a. Data collection and selection of case study

The observations on this day are from surface flux towers and five ∼60-km flight legs flown at ∼65 m AGL by the University of Wyoming King Air along the IHOP_2002 western track (Fig. 1). In contrast to the eastern track (LeMone et al. 2007b), this region had much less rainfall and vegetation. Furthermore, it has more heterogeneous soil types and land cover. The four surface flux sites along the western track [sites 1–3 maintained by NCAR, site 10 by the University of Colorado (CU)] were located on different types of surface—bare ground (site 1), ungrazed Conservation Reserve Program grassland (site 2), sagebrush (site 3), and heavily grazed grass (site 10)—allowing a good sample of horizontal variability from the surface as well as from the air.

Aircraft H and LE estimates are based on vertical velocity determined from the Rosemount 858AJ/1332 differential gust-probe system and a Honeywell Laseref SM inertial navigation system, with temperature from a reverse-flow thermometer developed at the University of Wyoming. Water vapor fluctuations are sampled using a Li-Cor-6262 gas analyzer and a Lyman-α instrument from NCAR. The Li-Cor measures infrared absorption by water vapor; while the Lyman-α measures absorption of ultraviolet radiation. The Li-Cor is standard on the King Air, was used for LeMone et al. (2003) and LeMone et al. (2007b), and provides stable measurements, while the Lyman-α has faster response but needs periodic calibration using a reference water vapor density; hence, we show results from both here. Surface H and LE are based on sonic temperature and vertical velocity from sonic anemometers, and mixing ratios derived from Campbell Scientific KH20 Krypton hygrometer water vapor densities.

The radiometric surface temperature T_s is sensed by a Heiman KT-19.85 radiometer on the King Air; and by Everest 4000.4GL sensors at the surface flux sites. Kang et al. (2007) indicate reasonable consistency between the aircraft and surface measurements, although L. Oolman (University of Wyoming 2007, personal communication) suggests there is a slightly cool daytime bias (∼1 K) in T_s due to pitting on the lens incorporating some effect of the air temperature at flight level. For comparison with HRLDAS values, we estimated the difference between T_s and 2-m temperature T₀ by subtracting the best-fit straight line to T₀ from the surface sites (average of 1815 and 1845 UTC) from the best-fit quadratic for the aircraft T_s for the flight leg centered at 1830 UTC. The aircraft normalized differential vegetation index (NDVI) is from Exotech radiometer data.

The soil and vegetation data used here were collected in several different ways. Recorded values of soil moisture at 5 cm at the NCAR sites and the profile at the CU site were measured using Campbell Scientific CS-615 probes; profiles at the NCAR sites were based on Decagon ECH₂O probes, installed and processed in partnership with the Hydrologic Science Team in the Department of Bioengineering of Oregon State University (OSU). Manual measurements of soil moisture were made using a MESA Systems TRIME FM-3 sensor on 29 and 30 May. On the same visits, NDVI measurements were made using a Cropscan MSR5 probe. We used soil temperatures from Campbell Scientific CS-107 probes at the NCAR sites, and REBS STP-I probes at the CU site. Soil heat flux was measured using REBS HFT-3 flux plates at all four sites. Soil characterization (i.e., mineral content, texture, and bulk density) was done for sites 1–3 by the OSU Hydrologic Science Team and for site 10 by Alfieri at CU. Further details are available from LeMone et al. (2007a).

We selected 29 May 2002 for this study for two reasons. First, the measured fluxes were heterogeneous, consistent with a strong north–south gradient in soil moisture; and second, we wanted to understand why HRLDAS did not do better in replicating the observations. A strong rain event 2 days previous deposited ∼80 mm of rain at site 1 near the south end of the track, and ∼10–30 mm at the remaining sites. The heterogeneous fluxes on this day and their impact on boundary layer depth are summarized in Kang et al. (2007). From Strassberg et al. (2008), the mean wind is from 194° at 4.8 m s⁻¹ at 65 m and the Monin–Obukhov length is −25 m. According to Kang et al., the PBL depth varied from about 1 km on the south end of the track to 1.3 km on the north end.

b. Flux calculation

Aircraft fluxes for each flight leg were found from covariances after subtracting out the linear trends for each variable and shifting the temperature and mixing ratio time series to account for time lags relative to the vertical velocity, which were induced by spatial separation on the aircraft and differences in sensor time response. The covariances were averaged in two ways: in overlapping 4-km running averages at 1-km intervals for looking at horizontal variability, and in 1-km bins for examining the effect of horizontal filtering on ΔLE/ΔH. The data processing is identical to that described in LeMone et al. (2007b), except that the individual legs were truncated so that the averages for all flight legs are at the same geographic points, eliminating the need to interpolate before averaging.

Surface fluxes, processed by NCAR for sites 1–3 and CU for site 10, are relative to half-hour averages. Details can be found in LeMone et al. (2007a) or at the NCAR Earth Observing Laboratory (EOL) Web site. (The processed aircraft and surface data are available at www.rap.ucar.edu/research/land/observations/ihop.php.) Observations along the flight track are summarized in Table 1.

c. HRLDAS

The HRLDAS model (Chen et al. 2007) is based on the Noah LSM (Mahrt and Ek 1984; Pan and Mahrt 1987; Noilhan and Planton 1989; Chen et al. 1996; Chen and Dudhia 2001a; Ek et al. 2003). We use 18 months of input data to obtain soil-moisture and temperature profiles that are physically realistic and consistent with past weather and with the physics package of its parent Weather Research and Forecasting (WRF) Model. The HRLDAS physics are as described in Chen et al. (2007), but we alter the Zilitinkevich coefficient for some runs. This will be discussed further after HRLDAS physics are introduced in section 3. We run HRLDAS on a 3-km grid.

Input parameters for HRLDAS consist of static and time-varying surface databases and historical meteorological data. The static databases include a 19-category land surface characterization based on 2001 MODIS data from the Department of Geography at Boston University (www-modis.bu.edu/landcover/index.html), and the 1-km resolution State Soil Geographic (STATSGO) soil data. Time-varying fields include the 0.15° monthly green vegetation fraction based on satellite-based climatological data collected between 1985 and 1990 (Gutman and Ignatov 1998). These are currently standard for HRLDAS (Chen et al. 2007), except for the MODIS land-cover data, which are used because of changes in land use along the western track. As in the case of HRLDAS with the default vegetation table, albedo and emissivity are defined according to vegetation type and are kept constant except for alteration for snow cover.

The meteorological data (i.e., temperature, humidity, wind, pressure, and downwelling longwave radiation) are from the 3-hourly NCEP Eta Data Assimilation System (EDAS), while downwelling shortwave radiation is from 0.5° Geostationary Operational Environmental Satellite-8 and -9 (GOES-8 and -9) data (Pinker et al. 2002), and rainfall is from 4-km hourly National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) Office of Hydrology stage IV rainfall (Fulton et al. 1998).

For 29 May, the input meteorological data are consistent with a near-cloudless fair-weather day, with almost no horizontal variability in downwelling radiation. The input downwelling radiation is ∼50 W m⁻² higher than the sites 1–3 average, almost completely due to differences in the longwave component. A half-hour¹ shift in the input downwelling solar radiation partially offsets this bias during the averaging period 1700–2100 UTC, but causes an artificially early sunset and leads to underestimates of H at 0000 UTC. Because of the latter bias, H values at 0000 UTC were recomputed for selected runs by averaging H at 2300 and 0000 UTC to obtain a model H at 2330 UTC for comparison to the observed 0000 UTC value. This corrects the timing of the solar radiation but shifts the other input data, so the true H estimates are likely between the original and “shifted” values. Estimated albedos and emissivities are close to input values. Input temperatures at 2 m are 1–2 K higher than observations between 1700 and 2100 UTC. Since there is not exact agreement, we will use the difference T_s − T₀ as well as T_s in evaluating HRLDAS. The western track is distant from the Next Generation Weather Radar (NEXRAD) radars, leading to errors in the HRLDAS input rainfall data. Figure 6 of Chen et al. (2007) shows a significant underestimate of the 26–27 May rain event at site 1, and overestimates at sites 2 and 3; with input rainfall totals from 10 May in agreement for site 1, and overestimates at sites 2 and 3.

a. Comparing HRLDAS and observations

Figures 2 –4 compare observations for 29 May 2002 on the IHOP_2002 western track with results from our control HRLDAS run for the variables it supplies to its parent NWP model, namely H, LE, and T_s.

Figure 2 shows H and LE from HRLDAS control along with the corresponding observations. Fractional random error for the 4-km averages is 0.12 for H and 0.34 for LE [LeMone et al. (2007a), based on Mann and Lenschow (1994)]. In the figure, the observed northward increase in H (decrease in LE) is consistent with the heavy rainfall at the south end of the track 2 days previous. HRLDAS H is higher and LE is mostly lower than what is observed, and the horizontal variability is not captured.

The differences between the model and observations appear to be real. The slight differences between surface and aircraft flux observations reflect true changes in the vertical. The small differences suggest that adjusting the aircraft data to surface values would bring the aircraft data closer to HRLDAS results, but not enough. To confirm this, we produced linear mean flux profiles interpolated to 1830 UTC from aircraft data and used the profiles to adjust the flight-level H and LE curves to surface values assuming a constant change with height. This procedure increased the H curve to 108% of its flight-level value and reduced the LE curve to 81%–94% of its flight-level value, far from enough to explain the discrepancy (not shown). Furthermore, if we shift “observed” aircraft H and LE curves left in Fig. 2 to correspond to their corresponding surface source regions—at most 2–3 km based on Song and Wesely (2003)—this is not enough to force H and LE to modeled values. For comparison, both H and LE in Kang et al. (2007) are similar to Fig. 2 except for a drop in H and a rise in LE at the northern end of the track and smaller averages due to their calculating fluxes relative to 4-km averages, which excludes the contribution of scales >4 km.

In Fig. 3, HRLDAS H is greater not only than the average observed H for most of the daytime hours, but it is also greater than the highest values observed at the surface. In HRLDAS, H becomes more negative (−64 W m⁻²) than any of the observed values at 0000 UTC, likely a result of the half-hour shift in input solar radiation. From section 2c, the “true” model H value at 0000 UTC is probably between −64 and −11 W m⁻², the value corresponding to the correct input solar radiation at 0000 UTC. HRLDAS LE lies within the range observed and is fairly close to the surface average. Like the modeled fluxes in Fig. 2, HRLDAS T_s (Fig. 4), does not exhibit the observed north–south gradient; and it slightly cooler on average than observed.

b. Application and interpretation of ΔLE/ΔH

2) HRLDAS: Why H and LE should be anticorrelated

In the foregoing, we argued that the H and LE variation in Figs. 2 and 5 that correspond to surface processes should be anticorrelated. Here, we show why H and LE should also be anticorrelated in HRLDAS for the conditions (nearly uniform radiative forcing) represented on 29 May, with a negative ΔH/ΔLE slope.

We start with the surface energy balance neglecting storage in the vegetation canopy:

View Expanded

where R_net is the net radiation, and G_sfc is the heat flux into the soil. If we rearrange (1a) slightly,

View Expanded

we can argue that higher (lower) values of H mean lower (higher) values of LE, provided the available energy R_net − G_sfc does not vary much horizontally. Thus, we expect H-versus-LE plots to show a negative slope around −1 under these conditions.

To show how ΔLE/ΔH deviates from −1, we express H, R_net, and G_sfc in terms of T_s − T₀, where T₀ is the air temperature at the lowest model level (i.e., 2 m). Provided T_s − T₀ ≪ T₀, R_net is given by

View Expanded

where σ is the Stefan–Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴), ε is emissivity, α is albedo, S_↓(1 − α) is the net downwelling shortwave radiation, and L_↓ is the downwelling longwave radiation [Ek and Mahrt (1991), modified to allow reflected longwave radiation].

Likewise, we replace T_s − T₁ with (T_s − T₀) + (T₀ − T₁) to express G_sfc as

View Expanded

where K_t is the soil thermal conductivity, a function of soil composition, soil porosity, and soil moisture, F_g is the green vegetation fraction, T₁ is the soil temperature in the first model soil level (0–10 cm), and Δz = 5 cm is the distance from the surface to the middle of the first model soil level. In this version of HRLDAS, K_t is computed following Peters-Lidard et al. (1998). The coefficient exp(−2F_g) in (3) describes “insulation” of the ground by overlying vegetation as an analog to the extinction of radiation. In its original form, the exponent as proposed by Choudhury et al. (1987) and applied by Peters-Lidard et al. (1997) was −βLAI, where LAI is the leaf area index. This term was changed to −βF_g in Ek et al. (2003), with the empirical coefficient β = 2 based on offline Noah runs.

Finally, the sensible heat flux H is written as

View Expanded

where ρ is the air density, c_p is the specific heat of air at constant pressure, c_h is an eddy exchange coefficient, and U is the wind at the lowest atmospheric model level (i.e., 2 m). In (4), we neglect the small correction (0.02 K) for the adiabatic lapse rate in T_s − T₀.

Rewriting (2) and (3) in terms of H using (4):

View Expanded

and

View Expanded

Finally, substituting (5) and (6) in (1b), we obtain the following:

View Expanded

The effects of horizontal variation of α and ε in (7) are small for the two land-cover classes represented, because their values are so similar: for grassland and cropland, respectively, α = 0.19 and 0.20 and ε = 0.96 and 0.985.

To get some idea about the behavior of the terms in (7), we use the results for the control run at 1800 UTC. To simplify, we calculate K_t for each soil type by inserting the appropriate input variables for each soil type into the Peters-Lidard et al. (1998) equations and then find the best-fit least squares straight line (|R| = 0.99) for K_t as a function of volumetric soil moisture Θ₁ in the range 0.15–0.35 to obtain the following:

View Expanded

where Θ₁ is the average for the top 10 cm of the soil and i designates the soil type. In (7), Θ₁= 0.23 ± 0.03, F_g = 0.37 ± 0.004, T₀ = 302.84 ± 0.49 K, T₁ = 298.4 ± 0.84 K, and ρc_pc_hU = 51.26 ± 1.41 W m⁻² K⁻¹. Using ε = 0.98, 4εσT ³₀ = 6.17 ± 0.03 W m⁻² making the radiation term 4εσT ³₀/(ρc_pc_uU) = 0.12 ± 0.003. Using Δz = 0.05 m and (8) to approximate K_t, the soil term in the H coefficient on the left-hand side of (7) averages 0.21 ± 0.05, leading to an H coefficient of 1 + 0.21 + 0.12 = 1.33 ± 0.05. Even though the individual numbers change along the track, the changes are such that the resulting H coefficient does not vary much. On the right-hand side, the radiation terms total to 735 ± 2 W m⁻², and the soil term is −47 ± 6 W m⁻², adding up to 687 ± 8 W m⁻².

The H coefficient in (7) is positive definite. This implies a negative ΔH/ΔLE slope if (i) the H coefficient and the right-hand side of (7) do not vary much horizontally, and (ii) LE and H vary horizontally significantly more than the right-hand side. Under these conditions, which appear to be satisfied on 29 May, HRLDAS supports the observational evidence for H and LE being anticorrelated. Indeed, the H coefficient in (7) could be related to ΔLE/ΔH. We will return to this topic.

c. The Zilitinkevich coefficient C

The one HRLDAS parameter modified in this study was the coefficient C in the Zilitinkevich (1995)³ equation used in the surface layer parameterization to compute the “scaling height” for heat and water vapor z_0h from the roughness height z_0m, which in HRLDAS is provided from a lookup table as a function of land-cover type. From Chen et al. (1997),

View Expanded

where u_* is the friction velocity, k = 0.4 is the von Kármán constant, ν is the kinematic molecular viscosity of air (∼1.6 × 10⁻⁵ m² s⁻¹), and C is an empirical coefficient set to 0.1 based on comparing model results and field data (Chen et al. 1997). In (9), u_*z_0m/ν is the roughness Reynolds number. In the Monin–Obukhov equations, z_0m is the height at which the average wind goes to zero, and z_0h is the height at which the air temperature T_air = T_s. Scalar transports at z < z_0m are assumed to be by molecular processes. It follows that (9) applies strictly for bare soil (e.g., see Zeng and Dickinson 1998); the documented complications related to the vertical distribution of temperature in vegetation of finite height and the influence of sunlight, wind, and so on (e.g., Garratt 1992; Brutsaert and Sugita 1996; Sun and Mahrt 1995; Sun 1999) are ignored. Thus, the height and density of the vegetation are felt through z_0m, LAI, and F_g. Moreover, Monin–Obukhov similarity (e.g., Paulson 1970) is assumed to apply down to z_0h. Based on measured u_* values, the default value of C = 0.1 in HRLDAS is equivalent to z_0h/z_0m ≈ 0.1 − 0.5 on 29 May, with larger values for smaller z_0m (a range of 0.03–0.12 m is used).

a. Introduction

In all, 22 HRLDAS runs (Tables 2 –5) were conducted to explore the sensitivity of HRLDAS H, LE, T_s, T_s − T₀, available energy H + LE, G_sfc, and ΔLE/ΔH to different input parameters and different values of C in (9); and to improve HRLDAS agreement with observations. For each run, modified values were introduced at 0000 UTC 29 May. The input parameters modified include F_g (Fig. 7), Θ₁ (Fig. 8), Θ₂ (Θ for 10–40 cm), soil type (Fig. 9), and z_0m. Land use (Fig. 9) and Θ for the third and fourth soil layers (60 and 100 cm thick, respectively) were left at their control values.

b. Effects of soil moisture and green vegetation fraction

Given the sparse vegetation along the western track, variability in soil moisture should strongly influence horizontal variability in H, LE, and T_s; this conjecture is supported by Alfieri et al. (2007). On 29 May, the decrease (increase) in LE (H) from south to north along the western track is consistent with the observed moister soils to the south (Fig. 10). In the figure, there is an overall northward decrease, with the lowest values at site 3, the highest values at site 2, and Θ₁ lying within the scatter except for site 3. At site 1, however, only the NCAR 5-cm soil moisture is for 29 May: because the soil was too wet to walk on, the site crews had to wait until 30 May to take manual measurements and bring the malfunctioning soil-profiling instruments back online. The soggy soil is consistent with over 80 mm of rainfall there 2 days previous (Fig. 11). From the air, the southern end of the track appeared to have saturated soils, with puddles up to 100 m in diameter (Fig. 12); indeed, one road looked impassible. We speculate that the HRLDAS soil moisture is too low along the southern part of the track for two reasons. First, the stage IV radar rainfall used for HRLDAS initialization underestimated the 26–27 May rain event by almost a factor of 2 (Fig. 6 in Chen et al. 2007). Second, the “extra” water in the Noah model is not stored in puddles that can either evaporate or soak into the soil; rather it is simply taken out of the model domain as “surface runoff.”

The lack of horizontal variability in H, LE, and Θ₁ and the too-shallow ΔLE/ΔH slope in the HRLDAS control run (Figs. 2 –6), combined with the foregoing evidence for a soaked south end of the track prompted the high soil moisture values at the south end of the track for the “extreme,” “dry north,” “wet north,” and “wetter north” scenarios in Fig. 8. The first two listed scenarios were based on the NCAR sites 1–3, while the wet north profiles gave equal weighting to site 3 and the CU site 10.

Since 2002 was a drought year, we also suspected that F_g used in the model was too high. This prompted a family of scenarios (Fig. 7) including the extreme, with almost no vegetation, the “high north” scenario, which allowed for less vegetation at the southern end of the track, and three scenarios (“KA step,” “KA smooth,” and KA average F_g = 0.25) with F_g based on King Air NDVI measurements, using the formula in Gutman and Ignatov (1998):

View Expanded

where NDVI_max = 0.52 and NDVI_min = 0.04.

From Fig. 13,changes in Θ₁ and F_g from their control values increase horizontal variation in both H and LE, but H remains too large and LE too small, while the available energy H + LE remains larger than observed values (Tables 1 and 2). Horizontal variability is induced primarily by imposed Θ₁ variability. This is illustrated by 1) significant horizontal variability in runs 2 and 8, for which F_g = constant; 2) the similarity of runs 8–10 with the same Θ₁ but differing F_g; and 3) the fact that changing F_g from 0.38 (run 10) to 0.01 (run 2) while keeping Θ₁ ∼ 0.4 at the southernmost point changes H and LE there by only ∼50 W m⁻². The run-to-run variation for runs 2–10 is greatest to the north because of a larger range in input soil moisture (Fig. 8). The effect of sand at the HRLDAS grid point at ∼36.83°N takes the form of excursions in H and LE that are reduced for lower soil-moisture values. All of these strategies steepen the ΔLE/ΔH slopes relative to the control run (Table 2). Eliminating points with Θ₁ < 0.1, where LE ∼ 0, steepens slopes from around −1 to around −1.1 (not shown), but values remain too shallow relative to observations.

The T_s simulations in Fig. 14 are more successful, with the runs with the greatest decrease soil moisture toward the north coming closest to reproducing the observed gradient. There is a slight low bias that increases toward the north.

Figures 15 and 16 illustrate the large sensitivity to soil moisture in HRLDAS. In the “zigzag” run (run 12 in Table 4), the soil moisture was subjectively modified so that peaks and valleys roughly corresponded to the horizontal variation in observed LE (cf. Figs. 2 and 8). Figure 15 (bottom) shows a reasonable match of modeled to observed LE along parts of the track (if we allow for slight dislocation of peaks), but at a price: both H and T_s have absurdly large horizontal fluctuations corresponding to the Θ₁ excursions. From the foregoing, the artificially large H amplitude follows from (7) and is consistent with the too-shallow ΔLE/ΔH slope for run 12 in Table 4.

c. Soil-type sensitivity

Figure 17 shows grassland H and LE values for run 11 (F_g = Θ₁ = 0.25, Table 4) to illustrate the role of soil type in HRLDAS. Aside from the sand point, the effect is fairly small. For G_sfc, the magnitudes increase with K_t, with the highest value for sand, and the lowest value for silty clay loam. Consistent with its high K_t, the sandy soil is coolest. The remaining variability is related to horizontal T₀ variability and the influence of the soil at lower levels.

d. Varying C in the Zilitinkevich equation [(9)]

From the foregoing, even large changes in Θ₁ and F_g, or setting the soil type to sand could not force good agreement between HRLDAS and observations along the whole track. Likewise, from Tables 1 –4, the ΔLE/ΔH value (−1.3) closest to observations is for the highly artificial all-sand run in (9) with F_g = 0.01. Similarly, the leg-averaged coefficient ρc_pc_hU in (4) had surprisingly small variation (leg averages 45–52 W m⁻² K⁻¹) for the first 12 runs, despite differences in soil moisture, soil type, and vegetation, which produced large variations in leg-averaged T_s − T₀ (Tables 2 –4). In contrast, observed ρc_pc_hU values found from (4) using surface data for the 1700–2100 UTC period averaged about 16.4 ± 2.6 W m⁻² K⁻¹ for the surface flux sites—roughly a factor of 3 lower than produced by HRLDAS. Chen et al. (1997) note that the exchange coefficient c_h is sensitive to (9). Thus, an additional 10 runs were designed to test the effects of C on ρc_pc_hU, the fluxes, ΔLE/ΔH, and T_s.

Figure 18 shows that the impact of C on ρc_pc_hU and ΔLE/ΔH is significant. In both cases, the best match to observed values is at C = 0.5. At least for the southern Great Plains during the summer, other researchers have also found that increasing C from its default value of 0.1 improved results. When Gutmann and Small (2007, manuscript submitted to Water Resour. Res., hereinafter GS) varied C in the Noah model using IHOP_2002 surface flux site data for dry, sunny days as input, predicted T_s matched observed values best for C values between 0.17 and 0.99; although simply using C = 0.5 did not improve H values. Trier et al. (2004) found using C = 1 in HRLDAS coupled to WRF produced boundary layer depths, T_s and mixing ratios more similar to those observed than C = 0.1, for the June 1998 convection-initiation case they simulated. For comparison, Zilitinkevich (1995) recommends C = 2, and using (9) in Zeng and Dickinson (1998) and assuming their exponent 0.45 for u_*z_0m/ν is not significantly different from 0.5 in our (9) yields C = 0.33, but they caution the relationship strictly applies to bare ground.

Figure 19 examines the effect of C for runs with control soil types: Θ₁ and F_g. Increasing C decreases H, making leg-averaged values closer to observations. The change in LE is small but new values are farther from observations. These changes are accompanied by a significant increase in T_s. Consistent with the T_s increase, H remains positive at 0000 UTC for C = 0.5 and C = 1 (Table 5). Leg-averaged T_s − T₀ values for C = 0.5 (run 17, Table 5) and C = 0.1 (run 1, Table 2) bracket the observed values (Table 2). The direction and relative size of the H and LE changes are consistent with the trends in Mitchell et al. (2004) when they changed C from 0.2 to 0.05.

From Fig. 20 and altering Θ₁ to better reflect observations and keeping C = 0.5, H, LE, and T_s become more consistent with observations, with the closest match for the soil moisture pattern we consider closest to observations [wetter north (WWN) Θ₁ = 0.4 to 0.22, run 19]. From Table 5, the higher WWN soil-moisture values lead to a slightly negative H at 0000 UTC (−25 W m⁻²), slightly lower than observed (3 W m⁻²), but not as negative as those for the C = 0.1 runs. Shifting the input data to account for the solar radiation time offset, the 0000 UTC H value for run 19 increases to +9 W m⁻², closer to both observations and the “corrected” value for the control run. Values of ΔLE/ΔH are similar to those observed (Tables 1 and 5; Fig. 5). However, T_s and H are still too high, and LE is too low at the south end of the track. These biases remain even if we shift the data to allow for fetch (less than one grid point, based on results of Song and Wesely 2003) or to correct for flux height changes.

For completeness, G_sfc is plotted as a function of latitude in Fig. 21 for run 19, the one closest to observations. Note a reasonable consistency with the surface data, although there are only three points for comparison.

Three more runs were conducted: (i) run 20, testing the effect of setting Θ₂ = Θ₁, where Θ₂ is the volumetric soil moisture in the second soil layer (10–40 cm);⁴ (ii) run 21, like run 20 but changing z_0m for grass from our default value 0.12 m to a smaller value, 0.08 m, and (iii) run 22, like run 20 but with F_g = 0.25. Runs 20 and 21 are compared with run 19 in Figs. 22 and 23. From the figures and Tables 1 and 5, the first two runs each improved agreement with observations, but the effect was small. Reducing F_g superficially eliminated the improvements from (i) and (ii), making run 22 more like run 19 in Table 5 and plots (not shown) more like run 19 in Figs. 22 and 23.

a. Physical significance of changing C

The coefficient C in (9) impacts the coupling between the surface and atmosphere: it changes the surface energy balance and T_s though altering the eddy exchange coefficient c_h, as illustrated in Fig. 18. This in turn follows from the Monin–Obukhov similarity flux–profile relationship [(A4) in Chen et al. 1997]. A smaller c_h in (4) reduces the transport of heat H from the surface, resulting in an increase in T_s. From (3), a higher T_s translates into more heat flux into the soil; the increase in G_sfc with C is obvious from Tables 2 –5. How LE should be affected is less obvious: from (1b), the slight reduction of LE with increasing C in Fig. 19 suggests that decreased R_net and increased G_sfc (both due to higher T_s) more than offsets the decrease in H. Mitchell et al. (2004) found that changing C from 0.2 to 0.05 increased midday available energy and H, with T_s and G_sfc decreasing and LE staying about the same, consistent with what we found.

The association of the results here along with those of Trier et al. (2004) and GS with summer conditions in the southern Great Plains suggests our results might be seasonal. We speculate that lower values of C might work better for the wintertime, when vegetation is dormant. In the case or dormant grasses, F_g ∼ 0 will treat the surface as bare ground in (3), leading to more flux into the soil than if LAI were used. As noted in the foregoing, lowering C decreases the flux into the soil, perhaps compensating for using F_g instead of LAI in (3).

b. Relationship between (7) and ΔLE/ΔH

In the foregoing, we discussed the possibility that the H coefficient in (7) could be related to ΔLE/ΔH. For the first 19 runs with control soil types, Fig. 24 compares the scatterplot based HRLDAS slope ΔLE/ΔH at 1800 UTC, to the slope based on the H coefficient in (7) evaluated for the same time using (8) to calculate K_t. Points with Θ₁ < 0.15 were not considered for the H coefficient or the slope. At lower Θ₁ values, (i) the curve used to estimate (8) becomes more nonlinear, and (ii) LE → 0, as illustrated for run 2 at the northern end of the track in Fig. 13. These low LE values lead to a flatter slope on the high-H end of the H-versus-LE plots. In Fig. 24, ΔLE/ΔH remains negative, although the two slopes diverge from the 1:1 line for larger negative values. Predictions would be perfect if the H coefficient and right-hand side of (7) were constant, suggesting there is more variability in both when the slopes are steeper (and C is larger, Tables 2 –5). Despite this departure, correlation coefficients for the HRLDAS best-fit slope lines remain consistently high.

c. Flux into the soil

From the foregoing, we can make several observations about G_sfc. First, other things being equal, G_sfc increases in magnitude as F_g decreases, a result of reduced “insulation” by the vegetation as represented by e^−2F_g in (3) (Tables 2 –5; Fig. 7). Second, G_sfc is largest for sand, a result of its high thermal conductivity compared to other equally moist soils (Table 3; Fig. 21). And finally, G_sfc increases with C, which contributes to the better match of H, LE, and H + LE to observations for the C = 0.5 runs (Tables 1 –5).

Since we measured F_g, T_s − T₁, Θ at 5 cm, NDVI, and G_sfc, we can estimate K_t from (3) and (8) as a consistency check. We did this for the two sites (2 and 3) with good data. In the observed case, G_sfc is calculated from the measured flux at 5 cm below the surface by using a correction based on the temperature change and heat capacity of the soil layer between the flux plate and the surface. The heat capacity is estimated from soil water content, soil bulk density, and the density of mineral particles, all of which were measured at each site. Based on surface NDVI measurements and (10), we estimated an F_g of 0.39 at site 2, and 0.36 at site 3—close to the control values.

Using data from 1700 to 2100 UTC in (3), K_t was 1.6 W m⁻¹ K⁻¹ for site 2 and 1.7 W m⁻¹ K⁻¹ for site 3. These values correspond to saturated soils at both sites based on (8)—clearly not correct. If we use 0.7 for NDVI_max and 0.08 for NDVI_min in (10) following Alfieri et al. (2007), F_g reduces to 0.24 and 0.21, respectively, and K_t becomes 1.20 for site 2 and 1.28 for site 3. From (8), these values correspond to Θ₁ of 0.3 at site 2 and 0.2 at site 3, closer to what is observed (Fig. 10). Applying Alfieri’s values in (10) for the aircraft data lowers the “observed” F_g from ∼0.25 to ∼0.13, which produces only a minor effect on H and LE from the foregoing.

d. Sensitivity of fluxes to z_0m

In this study, the “grassland” pixels are assigned a z_0m value of 0.12 m. Given the sparseness of the grasses along the western track, we thought it would be useful to test the impact of assuming a smaller value.

Thus, we decided to perform run 21, which was identical to run 20 except that z_0m = 0.08 m for grasslands. In Fig. 22, the grassland points associated with the same soil type (one of two silt loam points and four of eight clay loam points) stand out for runs 19 and 20 as slightly higher for H and lower for LE than the cropland points. Likewise, T_s tends to be higher for the grassland points than for the cropland points in Fig. 23. These excursions, small to begin with, are somewhat reduced, but not eliminated, for run 21.

To understand why the impact is so small, we consider the Monin–Obukhov relationships:

View Expanded

and

View Expanded

where L is the Monin–Obukhov length, z is height above the ground, and Ψ_h and Ψ_m are stability corrections to the logarithmic profiles.

For U = constant in (11), a decrease in z_0m decreases u_*. A smaller u_* in (9) produces a larger value of z_0h. Thus, in (12) a decrease in z_0m decreases both u_* and ln(z/z_0h), so the two effects compensate. From (9), (11), and observed data, ln(z/z_0h) decreased more than u_*, leading to a slight decrease in T_s − T₀ in (12) and a corresponding decrease in T_s in Fig. 23 for run 21. The effect on H and LE is more subtle, but results in values of LE slightly closer to observations, with little change in H.

e. The impact of changing initial conditions at 0000 UTC 29 May

In this study, we view HRLDAS as a tool to provide an initial physically realistic soil moisture profile along the western track. The soil moisture was subsequently modified at the top level to provide different values to explore sensitivity and to get closer to observed values. In run 20, setting the soil moisture at level 2 to the level 1 value improved results, but only slightly. Since roots extend down to level 3, “correcting” soil moisture at that level might improve HRLDAS results a little more. However, observations of the soil-moisture profile indicate that the high values of soil moisture had not yet had time to penetrate to those depths (see Fig. 11 of LeMone et al. 2007a).

It is clear, however, that the imposed soil moisture for the “sand” point was consistently too high. While the HRLDAS control Θ₁ at the sand point at ∼36.83°N was drier than the adjacent points (Fig. 8, presumably due to more rapid drainage), the imposed values in the sensitivity runs were intermediate between values on either side. These artificially high values probably exaggerated HRLDAS sand-value departures of H, LE, and T_s from the values on either side. Thus, with the exception of the control run, we used “no sand” values in Tables 2, 4 and 5 for parameters strongly influenced by the sand point.