Interpretable Soil Moisture Prediction with a Physics-guided Deep Learning Approach

Wang, Yanling; Hu, Xiaolong; Hu, Yaan; He, Leilei; Wang, Lijun; Song, Wenxiang; Shi, Liangsheng

doi:10.5194/egusphere-2025-4440

Preprints

https://doi.org/10.5194/egusphere-2025-4440

Preprints

18 Sep 2025

| 18 Sep 2025

Interpretable Soil Moisture Prediction with a Physics-guided Deep Learning Approach

Yanling Wang, Xiaolong Hu, Yaan Hu, Leilei He, Lijun Wang, Wenxiang Song, and Liangsheng Shi

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.

Received: 10 Sep 2025 – Discussion started: 18 Sep 2025

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Journal article(s) based on this preprint

19 May 2026

Interpretable soil moisture prediction with a knowledge-guided deep learning approach

Yanling Wang, Xiaolong Hu, Yaan Hu, Leilei He, Lijun Wang, Wenxiang Song, and Liangsheng Shi

Hydrol. Earth Syst. Sci., 30, 2973–2994, https://doi.org/10.5194/hess-30-2973-2026,https://doi.org/10.5194/hess-30-2973-2026, 2026

Short summary

Yanling Wang, Xiaolong Hu, Yaan Hu, Leilei He, Lijun Wang, Wenxiang Song, and Liangsheng Shi

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4440', Anonymous Referee #1, 18 Oct 2025
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
Synthetic vs. field data

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.
Interpretability not yet quantitatively tied to physics

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.
Citation: https://doi.org/10.5194/egusphere-2025-4440-RC1
- AC2: 'Reply on RC1', Yanling Wang, 15 Nov 2025
  
  We are very grateful to receive such valuable comments and suggestions provided by the reviewer. We have provided the response in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4440-AC2
RC2:
'Comment on egusphere-2025-4440', Anonymous Referee #2, 01 Nov 2025
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(𝑥_𝑖, 𝑥_𝑗) 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
- AC1: 'Reply on RC2', Yanling Wang, 15 Nov 2025
  
  We thank the reviewer for their valuable comments and suggestions. We have addressed each point in our responses, which are provided in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4440-AC1

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4440', Anonymous Referee #1, 18 Oct 2025
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
Synthetic vs. field data

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.
Interpretability not yet quantitatively tied to physics

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.
Citation: https://doi.org/10.5194/egusphere-2025-4440-RC1
- AC2: 'Reply on RC1', Yanling Wang, 15 Nov 2025
  
  We are very grateful to receive such valuable comments and suggestions provided by the reviewer. We have provided the response in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4440-AC2
RC2:
'Comment on egusphere-2025-4440', Anonymous Referee #2, 01 Nov 2025
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(𝑥_𝑖, 𝑥_𝑗) 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
- AC1: 'Reply on RC2', Yanling Wang, 15 Nov 2025
  
  We thank the reviewer for their valuable comments and suggestions. We have addressed each point in our responses, which are provided in the attached document.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4440-AC1

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (17 Nov 2025) by Bo Guo

I am still waiting for the comments from the third reviewer, but I think we should move forward at this moment. Based on the two reviewers’ reports and the authors’ detailed response, I see clear potential in this manuscript but also a need for a substantial and carefully implemented revision before it can be considered for publication in HESS. Both reviewers find the topic important and the overall modeling direction interesting. The paper introduces non-local neural network architectures for single-time-step, multi-depth soil-moisture prediction and demonstrates their performance on synthetic and ISMN field data. However, the reviewers also raise significant concerns about the clarity of the methodology, the framing of the “physics-guided” concept, and the way interpretability claims are supported.

Below is a summary of some of the key issues that need be addressed upon my own reading and my assessment of the reviewers’ comments (refer to the original reviewers’ comments for a complete list).

1. Revise the “physics-guided” framing and calibrate the claims
Both reviewers question the use of the term “physics-guided” given that the model does not actually encode governing equations or explicit physical constraints in the architecture or loss function. I agree that the current framing in the preprint over-states the level of physical embedding (e.g., title, abstract, and several statements emphasizing “physics-guided” gains and superior performance).

The authors indicated that they would replace “physics-guided” with “knowledge-guided” throughout the manuscript to better reflect that the design is inspired by conceptual understanding of soil water dynamics rather than coupled directly to the Richards equation or similar governing laws. I support this change, but the revised manuscript needs to be fully consistent:
• Ensure that the title, abstract, keywords, and conclusions are aligned with the “knowledge-guided” terminology and do not imply that physical equations are enforced.
• Calibrate the narrative so that “physics/knowledge guidance” is presented as structural guidance (e.g., directional masks, separation of four processes) rather than as a guarantee of physical correctness. Statements such as “highlighting the importance of physics guidance” need to be rephrased to emphasize qualitative plausibility, not strict physical enforcement.

2. Methodological clarity and internal consistency
Reviewer 2 in particular stresses that the methods section is currently difficult to follow, with ambiguities in the time-dependence assumptions, notation, and the construction of the knowledge-guided non-local operation. The revision should fully implement the clarifications promised in the authors’ response. Overall, the methods section should be readable and reproducible for hydrologists with some machine-learning background but not necessarily with specific expertise in non-local networks.

3. Experimental design: synthetic vs. field data and model baselines
Reviewer 1’s main substantive concern is that the synthetic experiments originally compared only SA-NLNN and PG/KG-NLNN, while LSTM baselines were used only on the field data, making it hard to attribute gains specifically to the knowledge-guided design. Adding LSTM_1 and LSTM_4 as baselines in the synthetic cases, including performance under varying noise levels, would help address this issue.

4. Interpretability claims and linkage to soil properties
Both reviewers appreciate the attempt to obtain interpretable non-local weight maps and relate them to soil texture/structure, but Reviewer 1 notes that, in the current form, the link to soil hydraulic parameters is qualitative and not quantified. The authors indicated that they will acknowledge this limitation and emphasize that the goal is qualitative insight rather than parameter estimation, providing additional synthetic examples (swapped layers, different Kₛ) to illustrate sensitivity of the weight maps to soil properties. If it is done well, this section can be a nice contribution, illustrating what non-local neural networks can reveal about vertical connectivity beyond black-box accuracy metrics.

5. Data description, initial conditions, and boundary forcings
Reviewer 2 asks for clearer description of the meteorological inputs (source, spatial/temporal resolution) and the use of reference vs actual evapotranspiration in the synthetic experiments. Reviewer 1 also asks for explicit statements on initial soil-moisture conditions and how the first step of multi-day forecasts is initialized.

6. Presentation and readability
Finally, both reviewers note issues of readability and organization (e.g., conclusive statements in the introduction, figure legends overlapping content, minor undefined symbols).

In summary, I concur with the referees that the study addresses an important problem and proposes a promising knowledge-guided non-local architecture for interpretable soil-moisture prediction. At the same time, the current version still requires substantial revision in framing, methodological clarity, experimental exposition, and the calibration of interpretability claims. I therefore recommend a major revision.

Please submit a thoroughly revised manuscript together with a detailed point-by-point response to all referee comments and the issues highlighted above.

Hide

AR by Yanling Wang on behalf of the Authors (18 Nov 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (24 Nov 2025) by Bo Guo

RR by Anonymous Referee #2 (01 Dec 2025)

RR by Anonymous Referee #3 (11 Jan 2026)

RR by Anonymous Referee #1 (12 Jan 2026)

ED: Reconsider after major revisions (further review by editor and referees) (18 Jan 2026) by Bo Guo

AR by Yanling Wang on behalf of the Authors (14 Feb 2026) Author's response

EF by Mario Ebel (02 Mar 2026) Manuscript Author's tracked changes

ED: Referee Nomination & Report Request started (03 Mar 2026) by Bo Guo

RR by Anonymous Referee #3 (07 Apr 2026)

Suggestions for revision or reasons for rejection

The authors have addressed most of my previous concerns, and the manuscript is recommended for publication subject to the following minor revisions.

Line 100 (Response 15): The revised explanation is still not sufficiently accurate. The main issues are as follows.

First, the manuscript overstates the defining characteristics of GNNs. The statement that GNNs “rely on explicit, pre-defined graph structures where topological relationships remain fixed” is too restrictive. While many GNNs do begin with an explicit graph, in many formulations the edge weights, adjacency, or effective interactions may also be learned, updated, or defined through attention mechanisms. Therefore, this is not a reliable criterion for distinguishing NLNNs from GNNs.

Second, the statement that “neighbor nodes typically share uniform transformation rules” is also not an appropriate discriminator. Although standard message-passing GNNs often employ shared functions, the actual interactions are not necessarily uniform, since they may depend on node features, edge features, attention coefficients, or edge types.

Third, the description of NLNNs as having “edges generated on-the-fly” is somewhat misleading. NLNNs are more accurately understood as computing pairwise affinities, often densely across all positions, based on the current features. This is better characterized as a dynamic, data-dependent, fully connected interaction pattern, rather than simply stating that they do not use a graph.

The authors should revise this section to present a more precise and technically accurate distinction between NLNNs and GNNs.

Line 215 (Response 32): The similarities and differences between NLNNs and transformers should also be explained more explicitly and clearly in the manuscript.

Hide

ED: Publish subject to minor revisions (review by editor) (17 Apr 2026) by Bo Guo

AR by Yanling Wang on behalf of the Authors (21 Apr 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (27 Apr 2026) by Bo Guo

AR by Yanling Wang on behalf of the Authors (27 Apr 2026) Manuscript

Journal article(s) based on this preprint

19 May 2026

Interpretable soil moisture prediction with a knowledge-guided deep learning approach

Yanling Wang, Xiaolong Hu, Yaan Hu, Leilei He, Lijun Wang, Wenxiang Song, and Liangsheng Shi

Hydrol. Earth Syst. Sci., 30, 2973–2994, https://doi.org/10.5194/hess-30-2973-2026,https://doi.org/10.5194/hess-30-2973-2026, 2026

Short summary

Yanling Wang, Xiaolong Hu, Yaan Hu, Leilei He, Lijun Wang, Wenxiang Song, and Liangsheng Shi

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This study introduces a new interpretable deep learning method that accurately predicts multi-depth soil moisture simultaneously without physical assumptions. The model provides insights into soil properties, while delivering precise predictions across diverse scenarios. Tested under various conditions, it outperforms traditional approaches, particularly when enhanced with basic physics. This tool can help improve water management by offering reliable and efficient soil moisture forecasts.


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Interpretable Soil Moisture Prediction with a Physics-guided Deep Learning Approach

Journal article(s) based on this preprint

Interactive discussion

Interactive discussion

Peer review completion

Suggestions for revision or reasons for rejection

Suggestions for revision or reasons for rejection

Suggestions for revision or reasons for rejection

Suggestions for revision or reasons for rejection

Journal article(s) based on this preprint

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