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Soil moisture (SM) plays an indispensable role in many practical applications, such as drought monitoring, hydrologic applications and agricultural management. Passive microwave remote sensing has proven capable of capturing changes in SM. However, the coarse spatial resolution (approximately 25–40 km) may greatly limit many regional hydrological and agricultural applications. In this study, we present a SM downscaling method based on the visible and shortwave-infrared (SWIR) remote sensing data toward improved spatial resolution of Soil Moisture Active Passive (SMAP) SM. In the proposed method, the Land Surface Temperature (LST), Normalized Difference Vegetation Index (NDVI), horizontally polarized Brightness Temperature (TBh), vertically polarized Brightness Temperature (TBv) and SWIR reflectance collected in Inner Mongolia from April to September 2018 and April to September 2019 are used as input data and combined with topographic information to downscale the SMAP SM L3 product from the original 36 km to 1 km. Random forest (RF) was used to link the input data and SMAP SM. Finally, 30 in situ station SM measurements distributed in Inner Mongolia and precipitation data were used to verify the downscaled SM. The results show that the correlation range of the downscaled SM and the in situ SM is 0.246 to 0.739, with an average of 0.535. The root mean square error (RMSE) range is 0.02 to 0.152 m3/m3, and the mean RMSE is 0.059 m3/m3. The ubRMSE has a range of 0.02 to 0.06 m3/m3, and the mean performance is 0.04 m3/m3. The bias ranges from −0.145 to 0.087 m3/m3, and the mean bias is 0.008 m3/m3. The downscaled SMAP SM can capture the spatial heterogeneity of the SMAP SM and the dynamic changes in measured soil moisture. The downscaled SMAP SM also has a high spatial correspondence with the original SMAP SM, providing more detailed soil water information than the original 36 km resolution.

Previous authors have studied unsteady flow in aquifer-aquitard systems with negligible storactivity in the confined aquifer layer. Formulae have been developed for groundwater level in the aquifer (or aquitard) and no adequate tables and graphs have been provided. In this paper, solutions for transient flow in an aquifer-aquitard system that consider storativity in a confined layer in response to both abrupt and uniform water level changes, as well as steady seepage rate from rivers (or canals), are developed. Analytical formulae for groundwater levels both in the aquifer and aquitard, and for seepage rate and total amount of water percolated from rivers, have been derived. To facilitate computation, graphs for the special functions involved in the proposed equations have been prepared.