1 Introduction

Land surface soil moisture (SSM) is an essential hydro-ecological parameter for monitoring energy, water, and carbon cycles (Seneviratne et al., 2010; Bateni and Entekhabi, 2012). Continuous SSM at fine spatial resolutions provides crucial information for hydrological models, precipitation forecasting models, land-atmosphere models, drought and flood forecasting, and vegetation growth monitoring (Krishnan et al., 2006; Wang et al., 2016; Dorigo et al., 2017). In general, soil moisture is acquired by using in-situ measurements (Dobriyal et al., 2012), including wireless sensor networks (Kerkez et al., 2012) and Cosmic-ray Soil Moisture Observing System (Zreda et al., 2012), which have helped overcome the sparse sampling and poor dynamic limitations of traditional in-situ methods. These ground-based measurements methods require continuous financial support and suitable ground conditions and are limited to small monitoring areas. With the development of active and passive microwave remote sensing techniques (Petropoulos et al., 2015), it becomes possible and more convenient to acquire SSM information dynamically at different spatiotemporal resolutions over large areas. A series of SSM products derived from various satellite-based microwave sensors has been released (Njoku et al., 2003; Parinussa et al., 2014; Meissner et al., 2018). However, with spatial resolutions of tens of kilometers, the current microwave-based SSM products are limited to large-scale monitoring applications.
Many approaches have been developed for downscaling these coarse scale SSM products. Some of these benefit from ancillary information that captures the variations of SSM at fine resolution, combined with correlated variables (Ge et al., 2019). There are two main sources of ancillary variables: active microwave data and visible/infrared data. Change detection based downscaling algorithms (Piles et al., 2009; van der Velde et al., 2015) and Bayesian merging methods (Zhan et al., 2006; Wu et al., 2017) have been proposed to downscale the coarse SSM by using active microwave data. The active microwave technique is highly sensitive to SSM and can even penetrate clouds, however it is greatly affected by soil roughness and vegetation. An alternative downscaling approach is to use fine resolution optical/thermal data. A number of downscaling algorithms have been developed to generate fine-resolution SSM, such as Disaggregation based on Physical And Theoretical scale Change (Merlin et al., 2015; Malbéteau et al., 2016), trapezoid-based methods (Yang et al., 2015; Babaeian et al., 2018), regression-based approaches (Duan et al., 2016; Liu et al., 2018) and geostatistical methods (Mukherjee, 2015; Jin et al., 2018). For downscaling with optical/thermal data, the statistical correlation between SSM and ancillary variables or physically based models have been explored (Peng et al., 2017).
Chauhan et al. (2003) proposed an empirical polynomial fitting downscaling approach using a polynomial regression at coarse spatial resolution to obtain the fine-spatial-resolution SSM. Since then, further polynomial fitting downscaling methods have been presented by employing multiple data sources or different ancillary parameters (Piles et al., 2014; Knipper et al., 2017), such as land surface temperature (LST), vegetation information, brightness temperature, albedo, evapotranspiration and terrain indices. Meanwhile, geographically weighted regression, which takes into consideration local characteristics (Song et al, 2019), and machine learning algorithms have been introduced into downscaling. Machine learning algorithms such as random forest and support vector regression (SVR) perform better in capturing the nonlinear relationships among variables and have been widely applied to downscaling SSM (Zhao et al., 2018; Abbaszadeh et al., 2019). Some studies directly combined the fine-resolution trend and coarse-resolution residual to predict the fine-resolution SSM (Im et al., 2016; Wei et al., 2019). Interpolation techniques such as bilinear interpolation and kriging interpolation have been generally used in residual analysis for approximating the actual fluctuations (Song and Jia, 2016; Chen et al., 2019). Geostatistical methods with a focus on the spatial correlation between variables have been increasingly applied in downscaling (Kaheil et al., 2008; Djamai et al., 2016). However, these downscaling approaches ignore the change in supports before and after downscaling. Due to the stratified heterogeneity in geographical variables, downscaling models for various stratifications established in the scaling process (Ge et al., 2019) are limited to the smaller samples captured by the model. The SVR approach, benefiting from its high generalization ability, could provide a solution to the small sample size problem (Srivastava et al., 2013).
Considering all the previous machine learning algorithms, this paper proposes a new machine learning-based geostatistical model that integrates SVR and area-to-area kriging (ATAK) to achieve spatial downscaling by fusing various ancillary variables. The proposed support vector area-to-area regression kriging (SVATARK) can tackle the modifiable areal unit problem, as well as model the complex nonlinear relationship among variables in the downscaling process. The downscaling approach was employed to predict 1-km-resolution SSM data by downscaling ESA’s 25-km-resolution SSM product, Climate Change Initiative (CCI), with consideration of land cover types. Downscaled SSM predictions were produced every eight days over the Naqu region in the central Tibetan Plateau (TP), and were evaluated using in-situ SSM measurements. A comparison of the SSM residuals obtained from the ATAK method versus the residuals from bilinear interpolation and kriging interpolation indicated advantages of the SVATARK downscaling approach.
The remainder of the paper is organized as follows. Section 2 describes the downscaling methodology, including the downscaling strategy during the experiment. Both the study area and the data sets are introduced in Section 3. Section 4 validates the downscaled predictions and discusses the comparison results. Finally, some conclusions are summarized in Section 5.