the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Sep 2025
Interpretable Soil Moisture Prediction with a Physics-guided Deep Learning Approach
Abstract. Soil moisture is a critical component of the hydrological cycle, but accurately predicting it remains challenging due to the nonlinearity of soil water transport, variability in boundary conditions, and the intricate nature of soil properties. Recently, deep learning has shown promise in this domain, typically by modeling temporal dependencies for soil moisture predictions. In this study, we propose non-local neural networks (NLNN) to convert this problem into a single-time-step, simultaneous multi-depth soil moisture forecasting. By facilitating mutual compensation among different depths, this method enables a representation of vertical heterogeneity and inter-layer connectivity without physical assumptions, leading to precise and efficient predictions in diverse scenarios. Our non-local operation design includes the embedded Gaussian operations and disentangled physics-guided operations, resulting in two variants: the self-attention non-local neural network (SA-NLNN) and the physics-guided non-local neural network (PG-NLNN). The models offer visual interpretability, providing insights into intricate mechanisms of soil moisture dynamics. Notably, the model guided by physics yields more stable and reasonable qualitative interpretations. With in-situ observations, we demonstrate that our proposed models perform satisfactorily. The physics-guided non-local operations significantly enhance accuracy and reliability. Additionally, our models adapt to diverse time-scale situations while maintaining high computational efficiency. Both models exhibit robust noise resistance, with physics guidance enhancing PG-NLNN’s noise resistance. In summary, our work addresses the soil moisture prediction challenge in a novel way, highlighting the potential of NLNN and the importance of incorporating physic guidance in data-driven models.
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Status: open (until 11 Nov 2025)
- RC1: 'Comment on egusphere-2025-4440', Anonymous Referee #1, 18 Oct 2025 reply
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RC2: 'Comment on egusphere-2025-4440', Anonymous Referee #2, 01 Nov 2025
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This manuscript presents an interesting and exploratory study addressing the critical challenge of soil moisture prediction within the hydrological cycle. Specifically, the authors developed two variants of non-local neural networks (NLNN), and the method effectively models vertical heterogeneity and inter-layer connectivity. The authors validated their approach using synthetic data and in-situ observations from the International Soil Moisture Network, highlighting the models’ interpretability and their robustness to noise. This approach, which attempts to learn soil water dynamics directly from data without relying on traditional physical assumptions, demonstrates the potential of integrating data-driven techniques with scientific knowledge, particularly in complex soil conditions such as wormholes and root water uptake.
However, despite the innovative research direction, the manuscript suffers from several issues, particularly in terms of the clarity of the methods. My specific comments are as follows:
- The claim of a “physics-guided” approach is a core theme, but the method lacks evidence of incorporating actual physical laws into the model structure or loss functions. The model constructed in this study essentially relies on data-driven feature interaction learning. The authors should either replace the term “physics-guided” with a more appropriate expression or explicitly incorporate more concrete physical information into the model.
- The authors mention various deep learning models in the introduction, including CNN, LSTM, Transformer, etc., and state that “the complex coupling of actual physical processes and the presence of unknown governing equations pose substantial challenges in practical applications,” based on which they propose the use of NLNNs in this paper. However, Graph Neural Networks (GNNs) can also incorporate spatial relationships into the model. The authors should expand the literature review to more clearly highlight the uniqueness of their approach.
- The authors include some conclusive statements in the introduction (e.g., "By integrating meteorological conditions and the spatial interactions of soil moisture within its four-part disentangled physics-guided operation framework, PG-NLNN demonstrates superior performance”). The introduction should mainly address the research background, motivation, scientific problems, and research content. Including such statements is useful for emphasizing the potential contribution of the paper, but it would be more appropriate to place them in the results or conclusion sections.
- The time dependency assumption presented in Section 2.1 needs further explanation. The sentence, "In our soil moisture forecasts at multiple depths, we assume that the soil moisture within the profile at the next time step depends on both the current meteorological conditions and the soil moisture from the previous time step," suggests that the soil moisture at time 𝑡1 and the meteorological conditions at time 𝑡2 determine the soil moisture at time 𝑡3. However, it is unclear why the soil moisture at time 𝑡2 does not influence the soil moisture at time 𝑡3. Please clarify the time dependency and provide the theoretical foundation for this assumption.
- The input symbol in Figure 2 should be consistent. The figure uses 𝑋𝑡, while the text uses 𝑠𝑚𝑡, which creates an inconsistency. It is recommended to unify the notation for better understanding for readers. Additionally, elements like 𝑊𝑘, 𝑊𝑞, and 𝑊𝑣 in the figure are not fully explained. It would be helpful to expand the caption to provide more detailed descriptions, aiding readers in better understanding the model structure.
- The model’s Physics-guided Operation section utilizes different mask layers to filter out specific data points while emphasizing useful information. This is similar to the self-attention mechanism in Transformers but with domain-specific adjustments. However, the authors have not provided the physical basis for this mechanism, nor have they discussed its advantages compared to the traditional Transformer mechanism. It is recommended to include the theoretical background of this mechanism and explain its specific advantages for soil moisture prediction to enhance the persuasiveness and originality of the work.
- In line 249 and in formulas (7), (8), and (9), 𝑓(𝑥𝑖, 𝑥𝑗) involves two variables, but the subsequent description mentions that the function is a mapping of three variables. The equation should either be modified or the description clarified to specify the actual number of input variables, ensuring consistency between the equation and the text.
- In lines 276–277, the authors mention that the LSTM input contains data from two time steps due to the delayed effect of meteorology on soil moisture. However, the authors do not explain why two time steps were selected or provide any physical or empirical justification. It is recommended to add the rationale and reasoning for this time window choice.
- Formulas (6) and (14–16) both use the symbol 𝑎 to represent the activation function, but the authors have not clarified whether the same function is used in both instances. If the activation functions differ, the notation should be distinguished to avoid confusion. Additionally, the explanation of LSTM variables lacks a description of the tanh activation function. It would be beneficial to add this explanation to maintain consistency between the notation and the equation definitions.
- In Section 3.1, the authors use reference evapotranspiration rather than actual evapotranspiration, which better reflects actual water consumption. It is recommended to clarify the reasoning behind this choice.
- In line 346, the authors list meteorological input variables but do not specify their time and spatial resolutions. It is recommended to provide this information and explain whether the data have been resampled to ensure the completeness and reproducibility of the model input descriptions.
- It is recommended to adjust the placement of the legends in Figures 6, 7, 11, and 14, especially in Figures 7 and 14, where it would be better to position the legend at the top of the figure to avoid obscuring important elements of the figure.
- In line 409, the term "significant errors" is used, but no statistical support is provided. It is recommended to either include p-values or replace “significant” with terms like “obvious” to avoid using the term without statistical backing.
Citation: https://doi.org/10.5194/egusphere-2025-4440-RC2
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- 1
This is a review of the manuscript “Interpretable Soil Moisture Prediction with a Physics-Guided Deep Learning Approach.” The authors propose non-local neural networks (NLNNs) for single-time-step, multi-depth soil-moisture forecasts, with two variants: a self-attention NLNN (SA-NLNN) and a physics-guided NLNN (PG-NLNN) that disentangles four influences (upper boundary, upper layers, same-depth memory, lower layers) motivated by gravity, capillarity, and retention. They test their models on both synthetic and field data. They compare the performance of the two models with LSTM baselines and show that the prediction uncertainty is smaller for the proposed NN models than for the LSTM models. They also show that the learned non-local weight matrices can be related to soil texture. This is an interesting direction of research.
I believe this manuscript contains many good ideas for further investigation. Thus, I encourage publication after a major revision.
Major points
It would be more natural to use the same set of models for both synthetic and field data. LSTM baselines are evaluated on field data; the synthetic section compares SA-NLNN vs. PG-NLNN but omits LSTM models on the same synthetic tasks. This weakens causal attribution of PG-NLNN’s gains to physics guidance rather than dataset characteristics.
Weight maps qualitatively reflect layering, but the link to soil texture/parameters is not quantified (e.g., correlation with (Ksat) contrasts or van Genuchten parameters across cases/sites).
Minor points
Line 159: `sm_1 … sm_n` are not explicitly defined.
Section 2: How did the authors determine the initial soil moisture for the synthetic and field data cases? Please specify exactly how the first step of multi-day forecasts is initialized in both the synthetic and field experiments.