heat flux plates, 3 HFT3 (Hukseflux, Delft, Netherlands) and 1 CN3 (Middleton, Melbourne, Australia) distributed radially about the tower at a depth of 3 cm, and SG was computed from 2 temperature profiles, each with copper-constantan thermocouples located at the 1-, 2- and 3-cm depths. When calculating SG, to account for the non-linear soil temperature profile we assumed that the mean temperature in the top 3 cm was (2r ] c m + T2cm)/3. V W C of the soil in the 0-15-cm layer was measured using 4 CS615 reflectometers (CSI) distributed radially about the tower. Wind speed (w) at the 5 m height was measured using model 05031 vaned propeller anemometer ( R M Young Co., Traverse City, MI), and presence of surface water was measured using model 237 leaf wetness sensor (CSI). Excluding the IRGAs, all instruments utilised factory calibrations. Climate data was recorded on a 23X data logger (CSI) networked to a site computer which also recorded digital (serial) signals from the sonic anemometer and IRGAs. 2.4.2 R o v i n g cl imate /EC system The roving tower was a C M 10 (CSI) tripod. A CSAT-3D anemometer-thermometer and an LI-7500 open-path IRGA were used to measure the turbulent fluxes. 15 An HMP45C temperature-RH probe at the 1-m height was used to measure SH and SLE-Rsnet and RLnel were measured using a CNR1 four-way radiometer. GT was measured using 4 soil heat flux plates, 2 HFP01 (Hukseflux) and 2 homemade by Dr. M Novak, UBC), and SG was computed from one temperature profile measured with copper-constantan thermocouples. All instruments were the same heights/depths as on the main tower. VWC of the soil was measured at 2-6 cm and also at 8-12 cm below the surface using 2 CS615 reflectometers. Data were logged using a CR5000 (CSI) data logger. 2.5 Data Analysis 2.5.1 Turbulent flux calculations The high-frequency IRGA and sonic anemometer-thermometer signals were temporally aligned by maximising the covariance of the IRGA signals with vertical wind speed. The IRGA signals were allowed to shift by up to 1 second with respect to the sonic signal, to allow for the fact that the delay between the 2 signals can change. This was particularly important with the open-path IRGA because the delay depends on wind speed and direction more than for the closed-path IRGA, as the open-path was placed further from the sonic array, and the delay varied depending on whether air passed first through the IRGA or the sonic arrays. The data were block averaged over 30-minute intervals, and three rotations were performed on each averaging period so that the mean vertical (w ) and lateral (v ) velocity components as well as the covariance between these velocity components (wV) were zero (Tanner and Thurtell 1969), where the prime indicates fluctuation from the mean. The relationship between the rotated and non-rotated flux was the same at the roving locations as it was at the main location (not 16 shown), being that the non-rotated flux was ca. 2% lower than the rotated flux. The small difference is expected when the measurements are made close to a solid surface (Finnigan et al. 2002). 2.5.2 D a t a qua l i ty con t ro l Limits were set for the averages, minima, maxima and standard deviations for the C O 2 and H 20 concentrations, Ta, u, radiation fluxes, and G, in order to remove periods when instruments were malfunctioning. Beyond this, data was visually inspected, and where required the high-frequency time series checked, before half-hourly fluxes were removed. Measurements of Rn were removed during the day and night if there was water indicated by the wetness sensor, as this caused Rup to tend to zero because the water was close to radiative equilibrium with the pyrgeometer. They were also removed at night when A > 0, as systematic low C during these half-hours was likely caused by a thin layer of condensation resulting in spuriously low magnitude net radiation measurements. Turbulent fluxes were removed when 45 < wind direction < 135 degrees from north, as C was systematically low when the wind came from these directions. This was likely due to flow distortion caused by the wind passing through the tower before the EC instrumentation, as the EC instrumentation was installed on the west facing side of the tower at both sites (see Appendix 3). 17 2.5.3 Methods of calculating C Four ways of calculating C for a given time interval were used: 1. The slope of the regression (calculated using the ordinary least squares relationship) of T against A (OLS method). An orthogonal regression was used, as this allows for the fact that there is random measurement error in A as well as T. 2. The mean of the ratio of T to A (MOR method). 3. The ratio of the mean of T to the mean of A (ROM method) 4. The ratio of the median of T to the median of A (ROMed method) 2.5.4 Spectral analysis Turbulent cospectra were calculated for w-Ta and W-H2O mixing ratios. Where different averaging times were used, the high-frequency data was amalgamated into a continuous time series for each respective trace before the cospectra were processed. The respective traces were linearly detrended, and filtered using a Hamming window, before the covariance was calculated for 100 logarithmically increasing frequency ranges and then averaged to 25 frequency ranges for the spectral plots. 2.5.5 Roving system calibration The roving system was placed close to the main system at both the beginning and end of the experiment to determine (a) whether calibrations were needed, and (b) whether they had changed over the course of the experiment. IRGAs and CSATs were within 1.5 m of each other, while the CNR Is were within 3 m of each other. The roving system soil 18 heat flux plates were placed approximately central with respect to the spatial distribution of main system soil heat flux plates. Comparisons of the fluxes did not change significantly between the two periods (not shown). Table 3 gives the coefficients of the linear regressions using data from both comparison periods. Based on the assumption that there should be no systematic difference between the fluxes measured by the systems when the two systems were close together because source areas for the respective fluxes were similar, the slopes and offsets obtained from the system comparison period were used as a calibration to correct the rest of the roving system data set. Table 3. Regression parameters for fluxes measured by the roving and main eddy covariance (EC) systems during the calibration periods: sensible heat flux measured by EC instrumentation (HEC), latent heat flux measured by the EC instrumentation (LEEC), net shortwave radiation flux (Rsnet), net longwave radiation flux {Rmet), and soil heat flux measured by the soil heat flux plates (Gj) Slope" Offset (W m"2 n R> RMSE, (W rn"2) H 0.99 + 0.25 273 1 3.88 LE 1.04 -0.02 211 0.99 5.90 Rsnet 1.00 -2.30 341 1.00 4.97 RLneI++ 1.06 + 3.90 125 1.00 2.65 R„++ 1.00 -10.00 125 1.00 4.35 G 1.20 1.20 335 0.97 7.25 Roving system = Slope * Main system + Offset. The number of data points for RLmt and R„ is less than the other fluxes because they were not logged during the first comparison period. 19 3 Results and Discussion 3.1 Accuracy of the measurement of A 3.1.1 Accuracy of the measurement of R„ at HJP02 Sources of error in measurements can be split into (a) calibration and (b) physical errors. The former refer to errors resulting from faulty calibration. Following Twine et al. (2000) calibration errors are discounted as sources of the systematic imbalance. The latter are caused by climatic effects on radiometers (Table 4), and any systematic spatial heterogeneity between the footprints of R„ and T, which may arise from (i) true spatial variability of the site in question and (ii) inclusion of the tower in the field of view of the net radiometer. Spatial variability of the site is discounted as the cause of the systematic imbalance because across multiple sites, this is a random error, and therefore would not cause a systematic imbalance (Twine et al. 2000), and also good agreement has been found between multiple instruments deployed at the same site (this study (not shown), Twine et al. 2000). 20 Table 4. Systematic errors in the measurement of R„ as given in the specifications for the CNR1 radiometer employed at HJP02. Column 3 gives the magnitude of the error during a typical midday situation"*", where the error has been assumed to have linear dependency. Cause Stated magnitude Magnitude for typical midday situation* There is a spectral gap between longwave and Small N / A shortwave bands resulting in radiation of wavelengths between 3 and 5 Lim not being measured Absorption of longwave radiation by the +15 W m " 2 for RSnet +7.5 W m"2 pyranometers when Rinel = -200 W i r f 2 Heating of the silicon window that covers the +25 W r n 2 for RLd + 12.5 W upward facing pyrgeometer due to absorption of when RSd= 1000 W m"2 shortwave radiation m 2 Temperature gradients induced by using the not stated for the N / A internal heater pyrgeometers, +10 W m"2 for the pyranometers Cooling of the window covering the upward not stated for the N / A facing radiometers at night due to the fact that it pyrgeometer, -15 has a higher thermal emissivity than the air W m"2 for the between the window and the sensor surface pyranometer Water deposition due to rain or dew on the Rinet tends to zero N / A window covering the upward facing pyrgeometer. Typical midday situation is when measurements indicate that Rsd ~ 500 W m" , Rsu = 75 W m"2, RLd = 350 W m"2, andR L u = 450 W i n 2 , givingR n = 325 W m"2. 21 The tower used at HJP02 was constructed of galvanized steel. The albedo (a) and thermal emissivity (e) of the tower were both estimated to be ca. 0.3 (http://www.uppco.com), and the radiometer's field of view (FOV) occupied by the tower was calculated to be ca. 5%. From these values, the albedo and emissivity of footprint viewed by the downward facing pyranometer and pyrgeometer measurement are given by ^footprint ~ 0.95agrOund + 0.05atOwer (12) ^footprint = 0.95 Aground + 0.05s, ower (13) Given that we measured af00,prin, = 0.15, Eq. 12 can be rearranged to give agrou„d = 0.142, and so the inclusion of the tower in the FOV caused af00tprint to be 5.5% higher than 2 • aground- For the typical midday situation, the measurement of Rsu = 75 W m" is an overestimation by 5.5%, or 5 W m"2. We assume that £ground = 0.95. From Eq. 13 s/ootprmt = 0.918, so inclusion of the tower in the FOV caused Sf00,prin, to be 3.5% lower than ground- Making the (questionable) assumption that due to the small diameter of tower bars and high clearcut wind speeds, i.e. high boundary layer conductance, there was efficient exchange of sensible heat between tower surfaces and the atmosphere, it follows that the tower was at approximately the same temperature as the air. The air (and therefore tower) would actually be cooler than the ground, (enhancing the reduction RLU), but for simplicity we make the assumption that they are in thermal equilibrium, which means that reduced thermal emissivity translated directly into reduced RLU, and so RLU was underestimated by 3.5%, or 16 W m"2 for our typical midday situation. 22 These errors in the upwelling radiative fluxes due to the inclusion of the tower in the FOV, as well as those detailed in column 3 of Table 4 imply that for the typical midday situation, R„ is overestimated by 31 W m" or 10%. At night, Rsnet was set to zero, so only the errors in RLd and REu persisted, and R„ being too negative would cause a systematic imbalance. Assuming that the tower was in approximate thermal equilibrium with the surface, it would have the effect of reducing RLU, which is not consistent with causing C to be < 100%. Rr.d would be decreased if the silicon window covering the pyrgeometer was cooler than the thermopile surface and increased if the silicon window were warmer. It was not possible to measure the window temperature of the CNR1 at HJP02, but at OJP, an Eppley Laboratory (Newport, RI USA) model PIR pyrgeometer (Barr et al. 2006) was used to measure RLd, which includes a measurement of the temperature of the window as well as the pyrgeometer sensor temperature. The window was generally cooler than the sensor-surface at night, and so the nocturnal correction was positive, with a magnitude of up to 5 W m"2. Given that the mean of nocturnal A at HJP02 when conditions were considered ideal was -27 W m-2, and nocturnal C under such conditions was ca. 90% (see Appendix 2), it is possible that a correction to RLd, similar to that applied at OJP, would increase nocturnal C to unity at HJP02. This analysis indicates that the error in R„ due to the inherent physical errors associated with making the measurement may be of the appropriate sign and magnitude to be responsible for a significant proportion of the observed imbalance during the daytime and alludes to the possibility that this may also be the case at night. Regardless of the accuracy of the instrument, inclusion of the tower in the FOV introduces 23 systematic heterogeneity between the footprint of A and the footprint of T, and so it cannot be expected that C = 100%. These errors need to be addressed on a site-by-site basis, accounting for specific instrumentation and tower geometry, before defensibly forcing the turbulent fluxes for closure. 3.1.2 Diurnal variation of C: implications for the accuracy of the storage fluxes Examining any systematic features in the diurnal variation of C may provide insight into the accuracy of A . Fig. 3 shows the diurnal variation of C at HJP02 during June 2003, 2004, and 2005. A physical explanation for the consistently low C during sunrise and sunset, which was seen throughout the year (not shown), may be that A was overestimated at these times, because the magnitude of G was overestimated. During these periods A was positive and T was negative or close to zero. Rn was negative, as was G, but with a larger magnitude, and the sun was above the horizon (clear-sky Rsd, Rpoi, calculated assuming constant atmospheric transmissivity from Stull 1998, > 0, not shown). When the sun's zenith angle was large, the amount of energy going into the above ground biomass and debris likely became decoupled from the soil heat flux due to the fact that the angle of incidence can remain low for the above ground biomass because much of it was perpendicular to the surface. At these times, there would be disproportionately more heat flux going into the above ground biomass than the soil surface (even if the net soil heat flux was negative). Gbiomass was not measured at HJP02, but it would make G less negative during these periods, and hence A would be negative or closer to zero, which would increase C. During the rest of the diurnal cycle this was 24 not a problem because (a) Gbhmass was in phase with SG, and (b) SG + Gbhmass was a relatively small percentage of A . If the ensemble average diurnal C were plotted for the entire summer, C would be low due to this effect for longer periods in the morning and afternoon because the time of sunrise and sunset would vary significantly, which is why only data recorded during June are shown in Fig. 3. The fact that SG (and Gbhmass, SH, and SLE) are ca. 90 degrees out of phase with the rest of the energy fluxes (i.e. the storage fluxes were positive in the morning, but negative throughout the afternoon) means that ensemble average diurnal variation of C allows a qualitative analysis of the accuracy of the sum of the storage fluxes, because C would systematically increase throughout the daytime if these fluxes were underestimated, and decrease if they were overestimated. The fact that C remains constant throughout the daytime (excluding sunrise/sunset) is therefore a strong indication that SG was well measured at HJP02. Standard deviations for a given half-hour M O R average were higher during nighttime, and during sunrise/sunset than during the day. This is because (a) fluxes were close to zero, and (b) turbulence can be intermittent at night (Stull 1988), and measured turbulent fluxes are dependent on turbulence. The former means that the ratio for individual half-hours can be large, giving a high standard deviation. The data set can become skewed due to this effect to the extent that the M O R method no longer accurately represents the average C, and because of this a limit was set for the M O R method so that for individual half-hours -100 < C < 200%. The diumal variation of C at OJP is shown in Fig. 4. C consistently increased throughout the day. Given that this behavior was not in phase with the variation of any of the climatic variables that dictate the state of the SL (e.g. Rsd, R H , u*), the likely 25 explanation is that energy storage change between the ground and EC measurement height was underestimated. Factors of 1.5 and 2, applied to (Sn + SLE + Gbiomass) and Gbiomass, respectively, made C constant throughout the day (not shown). 300 200 x ~ >« c LU 100 sunrise Time of day (CST) r 24 sunset Fig. 3. (a) Ensemble averages of R„ - G (available energy flux, A, solid line) and H + LE (total surface layer heat flux, T, dashed line). Data were recorded at HJP02 during June 2003, 2004, and 2005. (b) Mean of energy balance closure (Q for each half-hour, (MOR method, solid line) with error bars representing one standard deviation for each half-hour. Ratio of the mean of Tto the mean of A (ROM method, dashed line). 26 100 -o 50-(b) L 1 1 1 u \ i i 9 1 1 1 -\ I ' I I Il 1_ 6 12 18 24 Time of day (CST) Fig. 4. (a) Ensemble average of A (solid line) and T (dashed line). Data were recorded at OJP between day of year (DOY) 150-300, 2004 and 2005. (b) C using the MOR method (solid line) with error bars representing one standard deviation for each half-hour, and C using the ROM method (dashed line). The standard deviation for a given MOR value during the daytime was higher than at HJP02 (Fig. 3), which, serves as an indication that distinctly different processes influenced the variation of C at the 2 sites. This analysis implies that C at both HJP02 and OJP shows systematic diurnal variation that was likely at least partly due to the accuracy of the storage fluxes contained within A (at sunrise and sunset at HJP02, and throughout the daytime at OJP, due to 27 underestimation of Gbiomass)- Given that climatic variables such as Rsd, R H , u*, and stability all exhibit systematic diurnal variation, i f closure were analysed for dependencies using 1:1 plots of half-hour flux values, spurious relationships would be found. Analyzing C for dependency using either ensemble average diurnal variation or daily values can bypass this problem. We also note that the calculation of the stability parameter, zIL where z is height and L is the Monin-Obukhov length, is not independent of H and LE (or A, i f H and LE are first forced such that C = 100%), and so it is likely that use of zIL would result in spurious dependencies being found because if, e.g., H or LE is underestimated, L would be overestimated, thereby underestimating stability, leading to a spurious positive correlation between C and stability. Furthermore, i f T and N E E were forced for closure on a half-hour time scale, the fact that N E E contains diurnal variations would result in N E E being biased, because e.g. a large correction factor would be applied in the morning, when N E E can be more negative than in the afternoon due conditions being more conducive for photosynthesis. 3.2 Accuracy of the measurement of TEC When calculating turbulent fluxes, it is necessary system that response be fast enough to resolve all significant high-frequency covariance, and that the time period over which the covariance is computed is sufficiently long that there are no contributions to the cospectra at periods longer than the averaging time. This Section investigates both the high-frequency loss of W-H2O mixing ratio covariance due to the system response of the closed-path I R G A , and the loss of low-frequency covariance for both W-H2O and w-Ta cospectra due to insufficient averaging time. 28 3.2.1 U n d e r e s t i m a t i o n of high-frequency LEEc One method of estimating the high-frequency loss of LEEc is to calculate a transfer function (TF) using ensemble-average w-H 2 0 mixing ratio and w-Ta cospectra (TFH2o)- A n un-normalised TFH20 (Tr^o1™) was calculated as the ratio of the un-normalised w-H 2 0 mixing ratio cospectra to the un-normalised w-Ta cospectra, and then normalised by the value of T F H 2 o U N at a certain frequency (/}), below which it was assumed that no high-frequency degradation existed (i.e. T F was set to unity for frequencies below _/}). The underestimation of LEEc was calculated as the ratio of the integral over the entire frequency range of the w-Ta cospectrum multiplied by TFH20, to the integral of the w-Ta cospectrum over the same frequency range without the TF applied. Un-normalised cospectra were used because when individual cospectra were first normalised by the total covariance for the time period, loss of high-frequency covariance in the w-FLO mixing ratio cospectra resulted in incorrect normalisation factors being applied, and because there was a range of incorrect normalisation factors, ensemble-average cospectra became distorted. Implicit in this analysis is the assumption of spectral similarity between the SL fluxes at high-frequency (Stull 1988), and so high-frequency degradation of the W-H2O cospectra relative to the w-Ta cospectra was attributed to slower system response of the closed-path IRGA relative to the sonic anemometer-thermometer. Also the T F is only valid relative to the w-Ta cospectrum, because if there was high-frequency loss for HEc due to the system response of the sonic anemometer-thermometer, the true T F could not be calculated. 29 Fig. 5 shows TFH 2o for the closed-path IRGA at HJP02, for 3 RH stratifications. Data were recorded during July 2004 when H > 100 W m"2 and LE > 75 Wm - 2 . The mean RH for the low, medium, and high RH stratifications was 26, 53, and 72% respectively. The correlation of TFf^o1™ at low-frequency with RH is due to the correlation of the Bowen ratio with RH, i.e. when RH was high, the Bowen ratio was low, and so the ratio of un-normalised cospectra (which is the inverse of the Bowen ratio) was higher when RH was high. The reduction of the ratio of the cospectra at high-frequency indicates that LEEC exhibited high-frequency degradation at all RH stratifications. Furthermore the reduction appeared to begin at lower frequencies when RH was high. Selecting/; was somewhat subjective, but bearing in mind that there was not necessarily spectral similarity for the SL fluxes at low-frequency (due to different source locations), and that there was more variation in the cospectra at low frequencies due the fact the spectral bins contained fewer points, based on the data in Fig. 5 it was assumed that for low R H / = 0.3 Hz, and for high RH// = 0.05 Hz. Generally speaking, the slowest component of a closed-path IRGA system is the sample tube, and so comparison of the W-H2O cospectra for the closed-path system to the W-H2O cospectra for the open-path system (which measures air in-situ), shown in Fig. 6, can be used to gain confidence in the values of/. The cospectra contained in the data in Fig. 6 were for the same half-hours as for the corresponding RH stratifications in Fig. 5 Relative to the open-path, the closed-path system appears to exhibit high-frequency degradation above/= 0.3 Hz during the low RH half-hours, and above/= 0.05 Hz for the high RH half-hours. This independent method of determining/ provides confirmation of the values estimated from Fig. 5. 30 1.2 TO I 0.8 Q. If) O O M— o o CD 0.4 \ I \ I M i \ - -HJP02 0.001 0.01 0.1 f(Hz) 10 Fig. 5. Ratio of ensemble average vertical wind speed (w)-H20 mixing ratio cospectra to w-7; cospectra, stratified by relative humidity (RH): RH < 30 (solid line), 50 < RH < 57 (dashed line), and 60% < RH (dotted line). Data were recorded during July 2004 at HJP02 when HEC > 100 W m"2, LEEC > 75 W m'2, and C0 2 flux measured by the EC instrumentation (Fc) > 0 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 22, 20, and 18 respectively, and the mean RH for the low, medium, and high RH stratifications was 26, 53, and 72% respectively. 31 0,001 0.01 0.1 1 10 f(Hz) Fig. 6. Ratio of ensemble average W-H2O mixing ratio cospectra for the closed-path system to w-H20 mixing ratio cospectra for the open-path system, stratified by RH. Data were recorded at HJP02 during the same half-hours as the corresponding RH stratifications shown in Fig. 5. The impact that a given transfer function has on the measured covariance depends on what proportion of the true covariance was above fj. Fig. 7 shows the w-Ta cospectra for the same half-hours as shown in Fig. 5 and Fig. 6, but stratified by u*. The cospectra are un-normalised, so that the area under the curve represents the total covariance, or kinematic flux. Relative to the w-Ta cospectrum for all-u*, there was a greater proportion of high-frequency transport when u* was high, and less when u* was low, due to the 32 tandem effect that high u* half-hours correspond to high u half-hours, and so eddies were transported past the sensor at higher frequency, and for these roughly similar climatic conditions, low u* half-hours corresponded to more unstable conditions, which tend to exhibit a greater proportion of low-frequency transport (Finnigan et al. 2002). The underestimation of LEEc during the high and low u* half-hours shown in Fig. 7, due to the TFs based on the data in Fig. 5 is shown in Table 5. f(Hz) Fig. 7. Ensemble-average w-Ta cospectra stratified by friction velocity («*): u* < 0.4 (dashed line), all u* (solid line), and u* > 0.7 m s"1 (dotted line). Data were recorded at HJP02 during the same half-hours as the data shown in Fig. 5, and the low-, all-, and high-w. stratifications contain 13, 153, and 18 half-hours, respectively. 33 Fig. 8 shows TFH20 for data recorded at OJP. TFH20 shows less variation in the low-frequency for the RH stratifications, indicating that the Bowen ratio was not as strongly correlated with RH at OJP as it was at HJP02. TF H 2o U N shows similar reduction at high-frequency as at HJP02 (Fig. 5), indicating qualitatively similar high-frequency degradation of LEEC. As with the discussion of Fig. 5 for HJP02 data, the choice offi was subjective, particularly for the high RH stratification. However, based on the data in Fig. 8, for the low RH stratification, it was assumed that fi = 0.6 Hz, and for the high RH stratification, 2 TFs were calculated: firstly assuming/} = 0.4 Hz, and secondly assuming f, = 0.06 Hz. The w-Ta cospectra for the same half-hours that are shown in Fig. 8 are shown in Fig. 9. The w-Ta cospectrum peaked at lower frequencies than at HJP02, and so although there was a qualitatively similar shift to high/low frequencies during high/low u* periods, the proportion of transport at frequencies above / / was lower than at HJP02, and so the TFs calculated for OJP had less impact than at HJP02. The underestimation of LEgc during the high and low u* half-hours shown in Fig. 9, due to the TFs based on the data in Fig. 8 is shown in Table 5. A further point on the w-Ta cospectra for HJP02 (Fig. 7) and OJP (Fig. 9) is that regardless of the u* stratification, the covariance dropped to zero at high-frequency (at HJP02, when 100 frequency ranges were retained, the cospectra were closer to zero at the high-frequency cut-off than they are in Fig. 7, not shown, which is an artefact of using only 25 frequency ranges in Fig. 7), implying that the system response of the sonic anemometer-thermometer was sufficient to resolve all significant high-frequency covariance at both sites. 34 low RH - - med RH high RH > O J P 0.001 0.01 0.1 1 10 f(Hz) Fig. 8. Ratio of ensemble average W-H2O mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during July and August 2003 at OJP when HEC > 150 W m"2, LEEC > 100 W m"2, and FC < -5 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 21, 19, and 21 respectively, and the mean RH for the low, medium, and high RH stratifications was 35, 45, and 68% respectively. 35 all u, - - low u. high i f(Hz) Fig. 9. Ensemble-average w-Ta cospectra stratified by u*. u* < 0.4 (dashed line), all-w* (solid line), and u*> 1.1 m s"1 (dotted line). Data were recorded at OJP during the same half-hours as the data shown in Fig. 8, and the low-, all-, and high-u* stratifications contain 10, 109, and 9 half-hours respectively. 36 Table 5. Summary of the underestimation of LEEC due to high-frequency attenuation of H 20 variance in the sample tube of the closed-path IRGA. Transfer functions (TFs) were calculated based on the data shown in Fig. 5 (HJP02) and Fig. 8 (OJP) for the low and high RH stratifications, and set to unity below frequencies f. Underestimation of LEEc was calculated as the difference from unity of the ratio of the integral of the w-Ta cospectra over all frequencies with the appropriate TF applied, to the integral of the w-Ta cospectra over all frequencies without the TF applied. The w-Ta cospectra for the high and low u* stratifications are shown in Fig. 7 (HJP02) and Fig. 9 (OJP). Site RH stratification U* stratification //(Hz) Underestimatio n ofLEEC (%) HJP02 Low Low 0.3 5 Low High 0.3 8 High Low 0.05 24 High High 0.05 31 OJP Low Low 0.6 0 Low High 0.6 2 High Low 0.4 0 High High 0.4 3 High Low 0.06 3 High High 0.06 12 37 This analysis indicates that underestimation of LEEC due to attenuation of high-frequency H2O mixing ratio variance was significant, particularly at HJP02, where/} was closer to the spectral peak than at OJP. The impact on C would depend on the particular TF that was in effect, the content of the true W-H2O cospectrum, and the Bowen ratio during the measurement period. It was unclear whether the sample tubes were unusually dirty during the periods analysed, and further analysis detailing the progression of the TFs with time since a "good" sample tube was installed is required, both to correct archived values of LEEC, and develop a protocol for long-term EC monitoring. Similar analysis for Fc indicated that there was high-frequency degradation of Fc relative to HEc, but that the magnitude of the loss was not correlated with RH, as the TF for CO2 (TFC02) did not depend on RH ( see Appendix 1). The results in Table 5 may lead one to suspect that the systematic imbalance at HJP02 was entirely due high-frequency degradation of LEEC- This can be investigated by plotting C as a function of the ratio of LEEc to HEc, as in Fig. 10. For approximately similar climatic conditions, i.e. Rpot> 500 W m-2, C decreased as the ratio ofLEEc to HEc increased. However, if the imbalance were entirely due to underestimation of LEEC, C would equal unity when true LE was zero. Visual extrapolation of this graph indicates C was approximately 90% when LE = 0, so even when LE was very small, a systematic imbalance persisted (which was of the appropriate magnitude as to be consistent with the overestimation of R„ proposed in the previous Section). Furthermore, the imbalance also persisted at night, when LE was close to zero. 38 87.5 h L E E C / H E C Fig. 10. C as a function of LEEC I HEc- Data were recorded at HJP02 between May and September, 2004 and 2005, when clear-sky Rsd (RPot) > 500 W m"2, and have been bin averaged by LEECIHEC. Also shown is the standard error in the mean for each bin. 3.2.2 Loss of low-frequency covariance due to insufficient averaging time An averaging time that is too short would lead to a loss of low-frequency covariance, and tend to reduce the magnitude of the computed flux. Finnigan et al.(2002) present data where increasing the averaging (and coordinate rotation) period to 4 hours improved C to 100%. The w-Ta cospectra for HJP02 (Fig. 7) and OJP (Fig. 9) show marked differences at low frequencies. At HJP02 the covariance dropped to zero at low-frequency (the cospectra better approached zero when 100 frequency ranges were 39 retained, not shown), indicating that the 30-min. averaging time was sufficient to capture all of the low-frequency covariance, whereas at OJP, for both the low and all-w* stratifications, the cospectra did not drop to zero at low-frequency, indicating that SL fluxes were underestimated due to insufficient averaging time. Fig. 9 thereby provides significant qualitative insight into the systematic imbalance at OJP: when u* (and RH) was high, underestimation of L E E C became significant, being underestimated by up to 12% during the high-RH half-hours shown in Table 5, and likely more when R H was higher still. Conversely, when u* was low (or indeed average), there was significant covariance at periods longer than 30-min., and so TEC was underestimated due loss of low-frequency covariance. The positive correlation between C and u* during the daytime at OJP (Barr et al. 2006, Appendix 4) is consistent with the underestimation of TEc when u* was low, due to low-frequency loss, having greater impact than the underestimation of TEC when u* was high, due to high-frequency degradation of LEEC- Considering the cospectral content shown in Fig. 9, this would be expected, as it appears that the full low-u* cospectra would have greater contribution at frequencies lower than 10"3 Hz, than the high-w* cospectra have above/; Hz. In order to confirm that the 30-min. averaging time was sufficient at HJP02, and quantify the underestimation of TEC due to loss of low-frequency covariance at OJP, E C fluxes for the 2 sites were calculated using longer averaging periods. The regression parameters for TEC, calculated using a block average over longer periods, to the mean of the 30-min. fluxes that made up the longer periods are given in Table 6. As expected from the low-frequency content of the w-TA cospectra, longer averaging periods did not increase TEC at HJP02. Conversely, at OJP, TEC increased as averaging period increased. 40 When linearly-detrended fluxes were compared, the qualitative effect of increased averaging period was similar, but the slopes of the regression were ca. 2% lower (not shown). Table 6. Regression parameters for TEC computed using longer averaging period, against TEC computed using a 30-minute averaging period. The 30-minute fluxes were averaged over 2, 4, or 8 periods, for comparison with the 60, 120, and 240-minute fluxes, respectively, and the regressions included data for the entire diurnal cycle. Data were recorded during July 2004 at HJP02 and during July and August 2003 at OJP. Site Averaging Slope* (95% Intercept (W rrf ) n RMSE time(mm.) confidence bounds) (95% confidence bounds) (W m"2) HJP02 60 1 (1.03,0.98) 0.74(1.06, 0.43) 535 0.97 9.32 120 0.98 (0.96, 1.00) 3.62 (1.96,5.28) 266 0.95 9.71 OJP 60 1.04 (1.03, 1.05) -0.09 (-1.68, 1.5) 1331 0.98 26.85 120 1.07(1.08, 1.06) -1.8(-5.05,1.65) 664 0.96 35.23 240 1.1 (1.13, 1.08) 4.15 (-0.12, 8.42) 326 0.92 47.31 e.g. TEc60mm = Slope* TEc30min + Intercept Fig. 11 shows the ensemble-averaged cospectra for w-Ta (Fig. 11 (a)) and W-H2O mixing ratio (Fig. 11 (b)) recorded between 1000 and 1400 C S T at OJP during July and August 2003, for a 30-min. averaging period (solid line), and a 240-min. averaging period (dotted line), plotted so that the area under the curve represents the kinematic flux. It is clear from the low-frequency content of the cospectra that the 30-min. averaging period was insufficient, and that an averaging period of 240-min. was required to recover the low-frequency covariance. When the cospectra for the 60 and 120 min. averaging 41 periods were included, they terminated progressively closer to zero in the low-frequency (not shown). When similar analysis was applied to data from HJP02, the cospectra dropped to zero at low-frequency regardless of the averaging time (not shown), verifying that 30-min. period was sufficient These results provide qualitative explanation for the increase of TEC with averaging time at OJP. Quantitative consistency is indicated by the fact that the kinematic flux for the 30-min averaging period was 90 and 87% of the kinematic flux for the 240-min. averaging period for HEc and LEEc respectively , which is consistent with the slope of 1.1 given in Table 6 for the regression of TEC calculated using a 240-min. averaging time against TEC calculated using a 30-min. averaging time. 0.02 U o S u 0.01 P i I 2 E 0.0001 0.001 0.01 0.1 f(Hz) . — . — r " i — «•" I (a) w-T y ^ N . i i OJP X10" 3 i i i (b) w-H 2<0 mixing ratio OJP •'•'*• i i > 10 42 Fig. 11. Ensemble average cospectra of w-TA (a) and W-H2O mixing ratio (b) for 30-min. averaging period (solid line) and 240-min. averaging period (dotted line). Data were recorded at OJP between 1000 and 1400 CST during July and August 2003. The increased TEC at OJP when longer averaging periods were used resulted in increased C, to a maximum of 90% for the 240-min. averaging time, as detailed in Table 7. The remaining imbalance was likely not an artefact of insufficient averaging time, because, at least during the hours of 1000-1400 CST, 240-min. appeared to be sufficient to recover all of the low-frequency covariance (Fig. 11). Also, the underestimation of LEEC due to high-frequency attenuation of H2O variance likely did not account for such a large imbalance. No nocturnal u* threshold (u*th) was applied to the data before calculating the OLS closure given in Table 7, because the validity of comparing 240-min fluxes with non-contiguous 30-min fluxes was questionable, but such a treatment may have increased C for all averaging periods. However, it is also likely that when longer averaging periods were used, conditions were sometimes non-stationary within the averaging period, reducing covariance, and therefore C was reduced when the regression included fluxes from all times of day (as was the case for the values in Table 7). Similar analysis as shown in Fig. 11 but for data recorded between 0600 and 1000 CST is shown in Fig. 12. The 30-min. cospectra did not drop to zero at low-frequency, implying that a 30-min. averaging time was insufficient to capture the low-frequency covariance. The 240-min cospectra did drop to approximately zero at low-frequency, but relative to the 30-min cospectra, covariance was reduced at all frequencies. High frequency deviations of scalar concentration from the mean (or linear detrend) during non-stationary 43 conditions are not representative of physical transport phenomena, and therefore covariance with w would be reduced (it would unlikely be increased, as generally speaking the maximum covariance between w and scalar concentration that may be obtained is the true covariance). This may imply that during non-stationary periods such as the early morning, the averaging time required to capture all of the low-frequency covariance was necessarily too long to retain the high-frequency covariance, ergo E C fluxes cannot quantify the true ecosystem-atmosphere exchange in such circumstances. Clearly further investigation detailing the relative merits of long and short averaging periods during these times is required, but if it was the case that in such circumstances, 'long enough was necessarily too long', forcing the turbulent fluxes for closure would be the legitimate and required treatment. The similarity between the w-TA and W-H2O mixing ratio cospectra at OJP during such conditions implies that assuming the appropriate transfer function has been applied to correct for high-frequency degradation of LEEC, the Bowen ratio was likely well-measured, and therefore the turbulent fluxes should be forced for closure whilst retaining the measured Bowen ratio. Section 3.4 utilises 30-min fluxes to elucidate the similarity between TEC and N E E , but we note that the spectral similarity extended to the W-CO2 mixing ratio cospectra (see Appendix 1), which served as an initial indication that the same correction factor should be applied to N E E . Forcing for closure would need to be undertaken at the sub-diurnal time-scale, because both the accuracy of the SL flux measurements, and the true SL fluxes, contain strong diurnal trends, and so assuming that e.g. the accuracy of FC was equal during both midday and the early morning, would lead to a systematic bias. 44 This result places an onus on the accuracy of A , and particularly the storage fluxes. They are out of phase with R„ and TEC (and NEE) and so e.g. a constant underestimation (as was posited to be the case at OJP), would tend to make C low in the morning, and high in the evening, and so the closure-based correction factors would have a magnitude that varied with the true magnitude of the SL fluxes, thereby biasing long-term sums. 45 Table 7. Regression parameters for Tagainst A at OJP using different averaging periods for TEC- A was averaged over 2, 4, or 8 periods, for comparison with the 60, 120, and 240-minute fluxes, respectively. The data are for the same period as in Table 6. Averaging Slope* Intercept (W m") n R> RMSE time(mm.) (W m2) 30 0.84 7.2 2649 0.9 52.46 60 0.87 7.5 1328 0.94 43.33 120 0.88 8.2 661 0.94 42.83 240 0.9 15 316 0.91 50.31 u o S u e.g. Tio = Slope*^jo + Intercept x10~' © £ s s S u 0.0001 0.001 0.01 0.1 f(Hz) Fig. 12. Ensemble average w-Ta cospectra (a) and W - H 2 O mixing ratio cospectra (b) for 30-min. averaging period (solid line) and 240-min. averaging period (dotted line). Data were recorded at OJP between 0600 and 1000 CST during July and August 2003. 46 3.3 Spatial and temporal variability of the SL fluxes at H J P 0 2 -implications for the existence of venting 3.3.1 Similarity of C at different spatial locations - implications for the existence of systematic venting locations The roving locations were chosen to test the hypothesis that an imbalance arose at HJP02 due to systematic advection and subsequent venting at minor topographical features, and that some of the excess transport at the vent location was discemable to EC measurements. During the daytime venting would occur due to heterogeneities in airflow in the SL resulting in w> 0 at some locations, which would then induce advection. Transport due to w> 0 is not measured by EC systems but it is plausible that at such a venting position, turbulent transport would also be increased, and so qualification of venting with EC measurements would be possible. Conversely, at night, the fact that the SL is stable means that advection may be associated with drainage flows, which could all occur below the EC measurement height, and when turbulence resumes at some later time, all the transport may be turbulent (without w deviating from zero), and therefore quantifiable using EC. Table 8 details the spatial variation in C at HJP02, comparing C measured by the roving system with C at the main system during the same period (calculated using the OLS method). C at the roving location was considered to be different to the main tower location if the mean of the slope of the regression of one system was outside the 95% confidence limits of the slope of the other. At Location 1, C for the roving and the main systems was the same. At Location 2, the roving system appeared to achieve better 47 closure than the main system. However, if only wind directions for which the footprint was predicted to lie entirely within the clear cut were included, the slope of the closure regression decreased from 0.95 (0.91, 1.00) to 0.91 (0.83,0.99). The increased spread of the 95% confidence bounds was partly due to the reduced number of data points. If these rigorous conditions were applied, C at Location 2 was not significantly different to the main system. At Location 3, C for the roving system was significantly lower than at the main system. The probable explanation is that the footprint of A did not represent the footprint of T. The albedo of the footprint of A was lower, and therefore net shortwave radiation was higher. However, the footprint of TEC did not fall entirely within the slash pile, and so the high R„ was not representative the footprint of TEC- Fig. 13 elucidates this point, showing that A was 20% higher at roving Location 3 compared to the main location, whereas TEC was only 7% higher, which is consistent with the footprint of TEC falling partly, but not entirely, within the slash pile. This emphasizes the fact that when doing a C analysis it is necessary that the footprints of the respective components of Eq. 1 lie within the same homogenous area. This analysis indicates that there was no significant difference in C between any of the roving locations and the main system location caused by systematic venting. If systematic venting were occurring (and some of the excess transport at the venting point was turbulent), then none of the three locations was a venting position, and moreover, they were not sufficiently closer or further from a venting position that a significant difference in C was observed. 48 Table 8. (a)-(c). Regression parameters of T against A for the main system and roving system. (a) Location 1. Slope (95% Intercept (W m"2) N R2 RMSE confidence bounds) (95% confidence (W m"2) bounds) MainC 0.89 (0.86,0.91) -3.09 (-7.16,0.99) 252 0.96 21.64 Roving C 0.88 (0.86,0.91) -10.46 (-14.4, -6.51) 222 0.97 22.25 (b) Location 2. Slope (95% Intercept (Wm2) N R2 RMSE confidence bounds) (95% confidence (Wm2) bounds) Main C 0.84 (0.79,0.89) 3.55 (-1.35,8.45) 155 0.90 24.05 Roving C 0.95 (0.91, 1.00) -6.31 (-11.88,-0.75) 152 0.92 26.09 0.91 (0.83,0.99)+ -7.84 (-18.16, 2.48)+ Roving C when wind direction is such that the footprint for the roving turbulent fluxes is expected to lie entirely within clearcut. (c) Location 3. Slope (95% Intercept, Wm'2 N R> RMSE confidence bounds) (95% confidence bounds) (Wm2) MainC 0.82 (0.81,0.83) 3.00 (1.17,4.84) 812 0.94 22 AI Roving C 0.74 (0.73, 0.75) 3.1 (1.7, 4.36) 803 0.97 16.19 49 3.3.2 Temporal and spatial variability of the SL fluxes at HJP02 -implications for the existence of random venting locations Regardless of whether EC measurements are able to quantify transport at a vent location, the existence of venting would lead to increased variability in T relative to A , because the relative magnitude of advected fluxes would be correlated with climatic conditions, which exhibit strong diurnal and seasonal variations. If some of the excess transport at the vent location was discernable to EC, the variability of TEC would be further increased if the vent location were random, so that the distance from the tower varied. Fig. 13 utilises the roving data set to investigate spatial variation of TEC versus A . One statistic applicable to the evaluation of this data set is the statistical error, i.e. spread of the 95% confidence bounds, of the slope of the regression. The statistical error in the slope for A was ± 0.012, while for TEc it was ± 0.013. The same statistical errors when the two systems were side by side (not shown) were 0.015 and 0.011 for A and TEc, respectively. Separating the two systems did not significantly increase the scatter in TEC, and, moreover, TEC shows approximately the same scatter as A . This result implies that at any one point in time, TEC was well adjusted over a spatial scale on the order of the clearcut and so randomly located venting likely did not occur at HJP02. Further evidence to support this conclusion is that the coefficients of determination given in Table 8 were regularly > 0.95, which implies that the variation in Twas almost completely determined by the variation in A , and was therefore temporally well behaved. 50 0 200 400 Main A(Wm"2) MainTE C(Wm"2) Fig. 13 (a) Regression of A measured by the roving system against A measured by the main system, (b) Regression of TEC measured by the roving system against TEc measured by the main system. See Table 9 for regression parameters. The data were recorded while the roving system was at Location 3. 51 Table 9. Regression parameters for the spatial variation in A and the spatial variation in TEC at HJP02 (data shown in Fig. 13). Slope* (95% Intercept* (W m"2) (95% n R} RMSE confidence bounds) confidence bounds) (W m"2) A 1.21 (1.20, 1.22) -1.39(-2.87, 0.10) 870 0.98 19.056 TEC 1.07 (1.05, 1.08) -0.50(-1.87,0.86) 870 0.97 17.421 +Roving = Slope * Main + Offset. For the case of randomly located venting positions, if the measurement period was sufficiently long, the venting location would sometimes coincide with the tower location. In a dataset of many half-hour periods, TEC would therefore be positively skewed relative to A , as it would sometimes be very high. Fig. 14 shows the skewness calculated for fluxes at OJP and HJP02 after they were first binned by time of day. The systematic diurnal variation in skewness that is observed in Rsd, A and TEc in Fig. 14 (a) and (b) is expected because of the seasonal variation in Rsd, and the same pattern was seen in the skewness of Rpot (not shown). The skewness of Rsd was included as a reference for the 'base' skewness. Fig. 14 (a) shows that the skewness of TEC at OJP was systematically higher than the skewness of A . It is unclear whether this was an artefact of the insufficient averaging time (Section 3.2.2), or whether it was indicative of the existence of random venting at OJP. Fig. 14 (b) shows that the skewness of TEC at HJP02 was similar to the skewness of A , and therefore that turbulent fluxes were temporally well behaved, and so provides further evidence that randomly located venting likely did not occur at HJP02. 52 \ (b) HJP02 1 ,-1 • v / * s > > ^ / / / 1 1 in <D c CO -1 6 12 Time of day (CST) 18 Fig. 14. Diumal variation of skewness: A (solid line), TEC (dashed line), and Rsd (dotted line) at OJP (a) and HJP02 (b). Skewness was calculated from the half-hourly flux values, for each hour of the day, i.e. fluxes were first binned by hour of the day, and then the skewness was calculated for the distribution of all the fluxes within a given hour. Data were recorded during daylight hours (Rpol > 0 W m-2) between May and October, 2004 and 2005. 53 3.4 Similarity between S L fluxes From the theory of similarity of the transport of scalars in the SL, we would expect that if there was variation in C caused by either advection and subsequent venting, or loss of low-frequency covariance, then the relative magnitude of Fc would covary with TEC-Fig. 15 shows a light response curve for OJP data, stratified by C. The data were recorded during the summer, when downwelling photosynthetically active photon flux density (Q) was expected to be the primary forcing variable on NEE, i.e. when the temperature was above 5 °C, and there was no water stress on the trees. During this period there was no seasonal trend in C (not shown), which if coupled with the seasonal trend in Fc, could produce the results seen in this graph. This light response curve, stratified by C shows that during the daytime (Q > 0), for a given level of Q, the magnitude of Fc was reduced when C was low. The values of Fc for Q = 0 show that during the nighttime, the magnitude of Fc was also reduced during periods of low C. When measured NEE was plotted instead of Fc (not shown), the same pattern was observed, and so the reduction in the magnitude of Fc during low C periods-was not compensated for by Sco2- Furthermore, the behaviour was not explained by diurnal covariance of Fc and C, because for Q > 500 umol m"2 s"1, there was no diumal covariance of C and Fc. 54 2 i E -4 -6 1 -\ - » O J P "i " i . . . 20 < C <65 -65 < C < 85 - - 85<C<150 : % «E » --V \_ • •••I-. v ' - - I -•-J .j 1 0 400 800 Q (u. mol m" 2 s" 1) 1200 Fig. 15. Fc as a function of down welling photosynthetically active photon flux density ( 0 . Data were recorded at OJP during summer, 2004 and have been bin averaged, and stratified by C. C during the daytime (Q > 0) using the MOR method was 53%, 75%, and 102% for the low, medium, and high C stratifications respectively. Also shown is the standard error of the mean for each bin. 55 During the daytime Q is expected to be the main driver of NEE, whereas Fig. 15 implies that the fraction of NEE that is measured as F C , was dependent on C. This is consistent with the hypothesis that the variation in C was caused by the accuracy of the measurement of TEC, and that F C was affected in a qualitatively similar way. Approximate quantitative similarity is indicated by the fact that for Q > 400 umol m"2 s"1, C using the MOR method was 53, 75, and 102% for the low, medium and high C stratifications respectively, and that the ratio of the mean of F C for the low and medium stratifications to the mean of F C for the high stratification was 0.42 and 0.74, respectively. Further quantitative insight into the similarity between the SL fluxes can be gained by restricting analysis to periods that were thought to have similar climatic conditions, and looking at how the magnitudes of A, HEC, LEEc, and FC covaried as C varied. Half-hours were deemed to be similar when Q > 900 umol m"2 s"1, 8 < TA < 18°C and 0.07 < VWC < 0.2, as these measurements were independent of the measurements of A , TEC, and F C . Fig. 16 shows A, HEC, LEEC, and FC, for these 'similar' half-hours, all normalised by their respective values at C = 100%, for OJP during the summers of 2003, 2004, and 2005. A did not covary with C, and there was an approximately linear relationship between all three EC fluxes and C. 56 C(%) Fig. 16. Normalised fluxes plotted against C: A (dashed line), HEc (dot-dashed line), LEEC (solid line), and FC (dotted line), normalised by their respective means when 0.98 < C < 1.02. Data were recorded at OJP when (Q > 900 umol m"2 s"1, 8 < TA < 18°C and 0.07 < VWC < 0.2) during 2003, 2004, and 2005, and have been bin averaged, with 150 half-hours in each bin. When the respective storage terms were included in the SL fluxes the same pattern was seen (not seen). The fact that the normalised values of both HEC and LEEC were correlated with C is taken to imply that it was these fluxes that caused C to vary. A could only be responsible for the observed variation in C if it was overestimated by ca. 40% during periods of low C. When similar analysis was applied to the normalised 57 values of Q, T A , and VWC, they were all constant (not shown), which lends further weight to the conclusion that the half-hours shown in Fig. 16 were indeed, on average, similar, and makes it extremely unlikely that the variation in C was caused by the accuracy of A . Fig. 16 provides strong evidence that (a) the variations in C in the OJP data set were due to the variations in how much of the true sensible + latent heat exchange was measured as turbulent fluxes, i.e. variation in the ratio of 77 TEC, and (b) the variation in TI TEC was controlled by a process that had both a qualitatively and quantitatively similar impact on all of the turbulent fluxes. Regardless of whether this process was entirely the insufficient averaging time employed at OJP, or also included systematic advection and subsequent venting of SL fluxes, the data in Fig. 16 corroborates the results of the spectral analysis in Section 3.2.2, that TEC should be forced for closure while retaining the measured Bowen ratio, and that the same factor should be applied to F C . Similar analysis as presented in Fig. 16, applied to data from HJP02, is shown in Fig. 17. As was the case for OJP data, when Q, T A , and VWC were plotted, they were approximately constant (not shown), implying that on average the half-hours were indeed similar. In contrast to OJP, A was not constant, but was high when C was low, which is consistent with the hypothesis that variation in A caused at least some of the variation in C. LEEC was relatively constant, and HEC fell close to the 1:1 line. It is possible that this behaviour was entirely explained by the underestimation of LEEC- It was shown in Fig. 5 and Fig. 10 that LEEC was underestimated at HJP02 due to instrumentation issues, and therefore C was lower when the Bowen ratio was low (due to the tandem effect that LEEc was a large fraction of the energy balance, and that such half-hours tended to occur when 58 RH was high, and so the high-frequency degradation of LEEC was more pronounced). If T was constant for the half-hours shown in Fig. 17 then any decrease in H would be balanced by a corresponding increase in LE. If the increase in LE was not measured, then the behaviour see in Fig. 17 would be expected. The fact that F C was relatively constant may be a reflection of F C being correctly measured throughout these 'similar' half-hours. This analysis indicates that the variation in C at HJP02 was due to instrumentation issues affecting both A and LEEC, and this, combined with the fact that there was not similarity between FC and TEC, serves as a further indication that venting does not occur at HJP02. Considering this, and the results in Section 3.2.1 showing that the w-TA cospectra dropped to zero at both low and high-frequency, it seems likely that the only underestimation of SL fluxes was that due to instrumentation issues leading to high-frequency degradation of LEEc (and FC), and that the most defensible values for the SL fluxes would be to account only for these errors, thereby assuming that the remaining imbalance was due to the overestimation of A . 59 * i * • A i i HJP02 1.1 L E E C ^ ' 1 i _ -•' 1:1 1 H 0.9 EC 0.8 -:>f" r" F , x 0.7 " ' • *' 1 60 70 80 90 100 C(%) Fig. 17. Normalised fluxes plotted against C: A (dashed line), HEc (dot-dashed line), LEEC (solid line), and TC (dotted line), normalised by their respective means when 0.98 < C < 1.02. Data were recorded at HJP02 when (_> > 900 umol m"2 s"\ 8 < TA < 18 °C, and 0.07 < VWC < 0.16) during summer 2003, 2004, and 2005, and have been bin averaged, with 200 half-hours in each bin 60 4 Conclusions 1) There are systematic errors in the measurement of R„ that can be responsible for a significant portion of the imbalance. These errors are correlated with climatic conditions because they depend on climatic influences on the radiometers, and the climate would also influence the radiative inequality between the tower material and the ground surface (e.g. this would be different if they were wet than if they were dry). The magnitude of this error will therefore be correlated with NEE, and so NEE would be biased if the error in Rn were assumed to be constant (including zero). Rigorous quantification of the dependency of the error in R„ on climatic conditions, including the influence of the tower, is required before defensibly forcing the SL fluxes so that C = 100%. This needs to be done on a site-by-site basis, accounting for varying instrumentation and tower geometry. A 2) The magnitude of the storage fluxes between the ground and the EC height was likely underestimated at both HJP02 and OJP: due to the decoupling of Gthmass (which was not measured) and SG during sunrise and sunset at HJP02, and throughout the day at OJP. If the SL fluxes need to be forced for closure on a sub-diurnal time scale (due to the accuracy of EC measurements varying at such time scales) it is imperative to address the accuracy of the storage fluxes, because they are out of phase with the SL fluxes, and so failure to do so would introduce systematic biases. 3) LEEC was underestimated due to high-frequency attenuation of FLO mixing ratio in the sample tube of the closed-path IRGA. The impact on LEEC was positively correlated with RH due to the attenuation beginning at lower frequencies when RH was 61 high, and was posi t ively correlated wi th u*, illustrated by the fact that the w-TA cospectra had greater high-frequency content when u* was high. This error w o u l d be correlated with N E E because it depends on R H (which is correlated wi th RSd), and the B o w e n ratio (which is correlated wi th V W C ) , and so N E E wou ld be biased i f the S L fluxes are forced so that C = 100%, and the error in LEEc were assumed to be constant ( including zero). 4) Loss o f low-frequency covariance when a 30-min. averaging time was used was a significant issue at O J P , but not at HJP02 . Averaging times that were long enough to capture a l l o f the low-frequency covariance at O J P during periods when conditions were relatively stationary appeared to be too long to accurately resolve a l l o f the high-frequency covariance when conditions were non-stationary. A l s o , the shorter averaging times during these non-stationary conditions were insufficient to capture a l l o f the low-frequency covariance, raising the possibili ty that E C cannot accurately quantify ecosystem-atmosphere exchange during such conditions. 5) For data recorded at OJP , analysis o f the relative magnitudes o f the S L fluxes during ' s imi lar ' half-hours (that exhibited a range o f closure) indicated that the variation in closure was due to variations i n the accuracy o f TEC, and was a result o f micrometeorological processes that affected a l l 3 S L fluxes s imilar ly ( including, but not l imited to, varying impact o f the loss o f low-frequency covariance). Assuming that the recommendations made in conclusions 1-3 have been addressed, TEC should be forced for closure at O J P whi le retaining the measured B o w e n ratio, and the same factor should be applied to F C . 6) For data recorded at HJP02 , the S L fluxes were temporally and spatially we l l behaved, indicating that venting d id not occur. Furthermore, analysis o f the relative 62 magnitudes of the SL fluxes during 'similar' half-hours (that exhibited a range of closure) indicated that variations in closure were not due to micrometeorological processes that affected all 3 SL fluxes similarly, and so the SL fluxes should not be forced for closure. 63 References Aubinet, M., Grelle, A., Ibrom, A., Rannik, U., Moncrieff, J., Foken, T., Kowalski, A.S., Martin, P.H., Berbigier, P., Bernhofer, C , Clement, R., Elbers, J., Granier, A., Grunwald, T., Morgenstern, K., Pilegaard, K., Rebmann, C , Snuder, W., Valentini, R. and Vesala, T., 2000. Estimates of the annual net carbon and water exchange of forests: the EUROFLUX methodology. Advances in Ecological Research, 30: 113-176. Baldocchi, D.D., 2003. Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Global Change Biology, 9: 479-492. Baldocchi, D.D., Vogel, CA. and Hall, B., 1997. Seasonal variation of carbon dioxide exchange rates above and below a boreal jack pine forest. Agricultural and Forest Meteorology, 83: 147-170. Barr, AG. , Morgenstern, K., Black, TA. and McCaughey, J.H., 2006. Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of the CO2 flux. Agricultural and Forest Meteorology, submitted. Black, T.A., Den Hartog, G , Neumann, H.H., Blanken, P.D., Yang, P.C., Russell, C , Nexic, Z., Lee, X., Chen, S.G., Staebler, R. and Novak, M.D., 1996. Annual cycles of water vapour and carbon dioxide fluxes in and above a boreal aspen forest. Global Change Biology, 2: 219-229. 64 Blanken, P.D., Black, T.A., Neumann, H.H., den Hartog, G., Yang, P.C., Nesic, Z., Staebler, R., Chen, W. and Novak, M.D., 1998. Turbulent flux measurements above and below the overstory of a boreal aspen forest. Boundary-Layer Meteorology, 89: 109-140. Blanken, P.D., Black, T.A., Yang, P.C., Neumann, H.H., Nesic, Z., Staebler, R., den Hartog, G., Novak, M.D. and Lee, X., 1997. Energy balance and canopy conductance of a boreal aspen forest: Partitioning overstory and understory components. Journal of Geophysical Research, 102(D24): 28915-28927. Finnigan, J., 1999. A comment on the paper by Lee (1998): "On micrometeorological observations of surface-air exchange over tall vegetation". 97(1): 55-64. Finnigan, J.J., Clement, R., Mahli, Y., Leuning, R. and Cleugh, H.A., 2003. A re-evaluation of long-term flux measurement techniques. Part I: Averaging and coordinate rotation. Boundary-Layer Meteorology, 107: 1-48. Griffis, T.J., Black, T.A., Morgenstern, K., Barr, A.G., Nesic, Z., Drewitt, G.B., Gaumont-Guay, D. and McCaughey, J.H., 2003. Ecophysiological controls of the carbon balance of three southern boreal forests. Agricultural and Forest Meteorology, 117: 53-71. Kaimal, J.C. and Finnigan, J., 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York. Kanda, M., Inagaki, A., Letzel, M.O., Raasch, S. and Watanabe, T., 2004. LES study of the energy imbalance problem with edd covariance fluxes. Boundary-Layer Meteorology, 110: 381-404. Kljun, N., Rotach, M.W. and Schmid, H.P., 2002. A three dimentional backward Lagrangian footprint model for a wide range of boundary- layer stratifications. Boundary Layer Meteorology, 103: 205-226. Law, B.E., Falge, E., Gu, L., Baldocchi, D.D., Bakwin, P., Berbigier, P., Davis, K., Dolman, A.J., Falk, M., Fuentes, J.D., Goldstein, A., Granier, A., Grelle, A., Hollinger, D., Janssens, I.A., Jarvis, P., Jensen, N.O., Katul, G , Mahli, Y., Matteucci, G , Meyers, T., Monson, R., Munger, W., Oechel, W., Olson, R., Pilegaard, K., Paw, K.T., Thorgeirsson, Ff., Valentini, R., Verma, S., Vesala, T., Wilson, K. and Wofsy, S., 2002. Environmental controls over carbon dioxide and water vapor exchange of terrestrial vegetation. Agricultural and Forest Meteorology, 113(1-4): 97-120. Lee, X.H., 1998. On micrometeorological observations of surface-air exchange over tall vegetation. Agricultural and Forest Meteorology, 91(1-2): 39-49. Lee, X.H. and Black, T.A., 1993. Atmospheric turbulence within and above a Douglas-fir stand. 1. Statistical properties of the velocity-field. Boundary-Layer Meteorology, 64(1-2): 149-174. Mahrt, L., 1998. Flux sampling errors for aircraft and towers. Journal of Atmospheric and Ocean Technology, 15: 416-429. Massman, W.J., 2000. A simple method for estimating frequency response corrections for eddy covariance systems. Agricultural and Forest Meteorology, 104: 185-198. 66 Massman, W.J. and Lee, X., 2002. Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges. Agricultural and Forest Meteorology, 113(1-4): 121-144. McNaughton, K.G., 2004. Turbulence structure of the unstable atmospheric surface layer and transition to the outer layer. Boundary-Layer Meteorology, 112(2): 199-221. Monteith, J.L., 1981. Evaporation And Surface-Temperature. Journal of the Royal Meteorological Society, 107(451): 1-27. Schmid, H.P., 1994. Source Areas For Scalars And Scalar Fluxes. Boundary-Layer Meteorology, 67(3): 293-318. Schmid, H.P., 2002. Footprint modeling for vegetation atmosphere exchange studies: a review and perspective. Agricultural and Forest Meteorology, 113(1-4): 159-183. Stull, R.B., 1998. Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht. Tanner, C.B. and Thurtell, G.W., 1969. Anemoclinometer measurements of Reynolds stress and heat transport in the atmospheric surface layer. ECOM 66-G22-F, University of Wisconsin, Madison, Wisconsin. Twine, T.E., Kustas, W.P., Norman, J.M., Cook, D.R., Houser, P.R., Meyers, T.P., Prueger, J.H., Starks, P.J. and Wesely, M.L., 2000. Correcting eddy-covariance flux underestimates over a grassland. Agricultural and Forest Meteorology, 103: 279-300. 67 Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., Bernhofer, C , Ceulemans, R., Dolman, H., Field, C , Grelle, A., Ibrom, A., Law, B.E., Kowalski, A., Meyers, T., Moncrieff, J., Monson, R., Oechel, W., Tenhunen, J., Valentini, R. and Verma, S., 2002. Energy balance closure at FLUXNET sites. Agricultural And Forest Meteorology, 113(1-4): 223-243. Wofsy, S.C, Goulden, M.L., Munger, J.W., Fan, S.M., Bakwin, P.S., Daube, B.C., Bassow, S.L. and Bazzaz, F.A., 1993. Net exchange of CO2 in a mid-latitude forest. Science, 260: 1314-1317. 68 Appendix 1: Further spectral analysis Appendix 1 details TFco2U N for HJP02, OJP, and old aspen (OA, see Blanken et al. 1997 for a detailed site description), for comparison with TFmo™ provided in the main text. The graphs show that although Fc was underestimated at high-frequency, the underestimation was not correlated with RH to the same extent as it was for LEEC- We also show TFH20U N, and w-Ta cospectra for OA, to show the similarity with the equivalent OJP data. Finally we show the effect of averaging time on the w-C02 mixing ratio cospectra at OJP, for different times of day, to show similarity with the w-Ta and W-H2O cospectra given in the main text. 69 T 1 — 1 ' i i • I ' ' '— I ' ' i • . . . — - i » I O W R H • medRH i , \ : | high RH f(Hz) Fig. Al 1. Ratio of ensemble average w-CC»2 mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 30 (solid line), 50 < RH < 57 (dashed line), and 60% < RH (dotted line). Data were recorded during July 2004 at HJP02 when H> 100 W m"2, > 75 W m"2, and Fc > 0 umol m"2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 22, 20, and 18 respectively, and the mean RH for the low, medium, and high RH stratifications was 26, 53, and 72% respectively. 70 Fig. Al 2. Ratio of ensemble average W-CO2 mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during July and August 2003 at OJP when H> 150 W m-2, LE> 100 W m-2, and Fc < -5 umol nf2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 21, 19, and 21 respectively, and the mean RH for the low, medium, and high RH stratifications was 35, 45, and 68% respectively. 71 f(Hz) Fig. Al 3. Ratio of ensemble average W - H 2 O mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during July and August 2004 at OA when H > 150 W nf2, LE > 100 W m"2, and Fc < -5 umol m'2 s"1. The number of half-hours contained within the low, medium, and high RH stratifications was 21, 19, and 21 respectively, and the mean RH for the low, medium, and high RH stratifications was 35, 45, and 68% respectively. 72 f<Hz) Fig. Al 4. Ratio of ensemble average W-CO2 mixing ratio cospectra to w-Ta cospectra, stratified by RH: RH < 40 (solid line), 42 < RH < 48 (dashed line), and 60% < RH (dotted line). Data were recorded during the same periods as the corresponding RH stratifications shown in Fig. Al 3. 73 0.001 Fig. Al 5. Ensemble-average w-Ta cospectra stratified by u*\ u* < 0.42 (dashed line), all-w*(solid line), and u*> 1.1 m s_1 (dotted line). Data were recorded at OA during the same half-hours as the data shown in Fig. Al 3, and the low-, all-, and high-u* stratifications contain 13, 159, and 12 half-hours respectively. 74 x10 3 0.0001 0.001 0.01 0.1 1 10 i (Hz) Fig. Al 6. Ensemble average cospectra of w-Ta (a) and w-H20 mixing ratio (b) for 30-min. averaging period (solid line) and 240-min. averaging period (dotted line). Data were recorded between 0600 and 1400 CST during July and August 2003 at OJP. 75 A p p e n d i x 2: N o c t u r n a l C at H J P 0 2 C is often worse at night than during the day, because at night, there is often insufficient mixing to transport the SL fluxes past the EC measurement height. It is a matter of debate whether the SL fluxes advect to low points, where they are subsequently vented, or, conversely, u* flushing occurs; fluxes from low u* periods are simply measured as increased-fluxes when turbulence resumes. Fig. A2 1 compares T following low-w* periods with T following high-w* periods, and shows that for a given value of u*, the magnitude of T was not higher when the preceding period was calm than when the preceding period was turbulent, and therefore indicates that u* flushing did not occur at HJP02. Fig. A2 2 shows the nocturnal dependency of C on u* for this site. C improved as u* increased from 0-0.1 m s"1, and then plateaued, which implies that the appropriate u*h at HJP02 was 0.1 m s"1. For u* > u*'h, C did not depend on u*. Given that at night u* is the principal indicator of the state of the SL, it would be expected to be correlated with any variation in the validity of the EC measurements. The robustness of the plateau may therefore be an indicator that the remaining imbalance resulted from overestimation of A, rather than underestimation of T. 76 Fig. A2 1. Nocturnal TEc as a function of W*. Half-hours following periods of low u* (u* < 0.08 m s"1, open circles). Half-hours following periods with high u* (u* > 0.15 m s"1, crosses). Data were recorded at HJP02 between May and September, 2003, 2004, and 2005, and have been bin averaged. 77 O 6uh u. (m s"1) Fig. A2 2. C as a function of u* during the nighttime (Rpot < 0). Data were recorded at HJP02 between May and September, 2003, 2004, and 2005, and have been bin averaged with 200 half-hours in each bin. C was calculated using the ROM method, and error bars were calculated using dC2 = KdTj SJ2 + ydA; SA2 where 8T and 8^  are the standard deviations of T and A respectively. 78 Appendix 3 : The relationship between C and wind direction Fig. A3 1 shows C as a function of wind direction at HJP02 and OJP. C was low at both sites when the wind was from the east (90°). The likely explanation for low C during easterly winds was underestimation of TEC due to the influence of the tower on airflow. At both sites the EC instrumentation was installed on the west facing side of the tower, and so when the wind was from the east, air passed through the tower before reaching the EC instrumentation. This would have the effect that fluctuations of w no longer represented physical transport phenomena, and so covariance with scalar concentrations would be reduced. Based on the relationships in Fig. A3 1, half-hour fluxes were removed when 45 < wind direction < 135 deg. 79 100 o 45 90 135 180 225 270 315 360 Wind direction (deg from N) Fig. A3 1. C versus wind direction for HJP02 (solid line) and OJP (dashed line). Data were recorded during the summers of 2004 and 2005 when R p o t > 50 W m"' 80 A p p e n d i x 4: T h e influence of «* on C at O J P Fig. A4 1 shows the diurnal variation of C on low-u* days and high u* days at OJP. C was consistently higher at OJP on days when u* was relatively high. Fig. A4 2 compares C and the ratio of A and the ratio of TEc on days when u* was relatively high or in the morning, compared to the afternoon. There was a weak tendency for C (Fig. A4 2 (b)) to follow the same pattern as u* (Fig. A4 2 (a)). Fig. A4 2 (c) shows that the reason for the relative decrease in C on days when u* was (relatively) decreasing is that T was relatively high in the morning and low in the afternoon, whereas A was relatively constant. We therefore conclude that the diumal pattern of u* shows positive correlation with C, due to the impact on T. 81 4 0 1 - 1 -6 V OJP 12 18 Time of day (CST) Fig. A4 1. (a) ensemble average diurnal variation of u* for high-u* days (solid line) and low-w* days (dashed line), (b) ensemble average diurnal variation of C for high-w* days (solid line) and low-w* days (dashed line). Data were recorded at OJP between May and September, 2003, 2004, and 2005. 82 Time of day (CST) Fig. A4 2. (a) Diumal variation of u* on days when u* is relatively high in the afternoon compared to the morning (u*increasj„gll*, solid line) and days when u* is relatively low in the afternoon compared to the morning (u*deCreasmg_u*, dashed line), (b) Diurnal variation of C on days when u* is relatively high in the afternoon compared to the morning (Cincreasingji*, solid line) and days when u* is relatively low in the afternoon compared to the morning {CdecreaSing_u*, dashed line), (c) Ratio of 7decreasing_»* to Tincreasing_u* (dashed line) and ratio of Adecreasing_u* to Aincreasing_u* (solid line). Data were recorded at OJP between May and September, 2003, 2004, and 2005. 83 

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