Influence of Land Cover and Soil Moisture on the Horizontal Distribution of Sensible and Latent Heat Fluxes in Southeast Kansas during IHOP_2002 and CASES-97

a. Aircraft data: Fluxes, surface characteristics, and boundary layer depth

Aircraft data for both field experiments were collected using the University of Wyoming King Air gust-probe aircraft. For CASES-97, aircraft-relative winds were measured by a Rosemount 858AJ/1332 differential pressure gust-probe system. Aircraft position and motion relative to the ground were measured by a Honeywell Laseref SM inertial navigation system. Aircraft altitude was based on a King KRA5 radar altimeter for heights below 610 m and an APN159 radar altimeter for heights above 610 m. The mixing ratio Q was measured using the LiCor 6262 gas analyzer, the radiometric surface temperature T_s was measured with a PRT-5 radiometer, and potential temperature Θ was calculated from the pressure from a Rosemount 1201 sensor and air temperature measured as described in Friehe and Khelif (1992). Data were recorded at 50 Hz.

The King Air instrument package and software were slightly different for IHOP_2002. The normalized differential vegetation index (NDVI) was estimated from an Exotech radiometer, using the relationship

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where r₄ is the amount of electromagnetic radiation reflected in the near-infrared at 0.762–0.898 μm, and r₃ is the amount of electromagnetic radiation reflected in the red at 0.629–0.687 μm. The aircraft location was corrected using GPS to within 100 m horizontally (A. Rodi 2006, personal communication), so that T_s, NDVI, and aircraft video images could easily be correlated with surface features. A reverse flow thermometer measured air temperature, and a Heiman KT-19.85 radiometer sensed T_s. Data were recorded at 25 Hz.

Figure 1 shows the three tracks used for IHOP_2002 Boundary Layer Heterogeneity (BLH) missions, which were designed to document the effects of the surface on BL thermodynamic fluxes and structure. The flight-track locations extended from the Oklahoma Panhandle to southeastern Kansas, to sample a large range of precipitation, soils, and land-cover types. This paper focuses on the eastern track, shown in Fig. 2; fluxes on the western track are documented by Kang et al. (2007). From Table 1, the eastern track has greener and denser vegetation (higher NDVI), cooler T_s, and higher rainfall than the western track. The central track has intermediate characteristics.

Each King Air mission consisted of multiple straight-and-level legs along a single track, interspersed with soundings to check convective boundary layer depth (Table 2). In the IHOP_2002 BLH missions, some legs were always flown at ∼70 m above ground level (AGL), with at least one other height within the boundary layer (BL) represented. The flight pattern changed with the research emphasis, with more 70-m legs for flux missions, and legs divided more evenly between two and four heights for BL structure missions. For typical CASES-97 missions, four sets of legs at four levels within the BL were flown along the IHOP_2002 eastern track, with the lowest level at 30–40 m AGL. The lowest legs (below 100–150 m) were flown at a roughly constant height above the ground, while the higher legs were flown according to pressure altitude, so that altitude above the ground varied around the specified leg height.

“Total” grand-average IHOP_2002 and CASES-97 fluxes along the eastern track for a given day were calculated in a multiple-step procedure following LeMone et al. (2003). First, time series for Θ, Q, and vertical velocity W for each leg were detrended by subtracting out the best-fit line based on linear regression. Second, the mixing ratio was shifted 0.30 s earlier and the temperature 0.1 s earlier to correct for instrument time lag and the physical separation of the thermodynamic sensors from the vertical-velocity sensors on the aircraft.¹ Third, the resulting time series [θ(t), q(t), and w(t)] were multiplied to form θ(t)w(t) and q(t)w(t) time series. Fourth, these products were averaged into increments (0.01° longitude for CASES-97, 1 km for IHOP_2002) and converted to H and LE. For each leg, this procedure resulted in a set of 0.97- or 1-km segments whose fluxes, when averaged, are close to the leg-average fluxes. Fifth, data for each leg were smoothed using a 4-km running-mean average. Finally, the smoothed fluxes at corresponding points were averaged to form the grand-average leg. For IHOP_2002, the 1-km data for each leg were interpolated to common geographical points before averaging in time. While the interpolation has the effect of smoothing the 1-km data slightly, this should not significantly alter fluxes after smoothing with running means 4 km and longer to obtain statistical robustness.

For comparison, we calculated “high frequency” fluxes for the IHOP_2002 days using a procedure similar to that for the total fluxes except that the 1-km average fluxes for each leg were calculated using fluctuations relative to the corresponding 1-km mean.

We focus on the total fluxes because their magnitudes should be similar to measured and modeled surface fluxes. In the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE), high-pass filtering the data to remove fluctuations of wavelength >5 km resulted in underestimates in both H and LE (Grossman 1992; Kelly et al. 1992); in a more complete analysis, Lenschow et al. (1994) obtain a similar result. For the IHOP_2002 cases examined (Table 3), the leg-averaged high-frequency fluxes were between 77% and 88% of the leg-averaged total fluxes. The disadvantage is that the total fluxes include “mesoscale” motions, whose larger scales lead to more random error, and which may lead to a longer “memory” of the upstream surface. Further, linear-trend removal is not optimum when the time series include an abrupt change.

Table 4 shows estimates of the fractional random error σ*(F) for average total H and LE for each day. We calculated σ*(F) for each leg following Mann and Lenschow (1994) via

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and then combined the results for all N legs as described in LeMone et al. (2003). In (2), s is a scalar, L is the length of the flight leg (∼46 km), λ_F is the integral scale for ws, found from the ws − spectrum as described in Lenschow (1995), and r_w,s is the correlation between w and s. Relative to the values in the table, σ*(F) increases by a factor of ∼(46/4)^1/2 = 3.39 for 4-km averages along the grand-average leg. The IHOP_2002 random errors are comparable to those for CASES-97 in spite of more flight legs because changing the height of the lowest flight legs from 35 to 70 m leads to roughly a doubling of λ_F and thus a need for twice as many legs to get the same random error.

b. Surface-station data: Fluxes

Flux stations along the eastern track were all grassland sites, located at positions 7, 8, and 9 in Figs. 1 and 2. Half-hour averages of the terms in the surface energy budget (H and LE from eddy correlation, soil heat flux G_sfc, and net radiation R_net) from these sites are available at http://www.rap.ucar.edu/research/land/observations.php, along with meteorological variables (temperature and mixing ratio at 2 m, wind at 10 m, precipitation) and soil moisture at 5 cm. Also collected were 5- or 15-min profiles of several soil characteristics including soil moisture and temperature, at six depths to 0.6–0.9 m. The automatically recorded data were supplemented at 7–10-day intervals with photographs and manual observations of soil moisture and various vegetation characteristics. Because of instrument malfunction, the IHOP_2002 LE values used here were estimated as a residual from the surface energy budget. For the two CASES-97 case study days used here, LeMone et al. (2002) found that the fluxes were slightly underestimated, such that H + LE ∼ 0.9–0.94 (R_net − G_sfc). For IHOP_2002, LE was available after ∼12 June at station 9; the resulting residual was ∼0.1(R_net − G_sfc) but changed sign from day to day.

Because H was calculated from sonic temperatures using LE (Schotanus et al. 1983), the H measurements used here are too low by up to ∼10%–20% on days when the fast-humidity instrument malfunctioned (produced obviously too low LE). This estimate is based on iteratively correcting H using LE based on surface energy balance.

c. Comparison of aircraft and surface-station fluxes

For IHOP_2002, surface H values extrapolated downward from linearly regressed aircraft leg-average total H profiles are about 10% lower than fluxes based on tower measurements, with total leg-average LE values within 5% except for 30 May, when the values differed by ∼15%. Agreement is slightly better with corrected H. However, the H average for stations 7–9 is probably too low and the LE average too high, compared to the actual surface average, since all three sites are on grassland and the main other type of land cover (dormant winter wheat) should have higher H and lower LE than the green grasses. During CASES-97, King Air LE was similar to surface values given the large scatter, but H was up to 30% lower than the surface fluxes (LeMone et al. 2002).

d. Supplementary boundary layer depth estimates

The Argonne National Laboratory’s Atmospheric Boundary Layer Experiments (ABLE) facility radar wind profilers at Beaumont and Oxford, Kansas, were used to obtain boundary layer depth near the ends of the eastern track (Fig. 2). The vertical resolution is of the order of 60 m at Beaumont and 100 m at Oxford for CASES-97, and 60 m for both for IHOP_2002. Boundary layer height is defined as center height of the gate just below the maximum signal-to-noise ratio (SNR) drop-off rate with height (Coulter and Holdridge 1998).

The Wyoming Cloud Radar (WCR) was used to determined PBL depth along the flight track. The WCR is a 3-mm (95 GHz) multiantenna Doppler radar (Pazmany et al. 1994). During IHOP_2002, the radar’s two antennas looked vertically up and down from the aircraft; the along-beam data are resampled in 15-m gates after applying a spline fit to 4-m samples. The along-beam (vertical) resolution is O(30 m), and the nearest reliable gates are centered 120 m below and 105 m above the aircraft, resulting in a 225-m “blind” zone approximately centered on the aircraft. Echo strength is measured in terms of equivalent reflectivity, which is derived from power under the assumption that the scatterers are spherical water droplets.

The WCR BL depth z_{i_WCR} is determined from the equivalent reflectivity above plumes (Miao et al. 2006) after vertical (three gates or 45 m) and horizontal (10 s or ∼830 m) smoothing. Usually, z_{i_WCR} is found from the upward-looking beam, and defined as where the range-corrected reflectivity reaches a minimum—between the drop-off at plume top and the increase in reflectivity due to range-corrected noise. For the downward-looking beam, z_{i_WCR} is taken as the height of an arbitrary reflectivity value ranging between −28 and −26 dBZ. This level is characterized by a large reflectivity gradient. Since the scatterers are small insects trying to fly downward, reflectivity becomes small between plumes and BL depth is often not detectable there (Geerts and Miao 2005).

a. Environmental conditions

With the exception of 27 May (IHOP_2002) when light rain fell, the days examined (Table 2) had clear skies to scattered clouds, and wind from ∼SSW–SE, with speeds ranging from slightly less than 4 m s⁻¹ on 30 May 2002 to 10 m s⁻¹ on 29 April 1997. From Fig. 3, the rain and associated cloudiness significantly altered the surface energy budget on 27 May. Since our focus is on the effects of surface heterogeneity, 27 May will not be included in the analysis. The curves for net radiation (R_net), H, LE, and heat flux into the soil (G_sfc), are relatively smooth on the remaining six days, consistent with the lack of significant cloudiness (Fig. 3; Fig. 3 of LeMone et al. 2002; Fig. 9 of LeMone et al. 2000). The June days represent a single dry-down event (Table 2).

The land-use maps (Figs. 1, 2) show a higher density of crops (mainly winter wheat) to the west and mainly grasslands to the east, relative to the eastern track and for at least 100 km to the south. The band of winter wheat extends south to the Oklahoma–Kansas border; south of the border, the winter wheat band extends southwestward to beyond the Oklahoma–Texas border. Aircraft videos and surface site visits show land use along the flight track to be similar for CASES-97 and IHOP_2002. The dominant soil type along the flight track is silty clay loam (State Soil Geographic Database). Rainfall was ample (Table 1; Yates et al. 2001) and frequent (Chen et al. 2003, 2007) for both field programs, so the vegetation was not stressed.

b. Horizontal variability in low-level fluxes along the flight track

The H patterns, in Fig. 4 for IHOP_2002 and Fig. 5 for CASES-97, have consistent behavior for both experiments. For the IHOP_2002 days, there are H maxima around −96.9° (A) and −96.7° (A′), separated by a minimum from −96.77° to −96.8°. The pattern is reversed for CASES-97, with a well-defined H minimum around A on 29 April 1997 and a broader H minimum on 10 May 1997 spanning the same location; and secondary H minima around A′ on 10 May, and slightly west of A′ on 29 April. At the east end of the track, H increases eastward on three of the four IHOP_2002 days, and decreases eastward on the two CASES-97 days.

The LE patterns in Figs. 4 and 5 are not as well defined as the H patterns, with horizontal fluctuations sometimes less than the temporal standard deviations. Such behavior has also been noted by Mahrt (2000). However, there are LE minima around A′ for all the IHOP_2002 days except 22 June, corresponding to the IHOP_2002 H maxima. On 22 June, the LE minimum at A corresponds to the major H maximum, and the LE maximum corresponds to the H minimum east of A′. Also, the CASES-97 data show LE maxima near A that correspond roughly with the westernmost CASES-97 H minima and IHOP_2002 H maxima.

Except for the expected smaller values, amplitudes, and standard deviations, the IHOP_2002 fluxes relative to 1-km averages in Fig. 6 resemble those in Fig. 4 closely. The similarity of the flux trends near the leg ends suggests that linear trend removal to produce the fluxes in Figs. 4 and 5 did not have a significant effect.

Comparing Figs. 4 –6 to Fig. 7, the major features in the flux patterns are correlated with T_s, NDVI, and land-use patterns along the flight track. The T_s maxima and NDVI minima for IHOP_2002 correspond to areas of senescent-to-harvested (∼15 June) winter wheat, with the broadest extrema at A and A′, and more localized extrema at the riparian zone B. Locations A and A′ tend to have high H values and, to a lesser degree, low LE values. The low-T_s, high-NDVI areas correspond to green grass, low H, and to a lesser degree, high LE. In CASES-97, the patterns reverse, with low H, high LE, low T_s, and high NDVI over the winter wheat, which grows rapidly in late April through middle May; and high H, low LE, high T_s, and low NDVI over the grasslands, which are largely dormant on 29 April, and starting to green up by 10 May. The association of H and LE with T_s is discussed in more detail for CASES-97 in Grossman et al. (2005). The small horizontal T_s variability on 17 June 2002 relates to rain on 15–16 June (Table 2).

Table 5 lists the grand-average 4-km filtered flux-T_s, flux–NDVI, and T_s–NDVI correlations along the flight track, and shows that H is slightly more strongly related to NDVI than to T_s, while LE relationships to both are weaker. Not surprisingly, the largest correlations are for 22 June, which combined the smallest random error (Table 4) with the largest horizontal variability (Figs. 4, 6). For the three June days, the correlation of T_s with NDVI increases with time after rainfall (Table 2).

Some of the day-to-day differences between the flux distributions appear to be related to the range of land surface heterogeneity scales felt at flight level. We use two qualitative criteria, the scale length L_co and the stability as expressed by the Obukhov length −L (Table 2). The scale L_co (Raupach and Finnigan 1995), listed in Table 2, can be used as a crude measure of the minimum length scale that can affect flux distribution. It is based on the time scale for air from the surface to reach the top of the boundary layer, given by

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where U is the boundary layer wind speed, z_i is the boundary layer depth, C_co ∼0.8 (Mahrt 2000), and w_* is the convective velocity scale, w_* = [gz_i(_sfc/Θ_υ,sfc)]^1/3, where g is the acceleration of gravity, _sfc is the surface virtual temperature flux, and Θ_υ,sfc is the virtual potential temperature at the surface. The Obukhov length L is given by

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where u_* is the friction velocity and k is the von Kármán constant (here 0.4). In (3) and (4), we use values roughly applicable to the center time of the flight pattern (average for CASES-97, interpolated values for IHOP_2002). We include L since the effective flux footprint decreases in size and its peak becomes closer to the measurement site as the boundary layer becomes more convective (e.g., Schuepp et al. 1992).

The results, in Table 2, are consistent with the impact of smaller scales on the fluxes at flight level being reduced on days with strong wind and weak buoyancy flux. For IHOP_2002 and CASES-97, the westernmost H extremum at A is most prominent horizontally for 29 April 1997 and 17 and 22 June 2002, which have large L_co and −L. From Fig. 7, these differences are consistent with the winter wheat area being broader upstream (south) of A than upstream of A′. Conversely, the H extrema at A and A′ are comparable on 30 May 2002, 20 June 2002, and 10 May 1997, days with smaller L_co and −L, suggesting the fetch at A′ is large enough that the differences in fetch do not matter. For LE, the extremum at A dominates on 22 June 2002 and to a lesser degree on 29 April 1997. Both have large L_co and −L but perhaps more significantly also have the best statistical sample (Table 4). Note that the ∼2 km wide riparian zone at B does not have a clear impact on H or LE on any of the days observed.

a. Definition of Δ_xyLE/Δ_xyH and how it is estimated

In the foregoing, areas of high H often correspond to areas of low LE, and vice versa. To evaluate horizontal variability in IHOP_2002 and CASES-97 from a different perspective, we examine the slope of the best-fit straight line in plots of LE as a function of H, averaged over a given time interval, as illustrated for 29 April 1997 in Fig. 8. In the figure, H and LE varied by roughly 250 W m⁻², from high-H and low-LE values over bare ground to low-H and high-LE values over green vegetation, producing a slope Δ_xyLE/Δ_xyH = −0.92.

The association of higher LE values with lower H values (compared to the horizontal average) and vice versa, and the resulting negative Δ_xyLE/Δ_xyH slopes follow from the surface energy balance:

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as long as horizontal changes in H and LE are large compared to horizontal changes in R_net − G_sfc. Here R_net −G _sfc = constant, H + LE = constant, and Δ_xyLE/Δ_xyH = −1.

Based on CASES-97 data, LeMone et al. (2003) suggested that the available energy H + LE ∼ constant with clear skies and several days after the last rainfall. Clouds create a more complex net radiation field (Fig. 3), and the fluxes tend to be more uniform right after rainfall (Mahrt 2000; Yates et al. 2001; LeMone et al. 2003). To define the slope using surface-flux stations, a variety of land uses must be sampled (satisfied for CASES-97, but not for the IHOP_2002 eastern track, since stations 7–9 sample grassland only), and horizontal variability in H and LE must be greater than ∼100 W m⁻² (LeMone et al. 2003), based on the 50 W m⁻² uncertainty in the measurements (Yates et al. 2001).

Because the IHOP_2002 surface sites sample grassland only, we turned to aircraft data to estimate Δ_xyLE/Δ_xyH for the days in Fig. 4. In addition to the above requirements, slope estimates from aircraft data need a sufficient sample to overcome the positive Δ_xyLE/Δ_xyH slope that results from the atmosphere’s tendency to concentrate fluxes in the upwelling regions of large eddies (e.g., LeMone 1976; Grossman 1982). This often necessitates horizontal as well as temporal averaging (LeMone et al. 2003). Figure 9 shows Δ_xyLE/Δ_xyH as a function of horizontal averaging for IHOP_2002 (see Fig. 9 in LeMone et al. 2003 for a similar plot for CASES-97). As in Fig. 8, the slopes are based on least squares linear regression. Aircraft–surface slope comparisons for three days along the western track, where four surface stations sampled the range of land cover, show the best match for 3–5-km aircraft averages, precisely the range at which we would expect effects of boundary layer large eddies to be mostly filtered out (∼3 z_i; see Table 2; z_i values on the western track are similar for the days compared; Kang et al. 2007). Consistent with this, the slope in Fig. 9 tends to level off at averaging lengths >5 km. Thus we will use 3–5-km averages in slope comparisons, even though LeMone et al. (2003) suggested longer averages were needed to match surface slopes in CASES-97. Of course, a rigorous determination of the best average requires good aircraft statistics and corresponding surface data. The picture is complicated by potentially different footprints for H and LE (e.g., Kustas et al. 2006) and different atmospheric factors affecting H and LE at larger scales.

As in CASES-97, we could not determine reasonable Δ_xyLE/Δ_xyH slopes for all the days. The most robust slope estimates, both for aircraft and surface data, are for days with the longest dry-down and driest soils, 29 April 1997 and 22 June 2002. No amount of filtering is sufficient to make the slopes negative on 17 or 20 June. On 17 June, the high soil moisture and cool, near-uniform T_s (Fig. 4) results from recent rainfall; thus we expect LE due to evaporation from bare or sparsely covered ground is comparable to LE due to evapotranspiration over green vegetation (e.g., Yates et al. 2001). In such cases, horizontal variability in H and LE should be comparable to horizontal variability in the available energy R_net − G_sfc, with an H versus LE plot a cloud of points without a well-defined slope. Further, the rainfall distribution could be important. On 20 June, horizontal variability in available energy is significantly altered by clouds (Fig. 3), and only five low-level legs were flown. With only four days to compare, we will look at more days from CASES-97 and use land surface models.

b. Effect of the diurnal cycle on Δ_xyLE/Δ_xyH

IHOP_2002 aircraft flux patterns were centered on local solar noon (∼1800–1900 UTC; Table 1), while CASES-97 aircraft data used here were centered at ∼1630 UTC. Figure 10 shows the change of Δ_xyLE/Δ_xyH between 1515 and 2145 UTC, for an idealization of 22 June with two types of land cover, grass, and sparse vegetation. Over grasses, H peaks earlier than LE, and G_sfc is smaller in the afternoon than in the morning. If G_sfc, H, and LE over dormant vegetation are more symmetric about solar noon (true for CASES-97; see LeMone et al. 2000, 2002), the combined behavior of these two land-cover types makes the slope more negative with time (by ∼0.1 h⁻¹). The IHOP_2002 aircraft slopes for 22 June show a similar trend: for the first five legs, the 4-km-average slope is −1.25 (|R| = 0.4), shallower than the value for the second five legs, −1.5 (|R|=0.66), again a ∼0.1 h⁻¹ decrease. For CASES-97, half-hour-average plots of Δ_xyLE/Δ_xyH from half-hour-averaged surface-station data centered from 1745 to 2115 UTC revealed no obvious trend for 10 May, but 29 April slopes became shallower with time (+0.05 h⁻¹).

c. The association of shallower Δ_xyLE/Δ_xyH slopes with longer dry-down and drier soils

Figure 11 shows Δ_xyLE/Δ_xyH as a function of time for the three observed CASES-97 dry-down periods described in Fig. 7 of Yates et al. (2001), and for the modeled IHOP_2002 17–22 June 2002 dry-down period. For three of the four dry-down periods, Δ_xyLE/Δ_xyH becomes shallower with time after rainfall, with the final point of the 9–12 May CASES-97 sequence leading to the one exception. The IHOP_2002 slopes in the bottom frame are averages of the 4-km square model grids along the eastern track, from the High-Resolution Land Data Assimilation System (HRLDAS). HRLDAS, which is based on the Noah LSM, is described and evaluated in Chen et al. (2007). Diurnal effects are not a factor here, since the time of day is kept constant.

The relationship of Δ_xyLE/Δ_xyH to soil moisture is illustrated for both field programs in Fig. 12. The LSM slopes in the bottom two frames come from a variety of LSMs. For CASES-97, the slopes come from Fig. 5 of LeMone et al. (2003), and are based on the following three LSMs: SOLVEG (Nagai 2002), the Noah model (OSULSM; Pan and Mahrt 1987; Chen et al. 1996; Ek et al. 2003), and the National Center for Atmospheric Research (NCAR) LSM (Bonan 1996). The LSM data used to compute CASES-97 slopes were derived for 1-km squares as described in Chen et al. (2003), and smoothed with a ∼4 km running mean to be consistent with the corresponding aircraft fluxes. An additional version of the Noah model (Noah) for 1-km squares along the track is included because soil-moisture data from the other three are no longer available. Of the available CASES-97 model runs, it had the closest values to the modeled soil moisture in Chen et al. (2003). The CASES-97 LSMs are evaluated in Yates et al. (2003) and Chen et al. (2003).

The 5-cm volumetric soil-moisture values in Fig. 12 are computed to match the slope data to the degree possible. For the CASES-97 slopes based on the surface array (Fig. 2 of LeMone et al. 2003, sites 1–8), the corresponding soil-moisture values were averaged. The National Oceanic and Atmospheric Administration (NOAA) Twin Otter–based slope in Fig. 12a also uses the CASES-97 array average soil moisture, since its flight track was farther north within the array (Fig. 2, track 3, of LeMone et al. 2003). For the slopes based on the King Air, averages of IHOP_2002 sites 7–9 are used for 30 May and 22 June 2002, while the volumetric soil moisture at CASES-97 site 6 (closest to the eastern track) is used for the 29 April aircraft slopes. Horizontal variation of the Noah model soil moisture along the eastern track suggests that site 6 values are similar to track averages. For the CASES-97 array-averaged soil moisture for all three days, the spatial standard deviation is large (∼0.1), but the day-to-day trend is the same for all eight stations and consistent with the trend for the Noah LSM (Fig. 12b). For IHOP_2002, the range of soil-moisture values for sites 7–9 varies between 0.016 (17 June) and 0.057 (22 June), with the 30 May value = 0.027. HRLDAS soil-moisture values qualitatively follow the observed day-to-day trend.

Subject to the uncertainties discussed in the foregoing, all three frames of Fig. 12 suggest that Δ_xyLE/Δ_xyH becomes shallower with drier soils. The trend for the observations, in Fig. 12a is particularly striking, but must be interpreted with caution given the uncertainty in the slope and soil-moisture estimates. Correcting the slope data to a common time (1800 UTC) to allow for diurnal effects in Fig. 12a changes values from ∼0.1 to 0.15—a negligible effect.

As in the case of the observed slopes, the LSM values for CASES-97 in Fig. 12b are more well defined for 29 April than for 10 or 20 May. For 10 and 20 May, there is usually smaller horizontal variability and more scatter around the best-fit lines used to determine the slope in Fig. 5 of LeMone et al. (2003). Slopes based on poor statistical fits are omitted; hence the figure shows fewer points for 10 May (3) and 20 May (4) than for 29 April (6). Indeed, the horizontal variability in H and LE was not sufficient to define a slope even with surface data on 20 May.

Given the uncertainty in soil-moisture values, point-by-point comparisons of Δ_xyLE/Δ_xyH show the average LSM values match the surface slopes reasonably well for 29 April and 10 May (CASES-97), but the modeled slopes for IHOP_2002 are much shallower than those observed. This is consistent with HRLDAS significantly underestimating the soil moisture in Fig. 12c. The discrepancy is at least in part due to using as input the NCEP stage-IV radar-derived rainfall, which is up to 1/3 less than that observed at sites 7–9 (Chen et al. 2007). For CASES-97, 1-km-resolution gauge-corrected rainfall data generated as part of the experiment were used as input for the CASES-97 LSMs (Yates et al. 2001; Chen et al. 2003), leading to values more consistent with observations.

Collected in a nearby and similar geographic area, the FIFE data in Table 6 suggest similar behavior: Δ_xyLE/Δ_xyH is steepest for the wettest phase and shallowest for the driest phase. If one accepts the total FIFE fluxes as reasonable proxies for the daytime flux and assumes that the rainfall was reasonably spaced through the field observations, these figures are consistent with steeper slopes with wetter soils and/or shorter time between rain events.

d. Idealized Noah model runs

To examine the source of the Δ_xyLE/Δ_xyH differences further, we apply the Noah model to two pairs of idealized scenarios (Table 7) to represent CASES-97 (spring) and IHOP_2002 (summer). In each case, only two types of land cover—crops (winter wheat) and grassland—are represented according to changes in their green vegetation fraction Fg. The assumed soil depth is 2 m, the assumed root depth is 1 m, and there is no horizontal transport of water. Soil layers were 95% saturated at the beginning of the experiments, and allowed to dry down for 15 days. Diurnal forcing (net solar radiation) was consistent with clear skies and is the same for all runs.

The Δ_xyLE/Δ_xyH slopes for the four dry-down scenarios are represented by lines connecting noontime H and LE values for crops and grassland for each day in Fig. 13. In all cases, the steepest Δ_xyLE/Δ_xyH slopes occur immediately following rainfall. The range of flux values on each day is larger than observed because of the extreme initial conditions. Subsequently, the line connecting the two vegetation types rotates counterclockwise with time from a steep slope (between –1.8 and –2.6) to a shallower value (between −1.4 and −1.9) on day 15, and the range of values increases, as in the observations. For the vegetation type with Fg = 0.95, H and LE remain nearly constant² until around day 15, while the end of the line with low Fg moves down and to the right with time at a roughly 45° angle, as LE decreases and H increases with time. In the scenarios with Fg = 0.50 for the greener vegetation, both ends of the line move down their respective ∼45° time-evolution paths, but the Fg = 0.05 end moves slightly faster, again rotating the Δ_xyLE/Δ_xyH line toward shallower slopes with time.

From (5), the separation between the two time-evolution paths in each frame of Fig. 13 is determined by the value of R_net − G_sfc = H + LE. At a given time, the difference in R_net for the two vegetation types is small (true for CASES-97; see Fig. 9 of LeMone et al. 2000), so this separation is primarily because the heat flux into the soil is significantly larger for the low-Fg vegetation than for the high-Fg vegetation, resulting in smaller R_net − G_sfc for the lower-Fg vegetation. As long as this is true, the low-Fg time-evolution path (numbered symbols) will be closer to the origin (H + LE smaller) than the high-Fg time-evolution path (symbols at the other end of the Δ_xyLE/Δ_xyH lines). Because drier soil has lower thermal conductivity, G_sfc decreases with time. However, [∂(R_net − G_sfc)/∂t] = [∂(H + LE)/∂t] ∼ 0 in the scenarios shown, since the warming surface temperature T_s increases upwelling infrared radiation (∝T_s⁴) just fast enough for R_net to decrease at nearly the same rate as G_sfc. This makes the time-evolution paths (Δ_tLE/Δ_tH) parallel with a ∼45° slope. In some simulations (not shown), |(∂G_sfc/∂t)| > |(∂R_net/∂t)| for the lower-Fg vegetation, making [∂(R_net − G_sfc)/∂t] = [∂(H + LE)/∂t] > 0. This reduces the distance between the two time-evolution paths with time and allows Δ_xyLE/Δ_xyH to reach or exceed −1.

e. The effect of terrain on Δ_xyLE/Δ_xyH slopes

Knowing the association of grassland, shallow soils, and bedrock exposures with ridges, and the association of crops and deeper soils with nearby valleys along the eastern track (LeMone et al. 2000), we can speculate on how terrain would affect the modeled slopes in Fig. 13. For CASES-97 (spring), the dormant grasses should dry down faster than in the figure, because (a) the shallower soils will dry out faster, (b) surface runoff will make less moisture available, and (c) subsurface water will flow downhill. This will accelerate the “grassland” end of the Δ_xyLE/Δ_xyH line downward and to the right. We represent this dry-down “acceleration” by an arrow pointing down and to the right next to the grass time-evolution path (numbered symbols) in the top frames of the figure. Similarly, we use an arrow pointing upward and to the left to indicate some slowing of the dry-down for the crops (WW) due to water supply from surface runoff and subsurface flow. Together, these factors should produce an ∼ −1 slope more rapidly than the simulations represented in the figure.

Conversely, accounting for terrain in the IHOP_2002 (summer) scenario, the dry-down should be accelerated for the green grasses (down-right-pointing arrow next to the grass time-evolution path in the lower frames, and slowed in the valleys, where there is dormant or harvested crop with low Fg (up-left-pointing arrow). This slows down the evolution of Δ_xyLE/Δ_xyH to shallower slopes.

Figure 14 shows the impact of decreasing the Noah LSM grass-rooting depth (a crude proxy for “soil depth”) on Δ_xyLE/Δ_xyH. Decreasing the root depth from 1 m (the value corresponding to Fig. 13) to 10 cm leads to shallower slopes for the spring scenario, and steepens the slopes for the summer scenario, as expected. However, these changes are small compared to those associated with the length of dry-down (or equivalently, the amount of soil moisture). The effect of relative surface elevation on dry-down near the eastern track is supported by Fig. 15 of Grossman et al. (2005), which shows that T_s increases with elevation for a given land-use type in CASES-97. Thin soil at higher elevations is mentioned as a major factor. D. Gochis (2005, personal communication) modified the Noah model to include horizontal transport of water (“routing”) for a simulation of CASES-97 fluxes, and this resulted in slightly faster dry-downs on the ridges, with slightly higher H and lower LE with the routing included. This work is ongoing.