Estimation of spatial distribution of soil moisture on steep hillslopes by state-space approach (SSA)

Soil moisture is a critical variable that quantifies precipitation, floods, droughts, irrigation, and other factors with regard to decision-making and risk evaluation. An accurate prediction of soil moisture dynamics is important for soil and environmental management. However, the complex topographic condition and land use in hilly and mountainous areas make it a challenge to monitor and predict soil moisture dynamics in these areas. In this study, the determinants of soil moisture variability were determined by structural equation modeling, and then an attempt was made to estimate the spatial distribution of soil moisture content on steep hillslope using the state-space method. Herein, soil moisture at different depths (0-10, 10-20, and 20-30 cm) was monitored by portable time-domain reflectometer (TDR) along this hillslope (100 m × 180 m). It showed that the spatial variability of soil moisture decreased with increasing soil wetness, primarily in the topsoil (0-10 cm). Soil moisture was correlated with elevation (r = 0.28, 0.50, and 0.28), capillary porosity (r = 0.06, 0.37, and 0.28), soil texture (r for Clay: 0.20, 0.24, and 0.16; r for Sand: -0.25, -0.18, and -0.28), organic carbon (r = -0.31, -0.08, and 0.10) and land use (r = -0.01, 0.28, and 0.24) under different conditions (dry, moderate, and wet). Among these determinants, elevation made direct contributions to soil moisture variation, especially under moderate conditions, while land use made its impacts by altering soil texture. It is encouraging that the state-space approach yielded precise and cost-effective predictions of soil moisture dynamics along this steep hillslope since it gives the minimum root-mean-square error (RMSE) and Akaike information criterion (AIC). Moreover, soil organic carbon (AIC = -4.497, RMSE = 0.104, R² = 0.899), rock fragment contents (AIC = -4.366, RMSE = 0.111, R² = 0.878), and elevation (AIC = -3.693, RMSE = 0.156, R² = 0.629) effectively anticipated the spatial distribution of soil moisture under dry, moderate, and wet conditions, respectively. This study confirms the efficacy of the state-space approach as a valuable tool for soil moisture prediction in areas characterized by complex and spatially heterogeneous conditions.