the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Jan 2025
Two-dimensional Differential-form of Distributed Xinanjiang Model
Abstract. The distributed hydrologic models (DHMs) evolved from lumped hydrologic models, inheriting their modeling philosophy along with persistent numerical error issues. Historically, these models tend to use established one-dimensional (1D) methods for slope concentration, which often struggle to effectively represent complex terrains. In this study, we formulated a purely differential-form of mathematical equations for the distributed Xinanjiang model, and developed a fully-coupled numerical solution framework. We also introduced two-dimensional (2D) surface slope concentration equations, and derived 2D linear reservoir equations for subsurface slope concentration to replace their 1D counterparts. This culminated in the development of a Two-dimensional Differential-form of Distributed Xinanjiang (TDD-XAJ) model. Two numerical experiments and its application in a humid watershed were conducted to demonstrate the model. Our result suggested that: (a) numerical errors in the existing distributed Xinanjiang model were significant and may be exacerbated by a potential terrain amplification effect, which could be effectively controlled by the fully-coupled numerical framework within the TDD-XAJ model; (b) the 2D slope concentration methods showed enhanced terrain capture ability, and eliminated the reliance on flow direction algorithms used in 1D methods; and (c) the TDD-XAJ model exhibited improved simulation capabilities compared to the existing model when applied in Tunxi watershed, particularly for flood volume. This study emphasizes the need to revisit DHMs which stemming from lumped hydrological models, focusing on model equations and numerical implementations, which could enhance model performance and benefit the hydrological modeling community.
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Status: open (until 19 Mar 2025)
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RC1: 'Comment on hess-2024-377', Dengfeng Liu, 11 Feb 2025
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Comment
This work is a typical representation of the forward development in the current hydrological modeling field. By leveraging existing advanced numerical techniques, it reconstructs the traditional empirical, conceptual, and lumped hydrological model, transforming it into modern distributed hydrological model that can represent spatial heterogeneity and are based on complete systems of differential equations. Overall, I think this work is of great practical significance. In addition, the author’s writing is also quite mature and concise. Nevertheless, I still believe that this work should undergo major revision before it is suitable for publication, as the presentation of the results section remains insufficient for a mature study. My concerns are as follows:
1. I have reviewed the model code provided by the author and noticed that it is relatively concise pure Python code and dose not include many additional dependencies. I believe this is a strong advantage, as it suggests broader suage scenarios and greater potential for expansion. However, as an interpreted language, Python has a typical limitation in comparison to compiled languages like C, namely its lower efficiency. As a potential application for large domain modeling, I am concerned about the computational efficiency of the TDD-XAJ model. The author should at least provide a reference for efficiency, and clarify whether transitioning from a 1D modeling framework to a 2D framework would result in a significant decrease in computational efficiency. I believe the author should add a section to address these issues.
In addition, please include a description of the programming environment of the model, as well as the dependencies used, to help users clearly understand the usage scenarios.
2. I have some confusion regarding the channel unit modeling in Figure 4. In the previous sections (Section 2.1 and Figure 1), the channel units are explicitly defined as segments, with their lengths clearly specified in three ways. In these cases, the width of the channel units is significantly smaller than the grid size so that the rainfall can be neglected. However, in this test case (Figure. 4), the grid size (5m x 5m) is significantly larger than the channel width (20m). Does this mean that the channel units need to encompass multiple grids? I would ask the author to provide a corresponding diagram to clarify how spatial discretization and channel unit modeling are handled in the test cases.
A similar issue also applies to real basin modeling. Could you provide a diagram to illustrate how spatial discretization is carried out in the Tunxi watershed, including the definition of grid units and channel units?
3. Since the author emphasizes the advantages of the 2D method in capturing microtopography and presents it as a typical case of distributed modeling, the author should at least provide some results for spatial simulations. This would better illustrate the model's advantages and provide supporting evidence for the attribution.
Specifically, the author could provide some degree of spatial validation (for example), which is highly valued in the hydrological modeling community. If this proves challenging (due to data limitations or other reasons), an alternative could be to include a test case with more varied slopes (such as two or three different slope changes in the y-direction). In this more complex test case, testing the consistency between slope variations and simulation results would better highlight the advantages of 2D modeling.
4. The differences between Figure. 7b and Figure. 7c suggest that 1D modeling overlooks the interflow component in the y-direction, although this is not particularly clear. Could you include one or two time profile plots corresponding to different stages in Figure. 6g to further support this conclusion?
Below are some of my suggestions regarding the writing or presentation (although the paper is already well-written):
Specific issues
- Line 13-14: Please emphasize both the 2D diffusion wave and the 2D linear reservoir method in this sentence to enhance consistency with the paper.
- Line 58-59: Beven's alternative blueprint encompasses several key concepts, including Bayesian philosophy, model equivalence, and an emphasis on uniqueness. It would be beneficial to clarify which of these are closely related to the development of XAJ, although this may be considered a matter of fine-tuning.
- Line 342: Please clarify the model's inputs and outputs, and whether they differ from the original XAJ model.
- Line 359: “The synthetic V-catchment, first proposed by (Overton and Brakensiek, 1970)”, This appears to be an incorrect citation format.
- 6: The lower-left corner should be "subsurface" rather than "surface."
- 8: Highlight the inflection.
Citation: https://doi.org/10.5194/hess-2024-377-RC1 -
CC2: 'Reply on RC1', Zhongmin Liang, 25 Feb 2025
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Dear reviewer,
Thank you very much for your constructive comments on our manuscript. We have provided a point-by-point response to your comments in the attached document. We hope that our response effectively addresses your concerns.
Best regards,
Zhongmin Liang
Corresponding Author
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CC1: 'Comment on hess-2024-377', Ting Zhang, 15 Feb 2025
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In the study, a two-dimensional differential-form of distributed Xinanjiang Model was developed. This work is interesting and valuable. Through applying the proposed model, a good performance is achieved. But there are still some points that should be explained or revised before publication.
(1) There are many parameters in the proposed TDD-XAJ model, the authors should state the method for parameter calibration. If the calibration is done as stated in Line 432 (calibrated manually), a lot of work should done.
(2) Line 423, Daily scale hydrological data were used in the study. I think the constructed model can be used for flood events simulation. Why don’t you attempt to use sub-daily hydrological data?
(3) Line 456, the spatial distribution of the Oi has been zoomed into the upper left corner. I suggest the authors provide the spatial distribution of the entire area, and then zoom the upper left corner.
(4) In Table 2, average MAE statistics of model fluxes for a total of 500 parameter sets are provided using loosely coupled model. But the reference is the fully-coupled model. This cannot illustrate the better performance of fully-coupled model.
(5) Line 505, the 2 values cannot be found in Table 2.
(6) The simulation in the Tunxi watershed was only compared with 1 previous study in the same watershed. Is it possible to compare the results with previous research using other lumped or distributed models in the same or adjacent watershed?
Citation: https://doi.org/10.5194/hess-2024-377-CC1 -
CC3: 'Reply on CC1', Zhongmin Liang, 06 Mar 2025
reply
Dear reviewer,
Thank you very much for your valuable comments on our manuscript. We have provided a point-by-point response to your comments in the attached document. We hope that our response effectively addresses your concerns.
Best regards,
Zhongmin Liang
Corresponding Author
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CC3: 'Reply on CC1', Zhongmin Liang, 06 Mar 2025
reply
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RC2: 'Comment on hess-2024-377', Anonymous Referee #2, 26 Feb 2025
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This manuscript not only summarizes the progress achieved during past decades but also advances the field by establishing a complete system of differential equations for the distributed XAJ model, along with its numerical implementation. The manuscript provides a thorough analysis of both one-dimensional and two-dimensional concentration methods while addressing numerical error issues. The manuscript is well-written with promising application prospects. To strengthen the manuscript, I would like to propose several comments in the order of line numbers:
Line 55: It is more appropriate to describe this as “the widely-used three-water-sources lumped XAJ model.”
Line 56-66: While I agree the third phase highlighted the development of the distributed XAJ model, it is important to note that the original lumped XAJ model has continued to evolve in parallel. The authors should briefly acknowledge this progression.
Line 61: I believe the term “concentration method” is more appropriate here to maintain terminology consistency throughout the manuscript.
Line 126: “Deeper” in Figure 1 should be corrected into “Deep”, as referenced in Section 2.2.1. Besides, the slope-channel coupling diagram in this figure should be described in the text for clarity.
Line 145: The term “slope” is recommended instead of “hillslope”.
Line 153: Given the number of equations and variables, it is suggested to include a nomenclature section.
Line 343: The determination methods of 15 model parameters listed in the Table 1 requires detailed explanation. In addition, it is also necessary to explain the differences in model parameter from the original XAJ model.
Line 439: The equation of FVRE should be provided. Similarly, it is also suggested to provide the formulas of three channel cross-sectional hydraulic elements mentioned in Line 282.
Line 452: In the slope concentration methods comparison experiment, the authors systematically compared the 1D and 2D forms of the diffusion wave and linear reservoir methods based on idealized test cases. For the diffusion wave method, significant differences were observed between the 1D and 2D form, both in terms of hydrographs and surface storage. However, for the linear reservoir method, while the differences in hydrographs were noticeable (Figure 6g and 6h), the contrast in storage was less evident (Figure 7b and 7d). The authors should improve the visualization approach for Figure 7 such as by changing color schemes to make the comparison more clear.
Line 547-565: The authors analyzed the model's performance by applying it to the Tunxi watershed and examining the flow hydrograph at the outlet station, and the overall simulation results were satisfactory. However, as a distributed hydrological model, the authors should provide more details regarding the spatial simulation. Furthermore, it is suggested that the authors could include comparative results from stations within the watershed, if possible, as this would provide a more comprehensive evaluation of the performance of the TDD-XAJ model.
Line 591-595: In the final paragraph of the conclusion, the authors summarize the limitations of this study. The manuscript encompasses extensive research efforts. I understand that the journey from proposing a model to its refinement and maturity is a lengthy process, and this manuscript has done an excellent job methodologically, providing a solid foundation for future application and research. I recommend relocating this paragraph to the discussion part, where the potential application scenarios and future research directions of the model can be further explored.
Citation: https://doi.org/10.5194/hess-2024-377-RC2 -
CC4: 'Reply on RC2', Zhongmin Liang, 06 Mar 2025
reply
Dear reviewer,
Thank you very much for your constructive comments on our manuscript. We have provided a point-by-point response to your comments in the attached document. We hope that our response effectively addresses your concerns.
Best regards,
Zhongmin Liang
Corresponding Author
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CC4: 'Reply on RC2', Zhongmin Liang, 06 Mar 2025
reply
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