a. Atmospheric model—MM5

The atmospheric module of our coupled model is the nonhydrostatic version of MM5. MM5 is based on a fully compressible atmosphere in a rotating frame of reference, including terrain-following coordinates and a split semi-implicit temporal integration scheme. This is a well-studied, state-of-the-art mesoscale model designed to support basic atmospheric research and it has wide community support for further developments and refinements for a range of hydrometeorological applications. Various developments, physical parameterizations, and numerical techniques are described in the literature [see Anthes and Warner (1978), Dudhia (1993), Grell (1993), and references therein] and will not be repeated here.

This atmospheric model is a primitive equation model that solves a simultaneous set of eight nonlinear prognostic equations in the eight dependent variables (pressure perturbation, temperature, three components of velocity, water vapor, cloud water, and rain water). The model equations are described within a vertically stretched system. Also, the techniques of successive one-way nesting allows one to dynamically feed synoptic-scale features down to cloud scales.

Currently, MM5 uses multilayer Blackadar planetary boundary layer parameterizations to represent turbulent fluxes of heat, moisture, and momentum (Zhang and Anthes 1982). We note that although certain aspects of MM5 have been greatly improved over earlier versions, a popular version of the land surface parameterization is based on two studies—Deardorff (1978) and Carlson and Boland (1978)—done 18 years ago (Oncley and Dudhia 1995). Previous studies, however, have shown that the surface flux parameterizations used in earlier MM5 work reasonably well for long-term simulations, given appropriate values of required parameters (Oncley and Dudhia 1995). These parameters include albedo α, soil moisture availability M, surface emissivity ɛ, roughness length z₀, and thermal inertia λ_T. Currently, MM5 assigns constant values for these parameters based on 13 land-use categories. Oncley and Dudhia (1995) demonstrated that surface fluxes are quite sensitive to M. They suggested either to assume that the value of M is equal to the initial surface-layer soil moisture or to run MM5 iteratively to find the proper value of M. A key objective of this study is to explore the sensitivity of interactive soil moisture dynamics at a diurnal cycle. We will use MM5 in its original mode (with a time-invariant as well as time-varying soil moisture availability function) and in its coupled mode. In the coupled mode, we will couple a four-layer land surface model (described in section 2b) with MM5 in its nonhydrostatic mode with one of its high-resolution planetary boundary layer schemes, to simulate the diurnal cycle.

b. Land surface model

The land surface model used in this study is a variant of the land surface model developed by Viterbo and Beljaars (1995) for the ECMWF model. It is designed to compute different components of the surface energy and moisture budget over different land surfaces. Surface parameterizations are derived from Deardorff (1977, 1978), Abramopoulous et al. (1988), Hu and Islam (1995), and Viterbo and Beljaars (1995). Particular attention is given to capturing the principal physical mechanisms through a minimum number of parameters. Important features of the model are highlighted below.

• The surface heat and moisture budgets are represented by two partial differential equations (assuming snow-free ground). The total soil depth, number of layers, and boundary conditions are chosen such that all relevant timescales, ranging from diurnal cycles to seasonal cycles, are adequately represented.

• It uses an improved version of the discretization method for soil heat and moisture content. This improvement is achieved by minimizing the error produced by the force–restore approximation of the diffusion equation (Hu and Islam 1995).

• The evaporation rate from the canopy and from the bare soil consists of three components: evaporation of water from the wetted canopy, transpiration of soil water extracted by the root system, and evaporation from the bare soil.

• Soil hydraulic and thermal properties are characterized by using the Clapp and Hornberger (1978) and McCumber and Pielke (1981) formulations.

This land surface model has four soil layers, and each layer treats soil moisture movement with different timescales. Qualitatively, the first layer represents the diurnal cycle, the second layer represents variations between 1 day and 1 week, the third layer represents variations between 1 week and 1 month, and the fourth layer varies with timescales larger than 1 month. In addition to the four soil layers, there is a skin layer at the top that has no heat capacity and is in instantaneous equilibrium with atmospheric forcing, which allows quick response to the atmospheric condition change at the top. The depths of soil layer are taken in an approximate geometric relation as suggested by Deardorff (1978) and adopted by Viterbo and Beljaars (1995). It has been shown that four layers are sufficient to capture soil moisture dynamics from diurnal to seasonal cycles (Warrilow et al. 1986) The soil heat and moisture transfer are described by classical diffusion equations. The top boundary conditions are obtained from solution of the surface moisture and energy balance equations, and the heat and moisture fluxes from the bottom of the fourth layer are taken to be zero. The thermal diffusivity and moisture diffusivity are parameterized as a function of soil moisture and temperature (Clapp and Hornberger 1978). The surface temperature is computed from the surface energy balance equation:

_skT_skT₁αR_SR_TσT⁴_skH_s(1)

where Λ_sk is skin layer conductivity, T_sk is surface temperature, T₁ is first-layer soil temperature, R_S is downward shortwave radiation, R_T is downward longwave radiation, σ is the Stefan–Boltzmann constant, H_s is sensible heat flux, and LE is latent heat flux. The sensible and latent heat fluxes are parameterized as

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where ρ is air density, C_H is heat transfer coefficient, C_P is heat capacity of air at constant pressure, g is acceleration due to gravity, Z_L is the height of the lowest atmospheric layer, q_sat is the saturated specific humidity, and p_s is surface pressure. Also, |V|, T_L, and q_L are the wind speed component, atmosphere temperature, and specific humidity at the lowest atmospheric layer, respectively.

The surface temperature T_sk is solved from Eqs. (1) through (3) by obtaining the forcing data (R_s, R_T, |V|, T_L, q_L, p_s, Z_L, and precipitation) from the atmospheric module of MM5. The resulting T_sk, LE, and H_s are then fed back to the land surface boundary condition of MM5. The first-layer soil temperature is obtained from a difference equation representing the soil heat budget. In Eq. (3) the constants a_L and a_S are related to moisture availability function. In ECMWF, a_L and a_S are implicitly defined for three fractions of total evaporation: 1) fraction covered by the interception reservoir E_I, 2) vegetation fraction E_V, and 3) bare soil fraction E_B. The total evaporation is a linear combination of these three components. Because more than 85% of the FIFE area is covered by vegetation, we only describe the constants a_L and a_S defined in E_V:

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Variables r_a and r_c are aerodynamic resistances:

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where

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Here r_smin is minimum stomatal resistance of a single leaf, L_f is leaf area index, PAR is photosynthetically active radiation, θ is soil moisture, θ_pwp is soil moisture at permanent wilting point, θ_cap is soil moisture at field capacity, θ is average soil moisture, and a₁, a₂, and a₃ are related to canopy properties (Sellers 1985). In Eqs. (6) and (8), the soil moisture is obtained from a difference equation representing the soil water budget. For a detailed description of this land surface model, we refer the reader to Viterbo and Beljaars (1995).

We have performed a detailed validation of this land surface model using the FIFE data (Li and Islam 1999). We highlight some of the findings of model validation here. The soil moisture for the first two layers is simulated well by the model. There may be a slight underestimation bias for the deeper layers. The latent heat flux is modeled well, with a correlation coefficient of 0.92, a positive bias of 10.3 W m⁻², and a root-mean-square error of 20.87 W m⁻². Sensible heat flux, on the contrary, has a bias of −22.14 W m⁻², a correlation coefficient of 0.65, and a root-mean-square error of 31.06 W m⁻². Viterbo and Beljaars (1995) have also done an extensive validation for this model for a range of surface and climate conditions, including the FIFE in the United States, Cabauw in the Netherlands, and the Amazonian Rainforest Meteorological Experiment in the central Amazonia. A version of this land surface model is currently used as a host land surface model within the ECMWF model.

c. Land–atmosphere coupling

Two methods will be used to couple a land surface model with an atmospheric model: 1) control run, in which surface fluxes are computed using the original MM5 in which soil moisture is prescribed through a moisture availability function; and 2) coupled model, in which the land–atmosphere fluxes respond to dynamic space–time changes in both the atmospheric and land surface variables. These two different ways of coupling are used to design experiments and successively to identify strength of land–atmosphere interactions within a coupled land–atmosphere modeling environment. For each day, we will use three different representations of soil moisture availability function M for the control-run simulations: control 1, for which M is equal to a constant soil moisture; control 2, for which M is equal to a constant following Kondo and Saigusa (1990) parameterizations; and control 3, for which M is equal to time-varying soil moisture following Kondo and Saigusa (1990) parameterizations. Here, M is defined as follows:

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where F(θ) is a decreasing function of soil moisture that also depends on soil types, and D_atm is an increasing function of surface temperature. Although Kondo and Saigusa’s (1990) parameterization of moisture availability function [M_(Kondo)] is only applicable for bare soil, the parametric form of M_(Kondo) is somewhat similar to ECMWF’s parameterization of moisture availablity function [M_(ECMWF)], derived from Eqs. (3)–(6) as follows:

View Expanded

where r_c, similar to F(θ), is a decreasing function of soil moisture that depends on soil types but also considers the influence of vegetation [see Eq. (6)]. Given that FIFE is 85% vegetated, it is likely that the coupled MM5–ECMWF model would provide more realistic results.

a. Domain description and model specifications

We will simulate three cloud-free days: 15 August, 11 July, and 11 October from the FIFE 1987 near Konza prairie in Kansas. Our choice of days with no precipitation and little or no cloud allows us to use much simpler physics schemes (e.g., cloud scheme, radiation scheme, etc.) in the atmospheric part of the coupled model. This choice would also have minimal impact for simplified representation of land surface runoff and groundwater movement. These three days have a progressively smaller amount of surface soil moisture.

A 205 km × 205 km domain centered at the FIFE site (39.05°N, 96.53°W) is simulated with a medium-resolution grid (DX = DY = 5 km). There are nine model grids at the center of the simulation domain covering the FIFE site (15 km × 15 km). Lateral boundary conditions are obtained from the National Centers for Environmental Prediction (NCEP) reanalysis products for the corresponding periods. A similar three-dimensional domain with time-dependent lateral boundary conditions has been used successfully to compare simulated data with the collected dataset from the Hydrological Atmospheric Pilot Experiment site (Bougealt et al. 1991). Use of the NCEP reanalysis data allows us to provide time-dependent lateral boundary conditions over the FIFE area.

The initial and boundary conditions for the model simulation are from the NCEP reanalysis archive. For both the control and coupled model simulations, the Grell cumulus parameterization (Grell 1993) is used. For the control run (i.e., MM5 in its original mode, with a prescribed soil moisture availability function), surface properties such as albedo, roughness length, and heat capacity are specified according to one of the 13 land use categories. The moisture availability is specified in three different ways, as described above, using FIFE domain observations of surface volumetric soil moisture, which are 0.300 for 15 August 1987, 0.235 for 11 July 1987, and 0.139 for the dry case of 11 October 1987. For the coupled model simulation, the spatial distribution of soil texture is obtained from a lookup table with seven soil classes based on Zobler (1986). These seven soil classes are then reclassified into three soil classes: coarse, medium, and fine. Soil properties for these three classes are derived from Patterson (1990). The vegetation fraction is set as 0.85 following Viterbo and Beljaars (1995).

b. Metrics for comparison

Because several kinds of sensors and measurement techniques were used to collect surface data for the relatively small FIFE area, a random error (due to different sensors and measurement techniques) is expected to be present in the observations (Betts and Ball 1993). It is conceivable that random errors due to numerical diffusion and turbulence parameterizations could also arise in the simulations for the FIFE area. To minimize the effects of such random errors, we plan to compare statistical moments of the observed mean time series data and the control and coupled model outputs over the FIFE area. Betts and Ball (1993) successfully used similar mean time series data for the FIFE 1987 data to detect systematic errors in the ECMWF model.

To compare the model simulation results with the 30-min-averaged FIFE observation series, we take 30-min-averaged values of the model output quantities and further average the model output quantities over the model grids covering FIFE site. The mean, correlation coefficient, and bias are calculated for the following variables: net radiation Rn, ground heat flux G, sensible heat flux H, LE, evaporative fraction [LE/(H + LE)], mixing ratio q, and surface wind speed U and V.

a. Wet case—15 August 1987

Fifteen August is a cloud-free day during the Intensive Field Campaign—3 (IFC-3). On this day, net radiation averaged over a 12-h period was 392.10 W m⁻². There was about 80 mm of precipitation over the FIFE area on 12–13 August 1987, which resulted in a volumetric soil moisture as high as 0.30. Because the land surface soil water content is usually replenished by precipitation and the soil moisture drydown period lasts for several days, this day may be considered to be the beginning of a drydown period. On this day, the average surface wind velocity was 8.0 m s⁻¹, and the mixing ratio was 17.5 g kg⁻¹.

Figures 1a,b show net radiation and ground heat flux simulated by the three control simulations and the coupled model. The net radiation is simulated well by both models. It appears, however, that control 1 is slightly better than the control-2 and control-3 simulations. Root-mean-square error (rmse) and the bias are comparable for both the control and coupled-model simulations. For the ground heat flux, the coupled model shows greater bias when compared with the control run.

Figures 1c,d show the sensible and latent heat fluxes for the control and coupled model simulations. The statistical metrics are comparable for the control-1 and coupled-model simulations, while the control-2 and control-3 simulations yield a very high bias and root-mean-square error for latent heat flux. Table 1 compares statistical metrics for several variables for all the simulations. In terms of bias and rmse, the coupled model, in general, gives better results in simulating H, LE, q, U, and V.

Several points are worth noting from these figures and Table 1. First, in Figs. 1a and 1b, simulation of net radiation by the control (particularly Control 1) and coupled model are similar and they agree well with observations. Second, in Figs. 1c and 1d, better partitioning between sensible heat flux and latent heat flux is achieved by the coupled model around the local noon time (6 h after model starts), at which time the control runs overestimate the latent heat flux and underestimate the sensible heat flux. Because the simulated wind components (|U_L|² = u² + υ²) are similar for all the simulations, one may argue that differences in surface fluxes for the control run are not due to errors in surface wind. To understand the primary cause for differences in surface flux partitioning, one needs to look at the diurnal dynamics of soil moisture. The top-layer (0–7 cm) soil moisture drydown simulated by the coupled model shows a monotonic depletion of surface soil moisture from 0.30 to 0.25, but in the control-1 simulation soil moisture is kept at a constant value of 30%. This diurnal reduction in moisture availability is not considered in the control run, which consequently results in an overestimation of latent heat flux. For the control-2 and control-3 simulations, on the other hand, latent heat flux is overestimated because of the nonlinear relationship, proposed by Kondo and Saigusa (1990), between soil moisture availability function and soil moisture content. Results from the three control simulations demonstrate the sensitivity of specifying M in controlling the partitioning of surface fluxes. Note that, despite a reasonable simulation of net radiation, control simulations fail to reproduce accurate partitioning of surface fluxes because of inaccurate representation of soil moisture dynamics.

b. Moderate wet case—1987 July 11

Eleven July is another cloud-free day during the IFC-2. Net radiation averaged over a 12-h period was 400.90 W m⁻², and the 6-h peak average net radiation was 552 W m⁻². The observed soil moisture was 0.24, and the average surface wind speed and mixing ratio were 8.2 m s⁻¹ and 17.10 g kg⁻¹. In terms of average net radiation, ground heat flux, mixing ratio, and wind speed, this day is similar to 15 August 1987. Surface soil moisture, however, was lower on this day.

Table 2 compares performance of three control and coupled-model simulations. The net radiation is simulated well by both the models. Root-mean-square error, correlation between observed and model, and the bias are comparable for both the control-1 and coupled-model simulations. For the ground heat flux, the coupled model shows small bias; control 2 and control 3 show significant bias and large rmse. The correlation coefficient between the observed and simulated ground heat flux is low for all the simulations. Figures 2a,b show the sensible and latent heat fluxes for the control and coupled-model simulations. There is a large bias in the partitioning of fluxes for the control simulations, but the coupled model has provided a fairly accurate partitioning of radiative forcing into sensible and latent heat fluxes. For example, control 1 produced a negative bias of 88.5 W m⁻² for latent flux, and control 2 and control 3 yielded a positive bias of approximately 200 W m⁻². On the other hand, the coupled model has a bias of only 5.8 W m⁻² for latent heat flux.

For other quantities, such as mixing ratio and surface wind speed, similar results are obtained by both the control run and the coupled model. Based on the results of 15 August and 11 July, one may argue that a detailed coupling between land surface soil moisture and atmosphere is important under moderately wet land surface conditions.

c. Dry case—11 October 1987

On 11 October 1987 (a cloud-free day from IFC-4), a high pressure system was over the domain for the simulation period. The average surface wind speed was very low—1–2 m s⁻¹. The boundary layer was dry over the FIFE observation domain (mixing ratio is about 3.1 g kg⁻¹) and the sky was clear to partly cloudy. Them was only a small amount (∼2 mm) of precipitation during the previous day. The observed surface volumetric soil moisture content was about 0.14.

In this dry-case simulation, the surface latent heat flux was very small. Both the control and the coupled model underestimated the surface sensible flux, but the coupled model has a much larger bias. This bias is partly due to the large underestimation of net radiation by the coupled model. However, the correlation coefficients for surface fluxes are reasonably good from both model simulations (Table 3). The correlation coefficients for mixing ratio and surface wind (U and V) are also better for the control run. Overall, the results for this dry day show that the control run performs better than the coupled model in simulating daytime surface fluxes, mixing ratio, and surface wind speed. These results suggest that, for drier surface conditions, it may not be necessary to include a time-variant soil moisture representation for a coupled land–atmosphere model.

To isolate the influence of underestimation of net radiation on the land surface model, we have performed another simulation for 11 October 1987. In this simulation, the land surface model (described in section 2b) is integrated in its stand-alone mode. In other words, forcing for the land surface model (i.e., net radiation, wind speed, mixing ratio, etc.) is provided from the observed dataset. Figure 4 shows the time sequence of sensible and latent heat fluxes simulated by the stand-alone land surface model. Comparison of Figs. 3 and 4 clearly demonstrates an improvement of partitioning of surface fluxes. For instance, for the 12-h period, bias in sensible heat flux has reduced to 13.3 W m⁻² for the stand-alone model, as compared with −35.0 W m⁻² for the control run and −100.2 W m⁻² for the coupled model (Table 3). This result suggests that underestimation of net radiation is a key contributing factor for the underperformance of the coupled model. It turns out that in this case the coupled model overestimates the surface temperature, which caused an excessive loss of upward longwave radiation from the land surface.

In addition, there are very small differences between the model simulation results over the FIFE-area (15 km × 15 km)- and the entire-domain (205 km × 205 km)-averaged quantities (figures not shown). This result indicates that the spatial variations of the simulated fields may not be very heterogeneous at the model grid level. An implication of this lack is that the FIFE-averaged dataset may be used to detect systematic errors in large-scale model outputs. In fact, Betts and Ball (1993) have used FIFE 1987 data to detect systematic differences in ECMWF model output.