A dynamic soil moisture forecast framework considering non-stationary margins and structures

Accurate soil moisture (SM) forecasting is essential for hydrological and agricultural applications, particularly in the face of non-stationary climate conditions. This study developed a two-tiered modeling framework that combined a rolling forecast mechanism with non-stationary vine copula-based quantile regression models to improve SM forecast accuracy. Non-stationarity in hydrometeorological variables was assessed using the Mann-Kendall trend test, revealing statistically significant trends in over 97% of Yunnan Province, China. Then, a non-stationary vine copula model was constructed by embedding time-varying covariates into both marginal distributions and inter-variable dependence structures, enabling the model to dynamically capture both marginal and structural non-stationarity. Three temporal forecasting strategies—prediction, forecasting, and rolling forecast—were implemented to evaluate model adaptability and robustness. Model performance was benchmarked against three AI-based models (eXtreme Gradient Boosting (XGB), Random Forest (RF), and Long Short-Term Memory (LSTM)) and traditional quantile regression approaches. A suite of evaluation metrics was employed, including deterministic scores (e.g., Kling-Gupta Efficiency, KGE), probabilistic accuracy (e.g., coverage ratio, CR), and extreme-value diagnostics (e.g., total quantile error, TQE). Results demonstrated that non-stationary vine copula models outperformed stationary ones, achieving KGE values exceeding 0.90 in most regions, with structural (49.63%) and marginal (42.17%) non-stationarities contributing most to accuracy improvement. Among the methods, the rolling forecast with a sliding time window of 50 years emerged as the most reliable method, effectively mitigating "fake precision" by addressing biases from future information. Furthermore, the proposed model successfully identified and characterized agricultural droughts, including their frequency, duration, and severity. Taking the 2009~2010 winter-spring drought in Yunnan Province as an example, the model accurately captured its spatiotemporal evolution, demonstrating its potential in agricultural risk management and drought mitigation. Overall, this study highlights the necessity of incorporating non-stationarity in SM forecasting and presents a robust, interpretable, and operationally feasible framework for supporting drought preparedness and agricultural decision-making under climate uncertainty.