Soil moisture plays a crucial role in the hydrological cycle, but accurately predicting soil moisture presents challenges due to the nonlinearity of soil water transport and the variability of boundary conditions. Deep learning has emerged as a promising approach for simulating soil moisture dynamics. In this study, we explore 10 different network structures to uncover their data utilization mechanisms and to maximize the potential of deep learning for soil moisture prediction, including three basic feature extractors and seven diverse hybrid structures, six of which are applied to soil moisture prediction for the first time. We compare the predictive abilities and computational costs of the models across different soil textures and depths systematically. Furthermore, we exploit the interpretability of the models to gain insights into their workings and attempt to advance our understanding of deep learning in soil moisture dynamics. For soil moisture forecasting, our results demonstrate that the temporal modeling capability of long short-term memory (LSTM) is well suited. Furthermore, the improved accuracy achieved by feature attention LSTM (FA-LSTM) and the generative-adversarial-network-based LSTM (GAN-LSTM), along with the Shapley (SHAP) additive explanations analysis, help us discover the effectiveness of attention mechanisms and the benefits of adversarial training in feature extraction. These findings provide effective network design principles. The Shapley values also reveal varying data leveraging approaches among different models. The t-distributed stochastic neighbor embedding (t-SNE) visualization illustrates differences in encoded features across models. In summary, our comprehensive study provides insights into soil moisture prediction and highlights the importance of the appropriate model design for specific soil moisture prediction tasks. We also hope this work serves as a reference for deep learning studies in other hydrology problems. The codes of 3 machine learning and 10 deep learning models are open source.

The roughness of the land surface (z₀) is a key property, exerting significant influence on the amount of near-surface turbulent activity and consequently the turbulent exchange of energy, water, momentum, and chemical species between the land and the atmosphere. Variations in z₀ are substantial across different types of land cover, ranging from typically less than 1 mm over fresh snow or sand deserts up to more than 1 m over urban areas or forests. In this study, we revise the parameterizations and parameter choices related to z₀ in the Community Land Model 5.1 (CLM), the land component of the Community Earth System Model (CESM). We propose a number modifications for z₀ in CLM, guided by observational data. Most importantly, we find that the observations support an increase in z₀ for all types of forests and a decrease in the momentum z₀ for bare soil, snow, glaciers, and crops. We then assess the effect of those modifications in land-only and land–atmosphere coupled simulations. With the revised parameterizations, diurnal variations of the land surface temperature (LST) are dampened in forested regions and are amplified over warm deserts. These changes mitigate model biases compared to MODerate resolution Imaging Spectroradiometer (MODIS) remote sensing observations. The changes in LST are generally stronger during the day than at night. For example, the LST increases by 5.1 K at 13:30 local solar time but only by 0.6 K at 01:30 during boreal summer across the entire Sahara. The induced changes in the diurnal variability of near-surface air temperatures are generally of the opposite sign and of smaller magnitude. Near-surface winds accelerate in areas where the momentum z₀ was lowered, such as the Sahara, the Middle East, and Antarctica, and decelerate in regions with forests. Overall, this study finds that the current representation of z₀ in CLM is not in agreement with observational constraints for several types of land cover. The proposed model modifications are shown to considerably alter the simulated climate in terms of temperatures and wind speed at the land surface.

Artificial intelligence (AI) methods have created insurmountable performance in prediction tasks for geoscientific problems yet are unable to derive process insights and answer specific scientific questions. The geoscience community faces a dilemma of reconciling process comprehension with high predictive accuracy. Here we introduce a deep process learning (DPL) approach empowering neural networks to deduce intrinsic processes from observable data, wherein the intuitive physics of geosystems is directly coupled within the deep learning (DL) architecture as structural prior. We aim to incorporate as raw common concepts as possible as macroscopic guidance: on the one hand, to reduce interference with DL's data adaptability. On the other hand, to allow the information flow of the model to converge along specific paths toward the target output, thus enabling the potential to gain process insights with limited supervision. Illustrating its application to precipitation‐runoff modeling across the USA, DPL yields an ensemble median Nash‐Sutcliffe efficiency of 0.758 and Kling‐Gupta efficiency of 0.778 with robust transferability, compared to 0.762 and 0.751 for the state‐of‐the‐art DL model. The good match between internal representations of DPL and independent data sets of snow water equivalent and evapotranspiration, along with its superior capability for catchment water budget closures, demonstrates proficient process mastery. The study also highlights beneficial synergies from large‐scale data collaboration, promoting the organic unity of process understanding and predictive performance. This work shows a promising avenue for learning processes from big data and will benefit geoscientific domains that remain concerned with process clarity in the era of AI.

The parameters of the GR4J-CemaNeige coupling model (GR4neige) are typically treated as constants. However, the maximum capacity of the production store (parX1) exhibits time-varying characteristics due to climate variability and vegetation coverage change. This study employed differentiable parameter learning (dPL) to identify the time-varying parX1 in the GR4neige across 671 catchments within the United States. We built two types of dPL, including static and dynamic parameter networks, to assess the advantages of the time-varying parameter. In the dynamic parameter network, we evaluated the impact of potential evapotranspiration (PET), precipitation (P), temperature (T), soil moisture (SM), and normalized difference vegetation index (NDVI) datasets on the performance of dPL. We then compared dPL with the empirical functional method (fm). The results demonstrated that the dynamic parameter network outperformed the static parameter network in streamflow estimation. There were differences in streamflow estimation among the dynamic parameter network driven by various input features. In humid catchments, simultaneously incorporating all five factors, including PET, P, T, SM, and the NDVI, achieved optimal streamflow simulation accuracy. In arid catchments, it was preferable to introduce PET, T, and the NDVI separately for improved performance. dPL significantly outperformed the empirical fm in estimating streamflow and uncalibrated intermediate variables, like evapotranspiration (ET). Both the derived parX1 from dPL and the empirical fm exhibited significant spatiotemporal variation across 671 catchments. Notably, compared to parX1 obtained through the empirical fm, parX1 derived from dPL exhibited a distinct spatial clustering pattern. This study highlights the potential of dPL in enhancing model accuracy and contributes to understanding the spatiotemporal variation characteristics of parX1 under the influence of climate factors, soil conditions, and vegetation change.

Despite the remarkable advances in using deep learning for describing and predicting soil water flow, these models inherently cannot deepen our understanding of its underlying physical mechanisms as they are black‐box approaches. To address this issue, a novel data‐driven equation discovery approach has recently been widely used to facilitate scientific discovery in geoscience disciplines, including soil hydrology. However, due to the inherent complexity of soils, current data‐driven discovery approaches cannot deal with heterogeneous soil scenarios. In this study, we present a new group sparse regression theory and a deep learning framework to extend previous studies to be able to identify the governing equations for soil water flow in heterogeneous soils from observational data. Specifically, we focus on discovering equations from only time series of volumetric soil water content data, which are easily accessible. To accommodate it, the underlying assumption of the generalized soil‐water content‐based governing equation is utilized, and a coarse‐grained group sparsity theory is developed. Furthermore, we incorporate the proposed group sparse regression into a new deep‐learning framework: Extended‐DeepGS (Extended Deep‐learning‐based Group Sparsity). Through deep‐learning identification, it realizes simultaneous reconstructions of soil moisture dynamics and governing equations. A series of comprehensive numerical experiments are designed and conducted to test the performance of the theory and framework, and the results show its robustness. We also summarize the potential effects of soil heterogeneity on the discovery of equations. Finally, we discuss the limitations of the approach, which may inform future developments.