The surface soil moisture (SSM) products derived from microwave remote sensing have a coarse spatial resolution; therefore, downscaling is required to obtain accurate SSM at high spatial resolution. An effective way to handle the stratified heterogeneity is to model for various stratifications; however, the number of samples is often limited under each stratification, influencing the downscaling accuracy. In this study, a machine learning-based geostatistical model, which combines various kinds of ancillary information at fine spatial scale, is developed for spatial downscaling. The proposed support vector area-to-area regression kriging (SVATARK) model incorporates support vector regression and area-to-area kriging by considering the nonlinear relationships among variables for various stratifications. SVATARK also considers the change of support problem in the downscaling interpolation process as well as for solving the small sample size in trend prediction. The SVATARK method is evaluated in the Naqu region on the Tibetan Plateau, China, to downscale the European Space Agency's (ESA) 25-km-resolution SSM product. The 1-km-resolution SSM predictions have been produced every eight days over a six-year period (2010-2015). Compared with five other downscaling methods, the downscaled predictions from the SVATARK method performs the best with in situ observations, resulting in a 24.4% reduction in root-mean-square error with 0.08 m3·m-3 and a 8.2% increase in correlation coefficient with 0.72, on average. Additionally, anomalously low SSM values, an indicator of drought, had a record low anomaly in mid-July for 2015, as noted by previous studies, indicating that SVATARK could be utilized for drought monitoring.