On the estimation of soil moisture profile and surface fluxes partitioning from sequential assimilation of surface layer soil moisture

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1 Journal of Hydrology 220 (1999) On the estimation of soil moisture profile and surface fluxes partitioning from sequential assimilation of surface layer soil moisture J. Li, S. Islam* The Cincinnati Earth System Science Program, Department of Civil and Environmental Engineering, University of Cincinnati, P.O. Box , Cincinnati, OH , USA Received 25 June 1998; accepted 4 May 1999 Abstract Recent studies have shown that a variety of remote sensing techniques may be used for the estimation of soil moisture over large areas. The shallow moisture sensing depth of passive microwave measurements, however, limits the use of remotely sensed soil moisture for many land atmosphere interaction studies. In this study, a method is proposed for soil moisture profile estimation by sequential assimilation of surface layer soil moisture using a four-layer land surface model. A key difference between this and earlier approaches is that it evaluates the relative merits of daily assimilation of microwave measurements of surface soil wetness and measurements of rainfall for the estimation of soil moisture profile. We compare and contrast the profile estimation from assimilation of soil moisture and rainfall measurements using observed data sets from the Kansas prairie in the United States. Influence of measurement error, frequency of assimilation, and availability of precipitation measurements on the estimation of soil moisture profile is also explored Elsevier Science B.V. All rights reserved. Keywords: Soil moisture profile; Remote sensing; Data assimilation; Surface fluxes 1. Introduction Soil moisture is one of the most important variables that integrates much of the land surface hydrology and plays important roles in ecosystem dynamics and biogeochemical cycles. Intermittence in storm and interstorm dynamics, and heterogeneity in soil texture, vegetation, land use, and topography contribute to significant space time fluctuations in soil moisture. Consequently, the value of operational monitoring of soil moisture by in situ methods is * Corresponding author. Tel.: ; fax: address: shafiqul.islam@uc.edu (S. Islam) rather limited for regional and global scale problems. Currently, remote sensing techniques provide the most feasible capability to monitor soil moisture over a range of space and time scales (Schmugge et al., 1980; Jackson and Schmugge, 1989; Islam and Engman, 1996; Engman, 1997). Recent studies have shown that a variety of remote sensing techniques may be used for soil moisture measurements. Microwave techniques are widely used to quantitatively monitor soil moisture for a variety of topographic and vegetation conditions. Passive microwave radiometric measurements in the 1 5 GHz range are shown to be of great utility for soil moisture measurements (Njoku and Entekhabi, 1996). As Jackson (1993) noted, microwave remote sensing /99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S (99)

2 J. Li, S. Islam / Journal of Hydrology 220 (1999) offers a few advantages over other spectral regions: (i) the atmosphere and clouds are relatively transparent in the low-frequency microwave region; (ii) vegetation is semi-transparent at these wavelengths; (iii) large contrast between the dielectric properties of liquid water and dry soil; and (iv) measurement may be taken during day or night. Owing to reduced atmospheric attenuation and greatest vegetation penetration at large wavelengths, the low-frequency microwave range is considered the most suitable for soil moisture measurements. Another reason for choosing large wavelength radiation for soil moisture sensing is that the effective soil layer thickness for moisture measurements is a function of the wavelength. It is found that variations in brightness temperature are related most closely to the moisture content in a shallow near surface region. This shallow region is taken as a rule of thumb to be about one-tenth of the wavelength, i.e. about 2 cm of soil at 1.4 GHz (l ˆ 21 cm in air at 1.4 GHz). Although this is a good approximation of the moisture sensing depth, we must emphasize that actual sensing depth will depend on the magnitude of surface moisture and shape of the moisture profile. In any case, it is generally agreed that microwave measurements of soil moisture is limited to the top few (less than 10) centimeters of the soil column. This shallow moisture sensing depth imposes a serious limitation on the use of passive microwave measurements of soil moisture for land-atmosphere interaction studies. Because many of the land-atmosphere interaction processes depend on the profiles of the soil moisture and temperature to depth considerably larger than a few centimeters. Several promising approaches to estimate soil moisture profile have been proposed (Jackson, 1980; Camillo and Schmugge, 1983; Arya et al., 1983; Bruckler and Witono, 1989; Entekhabi et al., 1994). These approaches range from linear regression to knowledge based techniques that use prior information of hydrology and depth profile to inversion techniques that use combination of remotely sensed data and water balance models. Kostov and Jackson (1993) provided an excellent review of soil moisture profile estimation methods using remotely sensed surface moisture measurements. They concluded that proper integration and sequential assimilation of remote sensing of soil moisture and physical modeling appeared to be the most promising approach to solve the problem of profile soil moisture estimation. An illustration, using model generated data, of such an approach was provided by Entekhabi et al. (1994). They used hourly brightness temperature (to simulate microwave observations) from their model generated profiles and have shown that the estimated profile closely approximates the model generated profile during a one-week period of drying soil moisture conditions. To assess the robustness of this approach, an experimental verification is necessary. Also, the influence of frequency of microwave measurements needs to be evaluated before it can be used for routine assimilation of remotely sensed soil moisture for profile estimation. In this study, an alternative method is proposed for soil moisture profile estimation. Similar to many of the previous approaches, our proposed method utilizes a model that can predict the soil moisture profile with given initial and boundary conditions. A key difference between this and earlier approaches is that it will evaluate the relative merits of daily assimilation of microwave measurements of surface soil wetness and measurements of rainfall to estimate soil moisture profile. We will focus on the following two objectives in this paper: Estimate soil moisture profile from sequential assimilation of surface soil moisture and rainfall measurements using a detailed land surface model. Compare and contrast the profile estimation from sequential assimilation of soil moisture and rainfall measurements using observed data sets from FIFE. 2. Methodology 2.1. Estimation of the soil moisture profile using measurements of surface soil moisture and rainfall To use soil moisture (state variable) measurements from microwave sensors or rainfall measurements (flux) from radars or raingages for estimating soil moisture, we will use a land surface model in its stand-alone mode. We will use a state-of-the-art land surface model, developed based on the work of Viterbo and Beljaars (1995), in this study. The land surface model used here has four

3 88 J. Li, S. Islam / Journal of Hydrology 220 (1999) prognostic layers to calculate soil temperature and soil wetness. This model can capture land surface dynamics form the diurnal cycle to seasonal time scales. The model of Viterbo and Beljaars (1995) has been tested extensively with the ECMWF (European Center for Medium-Range Weather Forecasts) model and several observational data sets, and found to capture the physical processes and time scales very well. A brief description of the land surface model is given below Land surface model This land surface model is designed to compute different components of the surface energy and moisture budget and has four prognostic layers to calculate soil temperature and soil moisture. Surface parameterizations are derived from Deardorff (1977,1978); Abramopoulos et al. (1988); Hu and Islam (1995), and Viterbo and Beljaars (1995). 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 time scales, ranging from diurnal cycles to seasonal cycles, are adequately represented. The evaporation rate from the canopy and from the bare soil consists of three components: evaporation of water from the wetted canopy and soil, transpiration of soil water extracted by the root system, and evaporation from the bare soil. Soil hydraulic and thermal properties are characterized using the foemulations outlined by Clapp and Hornberger (1978). 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 while the heat and moisture flux from the bottom of the fourth layer is taken to be zero. The thermal diffusivity and moisture diffusivity are parameterized as a function of soil moisture and temperature (Clapp and Hornberger, 1978). There are four soil layers and the depths of the soil layers are taken in an approximate geometric relation (D 1 ˆ 7 cm, D 2 ˆ 21 cm, D 3 ˆ 72 cm, and D 4 ˆ 189 cm) 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 (Viterbo and Beljaars, 1995). To parameterize sensible and latent heat fluxes, we use transfer coefficients or resistances between the surface and the lowest atmospheric model level expressed as a function of the Obukhov Length (Beljaars and Viterbo, 1994). Advantages of using the Obukhov Length instead of a simpler formulation in terms of Richardson Number (Louis, 1979) are discussed in Beljaars and Viterbo (1994). We will take the roughness length for heat equal to that for moisture. The evaporation rate from the soil canopy system consists of evaporation of water from the wetted canopy E WC, transpiration of soil water extracted by the root system E tr, and evaporation from the bare soil E g. These three components of soil canopy evaporation are estimated following Noilhan and Planton (1989) and Viterbo and Beljaars (1995) Description of data For this study, we will use data sets from the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE) for the period between May and October The FIFE observations were made on a 15 km 15 km site. Betts et al. (1993) averaged the surface meteorological and flux data to obtain a single time series representative of the FIFE site. This is perhaps one of the most well studied and reliable data set suitable for a systematic analysis of soil moisture assimilation within a land surface model. This average data set has been useful for various land surface model development, calibration, and validation (Viterbo and Beljaars, 1995; Chen et al., 1996). For a detailed description of this data set we refer to Betts et al. (1993) and Betts and Ball (1998). We will use this average data set for our study. The data are 30 min averages of pressure, temperature, mixing ratio, wind speed, soil temperature at 10 and 50 cm depth, a radiometric skin temperature, incoming and reflected solar radiation, incoming long wave radiation, net radiation, and cloud cover. Surface flux measurements were made by both eddy correlation and Bowen ratio methods. Soil moisture was systematically measured at large number of sites

4 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 1. (a) Comparison of observed, predicted, and assimilated first layer soil moisture on a daily time scale (Julian Day : 28 May 16 October 1987). (b) Similar to (a) but for the second layer soil moisture. (c) Similar to (a) but for the third layer soil moisture. (d) Similar to (a) but for the fourth layer soil moisture.

5 90 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 1. (continued)

6 J. Li, S. Islam / Journal of Hydrology 220 (1999) by two methods: gravimetric method for the near surface layers and neutron probe method for depths up to 2 m. Our use of FIFE near surface gravimetric measurements of soil moisture as a surrogate of remote sensing measurements was motivated by the availability of a continuous data set of soil moisture for an extended period of time. In addition to soil moisture, as indicated earlier, several other forcing (radiative flux, precipitation, air temperature, etc.) and response (e.g. surface fluxes) variables are also available for the FIFE 1987 experiment. We have used a continuous data set extending over several months (28 May 16 October) from the FIFE 1987 experiment. We will evaluate the implications of using gravimetric surface soil moisture measurements as a surrogate of remotely sensed soil moisture Estimation of the soil moisture profile To evaluate the relative merits of sequential assimilation of microwave measurements of surface soil moisture and measurements of precipitation, we design two sets of experiments with the land surface model described in Section First, we run the model with the atmospheric forcing data (precipitation, radiation, etc.). With this forcing data, the model predicts the soil moisture and temperature for four different layers. In the second set of experiments, we use exactly the same set of forcing data that are used for the first set of experiments. However, as a surrogate of microwave observations of surface soil moisture, we use gravimetric measurements of surface layer soil moisture. Thus, the second set of experiments utilizes forcing data as well as microwave measurements of surface soil moisture to predict the soil moisture profile. In this study, we will use the so-called hard-update, i.e. predicted surface layer soil moisture will be replaced by observed soil moisture values during the assimilation phase. Our use of single daily assimilation of surface soil moisture is motivated by the fact that traditional passive microwave radiometer experiments have typically provided a daily observation of surface at a given wavelength (Jackson et al., 1997). A comparison of these two sets of predicted soil moisture profile with the observed soil moisture profile would provide an indication of relative merits of precipitation measurements and surface soil moisture measurements. We will also evaluate the influence of frequency of surface layer soil moisture assimilation on the estimation of soil moisture profile Compare both estimates of soil moisture profile with directly measured profile from FIFE 1987 Once the soil moisture profiles are predicted from the above two experiments, they can be compared with in situ measurements of soil moisture profiles. In situ measurements of the soil moisture profile are taken as the true value. For a specific layer, there are three time series here, W o, W p, and W m, denoting observed soil moisture, predicted soil moisture with precipitation (and other atmospheric forcing Table 1 Influence of random measurement error in rainfall on the prediction of surface soil moisture, sensible heat flux and latent heat flux without soil moisture assimilation No error 1% error 5% error 10% error First layer soil moisture (m m) Bias RMS error Correlation coefficient Sensible heat flux (W m 2 ) Bias RMS error Correlation coefficient Latent heat flux (W m 2 ) Bias RMS error Correlation coefficient

7 92 J. Li, S. Islam / Journal of Hydrology 220 (1999) Table 2 Influence of random measurement error in first layer soil moisture on the prediction of surface soil moisture, sensible heat flux and latent heat flux with soil moisture assimilation No error 1% error 5% error 10% error First layer soil moisture (m m) Bias RMS error Correlation coefficient Sensible heat flux (W m 2 ) Bias RMS error Correlation coefficient Latent heat flux (W m 2 ) Bias RMS error Correlation coefficient measurements) measurements, and predicted soil moisture with atmospheric forcing as well as sequential assimilation of daily microwave measurements, respectively. Absolute error, E, is defined as follows: E p i ˆ W p i W o i i ˆ 1; 2; 3; 4; E m i ˆ W m i W o i i ˆ 1; 2; 3; 4; where subscript p and m denote the same as above. E p and E m are compared with each other to evaluate the relative merits of sequential assimilation of precipitation measurements and surface soil moisture measurements. The state of soil moisture at the surface and in the profile plays an important role in the partitioning of sensible and latent heat fluxes and infiltration and surface runoff. We will also evaluate the adequacy of the two different soil moisture profiles, namely W p i and Wi m ; in partitioning the surface fluxes into sensible and latent heat fluxes. 3. Results and discussion 3.1. Estimation of the soil moisture profile Fig. 1 compares the observed, predicted, and assimilated surface soil moisture from the Kansas prairie during the FIFE 1987 campaign. It appears Table 3 Influence of different frequencies of assimilation of first layer soil moisture on the prediction of surface soil moisture and sensible and latent heat fluxes Assimilation every 12 h Assimilation every 24 h Assimilation every 48 h Surface soil moisture (m m) Bias RMS error Correlation coefficient Sensible heat flux (W m 2 ) Bias RMS error Correlation coefficient Latent heat flux (W m 2 ) Bias RMS error Correlation coefficient

8 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 2. (a) Estimation error of soil moisture for model alone and model with assimilation experiments for the first layer (Julian Day ). (b) Similar to (a) but for the second layer soil moisture. (c) Similar to (a) but for the third layer soil moisture. (d) Similar to (a) but for the fourth layer soil moisture.

9 94 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 2. (continued).

10 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 3. (a) Comparison of observed and model predicted daily average latent heat flux (Julian Day ). (b) Similar to (a) but with sequential assimilation of surface layer soil moisture measurements.

11 96 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 4. (a) Comparison of observed and model predicted daily average sensible heat flux (Julian Day ), (b) Similar to (a) but with sequential assimilation of surface layer soil moisture measurements.

12 J. Li, S. Islam / Journal of Hydrology 220 (1999) that soil moisture for the first two layers is predicted well by both the methods. Both the model and model with assimilation show several sharp peaks, which are not present in the observed data. There is a systematic underestimation of soil moisture for deeper layers for both the model and model with assimilation experiments. We speculate this to be a consequence of assuming a profile with homogeneous soil physical properties. To evaluate the value of including model dynamics, we compare model results with those of a simple persistence model for surface soil moisture and surface fluxes. There are certain difficulties, however, in implementing a simple persistence forecast model within the context of our study. For instance, the prognostic variables for the model are: soil moisture and temperature. Therefore, it is possible to compare the performance of the model with a simple persistence forecast model for soil moisture and temperature. Our focus in this study is to investigate the role of surface soil moisture assimilation in the partitioning of surface fluxes. Surface fluxes are measured as a function of several variables and hence a simple persistence model involves measurements of several variables which are not readily available for operational purposes. The data set from FIFE, however, have all the required data and we have compared the performance of our proposed model with a simple persistence model. Use of a persistence model shows better agreement for soil moisture (Persistence model results: Bias ˆ m/m; RMS error ˆ m/m; correlation coefficient ˆ 0.982), however, the proposed model does better for the estimation of latent heat flux (Persistence model results: Bias ˆ W m 2 ; RMS error ˆ W m 2 ; correlation coefficient ˆ 0.673) when compared to the model performance in Table 1 with no error. Fig. 2 (a) (d) show the estimation error in soil moisture from the model and model with surface soil moisture assimilation for the four layers. For the first two layers the model with microwave assimilation yield less error compared to the model alone. The difference between the model and the model with microwave assimilation diminishes for the bottom two layers. The mean error for the first layer soil moisture is 3.21% for the model and 2.26% for the model with microwave assimilation. While for the fourth layer the mean error is 3.94% for the model and 3.72% for the model with microwave assimilation Partitioning of surface fluxes Figs. 3(a) and 4(a) compare the daily average observed and model predicted latent and sensible heat fluxes. The latent heat flux is predicted well with a correlation coefficient of but with a positive bias of W m 2 and a root mean square error of W m 2. Sensible heat flux, on the contrary, has a bias of W m 2, correlation coefficient of 0.649, and a root mean square error of W m 2. Figs. 3(b) and 4(b) are similar to Figs. 3(a) and 4(a), but with daily microwave assimilated surface soil moisture. The bias has reduced approximately by a factor of two for both sensible and latent heat fluxes while the correlation coefficients remain statistically similar to the model alone-predicted values. The root mean square error for the latent heat flux with microwave assimilation is similar to that of model alone. While for sensible heat flux the assimilation reduces the root mean square error by about 7 W m 2. Based on these comparisons of soil moisture profile estimation and partitioning of fluxes, one may argue that daily assimilation of surface soil moisture value would improve the prediction of soil moisture profile and partitioning of surface fluxes. We however, note that in these experiments, actual in situ soil moisture measurements by gravimetric (surface layer soil moisture) and neutron probe (deeper layer soil moisture) methods are used as a surrogate of microwave measurements of soil moisture. In reality microwave measurements will be affected by the presence of vegetation, cloud, topography, and other surface heterogeneity effects. In the following section we will systematically evaluate the influence and tradeoff of random measurement error in microwave measurements of soil moisture and rain gage/radar measurements of precipitation. A key question we would like to address is that how much random measurement error we would have to incur to make the assimilated model prediction of soil moisture profile and surface fluxes comparable to those of model prediction alone.

13 98 J. Li, S. Islam / Journal of Hydrology 220 (1999) Influence of random measurement error So far, we have compared the relative performance of model and model with surface soil moisture assimilation in predicting soil moisture profile and surface fluxes. In these experiments, we implicitly assumed that there is no measurement error in the microwave measurements of surface soil moisture or in the atmospheric forcing. In addition, we have used gravimetric measurements of surface soil moisture as a surrogate of remotely sensed soil moisture. In reality, remotely sensed soil moisture is likely to have more error due to atmospheric effects, soil texture heterogeneity, and vegetation cover. Here, we will evaluate the influence of random error in microwave measurements of soil moisture in the prediction of the soil moisture profile as well as surface fluxes. We will also evaluate the trade-off between the random error in precipitation measurements and in microwave measurements of soil moisture. We introduce uniform random error of varying intensity ranging between 1 and 10% of the first layer mean soil moisture in the case of assimilated model prediction. Similar errors are also introduced in precipitation for the model prediction alone. Table 1 compares the performance of model prediction of surface soil moisture and partitioning of fluxes with errors in precipitation measurement, but without assimilation of surface soil moisture. It appears that error in precipitation measurements has nominal influence on model prediction of surface soil moisture and fluxes. For example, a 10% error in precipitation measurements results in a corresponding increase of and W m 2 in root mean square error for sensible and latent heat fluxes, respectively, while the bias increased by W m 2 for sensible heat flux and by W m 2 for latent heat fluxes. Changes in correlation coefficient, because of 10% error in precipitation measurements, are greater in the case of latent heat flux compared to sensible heat flux. It is curious to note that RMS error for the first layer soil moisture changed by only 0.1%. The influence of random error in microwave measurements of surface soil moisture and subsequent model assimilation appears more pronounced than the model prediction with error in precipitation measurements (Table 2). To isolate the influence of error in measurements of soil moisture and measurements of precipitation, in the case of model assimilation experiments, precipitation error is assumed to be zero. In the model assimilated prediction, for example, a 10% error in surface soil moisture yield a corresponding increase of and W m 2 in root mean square error for sensible and latent heat fluxed, respectively, while the bias increased by and W m 2 for sensible and latent heat fluxes, respectively. Changes in the correlation coefficient, because of 10% error in surface soil moisture, are more pronounced in sensible heat fluxes compared to those in latent heat fluxes. Comparison of these results suggests that in the presence of commonly encountered random measurement error, daily assimilation of microwave measurement of surface soil moisture would not improve the prediction of soil moisture profile and partitioning of fluxes compared to model alone prediction with or without error in precipitation measurements Influence of precipitation measurements To evaluate the role of precipitation measurements with and without sequential assimilation of surface soil moisture, we have performed another experiment. In this experiment, all the atmospheric forcings are kept the same but the precipitation is set to the climatological mean precipitation distributed uniformly over the period of experiment. Fig. 5(a) and (b) compare the observed, predicted and assimilated soil moisture for the first and second layer with climatological mean precipitation. It appears that the soil moisture prediction has significantly improved due to sequential assimilation when the precipitation is set to climatological values. In this experiment, the mean error for the first layer soil moisture is 5.37% for the model prediction with uniform precipitation and 3.30% for the model prediction with uniform precipitation and sequential assimilation of surface soil moisture, while for the fourth layer the mean error is 4.31% for the model with uniform precipitation and 4.12% for model with assimilation and uniform precipitation. The root mean square error and bias for latent heat flux are and W m 2 without soil moisture assimilation, and and W m 2 with soil moisture assimilation, respectively. While the root mean square error and bias for sensible heat

14 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 5. (a) Comparison of observed, predicted, and assimilated daily surface soil moisture with climatological mean precipitation. (b) Similar to (a) but for the second layer soil moisture. (c) Similar to (a) but for the third layer soil moisture. (d) Similar to (a) but for the fourth layer soil moisture.

15 100 J. Li, S. Islam / Journal of Hydrology 220 (1999) Fig. 5. (continued).

16 J. Li, S. Islam / Journal of Hydrology 220 (1999) flux are and W m 2 without soil moisture assimilation, and and W m 2 with soil moisture assimilation. Clearly, in the absence of precipitation measurements, use of climatological mean precipitation with sequential assimilation of surface soil moisture, even at a daily time scale, could improve our ability to predict soil moisture profile Influence of different frequencies of surface layer soil moisture assimilation As soil moisture measurements from potential remote sensing sources might only be available at daily time scale, all the above assimilation experiments have used daily updates of surface soil moisture. To evaluate the role of different frequencies of assimilation of surface layer soil moisture, we now focus on three different frequencies of assimilation: 12, 24, and 48 h. To obtain 12 h soil moisture values, we have used a linear interpolation between two successive days. Table 3 compares the influence of three different frequencies of soil moisture assimilation on the estimation of surface soil moisture and surface fluxes. Bias appears to increase when frequency of assimilation decreases, for example, for latent heat flux bias increases from to W m 2 when the frequency of assimilation decreases from 12 to 48 h. For surface soil moisture, root mean square error decreases as frequency of assimilation increases. An implication of this result is that if we further increase the frequency of soil moisture assimilation, bias and root mean square error would further go down. Nevertheless, sensitivity of frequency of assimilation is rather low. We speculate that this low sensitivity is related to dependence of soil moisture on time-of-day of assimilation as well as coarse temporal resolution of our soil moisture data. It is expected that surface soil moisture would change during a day as a function of radiative and evaporative forcing and lateral redistribution. It is unlikely, however, that remotely sensed soil moisture would be available at a temporal scale finer than twice a day. Given the availability of soil moisture measurements, one may argue that the daily assimilation of surface soil moisture would be adequate. We must emphasize, however, these results should be viewed as tentative and more experiments are necessary with finer resolution measurements to confirm these findings. 4. Discussion In the absence of any measurement error, daily assimilation of surface soil moisture predicts the soil moisture profile and partitioning of surface fluxes better than the model prediction alone. The improvement in profile prediction decreases, however, for deeper layers. This is not surprising given that the model has only four prognostic layers, and the distance between the two consecutive layers, increases geometrically as we go into the deeper layers. Inclusion of more prognostic layers could perhaps increase the predictive capability of the model, however, it would also require significant computational resources. Usually, an atmospheric model has layers in the vertical; if we include soil layers in the land surface model then the computational demand would be doubled and it would be almost impossible to simulate coupled land atmospheric processes over large domain for operational purposes. Comparison of predictions for the model and model with soil moisture assimilation, in the presence of measurement error, suggests that improvement in predictive ability with sequential assimilation of daily surface soil moisture decreases as we increase the intensity of random measurement error. For measurement error as low as 10% in microwave measurements of soil moisture, daily assimilation of surface soil moisture measurements would not improve our capability to predict soil moisture profile and partitioning of fluxes compared to model alone prediction without any assimilation. In the absence of any precipitation measurements, however, the improvement of profile estimation and surface fluxes partitioning due to sequential assimilation of soil moisture with climatological mean precipitation would be substantial. Preliminary analysis suggests that frequency of surface soil moisture assimilation between 12 and 48 h does not appreciably change the estimation error in predicting soil moisture and surface fluxes. In this study, we have used so-called hard-update, i.e. predicted surface layer soil moisture was replaced

17 102 J. Li, S. Islam / Journal of Hydrology 220 (1999) by observed soil moisture values during the assimilation phase. Recent studies (Entekhabi et al., 1994; Walker et al., 1998) have used Kalman filtering where updates were done by a statistically optimal estimate of the states (e.g. soil moisture) based on covariance of the model states and observations. Both of these studies have used model-generated data to test the performance of Kalman filtering updates. To assess the robustness of this approach, additional experiments with observed data are necessary. Results presented in this study should be viewed as tentative because it utilizes surrogate microwave measurements of soil moisture. In reality, microwave provides instantaneous measurements of soil moisture. Thus, additional experiments are needed with actual measurements of surface soil moisture from remote sensing to confirm and extend the findings of this research. Our preliminary analysis evaluates the merits of soil moisture profile estimation at a point. Results from these experiments provide an understanding of relative merits of precipitation measurements and microwave measurements of surface soil moisture for the estimation of soil moisture profile. To characterize the space time structure of soil moisture profile and surface fluxes partitioning, we need to extend the above methodology over large areas. This will require a distributed land surface model which incorporates spatially variable atmospheric forcing and surface parameters into the model formulations. Acknowledgements This research is supported, in part, by a grant from the National Science Foundation of the United States. Discussion with Elfatih Eltahir of the Massachusetts Institute of Technology and comments from anonymous reviewers have greatly improved this paper. References Abramopoulos, F., Rosenzweig, C., Choudhury, B., Improved ground hydrology calculations for global climate models (GCMs): soil water movement and evapotranspiration. J. Climate 1, Arya, L.M., Richter, J.C., Paris, J.F., Estimating profile water storage from surface zone soil moisture measurements under bare field conditions. Water Resour. Res. 19, Beljaars, A.C.M., Viterbo, P., The sensitivity of winter evaporation to the formulation of aerodynamic resistance in the ECMWF model. Bound. Layer Meteorol. 71, Betts, A., Ball, J.H., Beljaars, A.C.M., Comparison between the land surface response of the ECMWF model and the FIFE data. Q.J.R. Meteorol. Soc. 119, Betts, A., Ball, J.H., FIFE surface climate and site-average dataset J. Atmos. Sci. 55 (7), Bruckler, L., Witono, H., Use of remotely sensed soil moisture content as boundary conditions in soil-atmosphere water transport modeling 2: estimating soil water balance. Water Resour. Res. 225, Camillo, P.J., Schmugge, T.J., Estimating Soil moisture storage in the root zone from surface measurements. Soil Sci. 135, Chen, F., Mitchell, K., Schaake, J., Xue, Y., Pan, H.L., Koren, V., Duan, Q., Betts, A., Modeling land surface evaporation by four schemes and comparison with FIFE observations. J. Geophys. Res. 101, Clapp, R.B., Hornberger, G., Empirical equations for some soil hydraulic properties. Water Resour. Res. 14, Deardorff, J.W., A Parameterization of ground-surface moisture content for use in the atmospheric prediction models. J. Appl. Meteorol. 16, Deardorff, J.W., Efficient prediction of ground surface temperature and moisture with inclusion of a layer of vegetation. J. Geophy. Res. 83, Engman, E.T., Soil moisture, the hydrologic interface between surface and ground water. Remote Sensing and Geophysical Information Systems for Design and Operation of Water Resources Systems (Proceedings of Rabat Symposium S3, April IAHS Publ. No ). pp Entekhabi, D., Nakamura, H., Njoku, E.G., Solving the inverse problem for soil moisture and temperature profiles by sequential assimilation of multifrequency remotely sensed observations. IEEE Trans. Geosci. Remote Sensing 32, Hu, Z., Islam, S., Prediction of ground surface temperature and soil moisture content by the force restore method. Water Resour. Res. 31, Islam, S.I., Engman, E.T., Why bother for % of Earth s Water? Challenges for Soil Moisture Research. Eos, Trans. Am. Geophys. Union 77, 420. Jackson, T.J., Profile soil moisture from surface measurements. J. Irrigation and Drainage Div. 106 (IR2), Jackson, T.J., Schmugge, T.J., Passive microwave remote sensing system for soil moisture: some supporting research. IEEE Trans. Geosci. Remote Sensing 27, Jackson, T.J., Measuring surface soil moisture using passive microwave remote sensing. Hydrol. Processes 7, Jackson, T.J., O Neill, P.E., Swift, C.T., Passive microwave observation of diurnal surface soil moisture. IEEE Trans. Geosci. Remote Sensing 35, Kostov, K.G., Jackson, T.J., Estimating profile soil moisture from surface layer measurements-a review. Ground Sensing,

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