Decomposing Non-Stationarity for Soil Moisture Prediction: A Hybrid Statistical-Deep Learning Framework Integrating Periodic, Trend, and Residual Components

Abstract. The non-stationarity of hydro-meteorological processes has intensified under climate change, posing substantial challenges for accurate soil moisture (SM) prediction. To address the difficulty in distinguishing different sources of non-stationarity in conventional models, this study proposed a non-stationary SM prediction framework that integrated statistical methods with deep learning (DL) models. The framework focused on separating three types of non-stationary components — periodic fluctuations, long-term trend variations, and residual disturbances — and evaluated their effects on predictive performance. Specifically, independent models were first developed for different months to explicitly characterize periodic features. Statistical methods were then used to construct marginal distributions of hydro-meteorological variables, with physical covariates incorporated into distribution parameters to represent time-varying trends. Furthermore, Natural Gradient Boosting (NGBoost) was employed to perform secondary fitting of prediction residuals, thereby correcting random fluctuations that were not fully captured in the one-stage prediction. A gated recurrent unit with an attention mechanism (GRU-Attention) was selected as the core DL model, and SM prediction experiments were conducted across China to systematically evaluate the two-stage prediction performance under six modeling scenarios. Results showed that: (1) seasonal periodicity was the most robust predictive structure, whereas trend-related non-stationarity provided conditional rather than universal gain and residual learning improved performance only when the first-stage errors retained learnable structure; (2) the prediction skill was strongly organized by aridity, with the most stable performance concentrated in arid and semi-arid regions, while representative-grid and temporal-stability analyses revealed important local departures from regional mean predictability; and (3) the SHAP attribution identified a coherent dry-to-wet transition in dominant controls, from evaporation in hyper-arid regions to antecedent soil-moisture memory in arid regions and precipitation dominance in wetter regions, with tree-based importance rankings supporting the robustness of this driver hierarchy. From the perspective of non-stationary component separation, this study provides a new hybrid modeling approach for SM prediction and offers methodological support for hydrological forecasting, agricultural drought monitoring, and regional water resources management under complex climate change conditions.