Scaling and Uncertainty in Soil Moisture Modelling: A Probabilistic Deep Learning Perspective

Soil moisture plays a central role in terrestrial water and energy exchanges, yet its representation across spatial scales remains challenging due to strong heterogeneity, measurement uncertainty, and limited transferability of soil parameters. While deep learning models have shown skill in reproducing soil moisture dynamics at large scales, they are commonly applied deterministically, providing limited insight into predictive uncertainty and variability. Here, we apply a probabilistic deep learning framework based on Gaussian Mixture Long Short-Term Memory networks (GM-LSTMs) to model soil moisture dynamics and uncertainty across the contiguous United States using in situ observations from the International Soil Moisture Network. The model is trained and evaluated in a cross-validation setting on ungauged locations and forced with multiple meteorological datasets, with DayMet emerging as the most effective driver. Rather than focusing primarily on predictive performance, we use regional learning to examine how soil moisture dynamics and variability emerge across climatic, physiographic, and soil-textural gradients. We analyse the structure of predictive uncertainty using mixture entropy and Jensen-Shannon divergence to distinguish dispersion from distributional complexity. ... mehrThe model reproduces temporal dynamics and rank structure of soil moisture and outperforms ERA5-Land and SMAP benchmarks, while revealing systematic biases in absolute volumetric water content. Predictive uncertainty exhibits coherent spatial organization controlled by physiography and soil texture, and distinct moisture-dependent regimes consistent with established hydrological theory. Variability peaks at intermediate soil moisture states, in agreement with catchment-scale observations, indicating that signatures of soil moisture organization persist across scales. The results demonstrate that probabilistic data-driven modelling can provide physically interpretable information on soil moisture variability and uncertainty, and offer new perspectives on scale-robust patterns of land-surface hydrological behaviour in the absence of explicit small-scale process representation.