Land Surface Heterogeneity in the Cooperative Atmosphere Surface Exchange Study (CASES-97). Part I: Comparing Modeled Surface Flux Maps with Surface-Flux Tower and Aircraft Measurements

a. Atmospheric forcing and surface boundary data

The multiscale, gridded atmospheric forcing data used in this study are based on the measurements obtained from the S-Pol radar, the Next Generation Weather Radar (NEXRAD), and 10 surface-flux tower stations over the CASES-97 observation array for the period of 16 April–22 May 1997. The CASES site is located in the lower Walnut River watershed, Kansas, and a detailed description of the CASES-97 field experiment can be found in LeMone et al. (2000). The goal of CASES is to obtain a quantitative understanding of the interactions among the subsurface, the surface vegetation and soil, and the atmosphere—from the surface through the boundary layer into the free troposphere, over time-and space scales ranging from those associated with turbulence up to years and 100 km, respectively. The first episodic experiment, CASES-97, was conducted during April–June 1997 to look at the role of surface characteristics in determining the diurnal variation of wind, temperature, and moisture in the planetary boundary layer (PBL); to study rainfall and soil moisture scaling; and to test Weather Surveillance Radar-1988 Doppler (WSR-88D) precipitation-estimation algorithms.

Figure 1 shows the experimental array for CASES-97, and the numbers in the figure denote surface-flux stations, sited so that the surface data are in rough proportion to land use. These surface-flux stations sampled heat, moisture, and momentum fluxes using eddy correlation techniques. Near-surface temperature, wind, pressure, rainfall, net radiation, and (at stations 1–8) radiometric surface temperature were also measured. These observed atmospheric forcing and surface radiative fluxes were interpolated, using a cubic-spline interpolation algorithm, into a domain of 71 km × 74 km with a time interval of 30 min and at three spatial resolutions: 1, 5, and 10 km (Yates et al. 2001). Verified against observations, this interpolation approach produced satisfactory results for this type of land surface modeling study (Yates et al. 2001).

The gridded precipitation data were a hybrid product, merged from the high-resolution (roughly 100 m in space and 5-min in time) S-Pol radar operated for five heavy rainfall events and the continuous hourly 4-km NEXRAD observations. Although atmospheric conditions such as wind and temperature in this dataset resulting from the cubic-spline interpolation may appear homogenous, the use of a high-resolution rainfall field introduced much of the desired heterogeneity. Moreover, 1-km State Soil Geographic Database (STATSGO) soil texture and 1-km land-use cover maps (see Fig. 2) were used to capture the heterogeneity at small scales. The results show that 32% of the domain was covered by winter wheat (mostly in the western part), 62% of the domain is grassland (mostly in the eastern part), and the rest of the domain consists of urban area, water, and trees.

To initialize soil moisture at various depths in the three models, we ran a simple water budget model with eight-layers (soil depths are 0.05, 0.05, 0.1, 0.1, 0.1, 0.2, 0.2, 0.2 m) for a roughly 5-month spinup period (1 January–16 April 1997). This model used the precipitation obtained from Wichita's NEXRAD (WSR-88D) and analyzed atmospheric forcing conditions based on local weather station measurements. Three LSMs used the soil moisture field generated by the water budget model to further spin up in each model for another 10 days, because surface observations that we used to verify models started on 27 April 1997.

b. Validation data

Surface, aircraft, and remote sensing data were used in this study to evaluate the simulations by three land surface models and to study the scaling of surface heat fluxes. Data from the AVHRR were archived and corrected to derive the NDVI by Argonne's Atmospheric Boundary Layer Experiments (ABLE) group (Song et al. 2000), and the NDVI data were computed for the five CASES-97 intensive observation periods (IOPs): 28 April, 4 May, 10 May, 16 May, and 20 May 1997. The AVHRR data were obtained by direct reception of a National Oceanic and Atmospheric Administration satellite (NOAA-14), and the size of each satellite pixel is about 1 km. The satellite view angle varied from 48° to 44.58° on the three days, which has been taken into account in computing atmospheric corrections. With these views at the small solar zenith angles at the time of the satellite overpasses, the effects of bidirectional reflection on NDVI could be assumed to be negligible. The reflectances in the red waveband (channel 1, 0.58–0.68 μm) and near-infrared waveband (channel 2, 0.73–1.10 μm) were used to estimate NDVI.

2) Aircraft-derived heat fluxes

The aircraft-derived sensible heat flux is estimated from

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where the (′) is a departure from a linear trend over the flight leg, ρ is total air density, w is vertical velocity, θ is potential temperature, and N is the number of points in the average. We use θ because it is less sensitive to changes in aircraft altitude compared to temperature. Similarly, latent heat flux LE is given by

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where mr is mixing ratio, ρ_d is dry air density, and L is the latent heat of vaporization.

In theory, this captures fluxes due to eddies of wavelength up to the aircraft leg length, which extends up to 50 km. In practice, the larger eddies are only poorly sampled (e.g., Mann and Lenschow 1994), leading to large scatter in flux estimates, particularly for moisture. The alternative, to account for only the shorter wavelengths, usually leads to significant underestimation of fluxes (Desjardins et al. 1992; Betts et al. 1992).

To prepare the dataset for direct comparison with the surface data, we took the following steps. 1) We computed the fluxes at 1-km intervals along the leg using Eq. (1), and the primed quantities are still relative to the whole-leg linear trend. Thus the average of the 1-km fluxes will equal the total leg flux. 2) We interpolated the data to points lying at 0.01° increments in longitude (e.g., 97.00°, 97.01°, etc). And 3) we performed a four-point running mean and assigned the data to the center point. This four-point filter was selected by trial and error in a balance to reduce scatter but have an average over as small an area as possible. The result is close to the 4-km running average at 1-km intervals selected by Desjardins et al. (1992) in their comparisons of aircraft CO₂ fluxes to satellite-derived surface greenness index. The exact distance (in km) between the points in our case is given by

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where ϕ is latitude, and h is heading. Typical latitudes are 37.5°–37.6°; typical flight tracks and corresponding distances between points are ∼98° (0.9 km), ∼60° (1.0 km), or 65° (1.0 km).

c. Land surface models

Three land surface models with different degrees of complexity were used in this study to generate month-long multiscale surface-flux maps. The first LSM, the atmosphere–soil–vegetation model SOLVEG, consists of multilayer submodels for atmosphere, soil, and vegetation (Nagai 2002). For this intercomparison study, we used 10 atmosphere layers (height for each layer: 0.1, 0.3, 0.5, 0.7, 1.0, 1.5, 3.0, 5.0, 8.0, and 12.0 m), 7 soil layers (depths of layers: 0.02, 0.03, 0.05, 0.1, 0.2, 0.5, and 1.0 m), and 9 vegetation layers (same as the lower 9 layers of the atmosphere). The atmosphere submodel calculates momentum, heat, and water conservation and transport through diffusion, phase change of water, heat and water exchange with soil and vegetation, aerodynamic resistance, and turbulence production by the ground surface and vegetation. The soil submodel simulates the heat and water transport through heat conduction, water transport, phase change of water, reflection, absorption and emission of radiation at the ground surface, heat and water exchange with the atmosphere, and precipitation. The vegetation submodel evaluates heat and water budgets on the leaf surface, vertical flux of liquid water in the canopy, and transmission of solar and atmospheric radiation. Those submodels are linked with each other by heat and water exchange. Submodel variables include 1) atmosphere: horizontal wind components, potential temperature, specific humidity, fog water, turbulence kinetic energy, and turbulence length scale; 2) soil: soil temperature, volumetric water content, and specific humidity of air within soil; and 3) vegetation: leaf surface temperature, and leaf surface liquid water.

The second LSM, the National Center for Atmospheric Research (NCAR) LSM, utilizes the tile approach for representing multiple surface types within a grid cell and simulates the energy, momentum, water, and CO₂ exchange between the atmosphere and land accounting for ecological differences among vegetation types, and thermal and hydrological differences among soil types (Bonan 1996). A number of processes, including ecosystem dynamics (vegetation phenology), biophysical processes (radiative transfer within canopy, stomatal physiology), hydrologic processes (infiltration and runoff, water transfer within soils), and biogeochemical processes (photosynthesis, plant respiration, net primary production), are taken into account in this complex model. It is used here with six soil layers and one canopy layer.

Compared to SOLVEG and NCAR LSM, the third LSM [the so-called Oregon State University (OSU) LSM or National Centers for Environmental Prediction (NCEP)/OSU/Air Force/Office of Hydrology (NOAH) LSM] is a rather simple model. It is based on the work of Pan and Mahrt (1987) and extended by Chen et al. (1996) to include the modestly complex canopy resistance approach of Jacquemin and Noilhan (1990). It has one canopy layer and the following prognostic variables: soil moisture and temperature in the soil layers, water stored on the canopy, and snow stored on the ground. For the soil model to capture the daily, weekly, and seasonal evolution of soil moisture and also to mitigate the possible truncation error in discretization, we use four soil layers, and the thickness of each layer is 0.1, 0.3, 0.6, and 1.0 m, respectively. The total soil depth is 2 m, with the root zone in the upper 1 m of soil. The surface skin temperature is determined following Mahrt and Ek (1984) by applying a single linearized surface energy balance equation representing the combined ground/vegetation surface. Table 1 summarizes the major components (submodels) of these three LSMs. More detailed information can be found in the above-mentioned references.

a. Rapid greening process of grassland

The two dominant land-use types in our modeling domain of 5254 km² are grassland (pasture) and winter wheat. Modern-era land surface models often include an explicit treatment of vegetation and, hence, require the knowledge of a few primary vegetation parameters that includes the vegetation (land use) type, the fractional area of the vegetation (horizontal density), and the leaf area index (LAI) (vertical vegetation density). The vegetation fraction is defined as an area average shielding factor that represents the degree to which the foliage prevents shortwave radiation from reaching the ground and also is coupled to LAI (Deardorff 1972). Many land surface models refer to the green vegetation fraction as the fraction of canopy leaves that are photosynthetically active. LSMs use this variable to partition the total evaporation into direct evaporation from bare soils and plant transpiration via the uptake of water from the vegetation root zone. To a large extent, the definition of green vegetation fraction is similar to the fraction of photosynthetically active radiation (FPAR) (of the incident radiation in photosynthetically active wavelengths) that is actually absorbed by green, living vegetation.

LAI and green vegetation fraction can be specified as time varying parameters depending on vegetation type, or they can be derived from remote sensing data. One satellite-derived variable used the most frequently to characterize the vegetation characteristics is NDVI obtained from AVHRR. It is, however, difficult to simultaneously derive LAI and green vegetation cover from a single product NDVI, unless one of them is prescribed. According to Gutman and Ignatov (1998), it is more justified to prescribe LAI and derive vegetation fraction. In addition, while green vegetation fraction and LAI are about equally important, the natural variability (a priori uncertainty) in vegetation fraction seems substantially higher. Assuming a prescribed large LAI, Gutman and Ignatov (1998) suggested the following relationship to calculate the green vegetation fraction (f_g):

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They prescribed NDVI₀ = 0.04 (with a standard deviation σ₀ ∼ 0.03) and NDVI_∞ = 0.52 (with σ₀ ∼ 0.03) as seasonally and geographically invariant constants, which correspond to the NDVI_min and NDVI_max of the desert and evergreen clusters, respectively. The monthly, 0.15° global green-vegetation-fraction dataset, based on 5-yr climatology AVHRR NDVI, was derived using the above equation by Gutman and Ignatov (1998). It has been used in the NCEP Eta operational model and in the fifth-generation Penn State–NCAR Mesoscale Model (MM5; Chen and Dudhia 2001).

The NDVI data used here were collected during CASES-97 by an Argonne ground station from the NOAA polar-orbiting satellite high-resolution (0.0115°) image transmissions for the first five IOPs of CASES-97. We applied the above formulation to the CASES-97 NDVI dataset to compute the green vegetation fraction, which ranges from 0.48 to 1.0 for grassland and from 0.59 to 1.0 for winter wheat on 29 April. Photos taken at grass sites and aircraft videos, however, reveal that the grassland was brown and, hence, not photosynthetically active at the early stage of the field experiment, and that the grassland experienced a rapid greening so that at the end of experiment (i.e., 22 May 1997) it became greener than the winter wheat. Compared to these in situ data, the green vegetation fraction derived from NDVI using Gutman and Ignatov's algorithm seems to be overestimated for the grassland at its early growing season.

To demonstrate the significance of the greening of the grassland, the latent heat flux (LE) simulated by OSU LSM, using this vegetation fraction dataset, for a 1-km grid box dominated by grassland is shown in Fig. 3. Also shown for comparison in Fig. 3 is LE computed by OSU LSM using the vegetation fraction as assessed from photos, which is systematically lower than the former. Compared to LE measured at station 2 (observations available after 29 April), the simulation using the NDVI-based green-vegetation-fraction data overestimated the evaporation for late April and early May. Clearly, using the green vegetation fraction based on in situ data produced better agreement with observations. Other studies (e.g., Betts et al. 1997) also show the sensitivity of short-range weather forecasts of surface weather variables to the green vegetation fraction in coupled atmospheric models. Nevertheless, obtaining an accurate f_g from NDVI seems challenging. One has to assume a fixed LAI in order to compute f_g due to the close link between the two parameters (Carlson and Ripley 1997; Gutman and Ignatov 1998). It was suggested that the sensitivity of NDVI to LAI becomes increasingly weak with increasing LAI beyond a threshold value of typically 2 or 3 (Carlson and Ripley 1997). In our study, it seems that the vegetation fraction is overestimated when NDVI reaches some relatively high value (>0.45).

A few factors could contribute to the overestimation of green vegetation fraction using the above approaches and CASES-97 NDVI data. For instance, the max value of NDVI (0.52) suggested by Gutman and Ignatov (1997) was for evergreen clusters, which is lower than expected from the surface observations using a handheld multispectral radiometers. Their NDVI data were composite, while the CASES-97 NDVI data are corrected for atmospheric effects (Song et al. 2000). The composite data almost always have smaller NDVI values for terrestrial surfaces than the data that have been subjected to rigorous adjustments for atmospheric effects (such as the Argonne group did with LOWTRAN 7 in this work; M. Wesely 2001, personal communication). In addition, traditionally the NDVI transformation is computed as the ratio of the measured intensities in the red (R) and near-infrared (NIR) spectral bands using the following formula: NDVI = (NIR − red)/(NIR + red). For AVHRR data, NDVI is calculated from channel-1 and -2 radiance data, normalized for incoming solar radiation in the respective bands: NDVI = (band 2 − band 1)/(band 2 + band 1). The bandwidths of bands 1 and 2 are 0.58–0.68 and 0.725–1.10 μm, respectively. While band 2 is essentially near infrared, band 1 includes not only “red” but also “yellow and orange” spectral region. Hence, the AVHRR band 1 has a broader band than red and may yield higher NDVI.

This rapid greening of grass played a critical role in shaping the surface heterogeneity for the area investigated in late spring and early summer. The SOLVEG LSM did not originally explicitly consider green vegetation fraction. A number of sensitivity tests using CASES-97 data demonstrated that including a seasonality of vegetation significantly improved SOLVEG. To capture the heterogeneity in surface evaporation, one must rely on knowledge of vegetation characteristics; hence, methods for estimating these characteristics from satellite data need to be evaluated and improved in light of the new generation of Terra/Moderate Resolution Imaging Spectroradiometer (MODIS) sensors that have much narrow spectral bands.

b. Evaluation against surface-flux tower measurements

Latent and sensible heat flux, ground heat flux, and surface skin temperature measured at nine surface-flux tower stations were used to evaluate the simulations of three LSMs, and the results are shown in Fig. 4. In general, the three LSMs captured the observed tendency for winter wheat (sites 5, 6, and 7) to produce higher latent heat fluxes than grassland (sites 1, 2, 8, and 9). Similarly, they reproduced the observed lower sensible heat fluxes at the winter wheat sites and higher sensible heat fluxes at the grassland sites. Among the three LSMs, the NCAR LSM generally produces the highest latent heat fluxes and the lowest sensible heat fluxes for all sites. For the four grassland sites, all models tend to overestimate latent heat fluxes for sites 1, 2, and 8. The latent heat flux was found by eddy correlation for sites 1–8, while for site 9 it was computed as the residual of the surface energy balance equation using measured net radiation, and sensible and ground heat flux. As we will see later in section 3c, the latent heat flux computed from surface energy balance equation is higher. All three LSMs overestimated the observed sensible heat flux across all land-use categories, particularly for the three winter wheat sites. The averaged ground heat fluxes from observations and models were small, as expected, but the NCAR LSM had negative mean ground heat flux for the grassland sites 1 and 2. A negative ground heat flux would indicate a net energy transfer from a shallow soil layer to the ground surface. This discrepancy in the NCAR LSM may be partly due to its somewhat excessive evaporation and to the uncertainty in specifying the initial soil temperature profile. The OSU LSM generally overestimated the surface skin temperature, while the NCAR LSM had the lowest skin temperatures. SOLVEG and NCAR LSM appear to have overestimated evaporation for sites 3 and 4 (both located at bare soil or sparsely covered vegetation). The OSU LSM and SOLVEG models specified these two points with bare-soil characteristics. But NCAR LSM applied four subgrid cells to each of these two points and does not have “true” bare-soil points.

Examining modeled soil moisture fields for sites 3 and 4 reveals that the OSU LSM had lower surface soil moisture than the other two models throughout the simulation period, consistent with its lower evaporation. Interestingly, SOLVEG had drier surface soil but still overestimated the observed evaporation, because the incorporation of the water-vapor phase in SOLVEG allows water vapor to evaporate from its deep soil layers even in the absence of vegetation. Figure 5 shows the comparison of soil moisture between the three models and observations obtained at stations 7 (winter wheat) and 8 (grassland) at three depths. Soil moisture in the three LSMs had a faster response to precipitation in soil layers closer to the ground surface, as expected. However, soil moisture evolves differently in the three LSMs. For instance, more water was able to penetrate into the deeper soil layers of SOLVEG, while NCAR LSM was wetter than other two models after heavy rainfall events.

Another important factor contributing to the difference in simulating latent heat fluxes is the formulation of soil moisture stress. These three models account for the effect of soil-moisture stress on canopy resistance in their computation of plant transpiration. A more elaborated discussion about canopy resistance formulation used in the three LSMs is given in Part II in the context of examining the development of surface heterogeneity in model results. Both SOLVEG and OSU LSM use a relatively simple parameterization scheme for canopy resistance as documented in Jarvis (1976) and Noilhan and Planton (1989). The canopy resistance in this parameterization scheme depends on the minimum canopy resistance and is modulated by vegetation phenology parameters like LAI, air temperature, FPAR, vapor pressure deficit, and soil moisture. The soil moisture stress function F can be expressed as in Chen and Dudhia (2001):

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where F typically assumes a linear relationship in soil moisture stress between the field capacity Θ_ref and the wilting point Θ_w (both depending upon soil texture), and ranges from 1 when the soil is wet to 0 when the soil is dry. However, Chen et al. (1996) proposed a nonlinear soil moisture stress function to reflect (or to account for) the subgrid-scale variability in soil moisture. For instance, even though the area-averaged soil moisture represented by a grid box of an atmospheric model is at the wilting point (no evaporation according to F₄), the soil moisture in some subarea can be higher than the wilting point, and vice versa. To save computational time, a linear but broader range for soil moisture stress is suggested and a new set of values for field capacity and wilting point can be derived (e.g., Chen and Dudhia 2001), and SOLVEG and OSU LSM utilize these values in their simulations. Using the values of Θ_ref and Θ_w from Chen and Dudhia (2001), the soil moisture stress function for silty clay loam, the dominant soil texture in our CASES-97 simulation domain, is plotted in Fig. 6. The NCAR LSM has a complex formulation of latent heat flux for vegetated and nonvegetated surfaces, but it still employs a similar soil moisture stress function, named F here for the sake of convenience, which is

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where Θ_opt is the optimal water content for evapotranspiration, Θ_dry is the water content when evapotranspiration cases, T is the soil temperature, and T_f is the freezing point (Bonan 1996). Hence, conceptually, Θ_dry(Θ_opt) in Eq. (6) is equivalent to Θ_w(Θ_ref) in Eq. (5). This function is also plotted in Fig. 6 for comparison. It is clear that for a broad range of soil moisture (0.23–0.38), the NCAR LSM has higher F, and hence higher evaporation, than SOLVEG and OSU LSM. Noticeable also is the narrow responding range of F to soil moisture in NCAR LSM. For dry soil (i.e., less than 0.21 for this particular case), the NCAR LSM produces no evaporation. However, as mentioned above, because of its lower hydraulic conductivity, NCAR LSM remained wetter in root zone compared to SOLVEG and OSU LSM for most of the simulation, which leads to less soil-moisture stress on canopy resistance and, hence, higher vegetation transpiration. This is a major reason for the overestimated latent heat fluxes in NCAR LSM.

In order to assess the overall model performance, we used three statistical measures: 1) mean error (ME), which is often referred to as bias; 2) root-mean-square error (rmse), and 3) correlation coefficient. The ME and rmse of surface heat fluxes and surface skin temperature averaged for the entire simulation period are shown in Table 2. Consistent with results seen in Fig. 4, all three models overestimated evaporation at the three grassland sites 1, 2, and 8. SOLVEG and NCAR LSM also overestimated evaporation for the sparsely vegetated and winter wheat sites. When averaging over sites located at the same land-use cover, the model bias ranged from −22 W m⁻² (OSU LSM for winter wheat) to 56 W m⁻² (NCAR LSM for sparse vegetation). SOLVEG and OSU LSM have relatively small mean errors for latent heat fluxes over grassland sites.

The range of model ME for sensible heat fluxes was similar to that for latent heat fluxes, except that models tended to overestimate sensible heat fluxes, particularly for the winter wheat sites. The bias averaged for all sites is less than 29 W m⁻². OSU LSM and NCAR LSM performed well for grassland, while SOLVEG had the smallest errors for the sparsely vegetated site. OSU LSM and NCAR LSM tended to underestimate the ground heat fluxes. Averaged mean errors in surface skin temperature range from −2.7°C (NCAR LSM for the grassland site 2) to 5.7°C (OSU LSM for site 3), and OSU LSM (NCAR LSM) tended to overestimate (underestimate) surface skin temperature. SOLVEG had consistently the best estimates of surface skin temperature.

The OSU LSM and SOLVEG models had similar rmse ranges for latent heat and sensible heat fluxes, while NCAR LSM had larger rmse for latent heat flux. OSU LSM had the largest rmse in surface skin temperature among the three models. Errors in OSU LSM surface skin temperature calculation were not necessarily associated with the fact that it has a very simple vegetation layer, because large errors occurred over the sparsely vegetated sites 3 and 4. Rather, it seems to be the result of underestimating evaporation for these sites. Also examined are rmse and ME computed separately for daytime and nighttime model simulations; and, qualitatively, these statistics show very similar behavior to what seen from the averaged statistics. Nevertheless, daytime rmse and ME are larger than those for nighttime. This is not surprising given that the surface radiation fluxes are larger during daytime. Table 3 shows the correlation coefficients [as defined in Press et al. (1989)] for various parameters between model results and observations, which are averaged for grass sites, bare-soil sites, and winter wheat sites, respectively. As regards latent heat fluxes, the land surface models showed the best performance for winter wheat sites and performed more poorly for sparsely vegetated sites. On average, model surface skin temperature and sensible heat flux are more strongly correlated with the observations for grassland sites than for winter wheat and bare soil. Among the parameters, surface temperature has the highest correlation and latent heat flux the lowest. It is more difficult to model latent heat fluxes, which had more variability and more sensitivity to soil, atmospheric, and specific plant conditions.

c. Uncertainty in surface measurements

We should bear several factors in mind when comparing surface-energy components between observations and models. First, the longwave downward radiation, used to force all three LSMs, was computed by a simple function with an estimated error of about 30 W m⁻² (Yates et al. 2001), and this may explain some discrepancies. Another major factor concerns the surface energy closure in observations. It is a well-known problem that the independent measurements of the major surface flux components often do not balance the surface energy budget (e.g., Twine et al. 2000). One outstanding problem is that the usual “energy balance closure” (R_net = H + LE + G_s) neglects the heat storage in the canopy and energy associated with photosynthesis, which is probably a small term for CASES-97. Most reported results have shown the sum of sensible and latent heat fluxes measured by eddy covariance to be less than the difference between net radiation and soil heat fluxes. The residual, averaged for all CASES-97 sites, in surface-energy balance around solar noon was approximately 50 W m⁻² (Yates et al. 2001) with H + LE + G_s always being too small.

To evaluate the impacts of observational uncertainty on model verification, we adopted the approach of Twine et al. (2000) to “adjust” the measured surface latent and sensible heat fluxes. An adjustment factor R_a is defined as

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where R_net, H, LE, and G_s are the originally estimated net radiation, sensible, latent, and ground heat fluxes, respectively, from station measurements. The fluxes H, LE, and G_s are positive when they are directed away from the ground surface (e.g., during daytime). Assuming that the measured available energy R_net − G_s is representative of the site (Twine et al. 2000), adjusted LE_a and H_a are computed as the following to close the energy balance equation:

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As expected, the adjusted latent and sensible heat fluxes are generally larger than the “original” estimates, as shown in Fig. 7 in which both the original and adjusted estimates are plotted. Note that these two estimates differ the most for the sparsely vegetated sites, and the difference between them is close to the differences among three model results. Model ME and rmse based on adjusted fluxes are shown in Table 4. Utilizing these adjusted fluxes significantly improves NCAR LSM latent heat flux verification statistics, except for sites 8, 9, and 4 where ME does not change much. The OSU LSM and SOLVEG models now have better ME for sites 1 and 2, but worse scores for sites 5 and 6. Mean errors in SOLVEG and OSU LSM sensible heat fluxes were also improved for the majority of sites. Nevertheless, rmse, for both latent and sensible heat flux, increases in all three models. Adjusted data mostly affect the nighttime rmse (not shown). This may imply that applying the above approach for nighttime adjustment is problematic, because both LE and H are small compared to ground heat fluxes. Correlation coefficients based on adjusted measurements are slightly decreased (not shown) and decreased more for sensible heat fluxes.

It is out of the scope of the present study to discuss the best way to adjust surface heat flux measurements when the closure of the surface-energy budget is not satisfied. Rather, it is shown that such an adjustment could significantly affect model evaluation. The simple approach of adjustment used in this study seems to be problematic for nighttime heat fluxes, because it assumes that R_net − G_s is accurate, while in reality G_s may be a difficult component to estimate because of the soil heterogeneity at small-scale and uncertainty in computing heat storage in the top 5 cm of the soil.

d. Evaluation against aircraft measurements

The transects of aircraft flight legs during CASES-97 were located to sample heat flux across different land-use cover so that aircraft measurements would provide a snapshot of the effects of surface heterogeneity. Aircraft sensible and latent heat flux data were compared with 1-km gridded flux maps obtained from the three LSMs. These data were taken from the Wyoming King Air and NOAA Twin Otter aircraft for the five IOP days (29 April, and 4, 10, 16, and 20 May 1997). The aircraft data were smoothed and interpolated to roughly 1-km averages, which were then subjected to a 4-km running average. The overlapping portions of the flight tracks were then averaged. A slightly different averaging technique has been successfully done for CASES-97. Figure 11 of LeMone et al. (2000) shows a clear link between H and NDVI and CO₂ flux for 10 May when applying this averaging technique.

Points at the center of the 1-km flux-map grids that are closest to the corresponding aircraft points for the original unsmoothed 1-km aircraft fluxes were chosen for comparing with aircraft fluxes. Then we applied the same four-point running-average technique as used for the aircraft measurements. In general, the spatial fluctuations along flight tracks measured by the Twin Otter were smaller than those measured by the King Air. Also, the King Air had an onboard camera, allowing a better description of underlying land-use distribution. Finally, the King Air data have longer flight legs, and hence more samples, than the Twin Otter data. Thus we focused on the comparisons using the King Air data. However, data from both the King Air and Twin Otter aircraft were used to compute the correlation coefficients between model results and aircraft measurements.

Figure 8 compares heat fluxes based on model results from the three LSMs and King Air measurements for the morning averages of 29 April. Four flight legs were flown at ∼30 m above the ground in the morning and the length of the overlapping portion of the legs was about 43 km. The root-zone soil moisture generated by SOLVEG and OSU LSM is low and homogeneous along the flight tracks, while NCAR LSM is wetter and shows more heterogeneity because of its subgrid-cell configuration (Fig. 9). Nevertheless, the surface soil moisture along the flight tracks, shown in Fig. 9a, appears more heterogeneous than the deep root-zone soil moisture. Moreover, as mentioned above, the plant phenology in the CASES-97 domain was heterogeneous on this early spring day, because of the contrast between nongreen grassland in the east and green winter wheat in the west. This is reflected in the aircraft latent heat flux decreasing toward the eastern part of the CASES-97 domain. The heterogeneity in both land-use cover and soil moisture clearly has significant influences on model heat fluxes. The evolution of soil moisture was largely controlled by the variability of rainfall and land-use cover through vegetation transpiration processes. Both SOLVEG and OSU LSM seem to capture the major observed features in the spatial variability of latent heat flux: larger latent heat fluxes found at 96.85°, 96.7°, and 96.62°W. However, the three models failed to capture the relatively low evaporation at 96.91°W. Although the NCAR LSM has more variability than the other two LSMs, all three tend to have less variation than aircraft measurements. The NCAR LSM has a built-in subgrid-scale scheme that partitions each model grid cell into four subgrid cells and computes the grid average surface heat fluxes, providing an opportunity to account for more of the surface heterogeneity.

The King Air sensible heat fluxes are lower than the model fluxes, but their latent heat fluxes for this case are slightly higher. While the King Air–measured LE seems to be similar to the Twin Otter data, comparison of surface sensible heat fluxes to values obtained by extrapolating linearly to the surface suggest that the King Air values are 25%–35% too low compared to the unadjusted surface heat fluxes; and the Twin Otter values lie within 10%, except for 4 May, when they are 20% higher. Typical sensible heat flux profiles decrease approximately linearly from the surface to the top of the boundary layer, and it is generally accepted that aircraft-flux estimates are low [e.g., by 19%–25% according to Barr et al. (1997)]. Sun and Mahrt (1994) found both the mesoscale flux and the random sampling errors to be of the order of 10% of the turbulent flux for a flight track with strong surface heterogeneity. Comparisons of sensible heat fluxes revealed similar features of spatial variability as seen from latent heat flux comparison. Model results show large fluctuations in sensible heat flux in the areas with mixed land-use types, particularly in the areas where the fraction of cropland (i.e., winter wheat in this case) becomes significant. Again, the variability in modeled sensible heat fluxes along the flight leg has smaller amplitude than aircraft measurements.

The next comparison is for the morning of 20 May 1997. The overlapping portion of the four King Air morning flight legs was about 35 km. On 20 May both grassland and winter wheat were at their peak growing season, and heavy precipitation on 19 May almost saturated the soils across the CASES-97 domain. Soil moisture simulated by the three models is high and homogeneous along the flight tracks, and the soil at the surface is as wet as the deep root-zone soils (not shown). The Geostationary Operational Environmental Satellite (GOES) visible images show that the CASES-97 domain was mostly cloud free all morning. The CASES-97 domain was, therefore, essentially homogeneous in terms of plant photosynthetic capacity, surface soil moisture, and solar radiation forcing. In fact, all three LSMs produced fairly homogeneous surface heat fluxes along the flight tracks (Fig. 10). Again, sensible heat fluxes in the three models show less fluctuation than latent heat fluxes, which agrees with the trend seen from aircraft measurements. However, relatively larger spatial variability in both latent and sensible heat flux is evident in aircraft measurements.

Similar features seen from the above two examples are found in the comparisons using other IOP morning-averaged aircraft measurements. Correlation coefficients (R) between fluxes from the aircraft and the three models for all IOP morning averages are shown in Table 5. The OSU LSM (SOLVEG) produced better spatial variability, as compared to aircraft-measured latent heat fluxes, for the early (late) IOPs. Generally speaking, model sensible heat fluxes are correlated with aircraft measurements better than latent heat fluxes. Nevertheless, the correlation coefficients with aircraft measurements are much lower than those with surface station measurements, and this should not be a surprise. There are several factors contributing to this discrepancy.

First, one difficulty in comparing aircraft measurements with model results is certainly associated with differences in their spatial sampling or model resolution. As mentioned above, aircraft heat fluxes are computed at 1-km segments along the leg using Eqs. (1a) and (1b). Hence, it can be assumed that this segment-average flux is due to flux contributions from all land surface elements with different land-use cover, soil texture, terrain elevation, and soil moisture within the flux footprint. From a visual inspection of the King Air onboard camera data, some significant surface heterogeneity in land use occurs on scales of the order of 100 m. In contrast, two of the LSMs (SOLVEG and OSU LSM) assume a homogeneous underlying surface in each 1 km × 1 km model grid, while the third, NCAR LSM, assigns an arbitrary four-element subgrid-scale variability. Thus, we may expect less fluctuation in surface heat fluxes in the LSMs, even though we made an effort to perform the 4-km model-flux averaging in much the way as the technique used for processing aircraft fluxes.

Second, the footprint for the aircraft fluxes may not correspond to the kilometer squares over which the aircraft flew. Desjardins et al. (1992) found that fluxes sampled by aircraft at low levels correlated best with surface conditions slightly upstream. The correlation of flux with surface properties reached a peak at a separation of between 1 and 3 km, depending on wind speed, surface roughness, and stability. The averaged wind for the boundary layer was 10 m s⁻¹ from the south on 29 April, 5–6 m s⁻¹ from the south-southwest (SSW) on 10 May, and 6–7 m s⁻¹ from the east-northeast (ENE) on 20 May.

Third, atmospheric processes in addition to surface processes affect aircraft fluxes, at least on a transitory basis. Even over a horizontally homogeneous surface, converging air in large eddies sweep rising turbulent elements into their updraft regions. LeMone (1976) and LeMone and Pennell (1976) provide examples of horizontal roll vortices concentrating fluxes, but any large eddy should have a similar effect. Figure 11 shows an example of fluxes concentrated by the atmosphere for 20 May. Note the strong positive correlation between aircraft sensible and latent heat flux, with large values at 96.8°W and around 96.65°–96.7°W. The sum LE + H exceeds the net radiation by at least 150 W m⁻²; LE + H + G exceeds the net radiation locally by more than 200 W m⁻². Clearly, this type of atmospheric variability cannot be captured by 1D uncoupled LSMs, which involve only interations at the surface. In other words, land surface model results represent turbulence characteristics in equilibrium with the local surface, while events like that in Fig. 11 represent three-dimensional processes that involve larger scales.

Such large-amplitude events can dominate the entire morning average. For example, large heat fluxes found around 96.8°W in Fig. 10 reflect an event recorded in the first morning leg (Fig. 11). To see whether the correlation of modeled and observed fluxes along the flight tracks could be improved with the elimination of extreme events such as that in Fig. 11, different sets of legs were “resampled” and then used for computing correlation coefficients. For each morning average, one flight leg was alternatively dropped for morning leg averaging. As a result, only three flight legs for 29 April and two flight legs for 10 May were employed, and the correlation coefficients, based on such resampling, of the three models are shown in Table 6. For 29 April, utilizing only flight legs 1, 3, and 4 (i.e., eliminating the flight leg of 1601 UTC) produced better correlation coefficients for both latent and sensible heat fluxes. Recall that there were only three morning flight legs for 20 May, but removing flight leg 2 at 1643 UTC also seems to generate better correlations. Utilizing more samples may mitigate the dominance of one flight leg (Mahrt 1998), provided the large events do not stay in the same location from leg to leg. In a companion paper, LeMone et al. (2003, this issue) show how to determine whether surface effects can be separated from atmospheric effects through temporal and horizontal averaging.

Despite these limitations, model-flux maps are able to capture major heterogeneity induced by land-use cover and soil moisture. Notably, models appear to capture the spatial variability for the days when the land surface was significantly heterogeneous (e.g., 29 April and 10 May).

Moreover, the models did a reasonably good job in simulating the leg-averaged fluxes, as shown in Fig. 12. The models seem to have the same range of variation in latent heat fluxes as the aircraft measurements, while modeled leg-averaged sensible heat fluxes are systematically higher. Also note that the correlation coefficients for latent heat flux are slightly higher than these for sensible heat flux, and the leg-averaged heat fluxes are better correlated than along-leg flux variability. As shown in Fig. 11, aircraft LE + H + G can be larger or smaller than the net radiation in different parts of the flight leg. However, being averaged over the entire flight leg, LE + H + G is close to the net radiation.