Water Availability and the Spatial Complexity of CO 2, Water, and Energy Fluxes over a Heterogeneous Sparse Canopy

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1 798 JOURNAL OF HYDROMETEOROLOGY VOLUME 4 Water Availability and the Spatial Complexity of CO 2, Water, and Energy Fluxes over a Heterogeneous Sparse Canopy TODD M. SCANLON* Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia JOHN D. ALBERTSON Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina (Manuscript received 27 August 2002, in final form 23 January 2003) ABSTRACT The transient status of water availability to vegetation is central in shaping both the canopy-level processes as well as the spatial aspects of the turbulent exchange between the vegetation and atmosphere. This is examined by merging eddy covariance (EC) flux data with a detailed atmospheric model applied over a heterogeneous, remotely sensed surface. Eddy covariance measurements from a forested area near Mongu, Zambia, in southern Africa are used to parameterize a large eddy simulation (LES) model, which directly simulates the dynamical effects of the lower-atmospheric transport and mixing. High-resolution IKONOS satellite data are used to define the distribution of the leaf area index (LAI) and surface roughness over the 6.4 km 6.4 km study area. Fluxes along the bottom boundary of the three-dimensional model are represented by a Penman Monteith formulation for the canopy latent heat fluxes (LE c ), and CO 2 uptake by the vegetation (A c ) is added by drawing upon an observed bulk relationship from the EC data. Bare soil fluxes are modeled separately. The effect of water limitation on the vegetation fluxes is introduced by the parameter c, which acts upon the canopy conductance (g c ) in the form of a Jarvis-type limitation. LAI and vapor pressure deficit (D) of the canopy sublayer air are the other controls on g c. Five model simulations were conducted in which c was adjusted to represent various stages of vegetation water limitation. The results reveal a two-way spatial interaction between the vegetation and the canopy sublayer air, the characteristics of which are dependent upon c. For the well-watered cases, the spatial distribution of D was most predictable but its impact on the vegetation-controlled fluxes was unimportant, while in waterlimiting cases the distribution of D was least predictable yet most important in terms of its effect on the fluxes. Increased scaling complexity in estimating fluxes over heterogeneous vegetation was found to be associated with the more water-limited conditions. 1. Introduction The exchange of water, carbon dioxide, and energy between vegetation and the atmosphere is strongly tied to the transient status of the vegetation water availability, both in terms of photosynthetic processes and the dynamic coupling of surface fluxes with the state of the lower atmosphere. This paper focuses on the latter and considers the case in which the presence of a heterogeneous surface adds spatial complexity to the vegetation atmosphere exchange under various degrees of water availability. Locations where vegetation is subject * Current affiliation: Department of Civil and Environmental Engineering, University College, Cork, Ireland. Corresponding author address: Dr. John D. Albertson, Dept. of Civil and Environmental Engineering, Duke University, Box 90287, Hudson Hall, Durham, NC john.albertson@duke.edu to transient water limitation are commonly characterized by natural and human-induced vegetation heterogeneity (e.g., Chehbouni et al. 2000a), and understanding the impact of this heterogeneity on surface fluxes is critical for improving the reliability of flux estimates from remote sensing and improving the prognostic capability of meteorological and climate models. Since the fundamental exchange processes for water, CO 2, and energy are, in reality, operative on much finer spatial scales than those typical of remote sensing footprints or meteorological model grids, this demands a multiscale view of land atmosphere interaction that effectively bridges this gap in scales (e.g., National Research Council 1999). In this study, we examine the effects of soil moisture limitation on the relative importance of the vegetated surface structure versus meteorological coupling across neighboring landscape patches in terms of defining the spatial predictability of vegetation atmosphere exchange over a heterogeneous surface. Nonuniform distributions of vegetation (e.g., Cheh American Meteorological Society

2 OCTOBER 2003 SCANLON AND ALBERTSON 799 bouni et al. 2000b), along with the spatial and temporal variability of soil moisture (e.g., Famiglietti et al. 1999) and surface temperature (e.g., Moran et al. 1997; Kustas and Norman 2000) found within typical remote sensing footprints are integral in shaping both local and regional surface fluxes. Applications of surface energy balance models at various levels of detail using simple aggregation rules (e.g., Sellers et al. 1995; Kustas and Humes 1996; Moran et al. 1997; Kustas and Jackson 1999) have noted the potential for nonlinear scaling of fluxes over such surfaces. A more comprehensive assessment of the role that surface heterogeneity has in affecting the spatial component of land atmosphere exchange is one in which atmospheric surface-layer advection can exert a degree of nonlocal control on surface fluxes (e.g., Albertson et al. 2001a). This phenomenon has been identified experimentally (e.g., Oke 1979; Gay 1991; Hares and Novak 1992), been shown to confound the calculation of surface fluxes (e.g., Avissar 1992; Bonan et al. 1993; Seth et al. 1994; Gao 1995), and been handled analytically for an idealized physical setting (Guo and Schuepp 1994a,b). Owing to the spatial complexity of the heterogeneous surface examined in this study, we take the approach of numerically simulating the atmospheric turbulence to characterize the nonlocal controls on the surface fluxes. A large eddy simulation (LES) model is used to simulate the space and time evolution of large-scale turbulent eddies and their transport effects within the threedimensional atmospheric boundary layer (ABL). The version used for this application (Albertson and Parlange 1999a,b) simulates the turbulent flow described by the Navier Stokes equations written for wall-bounded flow subject to thermal stratification. The nature of the eddy properties and advective transport are implicitly taken into account with this technique. Previous studies have examined the effects of heterogeneous surfaces on ABL dynamics through applications of LES models with specified surface fluxes (e.g., Hadfield et al. 1991; Avissar and Schmidt 1998; Eastman et al. 1998; Raasch and Harbusch 2001), while others have allowed the surface fluxes to develop internally (e.g., Albertson and Parlange 1999a,b; Hobson et al. 1999; Albertson et al. 2001b). By allowing the surface fluxes to respond to the surrounding air properties, the feedback effects on the surface fluxes can be realized. This was analyzed in Scanlon et al. (2001), in which surface sensible heat fluxes yielded by an LES model were compared with those calculated using spatial mean atmospheric variables. It was demonstrated that local fluxes were moderated by a dynamic coupling between the air and surface temperatures. Albertson et al. (2001b), using a twosource representation of the surface to account for the separate fluxes from bare soil and vegetation, examined the nonlocal aspect of the atmospheric transport and showed a downwind propagation of a strong correlation between surface and air temperatures during advective conditions. Whereas Scanlon et al. (2001) and Albertson et al. (2001b) focused primarily on the sensible heat exchange and evapotranspiration from the vegetated fraction of the surface was represented by a potential rate, the present paper adds carbon dioxide exchange to the model as well as a regulation of the latent heat flux by canopy conductance through a Jarvis-type formulation (Jarvis 1976; Stewart 1988). Both vapor pressure deficit and vegetation soil water availability affect the local canopy conductance, and hence affect simulated water and carbon fluxes. Accounting for the effects of vegetation water availability on canopy conductance is an especially vital consideration for regions in which soil water status can often provide a limiting control on vegetation atmosphere exchange. An additional departure from previous LES applications is the use of functional relationships derived from eddy covariance (EC) flux measurements to parameterize the model in a distributed manner over a remotely sensed surface. Direct measurements have routinely shown that canopy conductance, g c, can be limited by the volumetric soil moisture,, that is available to the vegetation (e.g., Davies and Allen 1973; Oren et al. 1998). This control on transpiration by the vegetation water availability is consequential in shaping the partitioning of the net radiation between latent and sensible heat fluxes. Atmospheric dynamics over heterogeneous surfaces can be significantly affected by the relative magnitude of these fluxes, as can the potential microclimatic feedback effects on the canopy atmosphere exchange. Feedback on this exchange has previously been described in terms of the degree of coupling between the vegetation and the atmosphere (McNaughton and Jarvis 1983, 1991; Jarvis and McNaughton 1986), which is largely defined by the relative strengths of the canopy conductance, g c, and the aerodynamic conductance, g av. Although originally developed for homogenous surfaces, this conceptual framework can be applied to heterogeneous settings, where the spatial aspect of this coupling becomes an important consideration. Under decoupled conditions, g c is high and g av is low, leading to the formation of local microclimates that are decoupled from the regional atmosphere. Pronounced negative feedbacks exist between changes in g c and changes in transpiration. For instance, increases in g c lead directly to increases in stored water vapor within the relatively closed atmospheric microenvironment, thus decreasing the water vapor gradient across the foliage surfaces. The increased g c and decreased water vapor gradient have offsetting effects on the transpiration. For coupled conditions, in which g c is low relative to g av, microclimate effects are less important and thus local feedback is minimal. The vegetation fluxes are thus coupled with the regional atmosphere. As soil moisture is depleted and the status of the vegetation goes from being well-watered to waterlimited, the fluxes generally become more coupled with the regional atmosphere. Micrometeorological controls on the local fluxes are

3 800 JOURNAL OF HYDROMETEOROLOGY VOLUME 4 2. Study site The site selected for this study is a forested area near Mongu, Zambia (Fig. 1), where short-term flux measurements were taken in February March 2000 (Scanlon and Albertson 2003). Although technically classified as savanna vegetation, the definitive mixture of trees and grasses is dominated by trees, which have a fractional cover of 65% as measured by Scholes et al. (2002) for the relatively undisturbed canopy of the study site. Grass cover here is minimal, as confirmed by satellite observations (Scanlon et al. 2002), with the remaining surface area consisting of bare aeolian sand. Canopy cover heterogeneity is largely the result of disturbance, such as subsistence forestry, grazing, and fire. This canopy disturbance and regrowth has contributed to the patchiness of the land surface. Mean annual rainfall for Mongu is 879 mm with 94% of this amount received, based on a 20-yr average ( ), during the wet season months of October March. Convective thunderstorms are the predominant form of delivery for the rainfall. The meteorological data indicate that mean air properties, in terms of temperature (T a ) and specific humidity (q), are largely independent from the inferred aridity status of the vegetation (Fig. 2). For instance, during the wet (growing) season there is a 5% probability of a 2-week dry-down period following a rainfall event of 1 cm. After 2 weeks without rain, mean T a rises by only 1 C relative to its initial state and mean q is reduced by less than 1 gkg 1 relative to its initial state, indicating that the air properties at Mongu are controlled by factors active on a spatial scale significantly larger than those associated with convective rainfall events. FIG. 1. Location of Mongu, Zambia, where flux measurements were taken and used to parameterize the large eddy simulation model. evaluated in terms of nonlocal influences on the local canopy air properties as well as the degree of coupling between the vegetation and these air properties. In the present analysis, we consider a timescale over which the temporal means of the surface fluxes and atmospheric variables are stationary (i.e., 0.5 h) and apply the LES model to simulate the spatial aspects of vegetation atmosphere exchange over a heterogeneous surface. Our objectives in doing so are 1) to determine the spatial controls (structural versus meteorological) on the local surface fluxes under varying levels of vegetation water limitation, 2) to evaluate the predictability of the spatial distribution of fluxes and canopy-level air properties based upon the degree of local vegetation atmosphere coupling and the characteristics of nonlocal advective transport, and 3) to determine the effect of surface heterogeneity and associated nonlocal controls on fluxes in the calculation of regional aggregated fluxes. 3. Methods Key to the LES implementation for this study was the formulation and parameterization of the lower boundary conditions of the three-dimensional model that depict the distributed surface fluxes. This aspect of the modeling procedure is described first, followed by the details of the LES model implementation. The functional characteristics of the vegetation were drawn from direct field measurements (Scanlon and Albertson 2003) and an analysis of the relationships between the canopy-scale fluxes and the atmospheric forcing variables. Such a bulk representation is considered to be reasonable for atmospheric modeling at this spatial scale as an alternative to more complex multilevel or leaf-level designs (McNaughton and Jarvis 1991; Avissar 1993). Spatial information of the vegetation s structural distribution was obtained from high-resolution satellite data. An IKONOS satellite image, with a resolution of 1- m in the panchromatic and 4-m multispectral bands, was acquired for the Mongu area 1 month after the completion of field measurements in Normalized difference vegetation index (NDVI) was calculated from the red and near-infrared bands, and cloud cover ( 1% of total area) was removed by kriging. Vegetation fractional cover ( f ) and leaf area index (LAI) were determined from the NDVI field using the methods of Choudhury et al. (1994) and Norman et al. (1995), respectively. In light of LES computational considerations, the resolution of the surface was degraded to 50 m over the 6.4 km 6.4 km LES study area. Determination of the grid-cell momentum roughness lengths (z om ) and displacement heights (d o ) from the satellite data required more advanced image analysis, as the density and dimensions of individual trees had to be obtained from the high-resolution images. To do this, we thesholded the 1-m-resolution grayscale image

4 OCTOBER 2003 SCANLON AND ALBERTSON 801 FIG. 2. Solid curves for air temperature (T a ) and specific humidity (q) represent their mean departure from their initial starting values for the days subsequent to a rainfall event. These curves are positioned relative to their respective mean starting values, shown by the thin dashed lines. The thick dashed line is the probability of consecutive days without rainfall during the wet (growing) season of Oct Mar. Statistics are based on 20 yr of meteorological data from Mongu, Zambia. to remove shadows and bare soil, and overlaid spatially interpolated NDVI information from the 4-m-resolution IKONOS multispectral data. MATLAB (The Math- Works, Inc.) image granulimetry was then used to derive probability distribution functions of crown areas within each of the m pixels in the model domain. By assuming self-similar geometries for the trees and using crown area tree height relationships measured in the field (K. Caylor 2000, personal communication), we applied the method outlined by Jasinski and Crago (1999), based on the theoretical work of Raupach (1992, 1994), to estimate the distributed values of z om and d o. Surface fluxes were calculated using a two-source model, which treats separately the contributions to the overall flux from the bare soil and canopy (Albertson et al. 2001b). A modification to the two-source model described in Albertson et al. (2001b) is the addition of a canopy conductance that responds to both the vapor pressure deficit, D, in air surrounding the canopy as well as to the effects of vegetation water stress (i.e., soil moisture control) that may occur during dry-down periods. A Penman Monteith formulation (Monteith 1965, 1973), which incorporates g c, was used to model the canopy latent heat flux, LE c : Rnc cpdgav LEc, (1) (1 g av/g c) where is the slope of the saturation vapor pressure curve, Rn c is the net radiation for the canopy, c p is the heat capacity, is the psychrometric constant, and g av is the aerodynamic conductance, which accounts for both turbulent and quasi-laminar transport (Thom 1975; Choudhury and Monteith 1988). Assuming a linear relationship between g c and LAI (e.g., Wilson and Baldocchi 2000), and adopting a commonly used logarithmic relationship between g c and D (e.g., Brédaetal. 1993; Arneth et al. 1996; Oren et al. 1999), we distributed g c over the surface in the model domain by LAI gc [ m ln(d) b], (2) c LAI ref where c is a Jarvis-type parameter that ranges between 0 and 1 and describes the limitation to canopy conductance by the soil water availability, LAI ref is the LAI of the canopy within the estimated eddy covariance footprint ( 1.67), and m ( ) and b ( 0.106) are derived from boundary-line analysis (Chambers et al. 1985) of the measured g c versus D data. We selected a 0.5-h study period from the 8 days of flux measurements reported by Scanlon and Albertson (2003) and used the micrometeorological information during this time period as initial background conditions for the LES model (see Table 1). This midday period was preceded by a 2-day rainfall total of 20 mm, resulting in an assumed non-water-limited g c that falls along the m ln(d) b boundary line (i.e. c 1.0).

5 802 JOURNAL OF HYDROMETEOROLOGY VOLUME 4 TABLE 1. Initial background conditions for the LES mode 1. Date, time Air temperature (T a ) Specific humidity (q a ) CO 2 concentration (C a ) Vapor pressure deficit (D) Canopy conductance (g c ) Wind speed (u) Friction velocity (u ) Short wave incoming rad. (R swin ) Short wave outgoing rad. (R swout ) Long wave incoming rad. (R lwin ) Long wave outgoing rad. (R lwout ) CO 2 flux (F c ) Sensible heat flux (H) Latent heat flux (LE) Soil heat flux (G) Volumetric soil moisture ( ) Soil temperature at 5-cm depth 4 Mar 2000, 1130 LT 24.8 C g kg ppm mb m s 1 3.6ms m s W m W m W m W m mol m 2 s W m W m W m C For the addition of CO 2 to the model, we once again relied upon bulk relationships observed from the measured data to simulate the canopy carbon uptake. Water use efficiency (WUE) of the canopy can be defined by A c /LE c, where A c is the photosynthetic uptake of CO 2 by the vegetation. After removing the estimated bare soil contributions to the respective fluxes, the observed daytime WUE at Mongu is shown to be generally independent of g c (Fig. 3a), but sensitive to variations in C a /D (Fig. 3b), where C a is the CO 2 concentration of the air measured above the canopy. This ratio was chosen as the independent variable for modeling WUE because it can be physically related to the gradients between the intercellular and leaf boundary layer concentrations of CO 2 and water vapor, which drive the exchange of CO 2 and water vapor across the stomatal openings, and therefore affect the WUE ratio. The modeled relationship for A c derived from the observed data is ] c[ WUE max(c a/d) Ac LE, (3) K C /D where WUE max ( 0.15) and K m ( 42) are fitted parameters. The LES model domain for the simulations contained nodes in the horizontal and 120 nodes in the vertical directions, covering a spatial domain of 6.4 km 6.4 km 1.4 km. The atmospheric turbulence and scalar concentrations were updated in the 2 million nodes at an average time step of approximately 0.2 s, covering a total analysis timeframe of approximately 30 min. Boundary conditions of the model are periodic in the horizontal direction, consistent with the Fourierbased pseudospectral approach used in the numerical treatment of the flow field. For a full description of the fluid dynamics and numerical approach used in the atmospheric component of the LES model, the reader is directed to Albertson and Parlange (1999a,b). Prior to each model run, a 1-h-long spinup was performed to m a FIG. 3. (a) From the measured flux data, the water use efficiency of the vegetation (WUE) as a function of g c. (b) WUE as a function of the ratio C a /D, with the curve fit to the data represented by Eq. (3), as used in the model. bring the turbulence up to full development. A total of five simulations were performed, representing various degrees of soil water limitation on the canopy conductance. This was achieved by progressively reducing the c parameter in (2), starting with 1.0 (i.e., observed conditions) and then lowering this value by increments of 0.2 for subsequent model realizations. Implied with this reduction of the canopy conductance was a reduction in the volumetric soil moisture from its measured value so as to approximate a linear relationship between these two variables during water-limited conditions (e.g., Oren et al. 1998). In the absence of more detailed spatial information, we assumed a uniform distribution of soil moisture over the land surface. Soil respiration fluxes, R s, were modeled as a linear function of based upon the nighttime measurements with soil temperatures within a range of 4 C from that of the selected time period. Reductions in c and lead to higher canopy and surface soil temperatures, T c and T s, respectively. Energy balance models applied separately to the bare soil and the canopy were used to estimate these changes

6 OCTOBER 2003 SCANLON AND ALBERTSON 803 TABLE 2. Temperatures and soil resperation fluxes (R s ) estimated from energy balance mode 1 runs. c T s [ C] T c [ C] R s [ mol m 2 s 1 ] in temperature, shown in Table 2 along with the other variable inputs for the five model runs. After simulating the evolution of the instantaneous fields, the LES model outputs the time-averaged, threedimensional statistics for atmospheric turbulence and scalar concentrations, along with the two-dimensional surface fluxes. For the present analysis, we subsample the atmospheric output by considering only the air properties in the bottommost nodes of the model domain, referred to as the canopy sublayer, which corresponds to a vertical distance of approximately 1.8 m above the mean canopy height. We also focus our analysis on the vegetation-controlled fluxes and how they respond to this air in the canopy sublayer. The model results represent detailed spatial information that would be impractical to measure in a field setting. 4. Results The surface structure is defined, in part, by the distribution of LAI (Fig. 4a) as generated from the IKONOS multispectral bands and degraded to a 50-m resolution. Vegetation latent heat flux (LE c ) exhibits a similar spatial pattern to that of the LAI for the model run with no soil moisture limitation on g c ( c 1.0) (Fig. 4b), but the modeled LE c is visibly less correlated with LAI for the case having a high degree of water limitation ( c 0.2) (Fig. 4c). This can be explained in terms of the relative strengths of the atmospheric advection on LE c. The degree of coupling between the vegetation and regional atmosphere can be expressed in the form of LE dle (1 ) c dg (4) c (McNaughton and Jarvis 1983), where the decoupling coefficient varies between zero and one. As 1, the vegetation becomes decoupled from the regional atmosphere and, as a consequence, the latent heat flux becomes insensitive to changes in g c.as 0, the vegetation and atmosphere become highly coupled and LE c becomes sensitive to the evolving regional air properties. In calculating over the surface, we use the formulation of Martin (1989): 1 / g r/gav, (5) 1 / (gav g r)/gc g r/gav where g r is the radiative conductance (Monteith 1973). The relationships between and LAI for the two g c c FIG. 4. (a) Surface distribution of LAI derived from the IKONOS data. (b) Modeled LE c for the well-watered case ( c 1.0). (c) Modeled LE c for a water-limited case ( c 0.2). extreme simulations with respect to water availability ( c 1.0 and c 0.2) are shown in Fig. 5a. In general, the case with c 1.0 is more highly decoupled at given values of LAI relative to the water-limited c 0.2 case. For both cases there exists a positive and generally linear relationship between simulated and LAI. Figure 5b shows, as expected from Eq. (2), that the modeled g c exhibits a generally linear relationship with LAI. Scatter in the g c LAI relationships results from the impact of the evolving and spatially heterogeneous canopy sublayer air properties, specifically D, on the distributed values of g c. The magnitude of the scatter in g c is greater for the case c 1.0 compared with the case c 0.2. This greater scatter is not, however, manifest in the LE c LAI relationship. In fact, Fig. 5c shows a greater variability in LE c for like values of LAI in the water-limited c 0.2 case. Figure 5d shows this to hold true for the distributed fluxes of A c. The overall magnitudes of the fluxes are obviously reduced during water-limited conditions via a reduction in g c, but shifts in the structural versus meteorological controls on the local fluxes in the space domain are of principal interest for the present analysis. As previously shown in Figs. 4b,c, the spatial patterns

7 804 JOURNAL OF HYDROMETEOROLOGY VOLUME 4 FIG. 5. Model results for the two cases c 1.0 and c 0.2 showing (a) decoupling coefficient, (b) g c, (c) LE c, and (d) A c as a function of LAI. of the modeled LE c are qualitatively similar to the spatial patterns of LAI. However, as is visually evident in Fig. 4c, nonlocal (i.e., advective) controls on the surface fluxes do exist. Linear multivariate analysis shows that the spatial distributions of LAI and D together account for approximately 90% of the spatial variation in LE c (Fig. 6a), independent of the degree of vegetation water limitation. For the case c 1.0, LAI dominates the spatial control on LE c and the impact of variability in D is minimal. As water limitation increases ( c is reduced), the spatial distribution of D plays an increasingly important role in defining the spatial pattern of LE c and compensates for the decreasing importance of the local LAI. Although D and LAI are not fully independent (R for the most highly dependent case), this general pattern is descriptive of the spatial controls on LE c. In terms of the distribution of CO 2 uptake by the vegetation, shown in Fig. 6b, a similar relationship with respect to vegetation water availability is observed. With A c, there is an additional, small effect due to spatial variability in the atmospheric C a /D ratio. Although LAI and D have been shown to control a large portion of the spatial variability of the fluxes, it should be noted that the main operational distinction between these variables is that the distribution of LAI can be readily obtained with satellite data, while the spatial distribution of D is difficult to measure and is dynamic on short timescales. This raises the question of how the 0.5-h mean local values of D in the air are related to the underlying surface properties. Figure 7a shows the correlation coefficients between D and the LAI averaged over one-dimensional distances in the upwind direction. Instead of the local D in the canopy sublayer being most highly correlated with the immediately underlying LAI, D is most strongly a function of the LAI averaged over some distance upwind. For the case c 1.0, this distance is approximately 400 m. As c decreases to 0.8 and 0.6, this upwind averaging distance decreases. At the same time, the correlation strength between D and LAI also decreases as c decreases. During the drier conditions, D of the air above the canopy becomes linearly independent from the spatial distribution of LAI. This is despite the fact that the overall degree of spatial variability for D is higher for the drier case ( D 0.58 when c 0.2) than for the wetter case ( D 0.41 when c 1.0), where D is the spatial standard deviation of D. One impact of this surface control on D during wellwatered, decoupled conditions is that it causes the canopy WUE to be sensitive to the LAI in the influencing footprint (Fig. 7b). The range observed in WUE over the model domain for the case c 1.0 is to

8 OCTOBER 2003 SCANLON AND ALBERTSON 805 FIG. 6. Percentage of spatial variance in the modeled (a) LE c and (b) A c described by the LAI and canopy sublayer D distributions under differing levels of vegetation water availability, as described by c Portions of the forest canopy surrounded by dense vegetation will be in contact with air that is comparatively moist, thereby decreasing the gradient between the intercellular and extracellular specific humidity and allowing for less water loss with the uptake of CO 2. The spatial variability in CO 2 concentration in the layer above the canopy affects the WUE to a smaller extent relative to D. As c decreases, the spatial variability in D becomes linearly decoupled from the surface variability in LAI, leading to the WUE being controlled by factors not linearly related to the vegetation distribution. The degree to which the vegetation heterogeneity and dynamic meteorological coupling affects the overall large-scale fluxes can be evaluated by comparing the LES model results to an offline calculation, in which spatial variability is not considered for either the canopy sublayer air properties or vegetated surface. What this represents is uniform air properties over a coarse depiction of the vegetated surface. The offline calculations FIG. 7. (a) Correlation coefficients between localized canopy sublayer D and the LAI averaged over distances directly upwind. (b) Similar plot showing correlation coefficients between canopy WUE and the LAI. of LE c and A c use the same formulations as (1), (2), and (3), except spatial averages of, Rn c, D, LAI, C a, and g av are used instead as proxies for known regional meteorological conditions to compute the large-scale fluxes. The LES- and offline-calculated fluxes are compared for LE c (Fig. 8a) and A c (Fig. 8b). The absolute differences between the LES and offline estimates appear to be relatively small, however the percentage error increases for the drier conditions. For instance, there is a 17% error associated with calculating the regional mean LE c when the meteorological influence of the surface heterogeneity is not considered for the case c 0.2. The offline approach assumes precise knowledge of the spatial means of the canopy sublayer atmospheric variables such as, D, C a, and g av, information that is not readily obtainable. Any inaccuracies involved with the estimation of these mean meteorological variables could further compound this error. A simple way of extrapolating measurements made at a single point to the large region involves distributing the flux measurements as a linear function of LAI. The potential errors associated with doing so are illustrated

9 806 JOURNAL OF HYDROMETEOROLOGY VOLUME 4 FIG. 8. Mean (a) LE c and (b) A c for the 6.4 km 6.4 km area. LES- and offline-calculated fluxes are shown along with histograms of the areal mean fluxes calculated by scaling up measurements from various point-scale locations within the area. by the histograms in Figs. 8a,b, where the overall regional fluxes were estimated by considering the measurements made at particular locations and extrapolating these over the region. The suite of locations were chosen based on their LAI being within one standard deviation from the mean LAI in order to mimic a strategy of choosing representative monitoring locations for measuring fluxes. The greatest accuracy in estimating the regional flux is for the well-watered conditions. As c is reduced, the spread in the estimates becomes larger relative to the magnitude of the flux, with errors on the order of the mean flux. 5. Discussion The utility of using an LES model within the context presented here rests with its ability to provide realistic turbulent coupling over the surface in regard to the relative impact of local and nonlocal atmospheric effects imposed on the surface fluxes (Albertson et al. 2001a,b). Entrainment-related feedback on surface fluxes (e.g., McNaughton and Jarvis 1991; Jacobs and DeBruin 1992, 1997) is also handled implicitly by the LES model but, while being of potential importance over the course of the diurnal evolution of the ABL, this feedback process is not considered to be significant over the shorter time frame examined in this study. Additionally, due to the fact that the length scales of surface variability within the modeled area are much less than the height of the ABL, the locally defined impact of the entrainment processes on the surface fluxes is minimal (Albertson and Parlange 1999a). Consequently the present analysis focuses on the lower ABL dynamics. Surface-layer feedback, as originally considered (Jarvis and McNaughton 1986; McNaughton and Jarvis 1991) and modeled by Jacobs and DeBruin (1992, 1997) did not include the more top-down imposition of nonlocal advective effects that can be operative over heterogeneous surfaces. Two-dimensional second-order closure models, which have proven useful for simulating fluxes across a transition between two different types of surfaces (e.g., Kroon and DeBruin 1993; Baldocchi and Rao 1995) are not suited to the broad spectrum of surface heterogeneity present in most natural settings. The complexity of the surface illustrated in Fig. 4a calls for the application of a three-dimensional numerical model since the vegetated surface in the upwind direction from any particular location consists of an ensemble of roughness lengths and vegetation densities. The degree to which micrometeorological feedback effects are relevant in affecting the surface fluxes is, in the example presented here, largely dependent upon the state of the vegetation water availability. LES model output for the distributed values of LE c in the wellwatered case ( c 1.0) shown in Fig. 4b reveals that nonlocal effects do not appear to significantly influence the surface fluxes, as the distribution of LE c maps closely with the LAI field. Nonlocal effects are significant in defining the local air properties for the c 1.0 case, as shown in Fig. 7a, and this has an impact on g c (Fig. 5b), yet the canopy fluxes themselves are insensitive to the air properties (i.e., offsetting effects). The high canopy conductance and relatively low aerodynamic conductance leads to a decoupling of the vegetation fluxes from the regional atmosphere, as described by (Fig. 5a). For this well-watered case, the distributed LE c is, to a large extent, controlled by its equilibrium rate, which is a function of the available energy and the two passive conductances g r and g av, but is insensitive to moderate excursions in g c. The nonlocal effects on the vegetation fluxes are more significant for conditions in which there is limitation on g c by the soil water availability, as shown by the vertical scatter in Fig. 4c for the case c 0.2. Relative to the case c 1.0, the spatial mean of g c is reduced from to m s 1 and the spatial mean of g av is increased from to m s 1, the net result of which is an overall decrease in and consequentially a greater coupling with the larger atmosphere. For the

10 OCTOBER 2003 SCANLON AND ALBERTSON 807 dry case, LE c is strongly influenced by stomatal control, not only from the direct ecophysiological response of the vegetation to decreased soil moisture, but also from this enhanced coupling. Scatter in the LE c LAI relationship shown in Fig. 5c for the case c 0.2 is primarily the result of a nonuniform spatial distribution of D in the canopy sublayer air within the modeled 0.5-h period due to boundary layer mixing combined with the high degree of coupling between the vegetation and the atmosphere. This simulated effect is magnified for the A c LAI relationship shown in Fig. 5d due to the added impact of D on the modeled canopy WUE. The transition from local equilibrium to stomatal control on vegetation fluxes during dry-down periods, commonly observed at the point scale in the time domain (e.g., Hutley et al. 2000; Wilson and Baldocchi 2000), also has implications for the complexity of scaling on fluxes in the space domain. LAI is the most important factor in controlling the spatial distribution of the surface fluxes for this non-light-saturated canopy because it is a key parameter in both the equilibrium and stomatal-controlled rates of evaporation, in terms of Rn c and g c, respectively. During well-watered conditions, the distribution of LAI, which can be gathered from satellites measurements, controls approximately 90% of the spatial variance in LE c (Fig. 6a). As the water availability is diminished, the stomatal controls on LE c becomes increasingly dominant, and therefore canopy sublayer values of D provide an increasing control on the distribution of LE c. In contrast to LAI, the distributed canopy sublayer D cannot be easily measured or modeled. One-dimensional models are able to relate the canopy sublayer scalar properties to the underlying local fluxes and turbulent transport parameters (e.g., Jacobs and DeBruin 1992), however, for a heterogeneous surface with nonlocal advective effects, this task becomes prohibitively difficult. Model results indicate that the spatial pattern of D in the canopy sublayer can be qualitatively related to the distribution of the underlying vegetation during nonwater-limiting to moderately water-limiting conditions (Fig. 7a). Rather than D being most significantly influenced by the vegetation within its immediate vicinity, it is found to be most highly correlated with the LAI averaged over an upwind distance. This suggests a footprint effect, a concept previously developed to define the source areas for fluxes measured in the boundary layer (e.g., Schuepp et al. 1990; Leclerc et al. 1997), but also shown to be pertinent to the accurate determination of surface fluxes when heterogeneity exists (Guo and Schuepp 1994b). An interesting result of this footprint effect on the modeled surface fluxes is an increased WUE for vegetation when downwind of high LAI under wet conditions (Fig. 7b). For case c 1.0, the localized D is most highly correlated with average LAI over a distance of 400 m in the upwind direction (Fig. 7a). As c decreases, this distance is reduced due to the increased instability of the air that develops when the net radiation intercepted by the canopy is partitioned to a greater extent into the sensible heat flux component. The degree of correlation between D and the surface LAI becomes diminished when c is further reduced to 0.4 and 0.2. Factors that contribute to this are 1) a decreased contrast in the sources of water vapor and temperature over the heterogeneous surface, and 2) greater vertical mixing with the increased instability of the lower atmosphere. Increased spatial variance in canopy sublayer D for the dry conditions is a direct reflection of the enhanced vertical mixing between the canopy sublayer air and the air from within the full ABL. Unlike the wetter cases, the distribution of canopy sublayer D is independent from the surface LAI distribution and appears be more a property of the flow field. The LES model results suggest a two-way spatial interaction between the vegetation fluxes and the canopy sublayer air properties. For wet conditions, in which there is little limitation on g c due to water availability, the spatial distribution of the canopy sublayer air properties is shaped by the distribution of the vegetation structure. The vegetation fluxes, however, are decorrelated from the distribution of these air properties. In this scenario, the spatial distributions of the canopy sublayer air properties and the surface fluxes are relatively predictable since both are related to the distribution of the vegetation structure. This two-way spatial interaction becomes reversed during times in which the vegetation water availability limits g c. Under these conditions, the canopy sublayer air properties do not map well with the vegetation structure, but the distribution of vegetation fluxes is more highly correlated with the distribution of D. This leads to a relatively lower predictability for the spatial distributions of the air properties and the surface fluxes in the dry case. Surface heterogeneity-related effects can have an impact on the calculation of the overall fluxes, as illustrated by the comparison between the LES and offline fluxes in Figs. 8a,b. In general, the nonlocal effects tend to cancel out when their net effect is considered over a larger area, although the nonlinear relationship between D and g c may contribute to some of the differences seen between spatially aggregated LES fluxes and the offline fluxes. Point-scale flux measurements during dry conditions are highly sensitive to the air properties, and therefore if the localized air properties are not representative of the overall area, this can lead to relatively large errors on the upscaled estimates. This scaling problem can hamper the potential agreement between smallscale flux measurements (i.e., localized EC flux measurements) and large-scale one-dimensional model predictions based on remotely sensed surface conditions and mean air properties during times in which the vegetation is water-limited. 6. Conclusions Spatial information provided by the LES model indicates that there is a two-way spatial interaction be-

11 808 JOURNAL OF HYDROMETEOROLOGY VOLUME 4 tween the vegetation and the atmosphere that is sensitive to the status of the vegetation water availability. Under dry conditions, the spatial distribution of the vegetation fluxes is highly tied to the distribution of the canopy sublayer air properties, however, the air properties themselves are not locally reflective of the underlying surface. Under well-watered conditions, this two-way interaction is reversed: the air properties become highly spatially correlated with the underlying vegetation structure but have little effect upon the vegetation fluxes. The net result of this is that at times when the spatial distribution of D is most predictable it is unimportant in affecting the vegetation fluxes, while at times when D is least predictable it is most important in shaping the spatial distribution of fluxes. Scaling complexity involved in estimating fluxes over heterogeneous vegetation increases during the more water-limited conditions as a result of greater atmospheric influence in shaping the spatial distribution of the fluxes. Unlike LAI, which can be readily measured via remote sensing, the spatial distribution of the canopy sublayer air properties is difficult to measure or deduce, especially during dry conditions. Acknowledgments. Funding for this research was provided by a NASA New Investigator Program in the Earth Sciences award (NAG5-8670), along with support from the Biological and Environmental Research (BER) Program, U.S. Department of Energy, through the Southeast Regional Center (SERC) of the National Institute for Global Environmental Change (NIGEC). The comments of three anonymous reviewers helped to improve an earlier version of this manuscript. REFERENCES Albertson, J. D., and M. B. Parlange, 1999a: Natural integration of scalar fluxes from complex terrain. Adv. 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