1. Introduction
The dynamics of soil moisture and the partitioning of solar radiation at the land surface is key to hydrology (McCabe and Wood 2006), meteorology (Andrews et al. 2009), water resources management (Yang et al. 2018; Rigden and Salvucci 2015), and the terrestrial water cycle (Kumar et al. 2018). Soil moisture and surface heat fluxes can be measured with in situ flux networks (Dorigo et al. 2011; Baldocchi et al. 2001), but the extrapolation to regional scale is hindered by the uneven distribution of observation networks as well as their heterogeneous nature in space (Jung et al. 2011). Remote sensing is a promising technique for large-scale land variable monitoring, but energy fluxes have no unique signature that is detectable by remote sensing instruments (Sini et al. 2008). Although soil moisture can be detected using microwave remote sensing, the data are generally provided with low spatial or temporal resolution. For example, data from microwave radiometers (Petropoulos et al. 2015) or scatterometers (Brocca et al. 2017) are of low temporal sampling frequency (2–3 days) and coarse spatial resolution (30–50 km), while data from some synthetic aperture radar systems (Lievens and Verhoest 2011; Malenovský et al. 2012; Paloscia et al. 2013; Bauer-Marschallinger et al. 2018) are of fine spatial resolution (<3 km) but longer revisit interval. Furthermore, only soil moisture near the surface (<5 cm) can be measured as a result of the limited sensing depth of microwave instruments, while the soil moisture at larger depth, which is crucial for vegetation transpiration, remains undetectable.
To generate soil moisture and surface heat fluxes at finer spatial and temporal resolution, many studies have focused on simulations using surface energy balance models or land surface models (Su 2002; Vinukollu et al. 2011; Huang et al. 2015; Bastiaanssen et al. 1998; Kilic et al. 2016). These models have wide applicability under different climatic conditions and over various land cover types but often require a large suite of input data (Sini et al. 2008). Simpler approaches have also been developed that are based on empirical relationships with local indicators at finer resolution such as land surface temperature (LST) and vegetation indices (Tang et al. 2010; Yang et al. 2015; Zhang et al. 2015; Sadeghi et al. 2017; Zhao et al. 2017). Such methods are easy to implement but largely rely on historical data for model calibration and are often region-dependent.
In a departure from the direct modeling approaches, some studies estimate surface heat fluxes by assimilating LST time series into simple heat transfer schemes (Castelli et al. 1999; Boni et al. 2001; Caparrini et al. 2003, 2004a,b; Crow and Kustas 2005; Bateni and Liang 2012; Bateni and Entekhabi 2012b; Bateni et al. 2013; Xu et al. 2014, 2015, 2016; Abdolghafoorian et al. 2017; Xu et al. 2018, 2019; He et al. 2018). Such methods only require a limited amount of input data and are easily transferable to other regions. By coupling the heat transfer scheme with a soil moisture transfer scheme, Lu et al. (2016) improved the methodology by jointly assimilating in situ measured soil moisture and LST data. The rationale is that available energy partitioning between the sensible and latent heat fluxes at the land surface influences the daytime evolution of surface thermal condition, therefore the partitioning of available energy can be inferred from a series of LST observations, while assimilating soil moisture data further constrains the partitioning (Bateni and Entekhabi 2012a). The key is to estimate two parameters: a bulk heat transfer coefficient under neutral atmosphere 
Despite the improved surface heat flux and soil moisture estimates, only soil moisture data from the passive microwave radiometer have been used for assimilation, of which the spatial resolution (36 km) and temporal sampling frequency (2–3 days) are both very coarse. As a result of the spatial heterogeneity and limited memory of soil moisture (Dunne and Entekhabi 2006), using coarse resolution soil moisture data may limit the capability of the method to characterize the spatial pattern and the temporal dynamics of soil wetness condition, which directly influences surface energy partitioning. With the abundance of soil moisture data sources, deriving soil moisture products of higher spatial resolution or temporal sampling frequency has become possible. Potential data sources include the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E; Njoku et al. 2003), the Advanced Scatterometer (ASCAT; Bartalis et al. 2007), the Advanced Microwave Scanning Radiometer-2 (AMSR-2; Imaoka et al. 2010), the Soil Moisture Ocean Salinity (SMOS; Kerr et al. 2001), as well as the enhanced and combined active/passive products from the SMAP mission (Entekhabi et al. 2010). On one hand, soil moisture data can be obtained at higher spatial resolution (<10 km) using radar or through downscaling procedures, which can better characterize the spatial heterogeneity of soil moisture caused by differences in meteorological conditions or surface properties. On the other hand, multisource soil moisture data from different remote sensing platforms contain complementary information on soil moisture dynamics, which has great potential for better depicting the temporal evolution of soil moisture through data fusion. This provides great opportunity to explore the question that given soil moisture data at higher spatial resolution or temporal sampling frequency, how much improvement can be expected in soil moisture and surface heat flux estimates.
This study is based on the methodology developed in Lu et al. (2017) and focuses on evaluating the impact of different soil moisture data on the soil moisture and surface heat flux estimates through data assimilation using two comparative experiments. In the first experiment, GOES LST time series are assimilated together with the SMAP Level-3 enhanced passive soil moisture product (L3_SM_P_E), which is provided at finer spatial resolution (9 km). In the second experiment, the soil moisture dataset used for assimilation is a merged product derived from the SMAP and the SMOS mission to obtain observations at higher sampling frequency (quasi-daily). Results from both experiments are compared with those from Lu et al. (2017), which assimilated the SMAP Level-3 soil moisture product (L3_SM_P, 36 km/2–3 days) to evaluate the respective differences in surface heat flux estimates as well as soil moisture estimates at both the surface and the root zone. This is the first study that assimilates SMAP enhanced soil moisture product and the first to combine SMAP and SMOS products for improving surface heat flux and soil moisture estimates using data assimilation.
2. Methodology
a. Dual-source energy balance scheme
The methodology is based on a dual-source surface energy balance scheme, which was first proposed by Norman et al. (1995) and Kustas et al. (1996). In this scheme, the soil heat transfer is coupled to the soil water transfer. The key of this coupling is the tight interaction between soil moisture and latent heat flux: the modeled soil moisture influences the EF, which directly determines the partitioning of available energy at the land surface, while the estimated latent heat flux in turn serves as the sink term in the soil moisture modeling. The coupled heat and water transfer scheme is detailed in Lu et al. (2017).
Here the parameters a and b represent the influence from the soil and vegetation density, respectively, which will be estimated during data assimilation, and LAI (unitless) is the leaf area index.
To calculate 
b. Study area and data
The methodology is applied over an area (35.75°–37.24°N, 96.72°–98.21°W) in the U.S. Southern Great Plains (SGP) shown in Fig. 1. The study area is covered by 30 × 30 GOES LST cells at 0.05° resolution, or by 4 × 4 SMAP grid cells posted on a 36-km Equal-Area Scalable Earth-2 (EASE-2) grid. This area is selected because of the relatively dense flux network. The area is generally flat and mostly covered by grassland and cropland, with a small fraction of urban area and water bodies. The dominant soil types are sandy loam and silt loam. In situ flux measurements are available at four stations from the Atmospheric Radiation Measurement (ARM) network. Parameters H and LE are measured every 30 min by energy balance Bowen ratio (EBBR) instruments. In situ soil moisture observations are available at two stations from the U.S. Climate Reference Network (CRN; Bell et al. 2013) and the Soil Climate Analysis Network (SCAN; Schaefer et al. 2007), respectively. The soil moisture data are collected hourly at the depths of 5, 10, 20, 50, and 100 cm from the surface.
Land cover and soil types in the study area. The thick black lines represent SMAP 36-km grids; the dashed lines in red and black represent SMAP 9-km grids and GOES LST grids, respectively.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Land cover and soil types in the study area. The thick black lines represent SMAP 36-km grids; the dashed lines in red and black represent SMAP 9-km grids and GOES LST grids, respectively.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Land cover and soil types in the study area. The thick black lines represent SMAP 36-km grids; the dashed lines in red and black represent SMAP 9-km grids and GOES LST grids, respectively.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The input data include forcing and ancillary datasets for the model simulation, and remote sensing datasets for data assimilation. Precipitation forcing data are provided by the 3IMERGHH product from the Global Precipitation Mission (GPM; Hou et al. 2014; Huffman et al. 2015). Other meteorological data, including incoming shortwave 
Summary of datasets. The variables are explained in the text.
The ancillary data used include data on soil texture, vegetation, and land cover. The 3-km soil texture data, including sand and clay fraction and soil bulk density data, are provided by the National Snow and Ice Data Center (NSIDC; Das 2013). The soil texture data are used to calculate soil hydraulic properties using the ROSETTA software (Schaap et al. 2001). The LAI data (1 km, 8-day composite) used are the MCD15A2 product from the Moderate Resolution Imaging Spectroradiometer (MODIS; Knyazikhin et al. 1999). The land cover data are obtained from the ESA Climate Change Initiative (CCI; v1.6.1).
The data for assimilation include remote sensing observations for LST and soil moisture. The LST time series based on the geostationary observations from the GOES mission are obtained from the Copernicus Global Land Service (Freitas et al. 2013). Three remote sensing soil moisture datasets of different spatial and temporal resolution are involved in this study, including two operational products from the SMAP mission and a combined dataset from the SMAP and the SMOS mission. All soil moisture products are bias-corrected using the cumulative distribution function (CDF) matching approach before assimilation to reconcile for the difference between model simulations and observations in the long-term mean, variance and higher moments (De Lannoy and Reichle 2016).
One SMAP product is the Level-3 passive microwave soil moisture product (L3_SM_P). This data product is retrieved from the L-band microwave radiometer measurements, with a typical spatial resolution of 36 km and a revisit interval of 2–3 days (Entekhabi et al. 2014). The other SMAP product is the SMAP Level-3 enhanced passive microwave soil moisture product (L3_SM_P_E). L3_SM_P_E distinguishes itself from the L3_SM_P in that the soil moisture retrievals are posted on 9-km grids instead of 36-km grids. This is achieved by first interpolating the original Level-1B brightness temperature observations using the Backus–Gilbert optimal interpolation technique (Chan et al. 2018) to take advantage of the overlapping radiometer footprints. The interpolated brightness temperature “observations” are then used as the input to the baseline algorithm to generate soil moisture retrievals at 9-km resolution. Comparison against in situ observations suggests that the performance of the 9-km enhanced soil moisture product is comparable to that of the 36-km soil moisture product (Chan et al. 2018).
In addition, a merged product from the SMAP L3_SM_P product and the SMOS-IC (SMOS-INRA-CESBIO) product is also used. SMOS-IC differs from the operational SMOS Level-3 soil moisture product in the treatment of heterogeneous grid cells. The main goal of this product is to be as independent as possible from ancillary data. To achieve this goal, SMOS-IC considers grid cells as homogeneous to avoid uncertainties caused by ancillary data, which are used to characterize the heterogeneity of the grid cells. The schemes used for vegetation scattering albedo and soil roughness correction are also different. SMOS-IC product is posted on the same grids with the operational SMOS data. Comparison against European Centre for Medium-Range Weather Forecasts (ECMWF) soil moisture outputs suggests that SMOS-IC product yields higher correlations and lower unbiased RMSD (ubRMSD) than the operational SMOS soil moisture product over most pixels globally (Fernandez-Moran et al. 2017). Here SMOS-IC data are used in a data fusion process to fill in the gaps of SMAP L3_SM_P product between two SMAP descending overpasses (0600 LT). The original SMOS-IC data are first interpolated to the same grids as SMAP L3_SM_P at 36-km resolution. The interpolated SMOS-IC data are rescaled to model simulations and then used to fill in the gaps of SMAP L3_SM_P observations to achieve higher temporal sampling frequency. For days when only SMOS-IC data are available, the data are inserted into the SMAP L3_SM_P data stream as “additional observations.” On days with both SMAP L3_SM_P and SMOS overpasses, SMOS-IC data are not used. This is to enhance the temporal sampling frequency of soil moisture data while minimizing the perturbation of the original SMAP L3_SM_P data dynamics.
c. Data assimilation strategy
Soil moisture data and LST time series are assimilated into the coupled heat and water transfer model using different assimilation approaches. The main reason is the contrasting spatial and temporal resolution gap between the two datasets. As the spatial and temporal resolution of LST data is much higher than that of the soil moisture data, if assimilated jointly within the daytime window, the information contained in the soil moisture observations will be masked by the large number of LST observations. In addition, soil moisture observations are like a “snapshot” of the surface and represent instantaneous soil wetness condition, therefore filtering is better suited to update soil moisture state at the satellite overpass time. While the information on surface energy partitioning can be derived from the temporal evolution of a series of LST observations instead of the magnitude of each individual observation, hence smoothing is used instead of filtering for LST assimilation.
Here soil moisture data are assimilated using a particle filter (PF) at 0600 LT, while LST time series are assimilated using an adaptive particle batch smoother (APBS) within the daytime window (0900–1600 LT) when EF can be assumed invariant under clear-sky condition. The soil moisture profile is updated through soil moisture assimilation, while 
d. Experiment implementation
The experiment is run from day of year (DOY) 155 to 274 (120 days) in 2015 at a 30-min time step and 0.05° resolution. Six-hundred particles are used, which prove sufficient from a sensitivity test. Since the forcing data are coarser than the model grid cell, a “drop in the bucket” strategy is used to extract forcing data for each model grid cell. The forcing data from NLDAS-2 are also assumed representative during the 1-h period to accommodate the temporal resolution gap with model simulations. To account for the uncertainty of the forcing data as well as their heterogeneity within the data grid cells, perturbations are added which are summarized in Table 2. The perturbations are determined based on values suggested by previous studies (Luo et al. 2003; Dong et al. 2016; Lu et al. 2017). Sensitivity analysis indicates that model estimates are robust as long as the perturbations are within a reasonable range. The modeling errors for the heat and water transfer are assumed to be 0.1 K and 0.001 m3 m−3 following Lu et al. (2016). The observation errors for remote sensing soil moisture and LST data are assumed to be 0.04 m3 m−3 (Chan et al. 2016; Cai et al. 2017; Colliander et al. 2017) and 3 K (Lu et al. 2016), respectively. The ancillary data are spatially aggregated to the modeling scale, and the LAI data are also temporally interpolated to derive daily LAI values for each model grid cell.
Perturbations used for forcing data.
There are four parameters to be determined through data assimilation: a and b for calculating 
During daytime (0900–1600 LT), 
Two assimilation experiments are conducted to evaluate the impact of spatial resolution and temporal sampling frequency of soil moisture data. In the first experiment (hereafter 
3. Results and discussion
a. Improving spatial resolution of soil moisture observations
The observed mean surface soil moisture (0–5 cm, hereafter SSM) during the study period for the study area is plotted in Fig. 2 to examine the consistency and difference between the SMAP 36-km (L3_SM_P) product and 9-km (L3_SM_P_E) product. Both products show similar SSM patterns in the study area, demonstrating a clear dry–wet gradient from the southwest to the northeast. The areal mean SSM values generally agree well with each other, and the SMAP 9-km product better characterizes the spatial heterogeneity of SSM as a result of the enhanced spatial resolution. This is expected since both products are retrieved from the same original brightness temperature observations. The largest difference appears in the northeast of the area [grid cell (2, 1) of the SMAP 36-km product], which is influenced by the relatively high fraction of water body. A large lake exists in the northern part of the grid cell, which would greatly lower the observed brightness temperature and make the SSM retrieval less reliable. The soil moisture retrievals in that grid cell therefore should be used with caution.
Observed mean SSM during the study period for the study area from the SMAP 36-km (L3_SM_P) product and 9-km (L3_SM_P_E) product.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Observed mean SSM during the study period for the study area from the SMAP 36-km (L3_SM_P) product and 9-km (L3_SM_P_E) product.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Observed mean SSM during the study period for the study area from the SMAP 36-km (L3_SM_P) product and 9-km (L3_SM_P_E) product.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The SSM estimates from 
Assessment of SSM estimates from 
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Assessment of SSM estimates from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Assessment of SSM estimates from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
A statistical comparison of 30-min SSM estimates from 
Statistical comparison of 30-min SSM time series from 
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Statistical comparison of 30-min SSM time series from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Statistical comparison of 30-min SSM time series from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The performance of data assimilation is also assessed for the second layer (5–15 cm) and root-zone soil moisture (hereafter RZSM) in Fig. 5. A small difference exists between the thickness of modeled (90 cm) and observed (100 cm) soil column. To calculate RZSM, the model simulations are averaged along the soil column weighted by their respective layer thicknesses to derive a RZSM for the 0–90-cm soil column. The in situ soil moisture measurements are first linearly interpolated to get a soil moisture profile, and then integrated to get the RZSM for the 0–100-cm soil column. Both 
Assessment of the (a),(b) second layer (5–15 cm) and (c),(d) RZSM from 
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Assessment of the (a),(b) second layer (5–15 cm) and (c),(d) RZSM from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Assessment of the (a),(b) second layer (5–15 cm) and (c),(d) RZSM from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The 30-min H and LE estimates from 
Statistical comparison of 30-min H and LE estimates from 
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Statistical comparison of 30-min H and LE estimates from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Statistical comparison of 30-min H and LE estimates from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
b. Improving temporal resolution of soil moisture observations
Before merging the SMAP L3_SM_P product and the SMOS-IC product to obtain soil moisture data with higher sampling frequency, the histograms of SSM data from the original SMAP L3_SM_P product and SMOS-IC product (mapped to 36-km scale) are plotted in Fig. 7 to check the consistency between the two products using all the available data. SSM from both products falls in the range of (0, 0.45), and the distributions also show similar patterns. SMAP L3_SM_P product shows a slight wet bias compared to the SMOS-IC product, which may be caused by the difference in the remote sensing platforms or the soil moisture retrieval algorithms. Overall, the two products agree very well with each other in both the distribution and the soil moisture magnitude, which lays a good basis for data fusion. The SMOS-IC observations are then inserted into the SMAP L3_SM_P time series as “additional observations” following the procedures described in section 2b.
Histograms of the SMAP L3_SM_P product and SMOS-IC product in the study area during the study period at 36-km scale using all available data.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Histograms of the SMAP L3_SM_P product and SMOS-IC product in the study area during the study period at 36-km scale using all available data.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Histograms of the SMAP L3_SM_P product and SMOS-IC product in the study area during the study period at 36-km scale using all available data.
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The availability of soil moisture observations from the SMAP L3_SM_P product and SMOS-IC product in the 16 grid cells at 36-km scale in the study area is shown in Fig. 8. On average, there are 59 SMAP L3_SM_P observations and 40.7 SMOS-IC observations available during the 120-day study period for each grid cell. Out of the 40.7 SMOS-IC observations, 24.2 observations are from days without SMAP overpass, showing great potential for providing additional soil moisture information. When data fusion is conducted, the merged product provides 83.2 observations for each grid cell on average, which is a 41% increase over the SMAP L3_SM_P product. The merged product with enhanced temporal sampling frequency is expected to better characterize soil moisture dynamics.
The availabilities of the SMAP L3_SM_P product and SMOS-IC product in the study area during the study period. The colors indicate only SMAP L3_SM_P data available (red), only SMOS-IC data available (yellow), both data available (blue), and no data available (gray).
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The availabilities of the SMAP L3_SM_P product and SMOS-IC product in the study area during the study period. The colors indicate only SMAP L3_SM_P data available (red), only SMOS-IC data available (yellow), both data available (blue), and no data available (gray).
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The availabilities of the SMAP L3_SM_P product and SMOS-IC product in the study area during the study period. The colors indicate only SMAP L3_SM_P data available (red), only SMOS-IC data available (yellow), both data available (blue), and no data available (gray).
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The SSM estimates from 
Assessment of SSM estimates from 
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Assessment of SSM estimates from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
Assessment of SSM estimates from
Citation: Journal of Hydrometeorology 20, 4; 10.1175/JHM-D-18-0234.1
The estimates of soil moisture of the second layer and the RZSM from 
Statistical assessment of remote sensing soil moisture observations and model estimates against in situ measurements. The best performance in each category is shown in bold.
The 30-min H and LE estimates from 
4. Conclusions
In this study, the impact of enhanced spatial and temporal resolution of soil moisture data on the estimates of soil moisture and surface heat fluxes through data assimilation is evaluated using two comparative experiments in a predominantly grassland area in the Southern Great Plains. In the first experiment (
Although the 9-km SMAP L3_SM_P_E product is expected to better characterize the spatial heterogeneity of soil moisture, the improvement in soil moisture of the surface and deeper layers is in general not evident compared to those from 
Assimilating the merged soil moisture product outperforms all other assimilation strategies in soil moisture estimates of both the surface and the root zone at the two soil moisture stations. This benefits from the stronger constraints put on soil moisture dynamics. As a result of the enhanced temporal sampling frequency, soil moisture states are updated more frequently in 
Despite the differences in soil moisture estimates, no evident improvement in surface heat flux estimates can be seen from either 
Here the merged soil moisture data are generated directly from the SMAP and SMOS-IC soil moisture products for simplicity and easier comparison with previous studies (Lu et al. 2017). It should be noted that the aim is not to find the optimal approach for SMAP and SMOS-IC data fusion but to evaluate the impact when more frequent soil moisture sampling becomes available. A more rigorous data fusion should convert brightness temperature observations from SMOS to SMAP-like data using methods such as that proposed by De Lannoy et al. (2015) before performing soil moisture retrieval. The assimilation results are expected to be similar as a result of the similarity and consistency between the two missions. Other merged soil moisture products such as the ESA CCI soil moisture product (Dorigo et al. 2015, 2017) could combine the advantages of active and passive sensors and provide soil moisture data that are consistent in a long period with even higher temporal frequency (approximately daily), which is expected to further improve soil moisture estimates with this methodology.
One limitation of this study is the small domain and relatively short study period. In particular, the limited soil moisture heterogeneity and relatively uniform land cover type may reduce the added value of assimilating high-resolution soil moisture data. The impact of complex terrain and mixed land cover types should be further explored. Future studies should also evaluate the performance of the methodology at larger scales for a longer period and under different climate and soil wetness conditions, which may have an influence on the soil wetness control strength on surface energy partitioning.
Acknowledgments
The first author was financially supported for his Ph.D. research by the China Scholarship Council (CSC) (Ref. 201306040112).
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