Disaggregation of SMAP L3 Brightness Temperatures to 9km using Kernel Machines

In this study, a machine learning algorithm is used for disaggregation of SMAP brightness temperatures (T$_{\textrm{B}}$) from 36km to 9km. It uses image segmentation to cluster the study region based on meteorological and land cover similarity, followed by a support vector machine based regression that computes the value of the disaggregated T$_{\textrm{B}}$ at all pixels. High resolution remote sensing products such as land surface temperature, normalized difference vegetation index, enhanced vegetation index, precipitation, soil texture, and land-cover were used for disaggregation. The algorithm was implemented in Iowa, United States, from April to July 2015, and compared with the SMAP L3_SM_AP T$_{\textrm{B}}$ product at 9km. It was found that the disaggregated T$_{\textrm{B}}$ were very similar to the SMAP-T$_{\textrm{B}}$ product, even for vegetated areas with a mean difference $\leq$ 5K. However, the standard deviation of the disaggregation was lower by 7K than that of the AP product. The probability density functions of the disaggregated T$_{\textrm{B}}$ were similar to the SMAP-T$_{\textrm{B}}$. The results indicate that this algorithm may be used for disaggregating T$_{\textrm{B}}$ using complex non-linear correlations on a grid.

Spatial Scaling of Satellite Soil Moisture using Temporal Correlations and Ensemble Learning

A novel algorithm is developed to downscale soil moisture (SM), obtained at satellite scales of 10-40 km by utilizing its temporal correlations to historical auxiliary data at finer scales. Including such correlations drastically reduces the size of the training set needed, accounts for time-lagged relationships, and enables downscaling even in the presence of short gaps in the auxiliary data. The algorithm is based upon bagged regression trees (BRT) and uses correlations between high-resolution remote sensing products and SM observations. The algorithm trains multiple regression trees and automatically chooses the trees that generate the best downscaled estimates. The algorithm was evaluated using a multi-scale synthetic dataset in north central Florida for two years, including two growing seasons of corn and one growing season of cotton per year. The time-averaged error across the region was found to be 0.01 $\mathrm{m}^3/\mathrm{m}^3$, with a standard deviation of 0.012 $\mathrm{m}^3/\mathrm{m}^3$ when 0.02% of the data were used for training in addition to temporal correlations from the past seven days, and all available data from the past year. The maximum spatially averaged errors obtained using this algorithm in downscaled SM were 0.005 $\mathrm{m}^3/\mathrm{m}^3$, for pixels with cotton land-cover. When land surface temperature~(LST) on the day of downscaling was not included in the algorithm to simulate "data gaps", the spatially averaged error increased minimally by 0.015 $\mathrm{m}^3/\mathrm{m}^3$ when LST is unavailable on the day of downscaling. The results indicate that the BRT-based algorithm provides high accuracy for downscaling SM using complex non-linear spatio-temporal correlations, under heterogeneous micro meteorological conditions.

Disaggregation of Remotely Sensed Soil Moisture in Heterogeneous Landscapes using Holistic Structure based Models

In this study, a novel machine learning algorithm is presented for disaggregation of satellite soil moisture (SM) based on self-regularized regressive models (SRRM) using high-resolution correlated information from auxiliary sources. It includes regularized clustering that assigns soft memberships to each pixel at fine-scale followed by a kernel regression that computes the value of the desired variable at all pixels. Coarse-scale remotely sensed SM were disaggregated from 10km to 1km using land cover, precipitation, land surface temperature, leaf area index, and in-situ observations of SM. This algorithm was evaluated using multi-scale synthetic observations in NC Florida for heterogeneous agricultural land covers. It was found that the root mean square error (RMSE) for 96% of the pixels was less than 0.02 $m^3/m^3$. The clusters generated represented the data well and reduced the RMSE by upto 40% during periods of high heterogeneity in land-cover and meteorological conditions. The Kullback Leibler divergence (KLD) between the true SM and the disaggregated estimates is close to 0, for both vegetated and baresoil landcovers. The disaggregated estimates were compared to those generated by the Principle of Relevant Information (PRI) method. The RMSE for the PRI disaggregated estimates is higher than the RMSE for the SRRM on each day of the season. The KLD of the disaggregated estimates generated by the SRRM is at least four orders of magnitude lower than those for the PRI disaggregated estimates, while the computational time needed was reduced by three times. The results indicate that the SRRM can be used for disaggregating SM with complex non-linear correlations on a grid with high accuracy.

Downscaling Microwave Brightness Temperatures Using Self Regularized Regressive Models

A novel algorithm is proposed to downscale microwave brightness temperatures ($\mathrm{T_B}$), at scales of 10-40 km such as those from the Soil Moisture Active Passive mission to a resolution meaningful for hydrological and agricultural applications. This algorithm, called Self-Regularized Regressive Models (SRRM), uses auxiliary variables correlated to $\mathrm{T_B}$ along-with a limited set of \textit{in-situ} SM observations, which are converted to high resolution $\mathrm{T_B}$ observations using biophysical models. It includes an information-theoretic clustering step based on all auxiliary variables to identify areas of similarity, followed by a kernel regression step that produces downscaled $\mathrm{T_B}$. This was implemented on a multi-scale synthetic data-set over NC-Florida for one year. An RMSE of 5.76~K with standard deviation of 2.8~k was achieved during the vegetated season and an RMSE of 1.2~K with a standard deviation of 0.9~K during periods of no vegetation.