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    Land cover map of the upper Mississippi River basin, following the UMD classification (Hansen et al. 2000).

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    Schematic of the forward simulation of SMOS TB from subgrid vegetation tiles in VIC–CMEM.

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    Density scatterplots between 2011 VIC and SMOS SM (cm3 cm−3) (top) before and (bottom) after CDF matching.

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    The basin-averaged angular TB (K) signatures of the SMOS observations and baseline simulations by VIC–CMEM for 2011, along with the RMSE (K) and KGE (unitless) for (a),(b) ascending and (c),(d) descending orbits.

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    The 2011 annual mean ascending SM as a function of volume (%) (a) from SMOS and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (%; SMOS minus model) and (d) Spearman rank correlation.

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    The 2011 annual mean surface temperature (°C) (a) from ECMWF and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (°C; ECMWF minus model) and (d) Spearman rank correlation.

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    The 2011 annual mean ascending TBH (K) at 42.5° (a) observed by SMOS and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

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    The 2011 annual mean ascending TBV (K) at 42.5° (a) observed by SMOS and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

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    The basin-averaged angular TB (K) signatures of the SMOS observations and calibrated (case 10) VIC–CMEM simulations for 2011, along with the RMSE (K) and KGE (unitless) for (a),(b) ascending and (c),(d) descending orbits.

  • View in gallery

    The 2011 annual mean ascending TBH (K) at 42.5° (a) observed by SMOS and (b) simulated by the calibrated (case 10) VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

  • View in gallery

    The 2011 annual mean ascending TBV (K) at 42.5° (a) observed by SMOS and (b) simulated by the calibrated (case 10) VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

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    The 2011 annual mean (a) correlation, (b) mean ratio, (c) std dev ratio, and (d) KGE between SMOS TB and simulated TB (case 10) across all incidence angles, polarizations, and orbits.

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    The 2011 time series of ascending TB (K) at 42.5° as observed by SMOS and simulated by VIC–CMEM (case 10), over (a),(b) forest and (c),(d) cropland grid cells at (a),(c) H polarization and (b),(d) V polarization.

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Optimization of a Radiative Transfer Forward Operator for Simulating SMOS Brightness Temperatures over the Upper Mississippi Basin

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  • 1 * Laboratory of Hydrology and Water Management, Ghent University, Ghent, Belgium
  • | 2 Centre d’Etudes Spatiales de la Biosphère, Toulouse, France
  • | 3 Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland
  • | 4 European Space Agency, Noordwijk, Netherlands
  • | 5 Department of Civil Engineering, Monash University, Clayton, Victoria, Australia
  • | 6 ** Forschungszentrum Jülich, Jülich, Germany
  • | 7 Land Surface Hydrology Group, Princeton University, Princeton, New Jersey
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Abstract

The Soil Moisture Ocean Salinity (SMOS) satellite mission routinely provides global multiangular observations of brightness temperature TB at both horizontal and vertical polarization with a 3-day repeat period. The assimilation of such data into a land surface model (LSM) may improve the skill of operational flood forecasts through an improved estimation of soil moisture SM. To accommodate for the direct assimilation of the SMOS TB data, the LSM needs to be coupled with a radiative transfer model (RTM), serving as a forward operator for the simulation of multiangular and multipolarization top of the atmosphere TBs. This study investigates the use of the Variable Infiltration Capacity model coupled with the Community Microwave Emission Modelling Platform for simulating SMOS TB observations over the upper Mississippi basin, United States. For a period of 2 years (2010–11), a comparison between SMOS TBs and simulations with literature-based RTM parameters reveals a basin-averaged bias of 30 K. Therefore, time series of SMOS TB observations are used to investigate ways for mitigating these large biases. Specifically, the study demonstrates the impact of the LSM soil moisture climatology in the magnitude of TB biases. After cumulative distribution function matching the SM climatology of the LSM to SMOS retrievals, the average bias decreases from 30 K to less than 5 K. Further improvements can be made through calibration of RTM parameters related to the modeling of surface roughness and vegetation. Consequently, it can be concluded that SM rescaling and RTM optimization are efficient means for mitigating biases and form a necessary preparatory step for data assimilation.

Corresponding author address: Hans Lievens, Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, Ghent, Belgium. E-mail: hans.lievens@ugent.be

Abstract

The Soil Moisture Ocean Salinity (SMOS) satellite mission routinely provides global multiangular observations of brightness temperature TB at both horizontal and vertical polarization with a 3-day repeat period. The assimilation of such data into a land surface model (LSM) may improve the skill of operational flood forecasts through an improved estimation of soil moisture SM. To accommodate for the direct assimilation of the SMOS TB data, the LSM needs to be coupled with a radiative transfer model (RTM), serving as a forward operator for the simulation of multiangular and multipolarization top of the atmosphere TBs. This study investigates the use of the Variable Infiltration Capacity model coupled with the Community Microwave Emission Modelling Platform for simulating SMOS TB observations over the upper Mississippi basin, United States. For a period of 2 years (2010–11), a comparison between SMOS TBs and simulations with literature-based RTM parameters reveals a basin-averaged bias of 30 K. Therefore, time series of SMOS TB observations are used to investigate ways for mitigating these large biases. Specifically, the study demonstrates the impact of the LSM soil moisture climatology in the magnitude of TB biases. After cumulative distribution function matching the SM climatology of the LSM to SMOS retrievals, the average bias decreases from 30 K to less than 5 K. Further improvements can be made through calibration of RTM parameters related to the modeling of surface roughness and vegetation. Consequently, it can be concluded that SM rescaling and RTM optimization are efficient means for mitigating biases and form a necessary preparatory step for data assimilation.

Corresponding author address: Hans Lievens, Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, Ghent, Belgium. E-mail: hans.lievens@ugent.be

1. Introduction

The updating of land surface models (LSMs) through remote sensing data assimilation is well known for its potential to improve hydrologic model predictions (e.g., Pauwels et al. 2001, 2002; Crow and Wood 2003; Reichle et al. 2007; Pan et al. 2009). The significance of soil moisture SM observations for hydrologic predictions has fostered the development of remote sensing platforms, such as the Soil Moisture Ocean Salinity (SMOS; Kerr et al. 2001) and the Soil Moisture Active Passive (SMAP; Entekhabi et al. 2010) missions, dedicated to observing the dynamics of surface SM across time and space. These radiometer systems provide indirect estimates of SM, through the close relationship between the observed brightness temperature TB emitted by the earth’s surface and the SM content (Njoku 1977; Njoku and Entekhabi 1996). While it is possible to assimilate the derived SM products, there has been a strong interest in the direct assimilation of satellite-observed TBs (Reichle et al. 2001; Balsamo et al. 2006; Han et al. 2013), which circumvents the need for processing soil moisture retrievals. Moreover, this bypasses the need for ancillary parameters (e.g., surface temperature) and allows for the use of consistent parameters (e.g., soil and vegetation) between the LSM and radiative transfer model (RTM). The assimilation of TB observations directly requires the use of an RTM as a forward operator, to simulate the top of the atmosphere (TOA) TB.

An important prerequisite for the assimilation of TB observations into an LSM is that the observations need to be unbiased with respect to the model simulations (Reichle et al. 2004). This can be achieved through a priori processing of the TB observations, for example, through cumulative distribution function (CDF) matching. However, in the specific case of SMOS, which provides multiangular and multipolarization observations, CDFs would need to be matched for each incidence angle and polarization, while the correlations between these CDFs need to be accounted for. The latter poses major difficulties to the processing of the TB observations. Furthermore, for most climate regions (i.e., temperate and continental), TB displays a strong seasonal cycle dominated by temperature. As CDF matching only corrects for long-term differences, it will not lead to desirable results when scaling the TB. Alternatively, systematic differences can be mitigated within the coupled LSM–RTM framework. This allows for maintaining the SM–TB sensitivity of the observations, which would otherwise be affected by the CDF matching, and furthermore allows for simulating the observation error.

Unfortunately, the forward simulation of unbiased TBs through an LSM–RTM is far from straightforward because of several reasons. The first aspect is the complexity of the radiative transfer processes involved (De Lannoy et al. 2013). Major challenges in this context are the accurate characterization of vegetation and surface roughness contributions (Sabater et al. 2011; Vereecken et al. 2012; Rahmoune et al. 2013; Parrens et al. 2014; Martens et al. 2015). The second obstacle in TB simulation relates to the representation of the required RTM input states, such as soil temperature and soil moisture, which are generally obtained from an LSM. For instance, many studies have found large systematic differences between SM fields modeled through LSMs and those observed by satellite missions (e.g., Reichle et al. 2004; Gao et al. 2006; Sahoo et al. 2013). These can be attributed to several factors (Verhoest et al. 2015), such as approximations and shortcomings in both the retrieval and land surface models (De Lannoy et al. 2007); errors in model inputs, for example, soil texture (Han et al. 2014); and a mismatch in the horizontal and vertical representation (Wilker et al. 2006). While radiometer observations provide SM at scales of 10–40 km and are generally sensitive to only the top few centimeters (Escorihuela et al. 2010), LSMs typically operate at resolutions of 1–10 km and have their own definition of the top surface layer, often much thicker compared to remote sensing depths (Sahoo et al. 2013). In addition, LSMs may be optimized toward the simulation of streamflow or land–atmosphere fluxes, rather than SM representation (Koster et al. 2009). For these reasons, LSMs and satellite retrievals generally have different SM climatologies. Unfortunately, an established consensus on the climatology of SM over large domains, considering both LSMs and satellite retrievals, is currently lacking (Draper et al. 2013). Nevertheless, when LSM soil moisture is used as input to an RTM, its climatology has a substantial impact on the magnitude of biases in TB. This becomes evident when considering the sensitivity of TB to SM, that is, generally on the order of 2–3 K increase per 0.01 m3 m−3 decrease in SM for low vegetation at around 40° incidence angle (Jackson 1993). Finally, a third difficulty concerns the estimation of RTM parameters. The latter are typically estimated from local field experiments using ground-based and airborne radiometers (e.g., Sabater et al. 2011; Peischl et al. 2012), which may not always be appropriate for the simulation of spaceborne observations, for example, by SMOS, because of scaling effects. Unfortunately, large-scale studies on parameter optimization of RTMs are hardly available (Drusch et al. 2009; de Rosnay et al. 2009), and only a few studies have used actual SMOS TB data (De Lannoy et al. 2013; Montzka et al. 2013).

This study proposes a method for optimizing a coupled land surface and radiative transfer model framework to decrease the amount of biases in the simulation of multiangular and multipolarization SMOS TB observations. Therefore, the Community Microwave Emission Modelling platform (CMEM; Holmes et al. 2008; Drusch et al. 2009; de Rosnay et al. 2009) is coupled to the Variable Infiltration Capacity model (VIC; Liang et al. 1994, 1996, 1999). More specific, the study addresses ways for mitigating the mismatch in horizontal and vertical representation between model simulations and SMOS observations. Subsequently, the TB simulations from this model configuration are further matched to SMOS observations by calibrating the RTM parameters accordingly. Previous studies have addressed the global calibration of RTM parameters based on multiangular SMOS observations (De Lannoy et al. 2013) and local-scale calibration of temporally dynamic RTM parameters through data assimilation (Montzka et al. 2013). The novelty of this present study lies in its focus on the influence of the LSM soil moisture climatology on the TB simulations, the selection of the RTM calibration parameters, and the dependence of the calibration on the sensor configuration (i.e., distinguishing between ascending A and descending D satellite overpasses and horizontal H and vertical V polarizations). The study is applied on a regional scale, covering the upper Mississippi River basin in the central United States. The final aim of this study is to optimize an LSM–RTM framework that accommodates for the direct assimilation of multiangular and multipolarization TB observations from SMOS, in order to benefit surface water management.

2. Data and methods

a. Study site

The upper Mississippi River basin is located in the central United States. The basin covers an area of about 440 000 km2 and comprises portions of Minnesota, Wisconsin, Iowa, and Illinois. As can be seen in Fig. 1, the land use is primarily agricultural (corn, soybean, wheat, etc.). The northeastern part of the basin is mainly covered by forests. The basin is characterized by a lack of significant topography, which facilitates the retrieval of SM from satellite observations. The annual precipitation ranges from approximately 475 mm in the northern part to over 1300 mm in the southern part of the basin. The southern portion is prone to flooding because of strong summer precipitation, often enhanced by wet antecedent soil moisture conditions. Furthermore, the basin is equipped with an extensive meteorological network and is a part of the North American Land Data Assimilation System (NLDAS) domain (Mitchell et al. 2004). Finally, the catchment is characterized by a low contamination of radio frequency interference (RFI) in the SMOS L-band observations.

Fig. 1.
Fig. 1.

Land cover map of the upper Mississippi River basin, following the UMD classification (Hansen et al. 2000).

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

b. SMOS observations

SMOS provides regular (±3-day repeat period) observations of the TOA TB at the global scale, which are operationally used for SM retrieval through the European Space Agency (ESA) level 2 processor (Kerr et al. 2012). The TB and SM data in this study stem from the level 3 Centre Aval de Traitement des Données SMOS (CATDS) product (Jacquette et al. 2010), version 244. In essence, the level 3 algorithm is an extension of the level 2 prototype, employing multiorbit retrievals of vegetation parameters for the enhancement of SM retrievals over individual orbits.

The level 3 CATDS TB data are a global daily product in full polarization, available in ±25-km cylindrical projection over the Equal-Area Scalable Earth (EASE) grid. Note that the actual resolution of SMOS is ±43 km. The TB data are transformed from antenna polarization reference (X and Y) to ground reference (H and V) frame and are angle binned into fixed angle classes, stretching from 17.5° to 52.5°, with 5° bins. Both ascending and descending data have been extracted over the upper Mississippi basin from the beginning of January 2010 to the end of December 2011, with a separate processing of the A and D orbits.

Corresponding level 3 CATDS ascending and descending SM data are also extracted over the study area from 2010 to 2011 from the 1-day global product. Next to SM, the product also contains quality indices for soil moisture and RFI, as well as science flags indicating the presence of snow, frozen soils, etc. The SMOS data have been extensively filtered, preserving data when soil and air temperatures (according to the LSM forcings and simulations) are larger than 2.5°C, and product flags for snow and frozen soils [provided within the SMOS product through the European Centre for Medium-Range Weather Forecasts (ECMWF)] are zero, that is, indicating the absence of snow and frozen soils. As a consequence of this filtering, it is not expected that snow or frozen soil conditions will have a significant impact on further analysis. Finally, filters have been implemented to exclude data with a probability of RFI larger than 0.2 and urban or water cover fractions larger than 0.1 (fraction per SMOS cell).

c. The VIC

The Variable Infiltration Capacity model (Liang et al. 1994, 1996, 1999) is a distributed LSM, accounting for both water and energy balances. During the last decades, the VIC has been widely used in a number of applications (e.g., Maurer et al. 2001; Nijssen et al. 2001; Sheffield et al. 2003; Sheffield and Wood 2008). The gridcell size of the VIC can vary from 1 km to hundreds of kilometers, where each cell can be further subdivided into fractions representing specific vegetation types. In this study, the grid spacing was set to 0.125° × 0.125°, which approximately corresponds to 10 km × 10 km.

The simulations make use of the real-time forcing dataset (Cosgrove et al. 2003) prepared for the first and second phases of the NLDAS project (NLDAS-1 and NLDAS-2, respectively; Mitchell et al. 2004). Seven meteorological forcing fields were processed at an hourly time step and 0.125° spatial resolution: precipitation, 2-m air temperature, air pressure, vapor pressure, wind speed, and incoming short- and longwave radiation. Also, soil and vegetation parameters employed in the VIC were sourced from the NLDAS-1 project. The soil texture was derived from the State Soil Geographic (STATSGO) database (Miller and White 1998), whereas the elevation is described by the Global 30 Arc-Second Elevation (GTOPO30) database (Verdin and Jenson 1996). The soil texture and elevation data were averaged up to the 0.125° grid of the VIC. The land cover was extracted from the global 1-km University of Maryland (UMD) dataset (Hansen et al. 2000), based on which subgrid vegetation fractions were calculated for the coarser 0.125° model grid. Finally, the climatological vegetation leaf area index (LAI) was derived based on NDVI observations from the Advanced Very High Resolution Radiometer (AVHRR) satellite sensor (Gutman and Ignatov 1998). The LAI product (Myneni et al. 1997) was originally provided at 16-km resolution and subsequently resampled down to 0.05° through bilinear interpolation and reaggregated to 0.125°. Monthly averaged LAI values have been processed per subgrid vegetation tile.

The model simulations over the upper Mississippi are performed in full water and energy balance mode, where soil moisture and soil temperature in various layers are simulated on an hourly basis. The spinup time for the simulations was set to 1 year. The number of vertical soil layers has been set to 3, where the first layer represents the top 10 cm of the soil and the second- and third-layer depths vary between 10 and 250 cm. Note that this first-layer depth may differ from the layer depth observed by SMOS, which is limited to the top few centimeters (Escorihuela et al. 2010). Compared to the SMOS retrievals, the VIC SM simulations may consequently show a different long-term mean and dynamic range, as well as slower SM dynamics, because of the larger memory associated with thicker layer depths. Nevertheless, it was decided not to modify the first-layer depth of the VIC, as the model employs a one-source energy balance, and consequently depends on an equivalent surface and vegetation temperature. It should also be highlighted that, for this study, the VIC parameters were considered to be fixed, having been previously optimized for the purpose of streamflow simulations (Maurer et al. 2002) over the upper Mississippi basin. In this context, it is worth mentioning that a mismatch in vertical representation may also be found in operational applications, where it may not be possible to fine-tune LSMs for assimilation purposes because of computational restrictions and lack of data, particularly for large scales and remote catchments (Balsamo et al. 2009).

d. The CMEM

The RTM coupled to the VIC is the CMEM (Holmes et al. 2008; Drusch et al. 2009; de Rosnay et al. 2009), version 4.1. The CMEM is used as a forward operator to convert the simulated soil moisture and surface temperatures by the VIC into simulations of multiangular and multipolarization TOA L-band brightness temperatures at polarization :
e1
where (K) is the upward atmospheric contribution, (unitless) is the atmospheric opacity, and (K) is the TB at the top of the vegetation (TOV). The latter is calculated through a first-order tau–omega (τω) model (Jackson et al. 1982):
e2
where (K) is the effective temperature of the soil medium, (unitless) is the rough surface reflectivity, (unitless) is the vegetation transmissivity, (K) is the vegetation temperature, (unitless) is the scattering albedo, and (K) is the downward atmospheric contribution. As in most retrieval studies, the vegetation temperature is assumed to be equal to the effective soil temperature (Wigneron et al. 2007). The transmissivity of the vegetation can be expressed by
e3
where (unitless) is the optical depth of the standing vegetation and θ (°) is the incidence angle.
CMEM has a modular structure, allowing for different parameterization options for the respective contributions from atmosphere, soil, and vegetation. In general, the options selected for this study revert to the L-band Microwave Emission of the Biosphere (L-MEB) model formulation by Wigneron et al. (2007). The atmospheric contributions are described according to Pellarin et al. (2003). For the soil component, the effective temperature is approximated based on the surface temperature (K) and the deep-soil temperature (K) as
e4
where the weighting factor C depends on the SM content (Wigneron et al. 2001) by
e5
with and as semiempirical parameters depending on soil characteristics (mainly soil texture). As the RTM is coupled with the VIC, the VIC skin temperature and third-layer (variable thickness) soil temperature are used to approximate the and , whereas SM is approximated by the first-layer SM from the VIC.
The rough surface reflectivity parameterization is based on the formulation by Choudhury et al. (1979):
e6
where Q is the polarization mixing factor often set to zero for L band (Wigneron et al. 2001), q is the opposite polarization of p, h is the surface roughness, is the angular dependence of the surface roughness, and is the smooth surface reflectivity. The smooth surface reflectivity is given by the Fresnel equations and is a function of the dielectric constant. The relationship between dielectric constant and soil moisture is described by Mironov et al. (2004). Finally, the vegetation optical depth is based on the model by Wigneron et al. (2007), which expresses as a function of the optical depth at nadir (unitless):
e7
where is a parameter accounting for the influence of the incidence angle. The optical depth at nadir is given by
e8
with and being structural vegetation parameters. Despite that the vegetation optical depth is more closely related to the vegetation water content (VWC); it is usually derived based on LAI, as global LAI input data are more easily accessible (Wigneron et al. 2007). Although the LAI may be less suitable during the senescent phase of crops, the correlation between and LAI was found to be satisfactory for various crop types (Wigneron et al. 2007).

A set of baseline parameter values has been identified that corresponds to the parameter values that are used in the ESA level 2 processor, version 5.5.1 (Kerr et al. 2012). The list of parameters is given in Table 1 for each UMD land cover class. Note that for high vegetation types (classes 2–7 in Table 1), the annual maximum LAI is used in Eq. (8), whereas for low vegetation types (classes 8–13 in Table 1), monthly average values (the same as in the VIC) are employed.

Table 1.

The baseline RTM parameters for the UMD land cover types.

Table 1.

3. Optimization of the LSM–RTM framework

The assimilation of SMOS TB observations requires the coupling of an LSM with a forward radiative transfer scheme to provide unbiased simulations of multiangular and multipolarization TBs. To avoid difficulties encountered with a priori bias correction through CDF matching of the TB observations, this study aims to optimize the coupled LSM–RTM framework such that the processing of the observations can be bypassed. Therefore, a number of optimization experiments are investigated, which are further detailed in the following sections. A first experiment aims to investigate the impact of the LSM SM climatology on the bias in the TB simulations. Thereby, the SM simulations of VIC are rescaled to the climatology of SMOS through CDF matching, prior to propagation in CMEM. The climatology of the SMOS SM retrievals is chosen as the reference to assess the quality of the RTM parameters that are currently used operationally for SMOS retrievals, in the absence of persistent SM biases. A second experiment is dedicated to the calibration of RTM parameters based on multiangular and multipolarization SMOS observations.

a. Sample dataset

A sample dataset containing TB simulations by the coupled LSM–RTM and observations by SMOS was generated to investigate the optimization of the LSM–RTM framework. Data from 2010 were used for calibration and data from 2011 were used for validation. A schematic explaining the generation of the TB simulations through the coupled LSM–RTM is shown in Fig. 2. An important aspect of the proposed method is that it accounts for the mismatch in spatial resolution between the finescale LSM and coarse-scale SMOS observations, while conserving the subgrid vegetation description of the LSM.

Fig. 2.
Fig. 2.

Schematic of the forward simulation of SMOS TB from subgrid vegetation tiles in VIC–CMEM.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

For each SMOS TB swath (within the period of 2010–11), 25 random SMOS grid cells (EASE) within the upper Mississippi basin are selected. The random sampling is redone at each time step and is performed to limit the size of the dataset, while including data from various locations within the basin. Each of the selected SMOS grid cells covers a number (4–9) of finescale VIC grid cells, which in turn embed several vegetation tiles (forest, cropland, etc.). CMEM is then run for each individual VIC vegetation tile to simulate TB at both H and V polarization and eight angles, that is, from 17.5° through 52.5° (each 5°). Thus, all required input fields for CMEM are propagated from the VIC. These include soil moisture (first layer), soil temperatures (skin and third layer), sand and clay fractions, bulk density, land cover type, and LAI. The simulated TBs at each tile are then aggregated per VIC cell according to the vegetation fractions within each cell. Finally, the antenna pattern weighting function for each SMOS cell is used to aggregate the simulated TBs of the underlying VIC cells to the scale of the SMOS grid. Note that the antenna weighting function differs for each SMOS cell, as it relies on the incidence angle, the azimuth angle, and the footprint axis. A complete description of the weighting function can be found in Kerr et al. (2011).

Independent calibration and validation datasets have been generated for ascending and descending orbits to investigate the impact of the overpass on the calibration performance. The A and D calibration and validation datasets each contain a total of 8100 data pairs (at the SMOS grid) per polarization. These comprise TB simulations and observations at all eight angle bins with a frequency of occurrence according to the spatial coverage of the angle bin over each of the randomly chosen cell locations. This implies that inner angles (e.g., 42.5°) are slightly more present than the outer angles (e.g., 17.5° and 52.5°).

b. SM bias correction

It is known that LSMs and satellite retrievals often provide SM with a different climatology, expressed by the long-term mean and dynamic range. As argued previously, reasons can therefore be found in differences in representation (spatial resolution and layer depth) or shortcomings in both the land surface and retrieval models. Figure 3 (top) shows a comparison between the SM densities from SMOS and the VIC, revealing a bias of 0.17 cm3 cm−3 and correlation of 0.42. Notably, the VIC SM displays a decreased dynamic range compared to the SMOS retrievals. The wetter conditions and decreased dynamic range of VIC have previously been attributed to its lack of built-in undercanopy soil evaporation and its exponential decay of gravity drainage and plant transpiration with decreasing soil moisture (Pan et al. 2014). Additionally, they may be caused by the larger first-layer depth (10 cm) in the VIC as compared to the sensing depth interval of SMOS.

Fig. 3.
Fig. 3.

Density scatterplots between 2011 VIC and SMOS SM (cm3 cm−3) (top) before and (bottom) after CDF matching.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

When simulations from an LSM are used for the simulation of TB, the SM climatology will have a profound impact on the long-term mean and dynamic range of the TB simulations. Consequently, if SMOS SM retrievals for a given RTM parameter set are biased in comparison with the VIC SM simulations, this bias will inevitably propagate to bias in TB simulations, assuming that the VIC is coupled to an RTM with similar parameterization. Additionally, if the parameters of the coupled RTM would be calibrated without accounting for the possible bias in SM, the obtained parameter values could be unrealistic, in the sense that they are compensating for the divergent SM representation. Hence, there is a strong motivation to resolve part of the biases in TB simulations at the soil moisture level by rescaling the SM climatology of the VIC.

The bias correction of SM was performed through CDF matching, as is the suggested method by many studies (e.g., Reichle and Koster 2004). The CDF matching was applied to convert the VIC SM output to the climatology of the SMOS level 3 SM retrievals. The selection of the SMOS level 3 product as the reference allows us to assess and improve the operationally used RTM parameters for SMOS, eliminating the influence of the SM climatology. Note that remaining TB biases after SM CDF matching may still occur because of contributions of soil and vegetation inputs or parameters, model shortcomings or assumptions, forcing errors, biased temperature simulations, etc. The CDFs were computed using the nonparametric kernel-based method by Li et al. (2010). Thereby, SM values from 2010 were used to calculate the CDFs for each of the VIC and SMOS grid cells. Only time steps that were both covered in the VIC and SMOS datasets were used (0600 and 1800 local time for A and D orbits, respectively, on dates of SMOS overpasses). The matching coefficients for the CDFs were calculated on a pixel basis and stored in lookup tables (LUTs). Subsequently, the 2010 LUTs were used to rescale the VIC SM for 2011. As the model simulations are performed at a finer spatial scale compared to the SMOS observations, the same CDF for a coarse-scale SMOS grid cell was used to match the different finescale CDFs of the underlying VIC cells. It should be mentioned, however, that the rescaling may be suboptimal given the restricted time span (i.e., 1 year) for the construction of the CDF. The robustness of the rescaling function could be improved by considering larger datasets, which were, however, not available for this study. Nevertheless, Fig. 3 (bottom) shows that, although based on only 1 year of data, the CDF matching reduces the bias to 0.00 cm3 cm−3 and increases the Pearson correlation coefficient to 0.64 for the 2011 validation dataset. Finally, it is worth mentioning that the CDF matching of SM partly resolves the problems associated with a different SM representation between the LSM and the SMOS retrievals. More specifically, it modifies the long-term mean and dynamic range but preserves the ranking and the temporal variability, that is, SM memory.

c. RTM calibration

After modification of the input SM climatology, the parameters of the RTM are further optimized to decrease remaining biases in the SMOS TB simulations. The RTM parameters that are considered for calibration are h, , , , and , which were selected based on De Lannoy et al. (2013) and a sensitivity analysis. The and coefficients relate the optical thickness of the vegetation to LAI, the h and parameters describe the surface roughness and its angular dependence, and controls the vegetation scattering of microwaves.

It should be emphasized that the calibration of the RTM in this study is performed per land cover class (see Table 1) instead of on a pixel basis. Pixel-based calibration is difficult to achieve if the goal is to preserve the subgrid pixel heterogeneity in terms of vegetation types. Preserving subgrid variability in a pixel-based calibration would require a high number of parameter sets for each pixel, which would render the model coupling unfeasible. Finally, note that the calibration is not carried out for land cover classes with cover fractions below 1% (such as grasslands), as these may be subject to less accurate parameterization because of underrepresentation in the calibration dataset. Also, water and urban are not included, because the SMOS observations over cells dominated by the latter classes have been filtered.

The calibration of RTM parameters is performed using the particle swarm optimization (PSO; Kennedy and Eberhart 1995) algorithm. Example applications and details on PSO can be found in Scheerlinck et al. (2009) and Pauwels and De Lannoy (2011). Only a brief explanation and summary of the selected PSO parameter values are given here. The PSO algorithm iteratively explores the parameter space and minimizes an a priori defined objective function. The PSO algorithm modifies a number of parameter sets (or particles) by changing their velocity (speed and direction) based on the most favorable conditions encountered by an individual particle and the swarm of particles. Thus, the modification of individual particles expresses the cognitive aspect of the optimization algorithm, whereas the modification of the particle swarm accounts for the social aspect. In this study, the particle swarm size is set to 25 and the maximum number of iterations to 30. The inertia weight and cognitive and social parameters are set to 0.7, 0.7, and 1.3, respectively. The selected PSO parameter values are based on De Lannoy et al. (2013) and enforce a stronger social than cognitive effect on the optimization.

The objective function J to be minimized integrates the Kling–Gupta efficiency KGE, introduced by Gupta et al. (2009), together with a parameter penalty term as
e9
with
e10
where is the number of combinations of incidence angle bins θ, polarizations p, and orbits o, while refers to the number of calibrated RTM parameters. The variables and are weight factors for the different penalty terms, set to 100 and 1, respectively. These values have been selected to put fewer constraints on the parameter penalty compared to the KGE. Further, is the KGE for a specific θ, p, and o. The variable R is the correlation coefficient between the simulations and observations, MR is the ratio between the mean of the simulations and the mean of the observations, and SR is the ratio between the standard deviation of the simulations and the standard deviation of the observations. Note that the latter three criteria should ideally be equal to 1, through which the KGE becomes 1. The values from to are weights that can be assigned to specify the relative importance of the different criteria for the problem at hand. Although different weights have been tested, the aim of this study is not to perform a thorough optimization of the weights. Such optimization is a complex task and truly depends on the specific objectives of the calibration. Therefore, these weights are adopted as an indication of what could be possible. In this specific study, the weights have been set to , , and . The weights and were chosen such that emphasis is given to the optimization of the MR, in order to mitigate biases. The weight is set to zero, as the improvement in SR comes at the expense of an increase in bias. Moreover, as the SR simultaneously embeds the variability of TB in a temporal and spatial context (different grid cells and time steps are contained in the calibration set), compensating effects, for example, increasing spatial variability at the expense of temporal variability, needed to be avoided. Hence, SR is arguably less paramount to the optimization compared to R and MR. Finally, note that the cost function does not follow Bayesian parameter estimation approaches. While other studies have included the model and the observation errors to estimate RTM parameters and their uncertainties (De Lannoy et al. 2014), the primary goal of this paper is to find efficient parameter values, without a need to estimate the parameter uncertainty. This approach may result in suboptimal parameters because of overfitting, but no clear evidence thereof was found in this paper.
Besides the KGE, the objective function also minimizes parameter deviations from initial values to account for equifinality, that is, to select a single optimal parameter set from multiple parameter sets that yield a similar KGE. The deviation term is limited by the variance of a uniform distribution with boundaries , given by
e11

The initial parameter values have been taken from the baseline parameter set given in Table 1. The boundaries of the different parameters are given in Table 2 and indicate both the limits of the search area and the expected uncertainty in the prior parameter estimates. It should be noted that was not constrained to an initial guess, that is, the boundaries on are only an indication of the search space limits. The reason is the large variability of observed from experimental data (Wigneron et al. 2001).

Table 2.

RTM calibration parameters and selected boundaries.

Table 2.

The restriction to a realistic range of parameter values and the prior penalty term together preserve a realistic model sensitivity of TB to SM. This sensitivity is generally known to be an approximate 2–3 K increase in TB for a 0.01 m3 m−3 decrease in soil moisture around a 40° incidence angle for low vegetation (Jackson 1993). As denoted in De Lannoy et al. (2013), the sensitivity can largely decrease if, for instance, unrealistically high values for roughness and optical depth are used. In this case, the emission from the soil is very low, and thus the sensitivity of TB to SM is very low. Such unrealistic parameter values could be obtained when no parameter restrictions would be applied during the calibration.

d. Overview of the optimization experiments

A number of case studies, which are listed in Table 3, were performed in order to investigate several aspects in the RTM optimization. A first experiment aims at investigating the impact of the LSM SM climatology on the TB simulations with baseline RTM parameters (Table 1). Note that this experiment refrains from providing any recommendations on the optimal SM climatology (e.g., LSM versus SMOS), but aims to identify its impact on the occurrence of biases in the TB simulations. The experiment where CDF-matched soil moisture is used as input to CMEM, without RTM parameter calibration, is referred to as case 1 in Table 3.

Table 3.

RTM calibration cases.

Table 3.

In Table 3, cases 2–6 investigate the improvements in TB simulation after calibrating specific RTM parameters. Given the large impact of roughness on the climatological mean TB (De Lannoy et al. 2013), the h parameter is included in all cases. Case 2 explores the calibration of h only, whereas cases 3–5 simultaneously retrieve , ω, or and , respectively. Further, case 6 demonstrates the added value of a joint calibration of h, , and ω. Calibration cases 2–6 are performed on a dataset that includes both ascending and descending overpasses, as well as both H and V polarizations. Thus, no orbit or polarization-dependent parameters are considered in these cases.

Furthermore, cases 7–10 are designed to investigate the effect of the radiometer configuration on the calibration. In this context, it is investigated that a differentiation of the calibration between either polarizations or orbits, or both polarizations and orbits, may enhance the performance of the simulations. Finally, case 10 considers the calibration of a polarization-independent h, and polarization-dependent and parameters, while accounting for ascending and descending orbits separately.

4. Results

a. Baseline run

A baseline run, using the original VIC SM output and the RTM parameters of Table 1, was performed to simulate the SMOS TB observations over the upper Mississippi for 2011. Figure 4 shows the basin-averaged angular TB signatures for the ascending (Fig. 4a) and descending (Fig. 4c) orbits, comparing the SMOS observations with the VIC–CMEM simulations. As revealed by this figure, a large bias on the order of 30 K for H polarization and between 27 (at 17.5°) and 10 K (at 52.5°) for V polarization is found for ascending orbits. Descending orbits are exposed to slightly lower biases of approximately 20 and 5–15 K for H and V polarization, respectively, which are likely attributed to a lower probability of RFI in descending orbits. Figure 4 moreover displays the RMSE and KGE for each angle and polarization for ascending and descending orbits (Figs. 4b,d). In the case of H polarization, the RMSE increases with incidence angle, whereas the opposite trend is observed for V polarization, irrespective of the orbit. The KGE generally follows a similar behavior, with an increase in performance for lower (higher) incidence angles in case of H (V) polarization. Finally, the V-polarized simulations outperform the simulations at H polarization, mostly because of lower biases.

Fig. 4.
Fig. 4.

The basin-averaged angular TB (K) signatures of the SMOS observations and baseline simulations by VIC–CMEM for 2011, along with the RMSE (K) and KGE (unitless) for (a),(b) ascending and (c),(d) descending orbits.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

To support the further analysis of the optimization experiments, the SM output from the VIC is compared with the retrievals from SMOS. Figures 5a–d show the 2011 annual mean SMOS retrievals and simulations of SM over the upper Mississippi basin, their bias (SMOS minus VIC), and Spearman rank correlation, respectively. The comparison reveals a poor spatial agreement in SM patterns and a large wet model bias (as a function of volume) that ranges between −5% in the south to −30% in the northwest. Conversely, the correlation coefficient reaches up to 0.8 for most parts of the basin, demonstrating the agreement in temporal variations between SM simulations and retrievals, particularly in the southern and southwestern areas that are dominated by low vegetation types (see Fig. 1). The correlation results are consistent with comparison studies of SMOS SM products using local measurements (Al Bitar et al. 2012; Leroux et al. 2014). The forest area in the northeast is mainly characterized by a low temporal correlation between 0 and 0.5. This low correlation in forest areas may be explained by a less pronounced seasonal soil moisture cycle, in combination with the higher uncertainty of SMOS SM retrievals (Rahmoune et al. 2013). The latter is due to a decreased sensitivity of the SMOS L-band TB observations to SM under dense vegetation cover.

Fig. 5.
Fig. 5.

The 2011 annual mean ascending SM as a function of volume (%) (a) from SMOS and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (%; SMOS minus model) and (d) Spearman rank correlation.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Figures 6a–d show the 2011 annual mean skin temperature of ECMWF fields and the VIC simulations, their bias (ECMWF minus VIC), and Spearman rank correlation. The ECMWF fields are used as auxiliary information for soil moisture retrieval by the operational SMOS processor (Kerr et al. 2012). Therefore, a comparison between the ECMWF and VIC skin temperature simulations allows for assessing the possible impact of differences in temperature on the simulations of brightness temperature for SMOS. The comparison shows consistent spatial patterns between the ECMWF and VIC simulations, both displaying a small increasing gradient from north to south. The bias is homogeneous across the basin and ranges between 1° and 3°C. The temporal Spearman rank correlation is close to 1 for the entire basin. These results indicate that, apart from a small bias that is homogeneous across the study site, the VIC simulations are consistent with those used in the SMOS processor. Hence, the impact of temperature on the simulations of TB is expected to be minor.

Fig. 6.
Fig. 6.

The 2011 annual mean surface temperature (°C) (a) from ECMWF and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (°C; ECMWF minus model) and (d) Spearman rank correlation.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Figures 7 and 8 display the 2011 annual mean ascending SMOS TB observations at 42.5° incidence angle, the corresponding VIC–CMEM simulations, their bias, and Spearman rank correlation for H and V polarization, respectively. Compared to SM, the spatial correspondence between the observations and simulations becomes slightly more prominent, mainly driven by the influences of land cover. The bias is found to be particularly large (up to 50 K) over low vegetated areas at H polarization, whereas biases over forest areas are generally limited within 10 K. These results are consistent with De Lannoy et al. (2013), who found that the use of literature RTM parameters can result in TB biases of 10–50 K against SMOS observations. As for SM, the temporal correlation is especially high in portions dominated with low vegetation; compared to the SMOS retrievals, the correlations in TB over northern forest areas have increased.

Fig. 7.
Fig. 7.

The 2011 annual mean ascending TBH (K) at 42.5° (a) observed by SMOS and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Fig. 8.
Fig. 8.

The 2011 annual mean ascending TBV (K) at 42.5° (a) observed by SMOS and (b) simulated by VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

b. Optimization experiments

A set of optimization experiments was performed according to Table 3. Table 4 provides an overview of the performance of the different experiments in comparison to the baseline run for the year 2011. It is important to note that the evaluation criteria in this table are calculated based on the sample dataset (section 3a), which combines observations–simulations of different instants in time, spatial locations, and incidence angles. Consequently, regional or seasonal artifacts at specific angle bins are not evaluated by this approach and will be discussed in section 4c. In the following, the results of Table 4 are discussed, with emphasis on the impact of the LSM SM climatology, the choice of RTM calibration parameters, and the impact of partitioning the calibration between polarizations and orbits.

Table 4.

Evaluation of the calibration experiments based on the 2011 validation dataset. KGE and correlation R are unitless.

Table 4.

The importance of the SM climatology is evident when comparing the baseline run with case 1, where CDF matching of SM is performed prior to use in CMEM. Averaged over orbits and polarizations, the baseline yields a correlation of 0.67 and RMSE of 29.72 K, with the bias having an absolute value of 20.27 K [the unbiased RMSE (ubRMSE) is thus 21.73 K, given that ]. The corresponding KGE of the baseline equals 0.86. After CDF matching the VIC SM states, the RMSE decreases to 18.85 K, while the bias is reduced to 4.69 K. The unbiased RMSE is also slightly reduced to 18.26 K. This demonstrates that most of the bias, and a small part of the mismatch in variability, in the TB simulations is attributed to gross differences in the climatology of the SM simulations of the LSM against SMOS, with the baseline RTM parameters (Table 1) providing a reasonable simulation of TB once the SM climatology difference has been accounted for. The impact of SM climatology and the lack of any established consensus may as well partly explain the large variability in RTM parameters that can be found from modeling studies in literature [e.g., reviewed in De Lannoy et al. (2013)]. In addition to a decrease in bias and increase in accuracy, the CDF matching improves the Spearman rank correlation to 0.75 as a consequence of the nonlinear relationship between TB and SM. Finally, the KGE is increased from 0.86 to 0.94.

Cases 2–5 investigate the calibration of h alone and h in combination with , ω, and and , respectively. The results show that none of these calibration experiments are able to improve the simulations of case 1. This again justifies the use of baseline RTM parameters as given in Table 1, provided the model SM climatology is corrected. Only for case 6, which investigates the joint calibration of h, , and ω, is a slight improvement obtained. More specifically, the RMSE decreases with 1.5 K, with a minor decrease in bias of 0.2 K. These results are in line with De Lannoy et al. (2013), who observed calibration improvements after increasing the number of calibration parameters (including h and ω).

Given the minor improvements after the joint calibration of h, , and ω, this scenario is further investigated in cases 7–10, where independent calibrations for specific polarizations and/or orbits are carried out. It shows that separation of polarizations causes a slightly larger improvement compared to the separation of orbits, whereas treating both polarizations and orbits separately yields the largest improvement. In the latter case, a decrease of 0.6 K in RMSE and approximately 1 K in bias was found in comparison with case 6. Finally, case 10 indicates that there is no clear need to account for polarization differences in the calibration of h. Hence, the calibration case 10 may be proposed as the most optimal.

The improvement after separating ascending (0600 local time) and descending (1800 local time) orbits may be reasoned by the fact that, for ascending orbits, ionospheric effects are expected to be minimal, whereas surface conditions are close to thermal equilibrium. During descending orbits, the temperature gradients can be high (Jackson 1980). Also, the SMOS mission is known to be impacted by RFI (Oliva et al. 2012), and this impact is different for ascending and descending orbits as the instrument is tilted by 32.5° from nadir. The presence of low-level RFI in the ascending SMOS observations over North America due to the active presence of a military radar system in 2010–11 was highlighted in Collow et al. (2012) and De Lannoy et al. (2013). Several studies (Bircher et al. 2012; Leroux et al. 2014; Verhoest et al. 2015) have also shown that ascending and descending SMOS data reveal different statistics, supporting the need for different parameterizations. However, a caveat to the differentiation between orbits is the fact that this purposely introduces model bias to match the observation bias. If the objective would be to provide consistent time-independent simulations of TB, a differentiation between orbits may not be advisable. Finally, the use of polarization-dependent surface roughness and (particularly) vegetation parameters may be justified by differences in radiative transfer between polarizations as implemented in the L-MEB model (Wigneron et al. 2001) and validated using local radiometer and SMOS data (Wigneron et al. 2012).

c. Validation of calibration case 10

The calibrated parameters associated with case 10 are further used in a coupled VIC–CMEM simulation over the upper Mississippi for 2011. Table 5 shows the parameters obtained for ascending and descending orbits for each land cover class with a cover fraction larger than 1%, except for water and urban. The roughness of low vegetation types (e.g., wooded grassland and cropland) slightly increased, mainly for ascending orbits. The scattering albedo remained close to the baseline for ascending orbits, whereas a slight increase is observed for descending orbits. Furthermore, values for low vegetation are found to be larger than zero for all polarizations and orbits. Finally, large differences are occurring in even within classes of low and high vegetation types as this parameter was not constrained toward the initial parameter values. Nevertheless, the H polarization results may indicate a suboptimal performance of the initial value (equal to 2 for all vegetation types), as calibrated values are mostly in the range of 0–1. For V polarization, it is less clear to which values the calibration is converging.

Table 5.

The calibrated RTM parameters of case 10 for the UMD land cover types.

Table 5.

To demonstrate the improvements made with respect to the baseline, Fig. 9 shows the angular signature for the 2011 validation dataset. In comparison with Fig. 4, it clearly shows a reduction in bias (<10 K) over all angle bins. Furthermore, the RMSE decreases significantly to less than 20 K in all cases, whereas the KGE increases to above 0.9. Finally, after the RTM optimization, the TB simulations show a comparable accuracy (RMSE, KGE) over all angles, which was not the case for the baseline simulations (see Fig. 4).

Fig. 9.
Fig. 9.

The basin-averaged angular TB (K) signatures of the SMOS observations and calibrated (case 10) VIC–CMEM simulations for 2011, along with the RMSE (K) and KGE (unitless) for (a),(b) ascending and (c),(d) descending orbits.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Figures 10 and 11 show a comparison between the simulations and observations of the mean 2011 ascending TB at 42.5° incidence angle, after SM CDF matching and RTM calibration, for H and V polarization, respectively. Although the basin-averaged TB bias remains well below 5 K, considerable regional biases are still encountered. Particularly for H polarization, the simulated TBs in the northwest show a warm model bias compared to the SMOS observations, whereas the opposite is true in the southwest. Since large parts of these two regions share the same dominant land cover type (i.e., cropland), while the soil moisture bias has been almost completely removed through CDF matching, the remaining cause for the observed systematic differences can be found in measurement errors, forcing errors, biased temperature simulations, or the characterization of the vegetation. Specifically for vegetation, the level 3 SMOS retrievals employ static land use maps from ECOCLIMAP and related LAI. Based on this information, the optical thickness of the vegetation is dynamically retrieved in conjunction with soil moisture (Kerr et al. 2012). In the case of the VIC, the land cover is sourced from the UMD, with climatological monthly LAI parameters based on AVHRR satellite data. Consequently, regional differences in vegetation characterization may cause biases in TB, notwithstanding the unbiased soil moisture fields. Further removal of the regional bias would require pixel-based RTM calibration, or postprocessing, for example, through CDF matching of the TB simulations or observations. However, it should be recalled that the present study does not apply pixel-based calibration in order to preserve the subgrid vegetation variability of the VIC and simplify the coupling with the RTM. Finally, the Spearman rank correlation between the observations and simulations of TB is found to be particularly high over low vegetation, with correlations up to 0.9. Moreover, the correlation has increased after applying the SM CDF matching, as seasonal TB discrepancies have been reduced through adjusting SM that nonlinearly relates to TB.

Fig. 10.
Fig. 10.

The 2011 annual mean ascending TBH (K) at 42.5° (a) observed by SMOS and (b) simulated by the calibrated (case 10) VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Fig. 11.
Fig. 11.

The 2011 annual mean ascending TBV (K) at 42.5° (a) observed by SMOS and (b) simulated by the calibrated (case 10) VIC–CMEM, along with the corresponding (c) bias (K; SMOS minus model) and (d) Spearman rank correlation.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Figure 12 displays maps of R, MR, SR, and KGE, averaged over all angle bins, polarizations and orbits. In this case, the KGE has been calculated with weights (from W1 to W3) equal to one. The choice of equal weights is motivated by the fact that SR is considered a valuable criterion for pixel-based evaluation; no compensating effects can occur, for example, because of the embedding of spatial variability as in the calibration objective function. Again, the correlation coefficients are high over areas dominated by low vegetation, whereas slightly lower correlations are found in forest areas mainly in the north. The bias is low over most parts; however, a warm model bias (ratio of simulations over observations) is found in the northwestern cropland area, whereas a cold bias is observed in the south, dominated by cropland and wooded grassland. The ratio of the standard deviation shows a large contrast between low and high vegetation. While SR is close to one for low vegetation, a large underestimation of the TB variability is observed over forests. This may arguably be related to shortcomings of the model in the characterization of the surface emission and penetration depth over forest areas. As can be seen in Fig. 12d, the KGE is mainly influenced by R and SR, showing lower efficiencies in the forested northeast. Nevertheless, the KGE demonstrates the ability for accurately simulating TBs over low vegetation, with efficiencies between 0.6 and 0.8.

Fig. 12.
Fig. 12.

The 2011 annual mean (a) correlation, (b) mean ratio, (c) std dev ratio, and (d) KGE between SMOS TB and simulated TB (case 10) across all incidence angles, polarizations, and orbits.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

Finally, time series for 2011 of simulated and observed TB are shown in Fig. 13, for ascending orbits at 42.5°, at H and V polarization. The time series have been obtained for an SMOS pixel (latitude = 42.8260°, longitude = −91.1060°) covered for 82% by forest types and another pixel (latitude = 40.2180°, longitude = −88.5030°) covered for 95% by cropland. As was also revealed by Fig. 12, the forest simulations lack the temporal variability observed by SMOS, although seasonal patterns are captured well. Also, some of the SMOS observations might still be affected by errors such as those caused by RFI (e.g., the high TBH observation at day of year 150). A slight overestimation by VIC–CMEM is still observed in winter months for H polarization, whereas summer TBs are slightly underestimated at V polarization. Nevertheless, it should be noted that this figure provides an example for only one forest pixel. Hence, findings for this specific location are not necessarily true for other pixels dominated by forest cover. Over cropland, the simulations at both H and V polarization generally show a good correspondence with the SMOS observations. In this case, observations and simulations are characterized by high correlation and low bias, while exposing similar levels of variability.

Fig. 13.
Fig. 13.

The 2011 time series of ascending TB (K) at 42.5° as observed by SMOS and simulated by VIC–CMEM (case 10), over (a),(b) forest and (c),(d) cropland grid cells at (a),(c) H polarization and (b),(d) V polarization.

Citation: Journal of Hydrometeorology 16, 3; 10.1175/JHM-D-14-0052.1

5. Conclusions

To facilitate the direct assimilation of multiangular and multipolarization SMOS TB observations, the Community Microwave Emission Modelling Platform (CMEM) was coupled to the VIC. Such direct assimilation of TB observations can be of high value in time-constrained forecasting applications, for example, of hydrologic events, as it circumvents the need for SM retrieval data that are generally provided with longer time lag. However, the coupling of an LSM with RTM poses significant challenges when the objective is to simulate accurate and unbiased TBs in comparison with SMOS observations. This study shows that propagation of the VIC soil moisture and surface temperature fields through CMEM, using literature-based RTM parameters, may cause biases in TB that locally reach up to 50 K, with an average of about 30 K. A number of experiments were conducted in order to mitigate biases and improve the accuracy of the simulations.

The VIC SM is found to show mean annual discrepancies with the corresponding SMOS retrievals in the range of 10%–30% as a function of volume. Hence, optimization of the RTM using the direct SM output from the VIC may lead to unrealistic parameter combinations that decrease the sensitivity of TB to SM, thus motivating the rescaling of the VIC SM. After rescaling the VIC SM to the climatology of SMOS through CDF matching, the average TB bias reduced to less than 5 K, even with literature-based RTM parameterization. In addition to mitigating biases, the CDF matching of SM also increased the temporal correlation between the TB observations and simulations, as a result of the nonlinear relation of TB to SM. This demonstrates that the literature parameters, which are also employed in the operational SMOS retrieval algorithm, provide a realistic characterization of the surface and vegetation. Furthermore, it shows that in the case of L-band brightness temperature assimilation, some bias correction to the LSM SM state may be needed.

Through a series of RTM calibration experiments, optimal calibration parameters and associated RTM parameter values were selected for each land cover class present in the upper Mississippi basin. The calibration of surface roughness h alone, or in combination with the angular dependence , the scattering albedo ω, or the vegetation optical depth parameters, did not further improve the performance of the simulations. Only a combination of three calibration parameters, that is, h, , and ω, slightly decreased the RMSE (17.36 K) and bias (4.48 K) of the TB simulations. Further improvements in RMSE (16.68 K) and bias (3.79 K) were achieved by separating the calibration for H and V polarization and ascending and descending orbits.

Notwithstanding the improvements in the TB simulation, a spatiotemporal analysis revealed that considerable regional biases were still unresolved after the rescaling of the input SM and the optimization of RTM parameters. The largest regional biases (up to 20 K) occurred in the northwestern cropland area and wooded grassland area in the south, whereas other areas were generally characterized by biases below 5 K. It is expected that part of these remaining biases relate to biases in soil temperature, erroneous soil or vegetation characterization, or more fundamental model shortcomings, for example, in the model structure or physics. Part of the bias could possibly also be attributed to the SMOS TB data. A consummate bias removal can thus not be achieved by the present framework and may require further improvements in the model formulation. Finally, the spatiotemporal analysis also revealed a lack of variability in the TB simulations over forest, particularly over short time scales. In combination with lower temporal correlations, forest areas were therefore characterized by lower values of the KGE, which is a combined measure for correlation, bias, and variability. However, for most cropland and low vegetation areas, the coupled model was found to provide accurate TB simulations, characterized by KGE values of 0.6–0.8, which is a prerequisite for the assimilation of SMOS TB observations to benefit hydrologic applications.

Acknowledgments

The work has been performed in the framework of the ESA-STSE project “SMOS + Hydrology Study” and was partly funded through project SR/00/302 (Hydras+) financed by the Belgian Science Policy (BELSPO), and the CNES Terre, Océan, Surfaces continentales, Atmosphère (TOSCA) program. Furthermore, we would like to acknowledge the Jülich Supercomputing Center for granting computation time on JUROPA. Hans Lievens is a postdoctoral research fellow of the Research Foundation Flanders (FWO). Valentijn Pauwels is currently a Future Fellow funded by the Australian Research Council.

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