Improving heat transfer predictions in heterogeneous riparian zones using transfer learning techniques

Jin, Aohan; Shi, Wenguang; Zhou, Renjie; Zhan, Hongbin; Wang, Quanrong; Gu, Xuan

doi:https://doi.org/10.5194/egusphere-2024-4145

Preprints

https://doi.org/10.5194/egusphere-2024-4145

Preprints

16 Jan 2025

| 16 Jan 2025

Improving heat transfer predictions in heterogeneous riparian zones using transfer learning techniques

Aohan Jin, Wenguang Shi, Renjie Zhou, Hongbin Zhan, Quanrong Wang, and Xuan Gu

Abstract. Data-driven deep learning models usually perform well in terms of improving computational efficiency for predicting heat transfer processes in heterogeneous riparian zones. However, traditional deep learning models often suffer from accuracy when data availability is limited. In this study, a novel deep transfer learning (DTL) approach is proposed to improve the accuracy of spatiotemporal temperature distribution predictions. The proposed DTL model integrates the physical mechanisms described by an analytical model into the standard Deep Neural Networks (DNN) model using a transfer learning technique. To test the robustness of the proposed DTL model, the influence of the number of observation points at different locations, streambed heterogeneity (𝜎²_lnK =0, 0.2, 0.5, and 1.0), and observation noise levels (𝜎_{𝑁𝑜𝑖𝑠𝑒}=0.025, 0.05, 0.075) on the MSE values between the observed and predicted temperature fields. Results indicate that the DTL model significantly outperforms the DNN model in scenarios with scarce training data, and the mean MSE values decrease with increasing observation points for both DTL and DNN models. The mean MSE values for both the DTL and DNN models approach zero as the number of observation points increases to 200, indicating that both DTL and DNN models perform satisfactorily. Furthermore, increasing 𝜎²_lnK and 𝜎_{𝑁𝑜𝑖𝑠𝑒} raises the mean MSE values of the DTL and DNN models, with the DTL model exhibiting greater robustness than the DNN model, highlighting its potential for practical applications in riparian zone management.

Received: 25 Dec 2024 – Discussion started: 16 Jan 2025

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Journal article(s) based on this preprint

17 Oct 2025

Improving heat transfer predictions in heterogeneous riparian zones using transfer learning techniques

Aohan Jin, Wenguang Shi, Jun Du, Renjie Zhou, Hongbin Zhan, Yao Huang, Quanrong Wang, and Xuan Gu

Hydrol. Earth Syst. Sci., 29, 5251–5266, https://doi.org/10.5194/hess-29-5251-2025,https://doi.org/10.5194/hess-29-5251-2025, 2025

Short summary

Aohan Jin, Wenguang Shi, Renjie Zhou, Hongbin Zhan, Quanrong Wang, and Xuan Gu

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-4145', Anonymous Referee #1, 06 Mar 2025
This manuscript proposes a Deep Transfer Learning (DTL) approach to improve the accuracy of spatiotemporal temperature distribution predictions in heterogeneous riparian zones. Using transfer learning, the authors integrate analytical solution outputs for a homogeneous medium into a Deep Neural Network (DNN) and employ a 2D numerical model output for a heterogeneous medium as their synthetic data. They tested their approach by comparing the DTL to a DNN trained solely on synthetic data across various heterogeneous media and noise levels. Their findings indicate that the DTL model outperforms the DNN model in scenarios with limited training data and demonstrates greater robustness to data noise, which may have practical applications in riparian zone management.
The current version of the manuscript requires significant work. Essential information regarding the physical-based models used to train the DTL and DNNs is missing, as well as clarifications on the input and output variables of the machine learning models needed for testing and reproducing the work presented. Additionally, the authors should include the reasoning behind their sampling criteria and how it is linked to the physical process they are modeling, as well as highlight how their novel framework differs or adds from work done by previous authors. With the latter in mind, I cannot accept the manuscript in its current form.
Below, I have listed comments and suggestions, hoping they may help improve the manuscript’s quality.
Specific Comments
The physics-based models need further clarification.
The authors based their analytical and numerical models on previous work performed by Shi et al. (2023) and they present some of the equations and boundary conditions in the manuscript and the supplementary information. However, the manuscript does not clarify the actual domain of the system. Are they using the model's domain as the conceptual model presented in Figure 1? If so, why are the modeling results presented in a square? Is this an inset of the larger domain? If so, where is the inset located for the whole model? If it is not an inset, is the domain different from the one presented by Shi et al. (2023)? If so, why is its extent shorter than that of the original study? A clear description of the conceptual model and its boundary conditions should be included in the main manuscript to aid in the understanding of the physical process.

Additionally, the groundwater flow model and its boundary conditions are not mentioned. Is this the same model as the one used in Shi et al. (2023)? This should be included and clarified in the manuscript for an integral understanding of the process that the data-driven models are trying to reproduce.

Incidentally, part of the work looks into heterogeneity, and the authors present their heterogeneous fields. Nonetheless, there is no mention of which hydraulic conductivity value is used for the homogeneous case. The authors only mention variations in the Darcy’s fluxes (q_x and q_z) in line 167. How are these fluxes calculated? What values are used for head gradients? Are the variations of these Darcy’s fluxes related to boundary conditions or fluxes through the domain? I suggest including the Darcy flux equation and leaving the variations only to hydraulic conductivity to be consistent with the heterogeneous cases.

The authors only present the fields for hydraulic conductivity and absolute errors, and there is no plot of the temperature field they are trying to reproduce. Are these fields different from each other? How does the heterogeneous domain affect the temperature distributions? I suggest adding a figure with the temperature fields for the analytical and the numerical solutions so that the reader can understand how these fields vary throughout the domain and what the data-driven models are missing.

With respect to the machine learning models
The authors mention in line 15 that this work “[proposes] a novel Deep Transfer Learning (DTL) approach […] to improve the accuracy of spatiotemporal temperature distribution predictions.” However, a similar approach has been explored in Zhang et al. (2023) for the prediction of hydraulic heads in heterogeneous aquifers. The authors should clearly specify the improvements or modifications made to the framework compared to Zhang et al. (2023), beyond the difference in application.

In line 222, the authors mention that they restricted the number of epochs in the model training. Is there a reason why these models cannot be trained with different epochs until they reach the same convergence? Also, what about the other hyperparameters of the DNN models (i.e., number of nodes, number of layers, epochs, and activation functions, among others), have the authors considered testing a range of these parameters to get the best set of DNN?

Part of using these data-driven approaches is leveraging the current available data to predict variables that are difficult, expensive, or impractical to measure. With this in mind, the authors should be clear about what variables they are using as input to predict the temperature fields. Are they using the hydraulic heads and temperature of the stream? Are they using variables related to the geology of the site? Or are they using temperature data from previous timesteps? All of this is important because if we were to use these models to predict the temperature in a given field site, we would need to know what variables we should measure to be able to have an accurate prediction.

Furthermore, the authors should link their sampling criteria to the physical process they are trying to reproduce with data-driven approaches. For instance, grabbing more than 50 samples in a 1-meter cross-section with some spaced less than 0.1 meters horizontally is impractical and inefficient. I suggest the authors approach the sampling criteria as they were placed in the field, and are tasked to maximize the location of their thermistors or other measuring devices. This reviewer believes this approach can benefit the scientific community and add value to the manuscript.

Consider including an additional paragraph or sentences that describe other approaches to create physics-informed machine learning models (e.g., Arcomano et al., 2022; M. Raissi et al., 2019; Maziar Raissi & Karniadakis, 2018; Yeung et al., 2022).

I suggest the authors add more information in the discussion section. Where they highlight the importance of their work and how it relates to other approaches. I suggest also highlighting the transferability of this framework to other settings, as well as things that scientists should take into account.

Technical Corrections
Besides the comments described above, I have a few technical recommendations for the manuscript.
The manuscript has multiple sentences that are difficult to read or have grammatical errors. Among them are:
Lines 17-20 are difficult to read and contain variables that are not previously defined

The sentence in lines 22-23 is redundant, so consider removing it.

Grammar in line 89 “Newly proposed demonstrates”

In line 294 should be “centers” instead of “centres”

What do you mean by “it is postulated that the thermal and hydraulic properties of the streambed maintain uniformity”? (Lines 98-99). Are you referring to the fact that these variables remain constant throughout the simulation? Please clarify

It should be “no heat flux boundary” in line 102.

I recommend collapsing equations (1a) through (1c) to a single equation with a subscript i that is later described.

Line 144 states that “The hyperparameters θ_T for the fine-tuning model is acquired through the optimization of the loss function delineated by…” By definition, a hyperparameter cannot be estimated with model training. They are set by the user. I think that you mean “The parameters” instead of “The hyperparameters.”

Some variables, such as q_x and q_z, are not defined in the main manuscript. Since the manuscript should be self-contained, these variables should be specified in the text.

Remember to add the units of the Mean Square Error (MSE) values.

The text in Figures 5, 6, and 10 is difficult to read. Consider increasing the fonts. Also, include the units of the variables plotted.

Consider using the same y-scale for Figures 7, 9, and 11. This would aid in the comparison.

References
Arcomano, T., Szunyogh, I., Wikner, A., Pathak, J., Hunt, B. R., & Ott, E. (2022). A Hybrid Approach to Atmospheric Modeling That Combines Machine Learning With a Physics-Based Numerical Model. Journal of Advances in Modeling Earth Systems, 14(3), e2021MS002712. https://doi.org/10.1029/2021MS002712
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
Raissi, Maziar, & Karniadakis, G. E. (2018). Hidden physics models: Machine learning of nonlinear partial differential equations. Journal of Computational Physics, 357, 125–141. https://doi.org/10.1016/j.jcp.2017.11.039
Shi, W., Zhan, H., Wang, Q., & Xie, X. (2023). A Two-Dimensional Closed-Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones. Water Resources Research, 59(8), e2022WR034059. https://doi.org/10.1029/2022WR034059
Yeung, Y.-H., Barajas-Solano, D. A., & Tartakovsky, A. M. (2022). Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems. Water Resources Research, 58(5), e2021WR031023. https://doi.org/10.1029/2021WR031023
Zhang, J., Liang, X., Zeng, L., Chen, X., Ma, E., Zhou, Y., & Zhang, Y.-K. (2023). Deep transfer learning for groundwater flow in heterogeneous aquifers using a simple analytical model. Journal of Hydrology, 626,130293. https://doi.org/10.1016/j.jhydrol.2023.130293
Citation: https://doi.org/10.5194/egusphere-2024-4145-RC1
- AC1: 'Reply on RC1', quanrong wang, 16 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2024-4145/egusphere-2024-4145-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-4145-AC1
RC2:
'Comment on egusphere-2024-4145', Anonymous Referee #2, 04 May 2025
The manuscript by Jin et al. presents a novel Deep Transfer Learning (DTL) framework for improving the prediction of spatiotemporal temperature fields in heterogeneous riparian zones. The authors leverage analytical solutions in homogeneous domains to pre-train a DNN model, and subsequently fine-tune it for heterogeneous cases, thereby addressing the challenge of limited observational data. The study is well-motivated and addresses an important problem in hydrological modeling. The methodology is clearly described, and the results are well-documented through a series of comprehensive experiments.
I find the manuscript suitable for publication in Hydrology and Earth System Sciences after minor revisions. Below are my specific comments and suggestions for improving the manuscript.

General Comments
Scientific Merit and Novelty

The integration of physical knowledge via analytical solutions into DNNs using transfer learning is innovative and addresses a key limitation of purely data-driven models. The results convincingly demonstrate the improved robustness and performance of the proposed DTL framework, especially in data-scarce and noisy conditions.

Broader Context and Comparison to Existing Approaches

While the manuscript briefly mentions physics-informed neural networks (PINNs), a more direct comparison or a deeper discussion of how DTL differs from or complements PINNs would strengthen the manuscript. This would better situate the DTL approach within the broader landscape of hybrid modeling techniques.

Interpretability and Transferability

The paper focuses on model performance but does not explore the interpretability of the DTL model. A short discussion on whether the transferred physical knowledge can be traced or interpreted in the model outputs would be beneficial. Furthermore, although the authors mention possible extensions to solute transport or other applications, this is not demonstrated or discussed in detail.

Limitations and Domain Geometry

The authors acknowledge the limitation that analytical models assume regular geometries. This is an important point and could be expanded to discuss whether coordinate transformation, domain padding, or hybrid numerical-analytical datasets could mitigate this issue in future work.

Specific Suggestions
Section 2.2: Clarify why the tanh activation function is used rather than alternatives like ReLU. This choice may influence convergence and generalization.

Equation (2): Notation should be consistent with Equation (4). Clarify the definition of n (number of training samples).

Figures:

Consider including results for 200 observation points in the main figures, rather than relegating them to the Supplement, since these are discussed prominently in the text.

Conclusion
This paper presents a valuable contribution to the field of data-augmented hydrologic modeling. The proposed DTL framework offers a practical and effective solution for improving model accuracy under data limitations, with promising applicability beyond heat transport in riparian zones. With minor revisions and clarifications, this work will be a strong addition to the literature and of interest to the readership of HESS.
Citation: https://doi.org/10.5194/egusphere-2024-4145-RC2
- AC2: 'Reply on RC2', quanrong wang, 16 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2024-4145/egusphere-2024-4145-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-4145-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-4145', Anonymous Referee #1, 06 Mar 2025
This manuscript proposes a Deep Transfer Learning (DTL) approach to improve the accuracy of spatiotemporal temperature distribution predictions in heterogeneous riparian zones. Using transfer learning, the authors integrate analytical solution outputs for a homogeneous medium into a Deep Neural Network (DNN) and employ a 2D numerical model output for a heterogeneous medium as their synthetic data. They tested their approach by comparing the DTL to a DNN trained solely on synthetic data across various heterogeneous media and noise levels. Their findings indicate that the DTL model outperforms the DNN model in scenarios with limited training data and demonstrates greater robustness to data noise, which may have practical applications in riparian zone management.
The current version of the manuscript requires significant work. Essential information regarding the physical-based models used to train the DTL and DNNs is missing, as well as clarifications on the input and output variables of the machine learning models needed for testing and reproducing the work presented. Additionally, the authors should include the reasoning behind their sampling criteria and how it is linked to the physical process they are modeling, as well as highlight how their novel framework differs or adds from work done by previous authors. With the latter in mind, I cannot accept the manuscript in its current form.
Below, I have listed comments and suggestions, hoping they may help improve the manuscript’s quality.
Specific Comments
The physics-based models need further clarification.
The authors based their analytical and numerical models on previous work performed by Shi et al. (2023) and they present some of the equations and boundary conditions in the manuscript and the supplementary information. However, the manuscript does not clarify the actual domain of the system. Are they using the model's domain as the conceptual model presented in Figure 1? If so, why are the modeling results presented in a square? Is this an inset of the larger domain? If so, where is the inset located for the whole model? If it is not an inset, is the domain different from the one presented by Shi et al. (2023)? If so, why is its extent shorter than that of the original study? A clear description of the conceptual model and its boundary conditions should be included in the main manuscript to aid in the understanding of the physical process.

Additionally, the groundwater flow model and its boundary conditions are not mentioned. Is this the same model as the one used in Shi et al. (2023)? This should be included and clarified in the manuscript for an integral understanding of the process that the data-driven models are trying to reproduce.

Incidentally, part of the work looks into heterogeneity, and the authors present their heterogeneous fields. Nonetheless, there is no mention of which hydraulic conductivity value is used for the homogeneous case. The authors only mention variations in the Darcy’s fluxes (q_x and q_z) in line 167. How are these fluxes calculated? What values are used for head gradients? Are the variations of these Darcy’s fluxes related to boundary conditions or fluxes through the domain? I suggest including the Darcy flux equation and leaving the variations only to hydraulic conductivity to be consistent with the heterogeneous cases.

The authors only present the fields for hydraulic conductivity and absolute errors, and there is no plot of the temperature field they are trying to reproduce. Are these fields different from each other? How does the heterogeneous domain affect the temperature distributions? I suggest adding a figure with the temperature fields for the analytical and the numerical solutions so that the reader can understand how these fields vary throughout the domain and what the data-driven models are missing.

With respect to the machine learning models
The authors mention in line 15 that this work “[proposes] a novel Deep Transfer Learning (DTL) approach […] to improve the accuracy of spatiotemporal temperature distribution predictions.” However, a similar approach has been explored in Zhang et al. (2023) for the prediction of hydraulic heads in heterogeneous aquifers. The authors should clearly specify the improvements or modifications made to the framework compared to Zhang et al. (2023), beyond the difference in application.

In line 222, the authors mention that they restricted the number of epochs in the model training. Is there a reason why these models cannot be trained with different epochs until they reach the same convergence? Also, what about the other hyperparameters of the DNN models (i.e., number of nodes, number of layers, epochs, and activation functions, among others), have the authors considered testing a range of these parameters to get the best set of DNN?

Part of using these data-driven approaches is leveraging the current available data to predict variables that are difficult, expensive, or impractical to measure. With this in mind, the authors should be clear about what variables they are using as input to predict the temperature fields. Are they using the hydraulic heads and temperature of the stream? Are they using variables related to the geology of the site? Or are they using temperature data from previous timesteps? All of this is important because if we were to use these models to predict the temperature in a given field site, we would need to know what variables we should measure to be able to have an accurate prediction.

Furthermore, the authors should link their sampling criteria to the physical process they are trying to reproduce with data-driven approaches. For instance, grabbing more than 50 samples in a 1-meter cross-section with some spaced less than 0.1 meters horizontally is impractical and inefficient. I suggest the authors approach the sampling criteria as they were placed in the field, and are tasked to maximize the location of their thermistors or other measuring devices. This reviewer believes this approach can benefit the scientific community and add value to the manuscript.

Consider including an additional paragraph or sentences that describe other approaches to create physics-informed machine learning models (e.g., Arcomano et al., 2022; M. Raissi et al., 2019; Maziar Raissi & Karniadakis, 2018; Yeung et al., 2022).

I suggest the authors add more information in the discussion section. Where they highlight the importance of their work and how it relates to other approaches. I suggest also highlighting the transferability of this framework to other settings, as well as things that scientists should take into account.

Technical Corrections
Besides the comments described above, I have a few technical recommendations for the manuscript.
The manuscript has multiple sentences that are difficult to read or have grammatical errors. Among them are:
Lines 17-20 are difficult to read and contain variables that are not previously defined

The sentence in lines 22-23 is redundant, so consider removing it.

Grammar in line 89 “Newly proposed demonstrates”

In line 294 should be “centers” instead of “centres”

What do you mean by “it is postulated that the thermal and hydraulic properties of the streambed maintain uniformity”? (Lines 98-99). Are you referring to the fact that these variables remain constant throughout the simulation? Please clarify

It should be “no heat flux boundary” in line 102.

I recommend collapsing equations (1a) through (1c) to a single equation with a subscript i that is later described.

Line 144 states that “The hyperparameters θ_T for the fine-tuning model is acquired through the optimization of the loss function delineated by…” By definition, a hyperparameter cannot be estimated with model training. They are set by the user. I think that you mean “The parameters” instead of “The hyperparameters.”

Some variables, such as q_x and q_z, are not defined in the main manuscript. Since the manuscript should be self-contained, these variables should be specified in the text.

Remember to add the units of the Mean Square Error (MSE) values.

The text in Figures 5, 6, and 10 is difficult to read. Consider increasing the fonts. Also, include the units of the variables plotted.

Consider using the same y-scale for Figures 7, 9, and 11. This would aid in the comparison.

References
Arcomano, T., Szunyogh, I., Wikner, A., Pathak, J., Hunt, B. R., & Ott, E. (2022). A Hybrid Approach to Atmospheric Modeling That Combines Machine Learning With a Physics-Based Numerical Model. Journal of Advances in Modeling Earth Systems, 14(3), e2021MS002712. https://doi.org/10.1029/2021MS002712
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
Raissi, Maziar, & Karniadakis, G. E. (2018). Hidden physics models: Machine learning of nonlinear partial differential equations. Journal of Computational Physics, 357, 125–141. https://doi.org/10.1016/j.jcp.2017.11.039
Shi, W., Zhan, H., Wang, Q., & Xie, X. (2023). A Two-Dimensional Closed-Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones. Water Resources Research, 59(8), e2022WR034059. https://doi.org/10.1029/2022WR034059
Yeung, Y.-H., Barajas-Solano, D. A., & Tartakovsky, A. M. (2022). Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems. Water Resources Research, 58(5), e2021WR031023. https://doi.org/10.1029/2021WR031023
Zhang, J., Liang, X., Zeng, L., Chen, X., Ma, E., Zhou, Y., & Zhang, Y.-K. (2023). Deep transfer learning for groundwater flow in heterogeneous aquifers using a simple analytical model. Journal of Hydrology, 626,130293. https://doi.org/10.1016/j.jhydrol.2023.130293
Citation: https://doi.org/10.5194/egusphere-2024-4145-RC1
- AC1: 'Reply on RC1', quanrong wang, 16 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2024-4145/egusphere-2024-4145-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-4145-AC1
RC2:
'Comment on egusphere-2024-4145', Anonymous Referee #2, 04 May 2025
The manuscript by Jin et al. presents a novel Deep Transfer Learning (DTL) framework for improving the prediction of spatiotemporal temperature fields in heterogeneous riparian zones. The authors leverage analytical solutions in homogeneous domains to pre-train a DNN model, and subsequently fine-tune it for heterogeneous cases, thereby addressing the challenge of limited observational data. The study is well-motivated and addresses an important problem in hydrological modeling. The methodology is clearly described, and the results are well-documented through a series of comprehensive experiments.
I find the manuscript suitable for publication in Hydrology and Earth System Sciences after minor revisions. Below are my specific comments and suggestions for improving the manuscript.

General Comments
Scientific Merit and Novelty

The integration of physical knowledge via analytical solutions into DNNs using transfer learning is innovative and addresses a key limitation of purely data-driven models. The results convincingly demonstrate the improved robustness and performance of the proposed DTL framework, especially in data-scarce and noisy conditions.

Broader Context and Comparison to Existing Approaches

While the manuscript briefly mentions physics-informed neural networks (PINNs), a more direct comparison or a deeper discussion of how DTL differs from or complements PINNs would strengthen the manuscript. This would better situate the DTL approach within the broader landscape of hybrid modeling techniques.

Interpretability and Transferability

The paper focuses on model performance but does not explore the interpretability of the DTL model. A short discussion on whether the transferred physical knowledge can be traced or interpreted in the model outputs would be beneficial. Furthermore, although the authors mention possible extensions to solute transport or other applications, this is not demonstrated or discussed in detail.

Limitations and Domain Geometry

The authors acknowledge the limitation that analytical models assume regular geometries. This is an important point and could be expanded to discuss whether coordinate transformation, domain padding, or hybrid numerical-analytical datasets could mitigate this issue in future work.

Specific Suggestions
Section 2.2: Clarify why the tanh activation function is used rather than alternatives like ReLU. This choice may influence convergence and generalization.

Equation (2): Notation should be consistent with Equation (4). Clarify the definition of n (number of training samples).

Figures:

Consider including results for 200 observation points in the main figures, rather than relegating them to the Supplement, since these are discussed prominently in the text.

Conclusion
This paper presents a valuable contribution to the field of data-augmented hydrologic modeling. The proposed DTL framework offers a practical and effective solution for improving model accuracy under data limitations, with promising applicability beyond heat transport in riparian zones. With minor revisions and clarifications, this work will be a strong addition to the literature and of interest to the readership of HESS.
Citation: https://doi.org/10.5194/egusphere-2024-4145-RC2
- AC2: 'Reply on RC2', quanrong wang, 16 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2024-4145/egusphere-2024-4145-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-4145-AC2

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) (03 Jun 2025) by Heng Dai

AR by quanrong wang on behalf of the Authors (04 Jun 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (11 Jun 2025) by Heng Dai

RR by Anonymous Referee #3 (04 Jul 2025)

Suggestions for revision or reasons for rejection

General comments:
Thank you for the opportunity to review this thoroughly revised manuscript. The authors present a novel hybrid framework that combines simple analytical solutions for homogeneous systems with transfer learning techniques to address heterogeneous heat transfer problems in riparian zones. The topic is timely and of broad interest, and the methodology, which leverages well understood analytical models to inform data driven learning, represents a creative and potentially widely applicable approach. The revised manuscript is significantly improved in organization, clarity, and technical depth compared to the previous version, and I recommend acceptance after a few clarifications and minor edits.

First, the rationale for using both analytical and numerical models to generate training data and benchmarks would benefit from a more explicit explanation. Although the hybrid strategy intuitively combines the interpretability and low cost evaluation of analytical solutions with the flexibility of numerical simulations, the manuscript would be stronger if it contrasted this approach against purely numerical or purely statistical alternatives. For example, how does the introduction of analytical physics reduce the required volume of high fidelity simulations and how does it improve generalization to untested heterogeneous conditions? A brief discussion of these trade offs and any computational savings or improved convergence properties observed would help readers appreciate the advantages of the proposed framework.

Second, the choice of Shi et al. (2023) as the benchmark analytical model deserves further justification. The literature contains numerous analytical expressions for subsurface heat transport in riparian contexts; explaining why this formulation was selected (for example, because of its balance of simplicity and fidelity, its treatment of boundary conditions, or its previous validation against field data) would clarify its role in the study. If other models were considered but found less suitable, a sentence or two outlining those comparisons would reinforce confidence in the benchmark’s relevance.

Third, the description of the transfer learning workflow indicates that some network layers were frozen while others remained trainable, but the manuscript does not specify which layers were selected nor the criteria guiding these decisions. Since layer freezing can critically affect the retention of low level physical features versus high level adaptation to heterogeneous data, please detail which layers were frozen, which were fine tuned, and why. Were early convolutional filters preserved to encode general diffusion patterns while later dense layers were adapted to capture heterogeneity? Clarifying this architecture will help readers reproduce the experiments and understand how transfer learning choices influence model performance.

Fourth, the results demonstrate that transfer learning informed by analytical solutions performs remarkably well, even in heterogeneous systems that deviate from the homogeneous assumptions underlying the analytical form. It would be valuable to discuss potential reasons for this robustness: for instance, do the analytical solutions capture the dominant modes of heat propagation that persist under moderate heterogeneity? Is there a particular physical principle or scaling law embedded in the base model that remains valid across a range of conductivity contrasts? A short analysis of what features the network retains from the analytical initialization and how those guide learning in more complex settings would deepen insight into why the approach succeeds.

Minor issues:
1. In Lines 65-73 “DL” should be “deep learning”
2. In Line 87, “transfer learning” should be “transfer learning techniques”.
3. In Line 91, “power” should be “capability”.
4. In Line 106, L=0.32m is used in Section 2.1 or in all cases?
5. In Lines 138, 151 and 152, “physical information” should be “physical principles”.
6. In Lines 207-208, add references to support this point.

Hide

RR by Anonymous Referee #1 (14 Jul 2025)

Suggestions for revision or reasons for rejection

Thank you for submitting your manuscript addressing the comments previously made. This new version of the manuscript is in better shape. I only have a few comments and one technical correction that are presented below.

Specific Comments
1. To this reviewer, it is still not clear how the authors find the prescribed values for Darcy’s fluxes (qx and qz) in the analytical solution. The authors argue in their response (lines 91 to 96 in the response document) that the groundwater flow and heat transfer models are coupled through qx and qz, which they prescribed in the analytical solution. The numerical model has two boundary conditions where a constant head is set (Figure S2). Did the authors calculate the Darcy’s fluxes using the difference between these heads throughout the domain and the given hydraulic conductivity, or did they use the Darcy’s flux simulated results for a given cell within the domain? I recommend providing further clarification on this.

2. The main objective of the manuscript is to propose a novel physics-informed deep transfer learning (PDTL) approach to improve the accuracy of spatiotemporal temperature distribution predictions. The manuscript, as it is, works towards that goal and presents a promising methodology. My only concern is the use of the location in the domain as the only input variable for the machine learning model. This limits the transferability of the model to other potential locations and disconnects the association of the model to measurable physical variables, such as the temperature at the surface and the fluxes of water from the river to the underlying aquifer. Some of these limitations are already presented in the discussion, but I encourage the authors also to discuss the limitations of their selected input variables.

Technical Correction
1. The text in the axes of Figures 5, 6, and 9 is difficult to read. Consider increasing the fonts. Also, include the units of the variables plotted.

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ED: Publish subject to minor revisions (review by editor) (16 Jul 2025) by Heng Dai

AR by quanrong wang on behalf of the Authors (19 Jul 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (27 Jul 2025) by Heng Dai

AR by quanrong wang on behalf of the Authors (28 Jul 2025) Manuscript

Journal article(s) based on this preprint

17 Oct 2025

Improving heat transfer predictions in heterogeneous riparian zones using transfer learning techniques

Aohan Jin, Wenguang Shi, Jun Du, Renjie Zhou, Hongbin Zhan, Yao Huang, Quanrong Wang, and Xuan Gu

Hydrol. Earth Syst. Sci., 29, 5251–5266, https://doi.org/10.5194/hess-29-5251-2025,https://doi.org/10.5194/hess-29-5251-2025, 2025

Short summary

Aohan Jin, Wenguang Shi, Renjie Zhou, Hongbin Zhan, Quanrong Wang, and Xuan Gu

Supplement

https://doi.org/10.5194/egusphere-2024-4145-supplement

Model code and software

Python codes of the DTL and DNN models Aohan Jin https://github.com/Ahjin-CUG/TL

Aohan Jin, Wenguang Shi, Renjie Zhou, Hongbin Zhan, Quanrong Wang, and Xuan Gu

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

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Short summary

This study developed a novel deep transfer learning (DTL) approach, which integrates the physical mechanisms from an analytical model using a transfer learning technique. Results indicate that the DTL model maintains satisfactory performance even in heterogeneous conditions, with uncertainties in observations and sparse training data compared to the DNN model.


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