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

1. The physics-based models need further clarification.
   1. 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.
   2. 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.
   3. 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.
   4. 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.

1. With respect to the machine learning models
   1. 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.
   2. 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?
   3. 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.
   4. 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.
2. 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).
3. 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.

1. The manuscript has multiple sentences that are difficult to read or have grammatical errors. Among them are:
   1. Lines 17-20 are difficult to read and contain variables that are not previously defined
   2. The sentence in lines 22-23 is redundant, so consider removing it.
   3. Grammar in line 89 “Newly proposed demonstrates”
   4. In line 294 should be “centers” instead of “centres”
2. 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
3. It should be “no heat flux boundary” in line 102.
4. I recommend collapsing equations (1a) through (1c) to a single equation with a subscript i that is later described.
5. 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.”
6. 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.
7. Remember to add the units of the Mean Square Error (MSE) values.
8. The text in Figures 5, 6, and 10 is difficult to read. Consider increasing the fonts. Also, include the units of the variables plotted.
9. 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

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

1. 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.
2. 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.
3. 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.
4. 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.