Comparison between measured tracer fluxes and footprint model predictions over a homogeneous canopy of intermediate roughness

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1 Agricultural and Forest Meteorology 117 (2003) Comparison between measured tracer fluxes and footprint model predictions over a homogeneous canopy of intermediate roughness M.Y. Leclerc a,, N. Meskhidze a, D. Finn b a Laboratory for Atmospheric and Environmental Physics, University of Georgia, Griffin, GA , USA b Department of Civil and Environmental Engineering, Washington State University, Pullman, WA , USA Received 10 February 2003; accepted 11 February 2003 Abstract Fast response tracer flux measurements are compared against flux footprint predictions from both a Lagrangian stochastic simulation and an analytical solution to the equation of diffusion over a canopy of intermediate roughness. A turbulent tracer flux experiment was conducted over a peach orchard for a range of mildly unstable to very unstable conditions. For this purpose, a line source was used to release sulfur hexafluoride at treetop and fast response tracer flux instrumentation placed in the roughness sub-layer was mounted on four towers perpendicular to the line source to measure the vertical tracer flux. There was excellent agreement between Lagrangian simulated fluxes and their experimental counterparts. The analytical solution to the advection diffusion equation used also shows a good agreement with the tracer fluxes particularly far from the tracer source. These results suggest that for canopies of intermediate roughness, the flux footprint predictions from both models presented work very well, despite their simplifying assumptions Elsevier Science B.V. All rights reserved. Keywords: Tracer flux experiment; Advection diffusion equation; Langevin equation; Footprint; Stochastic modeling; Lagrangian simulation 1. Introduction The assessment of surface-atmosphere exchange from both satellite and airborne observations, aided by judiciously selected permanent surface flux measurement sites is a sine qua non condition to understand and monitor temporal and spatial changes in the earth s climate attributed to anthropogenic or biogenic causes. For logistical reasons, such flux monitoring stations must necessarily be few in number yet be representative of the local surface-atmosphere exchange. In this context, the identification of both the optimum Corresponding author. address: mleclerc@griffin.uga.edu (M.Y. Leclerc). number and the judicious placement of atmospheric flux measurement towers becomes of paramount importance to identify individual flux signatures that characterize the multiple and multi-dimensional eco-physiological, biophysical, and biogeochemical source/sink properties of a landscape. Fortunately, much progress has been made over the past decade during which studies aimed at assessing the spatial coverage of flux measurements took place. Today, the majority of micrometeorological field campaigns rely on the determination of the sensor footprint, a concept pioneered by Schuepp et al. (1990) and Leclerc and Thurtell (1990). The footprint refers to the identification of flux signatures from each surface source contributing to a point flux measurement /03/$ see front matter 2003 Elsevier Science B.V. All rights reserved. doi: /s (03)

2 146 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) (Leclerc and Thurtell, 1990). Footprint predictions now serve as blueprints in planning flux field campaigns and in the design of sampling characteristics. These methods also guide the subsequent analysis of flux datasets by providing both a quantitative tool to decompose flux measurements into their individual upwind sources, and an evaluation of the spatial size of the footprint envelope connected to these measurements. These studies have shown that, depending upon the physical properties of the underlying canopy, sensor placement level and atmospheric stability, the domain and shape of the footprint can vary dramatically within a given landscape and over short time intervals. Numerous studies have appeared since the Schuepp et al. (1990) and the Leclerc and Thurtell (1990) findings, thus augmenting our body of knowledge on the topic. These subsequent studies have contributed much to the field of spatial source-area analysis and include, to name a few, the works of Wilson and Swaters (1991), Flesch (1996) and Kljun et al. (2002) and Kljun et al. (2003) with inverse Lagrangian footprint methods; Horst and Weil (1992, 1994) with the use of their original realistic analytical solutions; Schmid (1994) with his three-dimensional footprint formulation; Haenel and Grunhage (1999) and Kormann and Meixner (2001) with new analytical solutions; Leclerc et al. (1997) with the determination of the gradual footprint decoupling between the surface and the atmosphere with height in the lower convective boundary layer; Karahabata et al. (1997) with the aircraft flux dataset of the BOREAS field campaign; Baldocchi (1997) with the identification of ground versus canopy layer contributions to flux footprints; Amiro (1998) and Stoughton et al. (2000) with the role of local climatology on flux measurements; Kurbanmuradov et al. (1999) with their theoretical Monte-Carlo formulation; Rannik et al. (2000) with Lagrangian and analytical solution theories to compare predicted footprints against flux measurements in inhomogeneous forested terrain; Cooper et al. (2003) with their footprint map of moisture lidar measurements and Markkanen et al. (2003) with their simultaneous use of higher-order closure model and Lagrangian simulation to determine footprints and fetches for fluxes over forest canopies of varying structure and density. Despite the widespread need for such guidelines, very little experimental work has been done that actually tests the various methods of footprint determination. One such study was conducted by Finn et al. (1996), over a short sagebrush canopy with sensors placed at both five and ten times the canopy height, well above the roughness sub-layer. While pioneering, the sagebrush study highlighted the need for flux footprint prediction methods to be validated above canopies with more significant roughness and in the region where most eddy-covariance flux measurements are made. In an effort to limit the sources of uncertainties, the present paper compares two widely used footprint prediction methods with a turbulent tracer flux experiment using a single source of known source strength and well defined location in the region immediately above a homogeneous rough canopy composed of evenly spaced, even height tree elements. 2. Footprint formulations Footprints have been studied mostly using three different model formulations: (1) analytical solutions to the advection diffusion equation, the forward approach (Schuepp et al., 1990; Horst and Weil, 1992, 1994; Schmid, 1994; Kaharabata et al., 1997, 1999; Haenel and Grunhage, 1999; Kormann and Meixner, 2001; Horst, 2001), and the inverse approach (Wilson and Swaters, 1991; Flesch, 1996; Kljun et al., 2002; Kljun et al., 2003); (2) the Lagrangian stochastic simulation (Leclerc and Thurtell, 1990; Luhar and Rao, 1994; Flesch, 1996; Kurbanmuradov et al., 1999; Kurbanmuradov and Sabelfeld, 2000), Rannick et al. (2000) with their analysis of measurements and predictions of footprint functions using sophisticated Lagrangian simulations and analytical solutions over an inhomogeneous forest canopy; and (3) Large-Eddy simulations (Leclerc et al., 1997). Analytical solutions are elegant and compact but are limited in their range of applications, in cases such as in-canopy footprint calculations. Lagrangian stochastic simulations are more versatile, can be used inside and over complex heterogeneous surfaces and, for most physical situations, describe well the physics of diffusion. The Large-Eddy simulation resolves the coarse features of the flow and, while remaining a computationally intensive method, constitutes a powerful research tool capable of providing valuable insight on the

3 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) behavior of flux footprints in complex flow conditions. This method was used to study the character of the footprint flux in the lower convective boundary layer (Leclerc et al., 1997). The challenge now resides in the examination of some of these footprint formulations over rough canopies in the roughness sub-layer region. Reynolds (1998) suggested that dispersion models when carefully parameterized, can accurately predict dispersion and flux within and above plant canopies. While many dispersion processes can be correctly accounted for, their correct treatment is more difficult when implemented in the vicinity of sources and sinks such as inside the canopy or in the region close to treetops. 3. Lagrangian model description The Lagrangian stochastic approach to turbulent dispersion is well known and will only be briefly described. For more details on the particulars of the method used, readers are referred to Leclerc et al. (1997). This type of simulation assumes a steady-state horizontally homogeneous flowfield in which streamwise velocity fluctuations are neglected. Vertical dispersion takes place by turbulent mixing and horizontal diffusion downwind by horizontal advection. It also considers the diffusion of a passive tracer which does not adhere to the surface or recombine with other molecules in the atmosphere, in a shear flow with vertically inhomogeneous turbulence. Above vegetated canopies, the assumption of Gaussian turbulence is sensible since the skewness of the vertical velocity is generally small. While the present simulation specifically addresses the effects of surface roughness and buoyancy on plume dispersion, it assumes horizontal homogeneity. The simulation assumes no step changes in surface properties. In essence, the vertical dispersion (by turbulence) and horizontal dispersion downwind (by horizontal advection) is numerically simulated by calculating the Lagrangian trajectories of hundreds of thousands of marked particles. The simulation is based on the Langevin equation which reproduces instantaneous velocities of individual particles. The tracer concentration at a specific location is linearly proportional to the time particles spent in a given volume with particle trajectories in space determined by integrating incremental changes in the Lagrangian velocities. The required input parameters are the tracer release height, measurement level, zero plane displacement and roughness length, friction velocity, standard deviation of the vertical velocity, Obukhov length and desired number of particles. The sonic anemometer data were used to calculate the friction velocity, the local standard deviation of the vertical velocity, and the Richardson flux number. The standard deviation of the vertical velocity for the other levels used the measured value corrected for height and atmospheric stability. The Lagrangian time scale was determined using the ratio of the Lagrangian length scale to the standard deviation of the vertical velocity and took into account atmospheric stability in a manner previously described in Leclerc et al. (1997). The zero plane displacement and the roughness length were obtained from measurements of wind profiles above the canopy (details described in Section 5.4). The simulations were run for thirteen periods. A minimum of 100,000 particles were used in the simulations. Particles were reflected at the zero plane displacement height. The time step is 0.1 the value of the Lagrangian timescale. This Lagrangian simulation has been shown to work well several time scales away from short canopies (Finn et al., 1996; Leclerc et al., 1997). 4. Analytical model description The reader is referred to Horst and Weil (1994) for an exhaustive description of the analytical solution to the advection diffusion equation used here. Horizontal homogeneity and negligible streamwise eddy diffusion are assumed. Their analytical solution (1994) is based on the van Ulden (1978) formulation. The reason for our selection of this analytical solution lies in its realism in the description of diffusion in the atmospheric surface layer as that solution takes into account both atmospheric stability and logarithmic wind profile above the canopy. The input parameters to this analytical solution are the source height, measurement level, Obukhov length, roughness length and zero plane displacement. The estimation of the shape parameter r uses power law wind profiles and surface-layer similarity theory corrections to the

4 148 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) diabatic wind profile (Dyer, 1974). The expressions for the r parameter are from Gryning et al. (1983) and are a function of the mean plume height and Obukhov length. These were later tested by Finn et al. (1996) and found to be generally satisfactory; results from the latter further demonstrated the weak dependence of the footprint on r. The values of A and B parameters used in the analytical footprint model are a function of r and were calculated following Finn et al. (1996), also based on the work of Gryning et al. (1983). The solutions are calculated for each of the thirteen turbulent tracer flux measurements periods and are non-dimensionalized with respect to the canopy roughness length. 5. Experimental design The experiment was conducted over a peach orchard at Hollonville, GA during July, August and September Table 1 presents the relevant information on date, tower location with respect to the line source, and atmospheric variables present during each experimental dataset (mean wind speed, mean wind angle, friction velocity, standard deviation of the vertical velocity, Obukhov length, eddy-covariance tracer flux and tracer source strength, respectively) corresponding to the tracer flux periods for the period over which the experiment took place. The canopy was pruned early in the spring and a combination of both hot summer and irrigation accelerated its growth. At the onset of the experiment, the flux measurement height of 6 m was nearly twice the canopy height of 3.1 m. Later in the summer, when the canopy had grown taller, the measurement height (unchanged) was roughly 1.5 times the canopy height of 4.2 m. An orchard was selected because (1) it represents a canopy considerably rougher than the sagebrush canopy where the only tracer flux footprint experiment was done (Finn et al., 1996) (2) orchard trees are planted symmetrically, making the site horizontally homogeneous, thus keeping site complexities to a minimum and (3) individual tree height variations are small. The canopy height was monitored weekly throughout the experiment and accounted for. The roughness length, z 0 and the displacement height, d, were and m, respectively Experiment layout Four 6 m towers were instrumented with a three-dimensional sonic anemometer/thermometer (Campbell Scient. Inc., Logan, UT) and a continuous fast response SF 6 analyzer (Benner and Lamb, 1985) to measure vertical tracer fluxes using the eddy covariance technique. The configuration of this experimental set-up is that of the release of a tracer at a known rate from one single (linear) source location with continuous high-frequency measurements of the tracer flux at several positions downwind. This is mathematically equivalent to a flux experiment in which a flux measurement at a tower results from the sum of all upwind sources within the footprint envelope in a natural system (from multiple discrete point sources in a tracer experiment). Rather than using the multiple sources-single flux sampling system, a method equivalent to a spatial decomposition of a typical eddy-covariance point flux measurement, the chosen configuration (one source-multiple flux sampling points) represents a more logistically feasible proposition. The alternate multiple sources configuration, an analog of biological emissions from discrete sources upwind from the flux measurement, requires simultaneous releases at different positions upwind to construct a flux footprint. Such an endeavor would require the use of multiple distinct tracers to mark each individual (tracer) source position along with complex multiple tracer analysis capability, something well beyond the scope of this experiment. A CR-10X data acquisition system (Campbell Scientific Inc., Logan, UT) collected 8 Hz time series data on PCMCIA cards using CSM1 Card Storage Modules. The data were subsequently transferred to a computer hard disk every h. Sulfur hexafluoride (SF 6 ) was selected as an atmospheric tracer because of its chemical inertness and stability, negligible atmospheric background and because of its high sensitivity to electron capture detection. To investigate the change of tracer flux with downwind distance, analyzers and sonic anemometers were placed at the same height (6 m) on masts located along the axis perpendicular to the line source as shown in Fig. 1. If the wind direction changed during the sampling period in a way such that zeroes were introduced in the record due to edge effects, that period was discarded. The data were selected on

5 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) Table 1 Meteorological and tracer release information Tower ū (m s 1 ) θ ( ) σ ( ) u (m s 1 ) σ w (m s 1 ) L (m) z 0 (m) w SF 6 (nkg m 2 s 1 ) Period July Period July Period na 24 July Period July Period July na 4 na na na na na Period September na na na na na Period September na na na na na Period September na na na na na Period September na na na na na Period September na na na na na Period September Period September Period September na na na na na 4 na na na na na Q (nkg m 1 s 1 )

6 150 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) Fig. 1. Areal photograph of the experimental site (24 August 1998, courtesy of the USDA) with configuration of the source receptor array. the basis of the quality of the dataset, mainly in the fast response tracer analyzer and the sonic anemometer signals. Computers, SF 6 standard gases and H 2 cylinders were kept in a temperature-controlled mobile laboratory with a small workshop equipped with electronic troubleshooting equipment. Fifteen minutes averaged quantities of wind speed and direction, standard deviation of wind direction, solar radiation, air temperature, relative humidity and barometric pressure were recorded using an on-site weather station MetData1 (Campbell Scientific Inc., Logan, UT). Lagrangian simulations were made prior to the experiment to anticipate the optimal distance from the release line source and the spacing between the towers. For this purpose, 5 years of wind speed and wind direction measurements from a nearby site (the University of Georgia Bledsoe farm, Williamson, GA is located within a 15 km radius of the experimental site) guided the orientation of the line source. Measurements of friction velocities, wind speeds, and Obukhov lengths using a three-dimensional sonic anemometer placed at that same site during a test deployment at the above site the previous summer provided the simulation input parameters to estimate footprint envelopes and optimum tower spacing to measure the footprint. Unstable and neutral stability conditions were selected for these simulations. As expected, the overall envelope of the footprint contracts or expands with each experimental period and shows a high sensitivity to the above parameters; it is thus difficult, nigh impossible to select tower spacings and distance from the line source which are optimum for all measurements made a posteriori. The spatial definition of a footprint envelope a priori required in the selection of optimal tracer release/ towers positions was made easier since wind speeds and surface heating vary modestly during most summer late mornings and afternoons in Georgia Data collection and analysis Wind profile measurements were made using four cup anemometers (Thornthwaite Associates, NJ). These anemometers were placed at treetop (h c ), 1.5h c, 2.5h c, and 3.5h c above the orchard. These were calibrated prior the experiment, and had a threshold

7 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) value of cm s 1. The data was collected prior to the tracer release experiment and the canopy height growth increase was subsequently used to adjust z 0 and d values throughout the tracer field deployment. z 0 and d values of and m were obtained from wind profiles averaged from ten 30 min periods taking the cup anemometer data at the upper levels. z 0 and d values agree with those published in the literature (Thom et al., 1975; Monteith, 1980). A three-dimensional coordinate rotation was made setting the mean lateral and vertical velocity to zero. Means, covariances, Obukhov length and Richardson flux numbers were then calculated for each half-hour period. Thirteen experimental runs were selected in this analysis. One-dimensional spectra of w and SF 6 are presented in Fig. 2. The SF 6 spectrum exhibits a short 5/3 slope in the inertial range as expected from the lower frequency response of this instrument. The spectrum of the SF 6 signal also shows that the frequency response of the analyzers was approximately 0.7 Hz. The cospectra of w and T, and of w and SF 6 are presented also in Fig. 3 and display the characteristic 7/3 slope. No forcing was made on the spectra. The reader is referred to Kay (1988) for a detailed treatment of the Welch and Yule Walker equations and methods used to calculate the spectra. Spectra obtained using these two methods are identical to one another in the inertial sub-range and exhibit a general agreement at the lower frequencies. Calculations in a manner similar to that used in Finn et al. (1996) suggest that flux loss corrections in the present dataset are less than 3% and 5% for unstable and neutral conditions, respectively Tracer release design Two 100 m line sources were deployed at the canopy top (h c ) in order to carry out the experiment for a broad range of wind directions as shown in Fig. 1. These line sources were made from (0.635 cm) copper tubing with stainless steel release ports ( cm i.d.) mounted equidistantly at 4 m intervals. The tracer was released a short time prior to each sampling period to ensure both full line pressurization and the establishment of steady plume conditions over the sampling array. The tracer release rate was continuously measured using a calibrated mass flow meter/controller (FC-2900V-4S, Tylan General) and a datalogger CR-21X (Campbell Scientific Inc., Logan, UT). The standard deviation of the flow meter output during the experiment (for 40 psig supply pressure) was 0.05 V (±0.007 Lm 1 )is<5% of the release rate. Fig. 2. Spectral energy density of (a) vertical velocity and (b) tracer concentration. The arrows show the inner (f i ) and the outer (f o ) scaling breaks of the inertial subrange for the tracer concentration spectrum.

8 152 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) Fig. 3. Cospectral energy density of (a) vertical velocity and temperature (Co wt ) and (b) vertical velocity and tracer (Co wsf6 ) on a log/log scale. In addition, individual release ports were monitored periodically to insure uniformity in the source strength along the line. Table 1 identifies the periods when each line source was used Tracer sampling system Fast response SF 6 analyzers (Rydock Co.) were used to make continuous fast response tracer concentration measurements. In these analyzers, an air sample is drawn through a catalytic reactor and mixes with H 2 which combusts with O 2 in the airstream and produces water. The wet sample stream then passes through semipermeable Nafion tubing to remove moisture before reaching a custom-built electron capture detector (ECD) using a short-range radioactive source of 200 m Cu of Tritium foil. The analyzer response is linear to approximately 10,000 parts per trillion (ppt) and the instrument s detection limit is approximately 25 parts per trillion. Flow restrictors and pumps are located downstream of the detector. In this experiment, each SF 6 analyzer was located inside a smaller version of a Stevenson screen, mounted near the canopy top. Continuous air samples were drawn through 0.16 cm polyethylene tubing place in the same control volume as that of the sonic anemometers. The velocity inside the tube was found to be above the minimum discharge velocity throughout the course of the experiment in a manner suggested by Lenschow and Raupach (1991). The tube length between the analyzers in the shelter mounted on the tower and the flux sampling point was kept short, at approximately 2 m. The inlet of the tracer analyzer was co-located with the three-dimensional sonic anemometer. Tests showed the typical response times (0 90% of peak height) for the four analyzers to be about 1 s. Finn et al. (1996) using an analyzer with a frequency response close to that of the present instruments, have shown that the flux loss with their analyzer to be typically 2 10% in their sagebrush study at 5 and 10 m in unstable conditions. Time delays between each sonic anemometer and its corresponding SF 6 analyzer were calculated using a cross correlation analysis between w and SF 6 time series and the flux data were corrected for the individual lag calculated between those two quantities (approximately 2 s). Time delays observed with this technique were also compared against time delay values obtained experimentally in the field and found to be in close agreement with the latter. Typical time delay differences between the cross-correlation technique and the experimental method were found to be less

9 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) Fig. 4. Validation of fractional flux density above the orchard using the Lagrangian simulation (solid line) and the analytical solution to the diffusion-equation (dashed line) for near neutral conditions (a) (z d)/l = , run no. 12, 22 September 1998 (b) (z d)/l = 0.016, run no. 10, 22 September Closed circles represent the experimental data points at each tower.

10 154 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) Fig. 5. Validation of fractional flux density above the orchard using the Lagrangian simulation (solid line) and the analytical solution to the diffusion-equation (dashed line) for unstable conditions (a) (z d)/l = 0.32, run no. 13, 23 September 1998 (b) (z d)/l = 0.15, run no. 2, 16 July Closed circles represent the experimental data points at each of the four towers.

11 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) than The tracer flux measurement uncertainty was estimated to be approximately 10 15%. The analyzers baseline stability is a function of several factors including temperature, pressure and also the condition (contaminated or not) of the Nafion tubing. The instruments were calibrated hourly during the experiment using commercial SF 6 /air mixtures (Scott-Marrin Inc., ±5% accuracy) spanning the range of concentrations observed in the field. All span and calibration periods were excluded from the computation of the mean fluxes. The detector s response is linear over the range of the concentrations obtained and gas standards spanning the ppt range were used. However, when the analyzer voltage output was outside the measured linear response region (i.e. near saturation), a situation that happened occasionally for the first analyzer, a fourth order polynomial fit was used to convert the voltage to concentration. Depending on the wind direction, tracer flux measurements were made at 6 m using the Northern line source (Fig. 1) at 8, 30, 55, 65 m downwind from the tracer source, or when using the Southern line source, tracer flux measurements were made at 9, 19, 42 and 55 m, respectively. 6. Results and discussion Fig. 4 compares tracer fluxes against those obtained from the Lagrangian simulations and the analytical solution. The disparity in fractional scalar fluxes between analytical and Lagrangian methods at the first tower close to the source in near-neutral conditions for run no. 12 ((Richardson flux number ((z d)/l = where z is the sonic anemometer level, d the zero place displacement and L the Obukhov length, mean wind speed ū = 1.34 ms 1 ) and run number 10 ((z d)/l = 0.016, with ū = 2.1ms 1 ) is readily apparent. Fig. 5 illustrates the footprint comparison above the peach orchard in unstable conditions using the Lagrangian simulation and the analytical solution for run no. 13 ((z d)/l = 0.32 and ū = 1.1 ms 1 on the 24th of July 1998 and run no. 2 (Richardson flux number of 0.15 and mean wind speed of 1.9 ms 1 on Fig. 6. Comparison of fractional flux density between the Lagrangian simulation above the orchard and above the sagebrush canopies and the tracer fluxes.

12 156 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) Fig. 7. Comparison of fractional flux density between the analytical solution above the orchard and the sagebrush canopies and the tracer fluxes. the 16th of July 1998). As suggested earlier in Fig. 4, these cases illustrate the fact that the analytical solution departs from the experimental data close to the source, a feature that proves to be even more salient and systematic in Fig. 7 shown later. The tracer flux data points coincide with the Lagrangian simulation footprint results. The identification of the exact tracer footprint breadth and location peak is tentative since flux gradients are steepest close to the source. This points out the difficulty of determining the cumulative footprint flux as a function of fetch, without additional measurements in the near field. Figs. 6 and 7 present non-dimensionalized fluxes predicted using both footprint predictions methods above a peach orchard canopy, and above a sagebrush canopy from the Finn et al. (1996) data. The reader is referred to Table 1 for details pertaining to the peach orchard dataset, including those of atmospheric stability, shown in those figures. The tracer fluxes have been non-dimensionalized with respect to both roughness length and tracer source strength. Both footprint methodologies are in broad agreement with the tracer flux data. In the near field, the Lagrangian simulations appear to better estimate the observed vertical fluxes at the first tower than the analytical solution for unstable to near neutral conditions within the limits of experimental uncertainties. This is likely because the diffusion is primarily a function of the distance from the source in the near field, and then becomes a function of the turbulence several length/time scales away in the far field (Taylor, 1921). The dispersion process with characteristic diffusion time scale t, is diffusive in the far field (t τ L ) and non-diffusive in the near-field (t τ L ). These physical characteristics are implicitly reproduced in the Lagrangian simulation. The analytical solution compares well with the tracer flux results at the three positions farthest from the line source. That solution departs from the 1:1 line for the peach orchard for the data at the first tower, since it is close to the source. Nonetheless, it can be seen that

13 M.Y. Leclerc et al. / Agricultural and Forest Meteorology 117 (2003) such analytical solutions, despite their simplifying assumptions, exhibit quite a favorable agreement with the present dataset. 7. Conclusions Two widely applied footprint prediction methods were compared against results from an eddy-covariance tracer flux experiment above a canopy of intermediate roughness with the flux instrumentation is placed in the roughness sub-layer, the region often chosen to make flux measurements. Sources of experimental errors include occasional edge effects from the line source, the limited precision of the electron capture detector, source strength variability, gas standard uncertainty, occasional overshoot, the difference between the measured tracer flux and the calibration standard value, and the small flux loss attributed to the sensor s frequency response. Both the Lagrangian and the analytical methods are shown to compare favorably against experimental results within the range of parameters used. Minor differences between the analytical model and both experimental results and Lagrangian simulations are observed mostly at the first tower, i.e. where the plume is still traveling close to the source. These differences may be attributed to the fact that Lagrangian simulations reproduce the physics of the diffusion from the release point where the diffusion is a linear function of the travel time/diffusion distance for short travel times. This feature was not previously seen in the sagebrush dataset given the larger distances from the (line) source involved. The physical characteristics of the changing dispersion process as particles move from the near field to the far field implicitly reproduced in the Lagrangian simulation form the basis for the strength of this method. The results presented in this paper suggest that in slightly unstable to near neutral conditions, the Lagrangian stochastic simulation compares most favorably with vertical fluxes within the limits of experimental uncertainties and model simplifying assumptions. While both models are found to work very well, the experimental evidence presented suggests that the Lagrangian stochastic simulation appears to be the method of choice to estimate the footprint when eddy-covariance flux measurements must be made close to sources and sinks (e.g. near treetop level), a constraint often dictated by logistical convenience and cost containment. This is despite the simplifying assumptions used in the Lagrangian simulation with regards to horizontal homogeneity in surface properties, streamwise diffusion, mean horizontal flowfield below the sonic level, and in-canopy influences. While this present tracer experiment provides a rare tracer flux dataset that covers most of the footprint envelope, additional tracer flux data points closer to the source in the region exhibiting the sharpest gradients would be helpful. The cumulative flux (the integral of the footprint) could then be effectively summed up to asymptotically approach 1 (total flux seen by a tower) not only for footprint predictions but also for the tracer dataset. Future work should now focus on the three-dimensionality of sources and sinks inside canopies, particularly in tall unmanaged canopies of multiple species, or those with important understories and complex vertical distribution of sources and sinks. Investigations regarding the influence of the presence of contrasting adjoining surfaces outside the fetch region should also be pursued. Linking model formulations to spatially inhomogeneous vegetated surfaces constitute additional and necessary valuable efforts which hold the promise to advance our much needed scaling-up efforts. Acknowledgements The authors wish to thank the reviewers for their insightful and most helpful suggestions. The US Department of Energy, Office of Science provided the financial support to make this experiment possible. We also wish to thank the University of Georgia Experiment Station, Hatch project and the Georgia Research Alliance for providing much of the tracer equipment needed to make this experiment possible. We acknowledge Jesus Mata for his multi-faceted help, Jim Rydock with his guidance in troubleshooting our analyzers, and the Gregg family for the use of their peach orchard. References Amiro, B.D., Footprint climatologies for evapotranspiration in a boreal catchment. Agric. Forest Meteorol. 90 (3),

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