Modeling Soil Moisture Dynamics and Variability Using Gaussian Mixture-Based Long Short-Term Memory Networks

Soil moisture plays a critical role in various hydrological processes, controlling groundwater recharge, infiltration, and the generation of overland flow. Additionally, it stands as a key determinant for the water supply essential for sustaining vegetation and agricultural crops. Soil moisture measurements using Time-Domain Reflectometry (TDR) sensors are labor-intensive and expensive, often requiring extensive setup and maintenance. Furthermore, because of the small support volume of these sensors, two of them placed at the same depth just a few meters apart can produce readings that vary by 20 volume percentage or more. These uncertainties are not random; rather, they reflect the small scale variability of e.g. soil texture, which largely controls soil water retention and thus soil moisture dynamics. To effectively model soil moisture and address these uncertainties, we need deep learning (DL) models that can not only make accurate predictions but also learn to represent the underlying variability. Here, we present a model that combines Long Short-Term Memory Networks (LSTMs) with Gaussian Mixture Models (GMMs), trained on a large dataset of uniquely placed in-situ soil moisture observations collected from the Attert experimental basins in Luxembourg. By training on in-situ soil moisture observations, our model aims to generalize soil moisture dynamics across spatial dimensions, temporal scales, and depths. Unlike traditional models that predict a single, deterministic value, the proposed network outputs weighted probabilistic distributions, providing a promising way to capture small scale soil moisture variability. With this approach we aim to evaluate the predictive performance of different Gaussian-Mixture LSTM (GM-LSTM) setups for soil moisture dynamics and to quantify observational variabilities and uncertainties. By temporal predictions and the assessment of variability we have shown that the developed model setup is capable to model the dynamical fluctuations of soil moisture, as well as to replicate the variability within the cluster site locations. In addition, we observed seasonal variations in the probabilistic model outputs, with lower uncertainty during dry periods and higher variability during wet phases, highlighting the ability of data-driven approaches to uncover relationships and offer additional insights into the dynamics of soil moisture systems. In summary, by using GM-LSTMs, we demonstrated that this modeling approach is capable of simultaneously predicting soil moisture dynamics while accounting for local-scale variability, which is important for improving drought monitoring and agricultural productivity.