1. Introduction

Improved assimilation of atmospheric sounding data over land from sensors such as the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) and the Special Sensor Microwave Imager (SSM/I) requires better estimates of the land surface microwave emissivity. Although this problem pertains to all of the land areas of the globe, the particulars are different for snow-covered and snow-free areas owing to substantially different dielectric properties of snow and ice as compared with snow-free areas. Microwave brightness temperature measured by spaceborne sensors over snow-covered areas originates from radiation emitted from the underlying surface, the snowpack, the vegetation, and the atmosphere. In theory, the dielectric constant of frozen water is altered relative to that of water in its liquid form, and the effect of snow on the emissivity can be used in algorithms to estimate snow water equivalence (SWE) from spaceborne emissions, typically at 18.7 and 37 GHz. In practice, though, the emissivity of snow depends not only on SWE but also on snowpack microstructure, especially grain size and temperature.

These complications with SWE retrievals have motivated an alternative approach, which focuses on top of the atmosphere (TOA) emissions in the microwave frequencies and attempts to assimilate satellite radiance observations with model predictions rather than retrieving SWE. This approach is particularly relevant for applications such as the retrieval of atmospheric moisture in which the SWE problem is incidental. However, even where there is a motivation to update land surface variables, such as SWE, the assimilation of brightness temperatures (T_b), rather than derived the SWE products, requires knowledge of snow physical properties because they affect the (surface) emissivity. National Centers for Environmental Prediction (NCEP) operational models currently use the Community Radiative Transfer Model (CRTM), which predicts TOA microwave and infrared radiances and brightness temperatures. CRTM is generally much more sophisticated in its representation of atmospheric radiative transfer than of the land surface. The land surface emissivity in CRTM is based on snow depth and surface temperature, from which they use an empirical regression for grain size as inputs into the land emission model (Weng et al. 2001). Whether or not snow is present is determined by the output of the (Noah) land scheme snow depth prediction, which is updated daily using (in operations) a direct insertion approach. The observations are the Air Force Weather Agency (AFWA) global snow depth analysis (SNODEP), which is based on the interpolation of daily station reports (K. Mitchell 2007, personal communication).

The approach we propose to develop in this paper is a part of a broader National Oceanic and Atmospheric Administration–National Aeronautics and Space Administration (NOAA–NASA) Joint Center for Satellite Data Assimilation (JCSDA) sponsored project that is intended to incorporate recent improvements in snow emissions modeling into CRTM. The current approach for estimating snow emissivity in CRTM will be compared with one, or a combination of, forward snow emission models (SEMs) coupled with the Noah land surface scheme. Technically, the objective of the present contribution is twofold: i) to test a new methodology for estimating microphysical snow forcings by a land surface scheme and ii) to evaluate the feasibility of coupling the land surface scheme with SEMs in terms of accuracy of T_b predictions. The first objective is accomplished by improving the existing parameterization of snow physics in the Variable Infiltration Capacity (VIC) model (Liang et al. 1994). The new algorithm accounts for snow metamorphism, compaction from the weight of new snowfall, and an effective internal snowpack compaction. It also calculates the average snow grain size using a crystal growth equation. In the future, this parameterization is intended to be transferred into the operational Noah model to improve CRTM estimates of snow T_b. To accomplish the second objective, we evaluate the performance of three SEMs coupled with the VIC model using AMSR-E satellite observations of T_b (at 18.7, 37, and 89 GHz for both horizontal and vertical polarization) at two sites from the NASA Cold Land Processes Experiment (CLPX) in Colorado during the winter of 2003. The three SEMs are the Microwave Emission Model of Layered Snowpacks (MEMLS) of Mätzler and Wiesmann (1999), a modification of the Land Surface Microwave Emission Model (LSMEM) of Gao et al. (2004), and the Dense Media Radiative Transfer (DMRT) model of Tsang et al. (2000). Additionally, an example of the multimodel T_b estimate, based on Bayesian model averaging, is computed and compared to AMSR-E measurements. It demonstrates, using a bootstrap validation procedure, that the multimodel estimate increases the mean prediction accuracy as well as provides a nonparametric estimate of the error distributions.

As discussed above, the motivation of this paper is assessing the assimilating current satellite microwave brightness temperature (from AMSR-E) into microwave emission snow models (often referred to as forward models). The reader should recognize the multitude of challenges in this assimilation, which include the poorly posed problem of predicting microwave emissions as a result of their sensitivity to snow depth, the freeze–thaw cycle that affects snow grain morphology, the development of layering, and snowpack water. The challenge also includes scaling effects from the low-resolution (25 km) AMSR-E pixel resolution and the spatial heterogeneity in vegetation, topography, and snowfall. Therefore, this paper focuses mainly on the most favorable period within CLPX to best assess our ability to assimilate AMSR-E brightness temperatures.

This paper is organized as follows: section 2 provides a description of the new snow module implemented in VIC. The three SEMs used in this study are discussed in section 3. The mathematical formulation of the Bayesian model averaging is given in section 4. The CLPX 2003 measurements and the models’ setup are described in section 5. The results are discussed in section 6. The paper closes with the summary and a short discussion of future research directions in section 7.

2. Variable Infiltration Capacity model

b. Modification of snow module

In this study, a new snow densification algorithm in VIC (see Andreadis et al. 2008) was used to account for the significant effects of snow density and depth on microwave emissivity. Originally, VIC used a constant density of 50 kg/m³ for newly fallen snow and accounted for densification by compacting the snowpack with the weight of new snowfall. Rather than a constant value, we incorporated the algorithm by Hedstrom and Pomeroy (1998) that calculates the density of fresh snow based on air temperature. We also modified the snow densification algorithm by calculating a compaction rate according to Jordan (1991). This model accounts for settling as a result of snow metamorphism, compaction from the weight of new snowfall, and an effective internal snowpack compaction. In addition, a snow crystal growth algorithm was added to the model based on the one used by the snow thermal model SNTHERM (see Jordan 1991). This algorithm is based on the equation that describes growth by sintering in metals and ceramics:

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where d (mm) is the average grain size, T (K) is the temperature, and a, b are adjustable parameters. For dry snow in SNTHERM, we considered using a simple function of the form

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where T_s (K) is snow temperature, P_a (hPa) represents the atmospheric pressure, z (m) is snow depth, and g₁ (m⁴ kg⁻¹) is an adjustable parameter (here we used the value of 7 × 10⁻⁷). The value of effective diffusion coefficient for water vapor in snow D_eos at 1000 hPa and 0°C is 0.92 × 10⁻⁴ (m² s⁻¹), and the value of variation of saturation vapor pressure with temperature relative to phase C_kT (kg m⁻² K⁻¹) can be calculated by Eq. (20) in Jordan (1991). Note that d in (2) is expressed in meters. When implementing (2) in VIC, we approximated the absolute vertical thermal gradient ∂T_s/∂z by |T_s − T_g|/Δz, where T_g (K) is ground temperature. For wet snow when liquid water content θ_l within the snowpack exceeds a threshold (0.0001), grain growth rate increases and, as proposed by Jordan (1991), is modeled using the similar growth function to that for dry snow:

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Here, θ_l is set to a maximum of 0.09 if it exceeds that value, and adjustable parameter g₂ is taken as 4 × 10⁻¹² (m² s⁻¹). The grain size estimated by the model is a depth-weighted average of the grain size of newly fallen snow (taken as 0.1 mm), and the grain size of the existing snowpack is obtained from (2) or (3).

3. The snow emission models

In this section, we provide a brief description of the three SEMs used in this study. For the sake of clarity, the key aspects of these models are listed in Table 1. Before characterizing each individual model, we introduce the inputs required by the models. The inputs are nearly the same for all models and include snow depth, snow density, snowpack temperature, ground temperature, and surface roughness of the air/snow boundary, except that the LSMEM and DMRT models require the “mean grain size” of snow particles as an input, whereas the MEMLS model requires the “correlation length.” The mean grain size is taken as the radius of spherical ice particles approximating the ice grains in snow. The correlation length is related to snow grain size, shape, and volumetric distribution of snow grains (e.g., Jin 1993). However, this relationship is not straightforward (see, e.g., Pulliainen et al. 1999). To derive a value for the correlation length from the mean grain size, we multiplied the value of the mean grain size by the factor of 0.15 (C. Mätzler 2006, personal communication). This was done so comparisons can be made with results for models using either the mean grain size or a correlation length as inputs.

4. Bayesian model averaging

Bayesian model averaging (BMA) is a statistical method that infers from an ensemble of competing predictions the probabilistic prediction that possesses more skill and reliability than the original ensemble members (Raftery et al. 2003). BMA has been principally used in generalized linear regression applications. Recently (Raftery et al. 2003, 2005), it has been successfully applied to numerical weather prediction. In this study, we apply BMA to construct multimodel brightness temperature predictions using individual predictions from the three SEMs described in section 3. The BMA scheme is briefly described below.

a. Problem statement

Let y be a scalar quantity to be forecast, and let f_k be the forecast of y produced by model k. The forecast f_k is then characterized by a conditional probability density function (pdf), g_k(y|f_k), which can be interpreted as the pdf of y conditional on f_k, given that f_k is the best forecast in the ensemble. The BMA predictive pdf for the k-member ensemble of forecasts can be written as the following mixture model (see Hoeting et al. 1999; Raftery et al. 2003, 2005):

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where w_k is the weight such that ∀_kw_k ≥ 0 and Σ^K_k=1w_k = 1. When predicting the brightness temperature, it is reasonable to assume that g_k(y| f_k) ∼ N(μ_k,σ²_k). Note that although the latter conditionals are Gaussian, (4) is a nonparametric Gaussian mixture model (McLachlan and Peel 2000). The model is fitted to data sample χ = {y_t, f_1,t, f_2,t, . . . , f_K,t}^t=N_t=1, where the subscript t denotes time, f_k,_t is referred to as the kth forecast in the ensemble for time t, and y_t represents the corresponding verification. An estimate of the parameter vector θ = [w₁, . . . , w_k, μ₁, . . . , μ_k, σ₁, . . . , σ_k]^T is obtained by maximizing the log-likelihood function

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Because (6) cannot be solved analytically, we solve it using the expectation–maximization (EM) algorithm.

b. Solution by the EM algorithm

The EM algorithm (see Dempster et al. 1977; McLachlan and Krishnan 1997) is an iterative procedure that alternates between two steps, the expectation (E) step and the maximization (M) step. It starts with an initial guess, θ₀, for the parameter vector θ. In the E step, the posterior probabilities ẑ_k,t are estimated given the current guess for the parameters. For the BMA in (4), the E step is

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where the superscript j refers to the jth iteration of the EM algorithm, and g[y_t|μ^(j−1)_k,t, σ^(j−1)_k] is a normal density with mean μ^(j−1)_k,t and standard deviation σ^(j−1)_k evaluated at y_t. The mean is modeled as a function, ϕ, that depends on f_k,_t and a set of parameters, β_k. We choose a local model that has linear parameters:

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The other choice to make is ϕ, the form of the local model. In the absence of any prior information, a local linear model is a good choice [so ϕ₁( f_k,_t) = 1 and ϕ₂( f_k,_t) = f_k,_t]. For simplicity of further notation, we define the posterior-weighted average of a quantity x as

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The M step then consists of estimating the w_k, μ_k, and σ_k using the current estimates of z_k,_t as weights. Thus,

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The E and M steps are then iterated to convergence, which we defined as changes no greater than some small tolerance ɛ in the log-likelihood. The above algorithm provides a general setting for BMA with Gaussian conditionals. Sometimes, if the data sample χ is scarce, some adjustments are needed to keep the number of parameters entering EM, that is dim(θ), low compared to the sample size. A simplification that we incorporated here is that instead of estimating the coefficients β_k iteratively using (13), we fixed their values prior to EM by performing linear regression of y_t onto each f_k,_t, as in Raftery et al. (2005).

c. BMA predictive mean and variance

The predictive mean and variance of (4) can be expressed as (Raftery et al. 2003)

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In essence, the expected BMA prediction is the average of individual predictions weighted by the likelihood that an individual model is correct given the observations. There are several attractive properties to the BMA prediction. First, the BMA prediction receives higher weights from better performing models because the likelihood of a model is essentially a measure of the agreement between the model predictions and the observations. Second, the BMA variance is essentially a second-order uncertainty measure of the BMA prediction. It contains the following two components: i) the between-model variance and ii) the within-model variance, as shown in the first and second terms of the right-hand side of (17). This measure is a better description of predictive uncertainty than that in any nonBMA scheme, which estimates uncertainty based only on the ensemble spread (i.e., only the between-model variance is considered) and, consequently, results in underdispersive predictions (Raftery et al. 2003).

5. Data description and model identification

Meteorological measurements were recorded in 10-min intervals at 10 sites within the CLPX small regional study area (SRSA) located in north-central Colorado (39.5°–41°N, 105°–107.5°W) between 20 September 2002 and 1 October 2003. In this study, we used data records from two meteorological towers within the Fraser mesocell study area (MSA), Fraser Alpine (FA) and Fraser Experimental Forest headquarters (FHQ), from the period of 1 February to 31 May 2003. The dataset included air temperature, atmospheric pressure, relative humidity, wind speed and direction, and shortwave and longwave radiation as well as snow depth [see Feng et al. (2008) for a detailed description of these data]. The observed 10-min values were averaged to 1-h intervals to conform to VIC input requirements. It is important to stress that precipitation was not directly measured at the two CLPX sites. Therefore, for both FA and FHQ sites, we used hourly precipitation data based on 1/8th degree (∼12 km) hourly merged gauge–radar precipitation product available from the North American Land Data Assimilation System (NLDAS). Driven by the above mentioned meteorological forcings, VIC was integrated with the time step of 1 h at both FA and FHQ sites. The three SEMs described in section 3 were then forced with the ground temperature, snow temperature, depth, density, and grain size from VIC. The estimates of T_b were obtained for passive microwave frequencies at 18.7, 37, and 89 GHz for both horizontal (H) and vertical (V) polarization except for DMRT, which currently cannot handle a 89-GHz channel. Further, the T_b simulations were restricted only to dry snow conditions. This was because the retrieval of SWE is not possible when liquid water content in snow increases as a consequence of melting. The penetration depth at microwave frequencies when snow is wet is of the order of a few centimeters as a consequence of the absorption coefficient, which limits our capability of deriving SWE/SD (where SD is snow depth) in wet snow conditions from microwave data in general. Moreover, LSMEM and DMRT versions used in this study can only estimate T_b for dry snow. Next, the estimated T_b was compared to the Aqua AMSR-E satellite data at the incidence angle of 55°. These data were gridded to the geographic (latitude–longitude) grids of the CLPX 2003 large regional study area (LRSA) and interpolated from swath space using inverse distance squared resampling (Brodzik 2003). The grid resolution was approximately 1/4° (∼25 km), so both FHQ and FA sites are located within the same AMSR-E pixel.

6. Results

b. Comparison of brightness temperatures

Brightness temperature predictions at 18.7 and 37 GHz, computed by means of the LSMEM, MEMLS, and DMRT models; and at 89 GHz, by means of the LSMEM and MEMLS models; at both the FHQ and FA sites were first corrected for tree emissions in the analyzed AMSR-E pixel using the following formula:

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where f represents fractional tree cover, T_b,tree is the brightness temperature of trees and T_b,model is raw estimate of brightness temperature from a particular SEM. Here, Fraser area f = 0.53, and T_b,tree was taken as the mean of the distribution of brightness temperatures for trees (see Tedesco et al. 2005 for details), that is, 268 K at 18.7 GHz and 271 K at 37 GHz. At 89 GHz, the value of T_b,tree was assumed to be 272 K. Figure 2 shows T_b estimates for FHQ site together with the corresponding AMSR-E measurements (ascending and descending overflights are grouped together).

It is clear that for 18.7 and 37 GHz, all three SEMs overestimate AMSR-E brightness temperature in the beginning of the study season [1 February–13 March 2003; time index 0–1000 (hour)]. Although there are many factors that can contribute to overestimation, one factor is that the value of T_b,tree might be too high, which could occur if the trees were snow covered. Another problem, especially in the case of 37 GHz T_b, is that the grain size estimates by VIC might be too low. On the other hand, the overestimation is not present at 89 GHz (both horizontal and vertical). This can be explained considering that, in general, values of T_b at 89 GHz are strongly influenced by the diurnal freeze–thaw cycles at the surface of snowpack. The surface is usually cooler and dryer than deeper layers of snowpack. Note that in Fig. 2, the variability in both estimated and measured T_b decreases with the decrease of the frequency. Additionally, 37- and 89-GHz channels are generally more sensitive to the attenuating influence of the snowpack than the 18.7-GHz channel, which is influenced by the soil underlying the snowpack, especially for thin snowpacks. For these two channels, LSMEM estimates of T_b exhibit large fluctuations compared to the other two models. This can be attributed to the sensitivity of LSMEM predictions of T_b to the variability in the average temperature of the snowpack T_snow (cf. the plot of VIC predictions of T_snow at FHQ site in Fig. 3 with LSMEM T_b predictions at 37 and 89 GHz in Fig. 2). Another important aspect in Fig. 2 is that the AMSR-E data have a pronounced early summer snowmelt signature (increasing trend in measured T_b). This snowmelt event is not adequately reproduced by SEMs. The reason for that is twofold. First, we restricted our simulations to dry snow conditions, and the brightness temperature of dry snow is much lower than that of the wet snow. Second, as mentioned in section 6a, the VIC prediction of the timing of the snowmelt was delayed. For the FA site (Fig. 2), it is evident that the results are worse than for the FHQ site, especially at 37 and 89 GHz (both horizontal and vertical). In the second half of the study season, there is a U-shaped feature in the predicted T_b time series, which is obviously caused by the rise and rapid decrease in grain size, as depicted in the lower panel of Fig. 1. This grain size pattern may be attributed to the overestimated snow depth at FA (see section 6a). To help study the polarization effects, Fig. 4 shows the AMSR-E and model-predicted polarization differences (horizontal minus vertical) for 18.7, 37, and 89 GHz at the FHQ (left) and FA (right) sites. The models provide larger polarization differences than those observed by the AMSR-E sensor for two reasons. First, in this study a single-layer approximation to model snowpack was used (multiple layers tend to reduce the polarization differences). Second, other factors in the scenes observed by the sensor, such as vegetation, might also decrease the magnitude of polarization differences. Another interesting effect in Fig. 4 is that LSMEM-predicted differences are larger than what the other models predict, probably because LSMEM assumes that 96% of scattering occurs in the forward direction. Nevertheless, the polarization difference magnitudes appear to be relatively similar for all three models with the exception of DMRT, which shows a large increase at the FHQ site during the snowmelt event in late spring.

c. BMA and multimodel brightness temperature prediction

The differences between observed and modeled snow T_b can be due to the following: i) the misrepresentation of snow properties (especially gain size) by the models at spatial scales is equivalent to the AMSR-E surface footprint size, ii) the AMSR-E T_b is actually a combination of T_b contributions from the snow, ground, vegetation cover, and atmosphere, and iii) instrumental and input errors. Individual SEMs capture only some of these uncertainties and then probably only partially, depending on the frequency channel used and the adequacy of parameterization of snow emission physics. Accordingly, by trying to select the “best” SEM out the multimodel ensemble, some sources of uncertainty captured by the remaining SEMs might be ignored, thus underestimating the total uncertainty in T_b estimates. To tackle this problem, we constructed multimodel AMSR-E T_b predictions using the BMA technique described in section 4. Given the difficulties at FA described in the previous section, the BMA analysis is performed only for the FHQ site.

1) Bootstrap validation for BMA

The simplest approach for assessing the performance of the BMA predictions is to define an error measure, split the entire data sample deterministically into a training set and an independent testing set, fit the BMA using the training set, and estimate the error on the testing set. Because the total number of available AMSR-E measurements in our study period was only 193, this approach is problematic because the results would highly depend on the (deterministic) way the data would have been split. To resolve the problem, we used the following bootstrap validation procedure. By randomly sampling without replacement from the original data, we generated B = 30 independent replicates of the training data (145 points, which is 75% of the total sample size) and the testing data (48 points, which is 25% of the total sample size). Then, we refitted the BMA scheme to each of the training replicates and examined the behavior of the fits using corresponding replicates of the testing data. If Y = {y*bval, ŷ*bval}Nvaltval=1 is the bivariate set of estimates of the BMA predictive mean in (16) and associated AMSR-E verifications in the bth bootstrap testing set, then the estimate of the average bootstrap prediction error for the BMA scheme is

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where N_val denotes the number of points in the bth testing set, and ɛ(·) is the loss function for measuring errors. A typical choice of the loss function is the root mean squared error (RMSE),

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In addition, we calculated the mean absolute error (MAE),

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which is similar to the RMSE but is less sensitive to large forecast errors. For small or limited datasets, the use of MAE is sometimes preferred.

2) BMA results

To initialize the EM fitting procedure, for each frequency channel and for each polarization, the variances of the conditional Gaussian pdfs on the right-hand side of (4) were taken as variances of individual SEMs T_b estimates, respectively. Figure 5 shows an example of the fitted conditionals and predictive BMA pdf of 37-GHz (vertical) T_b at FHQ site at 0800 UTC on 20 March 2003. Note that these estimates were obtained by running the EM on one of the replicates of the bootstrap training set. There was a disagreement among the raw ensemble member predictions: two of them (LSMEM and MEMLS) were around 260 K, whereas the other one (DMRT) was around 270 K. This difference of 10 K is quite large. After estimating the ensemble member conditional means (hereafter the bias-corrected T_b estimates), the raw SEMs predictions were shifted toward verifying the AMSR-E observation (cf. raw SEMs predictions with the means of the Gaussians in Fig. 5). The latter turned out to be outside the raw ensemble range. The resulting BMA predictive mean slightly overestimates AMSR-E T_b. However, it is much more accurate than the raw SEMs estimates. Because each MEMLS and DMRT bias-corrected T_b underestimates the verifying observation and LSMEM T_b overestimates it, the BMA predictive pdf is positively skewed. The values of the weights of the model-conditional components of this pdf were 0.6 for LSMEM, 0.36 for DMRT, and 0.04 for MEMLS. The small weight for the MEMLS component is due to the high correlation (0.87) between LSMEM and MEMLS T_b predictions. This implies that if the LSMEM prediction is known, the additional information from the MEMLS prediction is much less than it would be if the two predictions were uncorrelated. Figure 6 shows the time evolution of one bootstrap realization of BMA predictive pdf, its mean, and the standard deviation envelopes at the FHQ site for all analyzed frequencies and polarizations. It is clear that the variability of the AMSR-E data is well described by the BMA standard deviation envelopes. Moreover, the BMA predictive mean approximates AMSR-E T_b better than raw SEMs predictions in Fig. 2. This is confirmed in Table 2, which compares the average bootstrap values of RMSE and MAE of BMA predictive mean with raw SEMs predictions. The values are stratified according to frequency and polarization and refer to the training and testing set averages separately. In general, the values of both RMSE and MAE for the BMA predictive mean are lower than those for the raw individual SEMs predictions. The BMA scores are better for vertical polarization than those for horizontal polarization for all frequencies. Moreover, as expected theoretically, MAE estimates are slightly smaller than RMSE estimates. This indicates the sensitivity of the latter statistic to outliers. The highest improvements in the prediction accuracy are found for the 37-GHz (V) channel. Here, the differences between the corresponding estimates of RMSE and MAE for the BMA predictive mean and the best performing models (LSMEM and MEMLS) on the testing set are about 3.5 and 3 K, respectively. The best prediction accuracy of the BMA scheme is found for 18.7-GHz (V) channel. The testing set estimates of RMSE and MAE are as low as 6.78 and 5.44 K, respectively. This is due to the relatively small variability in the corresponding AMSR-E measurements. Conversely, for 89 GHz in which the variability is large, the errors in the BMA predictions are large too. With regard to the errors of raw SEMs predictions, the best performing model is LSMEM, with slightly better RMSE and MAE scores than MEMLS and much better scores than DMRT for 18.7 (H), 37 (H), and 37-GHz (V) frequency, respectively. Another important feature of the results in Table 2 is the reasonable agreement between the mean error estimates for the training set samples and the testing set samples. This indicates that on average, the BMA model is robust against overfitting. To further examine the robustness of the RMSE and MAE, we estimated their standard deviations. These results are listed in Table 3. Clearly, the dispersion around the mean value in the bootstrap samples of RMSE and MAE for the training set is much smaller than in those for the testing set. This is because the size of the testing set is only 25% of the total number of AMSR-E measurements, which in turn makes the bootstrap error estimates on the testing set more vulnerable to sampling effects, to the presence of outliers, and to the nonstationarity in AMSR-E data as a result of the snowmelt event at the end of the study season. On the other hand, the standard deviations of both RMSE and MAE of the BMA scheme never exceed ±1 K, which confirms the robustness of the results in Table 2.

7. Summary and outlook

In this paper, brightness temperatures of snow at 18.7 and 37 GHz were simulated by three SEMs (LSMEM, MEMLS, and DMRT) and at 89 GHz by two SEMs (LSMEM and MEMLS) coupled with the VIC land surface scheme using data from the FHQ and FA sites collected during the CLPX 2003 experiment. The objective of this study was to assess the feasibility of the coupling in terms of the quality of T_b predictions. Because we simulated hourly time series of T_b for the period of February–May 2003, the natural way to validate our simulations was to compare them to satellite AMSR-E measurements. All the analyzed SEMs had common inputs predicted by VIC. The latter was driven by a combination of in situ and NLDAS forcings, which introduced a scale discrepancy between the SEMs predictions and the AMSR-E observations. In the beginning of the study season at 18.7 and 37 GHz, all the models overestimated the AMSR-E T_b at the FHQ site. This may have been caused either by trees covered by snow in the AMSR-E pixel or by an underestimation of the average snow grain size. Also, the signature of early summer snowmelt event in the AMSR-E measurements was not well captured by the SEMs at all analyzed frequencies. The reason for that is because in our investigation, we only considered dry snow conditions. Thus, T_b was underestimated compared to the T_b signature of wet snow that would be measured by AMSR-E. In general, except for the 89-GHz channel, the variability range of AMSR-E measurements of T_b was not well captured by SEMs. In particular, MEMLs and DMRT produced oversmoothed T_b estimates. LSMEM predictions, on the other hand, turned out to be sensitive to the average snow temperature fluctuations. This was particularly pronounced at 37 and 89 GHz. The penetration depth of the latter frequency channel is small, so effective fluctuations in snowpack surface temperature govern the dynamics of T_b. Our simulations were less successful at the FA site because the spatial variability of snow depth was highly influenced by snowdrift. This phenomenon is not accounted for in the current version of VIC, so the simulation of the microphysical snow properties at FA was of poor quality. As a result, the simulated T_b exhibited some artifacts as explained in section 6a.

Apart from considering the individual SEMs predictions, we proposed a new multimodel procedure for estimating the AMSR-E brightness temperature of snow based on an ensemble of SEMs (LSMEM, MEMLS, and DMRT) coupled with the VIC land surface scheme. The procedure is based on BMA and offers not only an adequate nonparametric description of the T_b predictive pdf, but it also improved the T_b prediction accuracy compared to individual SEMs results. This is because, to some extent, BMA reduces the effects of scaling, model error sources, atmospheric contribution to radiative transfer, and sparseness of AMSR-E measurements—problems that are notorious when comparing satellite snow T_b with SEMs predictions. Using a simple bootstrap validation procedure, we have shown that the BMA predictive mean outperformed the predictions of individual SEMs in terms of RMSE and MAE scores, particularly for 37 GHz. The results for 18 GHz (H) were also encouraging. Another interesting feature of BMA results was its low variability (less than 1 K) around the bootstrap estimates of the aforementioned error measures, which confirms the robustness of the presented results. Despite the increased precision of BMA estimates of T_b compared to SEMs predictions, our preliminary results have shown that the errors of BMA were still significant.

There are a number of issues that need further investigation to improve the BMA T_b estimates to make them useful in hydrometeorological practice. i) Additional research is needed to better understand the influence of atmospheric moisture profiles on T_b estimates from SEMs. An attractive option here would be to implement the ensemble of SEMs as a microwave surface module of CRTM and run it in the coupled mode with atmospheric absorption and atmospheric scatter modules. ii) It is critical to further understand the influence of the mean grain size (or correlation length in the case of MEMLS) on the SEMs performance. Because the measurements of this parameter are not usually collected systematically, perhaps a better option would be to compute an “effective” grain size by simply calibrating this parameter to produce T_b estimates that match AMSR-E T_b as closely as possible. Note that this effective value would automatically account for any potential scaling mismatch. Some preliminary results of the parameter calibration approach for LSMEM—applied for soil moisture retrievals though, not for snow T_b estimation—are given in Pan et al. (2006). And, (iii) the final issue concerns the use of BMA predictive pdfs in data assimilation. These pdfs could, for example, be applied to construct the nonparametric likelihood operators in particle filters, offering enhanced quality of the updates of variables that describe snowpack evolution in land surface models.