A hybrid model for streamflow prediction addressing spatial connectivity and non-stationary dynamics with adaptive graph learning and multiscale decomposition

Nan, Yueming; Tao, Lizhi; Yang, Dong; Zou, Haibo; He, Yufeng; Cui, Zhichao; Luo, Yuanbo

doi:10.5194/egusphere-2025-4171

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https://doi.org/10.5194/egusphere-2025-4171

Preprints

04 Sep 2025

| 04 Sep 2025

A hybrid model for streamflow prediction addressing spatial connectivity and non-stationary dynamics with adaptive graph learning and multiscale decomposition

Yueming Nan, Lizhi Tao, Dong Yang, Haibo Zou, Yufeng He, Zhichao Cui, and Yuanbo Luo

Abstract. Accurate streamflow forecasting remains a challenge due to the pronounced nonlinearity and multiscale variability inherent in hydrological processes. In this paper, a hybrid logarithmically transformed complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-based the spatial graph gated recurrent unit with adaptive graph structure (LCEEMDAN-ASGGRU) model is proposed to improve streamflow forecasting. The hybrid model is validated by forecasting daily streamflow at 14 stations in the Poyang Lake basin, a region characterized by complex river-lake interactions and significant spatial variability in streamflow magnitudes among stations. Results demonstrate that the LCEEMDAN-ASGGRU model shows superior predictive accuracy compared to benchmark models, achieving a mean Nash–Sutcliffe efficiency coefficient of 0.888 and mean root mean squared error of 264. The adaptive graph structure is spatially interpretable, closely aligning with known hydrological flow paths, while simultaneously capturing temporal similarity patterns among stations. In addition, a hidden Markov model with Gaussian Mixture Regression is used to quantify predictive uncertainty. Compared with other models, LCEEMDAN‑ASGGRU yields the most reliable forecasts. This study demonstrates the effectiveness of coupling logarithmic transformation, CEEMDAN decomposition, and adaptive graph learning with graph neural networks, providing a novel integrated approach for improving streamflow forecasting accuracy under complex hydrological conditions.

Received: 26 Aug 2025 – Discussion started: 04 Sep 2025

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Yueming Nan, Lizhi Tao, Dong Yang, Haibo Zou, Yufeng He, Zhichao Cui, and Yuanbo Luo

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-4171', Anonymous Referee #1, 28 Oct 2025
This study proposes a hybrid model (LCEEMDAN-ASGGRU) integrating logarithmic transformation, CEEMDAN decomposition, and adaptive graph neural network for streamflow forecasting. The research topic holds practical application value, with systematic empirical studies conducted in the Poyang Lake Basin. However, the paper has several areas requiring improvement in terms of innovation, experimental design, and technical depth. Major revisions are recommended before considering publication.
My comments are provided as follows:
Major Comments
The combination of CEEMDAN with deep learning has been explored in recent literature (e.g., Xu et al., 2024). Furthermore, logarithmic transformation represents a standard preprocessing technique that cannot be considered a primary contribution. The authors should clearly articulate what distinguishes their approach from existing methods and explicitly states the novel aspects of the proposed framework.

(Line 244) “Each variable (streamflow, precipitation, and temperature) at each station was decomposed into eight IMFs and one residual component.” The manuscript states that each variable is decomposed into eight IMFs plus one residual component without providing theoretical or empirical justification. This parameter selection requires thorough discussion including sensitivity analysis of IMF numbers, and comparison with alternative decomposition levels.

In terms of the model design, LCEEMDAN-ASGGRU feeds nine decomposed components into ASGGRU individually to construct nine sub-models, with the final prediction result derived as the average of these sub-models. This design appears to overlook the interactivity among the decomposed components, rendering the approach more akin to an ensemble model rather than a truly integrated hybrid framework. It is therefore requested that the authors explain the rationale behind treating the nine sub-models as independent entities instead of exploring the interactive fusion of their training features. Why was the potential for synergistic information exchange between decomposed components not considered in the model architecture?

Minor Issues
(Line 22) The phrase “mean root mean squared error of 264” lacks units, which is essential for RMSE (a dimensional metric). Please thoroughly review the entire manuscript and correct the notation for all dimensional units to ensure clarity and rigor.

(Figure 1) Elevation values in the figure require associated units. Additionally, the manuscript mentions five major rivers (Ganjiang, Fuhe, Raohe, Xinjiang, and Xiushui) as key tributaries of the Poyang Lake Basin, but these rivers are not explicitly displayed in Figure 1. Given the statement that “Figure 1 shows the spatial distribution of selected stations, covering the five major river systems that drain into the Poyang Lake,” the five corresponding sub-basins should be clearly labeled in the figure to align with the textual description.

(Figure 3) (Figure 3) The model framework diagram necessitates optimization for clarity: (1) The meaning of “T1-T4383” following normalization is not clarified, please add explicit annotations to define these variables; (2) Relocating this framework diagram to Section 3.1 (Methods) would better facilitate readers’ understanding of the model structure prior to discussing results; (3) The arrow placement between the 4th, 5th, and 6th sub-diagrams is ambiguous and fails to illustrate the data transfer and computational flow from the upper to lower layers of the model; (4) The boxes in the last two sub-diagrams are incomplete, and the label “LCEEMDAN-ASGGRU” is misleading, which should refer to the prediction output rather than the model name.

(Sections 4.1–4.2) The content in these sections focuses on experimental design and comparative model settings, which is misclassified under the Results section. It is recommended to create a dedicated chapter (e.g., “Experimental Setup” or “Comparative Models”) following the Methods section to house this material. Furthermore, the abbreviations DTWSGGRU and FDSGGRU are used without prior definition.

(Section 4.5) The authors should explicitly justify the selection of stations S4 and S5 for detailed analysis, i.e., clarify their representativeness. Additionally, Figure 9 suffers from insufficient resolution, making its core message unintelligible.

(Line 433) “In particular, connections such as S3→S10, S4→S14, S7→S11, and S13→S7 reflect physically consistent upstream–downstream dependencies that are embedded in the true hydrological topology.” However, the figure also shows S10→S3. Therefore, it is necessary to provide a detailed explanation of the adjacency matrix, clarifying that it encodes not only hydrological upstream–downstream relationships but also spatial meteorological correlations (attributed to the inclusion of precipitation and temperature data) to resolve this apparent contradiction.

The terms “streamflow” and “runoff” are mixed throughout the manuscript.

The standard deviations of the 10 repeated experiments should be reported.
Citation: https://doi.org/10.5194/egusphere-2025-4171-RC1
- AC1:
  'Reply on RC1', Lizhi Tao, 12 Nov 2025
  Dear Anonymous Referee,
  We sincerely thank the reviewers for their constructive and insightful comments. Your feedback has substantially improved the quality, clarity, and organization of our work. The following is our brief response and all revisions will be fully reflected in the resubmitted manuscript.
  Comments from Reviewer #1:
  This study proposes a hybrid model (LCEEMDAN-ASGGRU) integrating logarithmic transformation, CEEMDAN decomposition, and adaptive graph neural network for streamflow forecasting. The research topic holds practical application value, with systematic empirical studies conducted in the Poyang Lake Basin. However, the paper has several areas requiring improvement in terms of innovation, experimental design, and technical depth. Major revisions are recommended before considering publication.
  Reply:
  We thank you for the thoughtful and constructive feedback. Below, we provide responses to each comment, along with explanations of how the suggested changes will be incorporated into the revised manuscript.
  My comments are provided as follows:
  Major Comments
  The combination of CEEMDAN with deep learning has been explored in recent literature (e.g., Xu et al., 2024). Furthermore, logarithmic transformation represents a standard preprocessing technique that cannot be considered a primary contribution. The authors should clearly articulate what distinguishes their approach from existing methods and explicitly states the novel aspects of the proposed framework.
  
  Reply:
  Thanks for your comment. We agree that the combination of CEEMDAN with deep learning has been explored in recent literature. Existing work typically combines CEEMDAN with classic deep learning models, such as LSTM, GRU, and CNN, and does not incorporate the spatial dependence between hydrological stations into the model (Ghanbari-Adivi and Ehteram, 2025; Li et al., 2023).
  The novelty of our work lies in the integration of CEEMDAN decomposition with a graph-based neural network, which explicitly captures spatial dependencies across multiple hydrological stations at different frequencies. By coupling CEEMDAN's multi-scale temporal decomposition with the spatial graph gated recurrent unit, our approach simultaneously captures both the intrinsic temporal characteristics of streamflow at different frequencies and their spatial propagation patterns across the watershed network. We will make revisions to the manuscript, treating the logarithmic transformation as a standard preprocessing technique rather than considering it as a major contribution. The relevant statements will be provide in the revised manuscript.
  [1] Ghanbari-Adivi, E., Ehteram, M., 2025. CEEMDAN-BILSTM-ANN and SVM models: two robust predictive models for predicting river flow. Water Resour. Manage. 39, 3235–3271. https://doi.org/10.1007/s11269-025-04105-w
  [2] Li, H., Zhang, X., Sun, S., Wen, Y., Yin, Q., 2023. Daily flow prediction of the huayuankou hydrometeorological station based on the coupled CEEMDAN–SE–BiLSTM model. Sci. Rep. 13, 18915(2023). https://doi.org/10.1038/s41598-023-46264-z.
  (Line 244) “Each variable (streamflow, precipitation, and temperature) at each station was decomposed into eight IMFs and one residual component.” The manuscript states that each variable is decomposed into eight IMFs plus one residual component without providing theoretical or empirical justification. This parameter selection requires thorough discussion including sensitivity analysis of IMF numbers, and comparison with alternative decomposition levels.
  
  Reply:
  Thank you for the suggestion. In our implementation using the PyEMD library's CEEMDAN with its default parameters, the algorithm adaptively determined the number of IMFs, resulting in varying counts across different variables and stations. Specifically, precipitation series decompose into 10 or 11 IMFs, streamflow into 9 or 10, and temperature into 8 or 9. Using these counts directly would make the input channel sizes inconsistent across variables or stations. To align channels, we merge all components slower than IMF8 (i.e., IMFs with indices > 8) into a low-frequency aggregated residual. This preserves exact reconstruction while ensuring a consistent number of channels across variables and stations. We will revise the manuscript to clearly describe this representation.
  We acknowledge your point that this design choice warrants empirical justification. Therefore, we will conduct a sensitivity analysis to compare the model's performance under different decomposition levels (e.g., using 5, 6, and 7 IMFs). This will provide the necessary empirical grounding for our parameter selection.
  In terms of the model design, LCEEMDAN-ASGGRU feeds nine decomposed components into ASGGRU individually to construct nine sub-models, with the final prediction result derived as the average of these sub-models. This design appears to overlook the interactivity among the decomposed components, rendering the approach more akin to an ensemble model rather than a truly integrated hybrid framework. It is therefore requested that the authors explain the rationale behind treating the nine sub-models as independent entities instead of exploring the interactive fusion of their training features. Why was the potential for synergistic information exchange between decomposed components not considered in the model architecture?
  
  Reply:
  Thank you for your thoughtful comment. The final prediction is obtained by summing, not averaging, the outputs of the sub-models. This summation is the inverse operation of the decomposition and is the standard, principled method for reconstructing the original signal from its components, ensuring numerical fidelity.
  Regarding the question of interactivity, we will add an experiment in which each target component is predicted using all components as inputs (i.e., cross-scale features are concatenated) and discuss whether cross-scale fusion improves performance.
  Minor Issues
  (Line 22) The phrase “mean root mean squared error of 264” lacks units, which is essential for RMSE (a dimensional metric). Please thoroughly review the entire manuscript and correct the notation for all dimensional units to ensure clarity and rigor.
  
  Reply:
  Agree. We will revise the manuscript and add the physical unit m³/s for the root mean square error. We will also review the entire manuscript, including the main text, tables, and figures, to ensure consistent unit notation throughout.
  (Figure 1) Elevation values in the figure require associated units. Additionally, the manuscript mentions five major rivers (Ganjiang, Fuhe, Raohe, Xinjiang, and Xiushui) as key tributaries of the Poyang Lake Basin, but these rivers are not explicitly displayed in Figure 1. Given the statement that “Figure 1 shows the spatial distribution of selected stations, covering the five major river systems that drain into the Poyang Lake,” the five corresponding sub-basins should be clearly labeled in the figure to align with the textual description.
  
  Reply:
  Thank you for your suggestions. We have revised Figure 1 as follows: (i) the elevation colour scale now includes units (metres); (ii) the five major tributaries of the Poyang Lake basin (the Ganjiang, Fuhe, Raohe, Xinjiang, and Xiushui) have been clearly labelled and marked.
  (Figure 3) (Figure 3) The model framework diagram necessitates optimization for clarity: (1) The meaning of “T1-T4383” following normalization is not clarified, please add explicit annotations to define these variables; (2) Relocating this framework diagram to Section 3.1 (Methods) would better facilitate readers’ understanding of the model structure prior to discussing results; (3) The arrow placement between the 4th, 5th, and 6th sub-diagrams is ambiguous and fails to illustrate the data transfer and computational flow from the upper to lower layers of the model; (4) The boxes in the last two sub-diagrams are incomplete, and the label “LCEEMDAN-ASGGRU” is misleading, which should refer to the prediction output rather than the model name.
  
  Reply:
  Thank you for the suggestions regarding Figure 3. “T1–T4383” denote time indices. After standardization, the sequence consists of 4383 daily time steps (day 1 to day 4383). We will add an explicit annotation in the figure caption to clarify this, and we will also improve all arrows for readability. In addition, the label in the last sub-diagrams currently shown as “LCEEMDAN-ASGGRU” will be corrected to “Prediction output”.
  Figure 3 presents the entire LCEEMDAN-ASGGRU pipeline and is intentionally placed in Section 3.4 (Proposed LCEEMDAN-ASGGRU model) to facilitate readers’ understanding of the overall model structure before the Results section. Section 3.1 only introduces the CEEMDAN algorithm and is therefore not an appropriate location for the full model diagram.
  (Sections 4.1–4.2) The content in these sections focuses on experimental design and comparative model settings, which is misclassified under the Results section. It is recommended to create a dedicated chapter (e.g., “Experimental Setup” or “Comparative Models”) following the Methods section to house this material. Furthermore, the abbreviations DTWSGGRU and FDSGGRU are used without prior definition.
  
  Reply:
  Agree. We will revise the manuscript organization accordingly. Specifically, the current Sections 4.1 – 4.2 will be moved out of the Results section and placed after the Methods as a standalone section (“Experimental Setup and Baselines”). We will define the abbreviations DTWSGGRU and FDSGGRU.
  (Section 4.5) The authors should explicitly justify the selection of stations S4 and S5 for detailed analysis, i.e., clarify their representativeness. Additionally, Figure 9 suffers from insufficient resolution, making its core message unintelligible.
  
  Reply:
  Thank you for the comment. We selected S4 and S5 because they are representative extremes within our study set of 14 stations. S4 exhibits the lowest streamflow across all sites, whereas S5 exhibits the highest. In addition, S4 and S5 are located at the headwater (most upstream) and terminal (most downstream) positions. This selection helps illustrate the model’s behavior and provides evidence of its reliability at the extreme stations. For Figure 6, we will add a more detailed description and correct the labeling errors. Regarding Figure 9, we will replace it with a high-resolution version.
  (Line 433) “In particular, connections such as S3→S10, S4→S14, S7→S11, and S13→S7 reflect physically consistent upstream–downstream dependencies that are embedded in the true hydrological topology.” However, the figure also shows S10→S3. Therefore, it is necessary to provide a detailed explanation of the adjacency matrix, clarifying that it encodes not only hydrological upstream–downstream relationships but also spatial meteorological correlations (attributed to the inclusion of precipitation and temperature data) to resolve this apparent contradiction.
  
  Reply:
  Thank you for the helpful comment. You are correct, the learned adjacency is not a pure river-routing graph. Because it is learned from streamflow, temperature, and precipitation time series, it encodes not only hydrological upstream–downstream relations but also spatial meteorological correlations. We will clarify this more rigorously in Section 4.4.
  The terms “streamflow” and “runoff” are mixed throughout the manuscript.
  
  Reply:
  Thank you, we will standardize the terminology in the revision.
  The standard deviations of the 10 repeated experiments should be reported.
  
  Reply:
  Thank you, in the revision we will report the standard deviations across the 10 repeated runs for all metrics (NSE, RMSE).
  
  Citation: https://doi.org/10.5194/egusphere-2025-4171-AC1
RC2: 'Comment on egusphere-2025-4171', Anonymous Referee #2, 03 Nov 2025

Overall comment
This paper addresses the problem of daily streamflow forecasting of multi-station by applying CEEMDAN decomposition to extract multiscale dynamic features, and an adaptive graph recurrent network to capture spatiotemporal dependencies. The authors also discuss the advantages of uncertainty-based interpretation. Overall, the manuscript is clearly written and generally well organized. However, the proposed approach mainly combines existing techniques rather than introducing a truly novel methodology. The framework—decomposing the time series, modeling each component separately, and then reconstructing the final output—is quite common in the literature. Moreover, the model appears to focus on only one-step-ahead forecasting, which limits its practical value for real-world hydrological applications. Therefore, I don’t recommend the publication of the manuscript in HESS in its present form.
Specific comments
L120: Figure 1 is not clear, and this issue persists throughout the manuscript. Figures in general need to be improved in clarity and readability.
L202: The abbreviation Aadp is not defined.
L208: The meaning of arrow in the lower right corner of Figure 2 is unclear.
L212: Is SGGRU proposed by the authors’ team, or is it based on Zhao et al. (2020)? Please clarify.
L257: Corresponding to the logarithmic and standardization steps in Step 1 and 3, shouldn’t inverse standardization and inverse log-transformation be applied before combining the final results? (Figure 3 indicates such steps are needed.)
L360: What does the learned graph structure of ASGGRU look like after training? Please provide a visualization. Which also makes me confused in L436.
L421: From Figure 6, the ASGGRU results exhibit notable under- and over-estimations of flood peaks, and perform no better than DTWSGGRU and FDSGGRU. This appears inconsistent with the performance metrics reported in the text. Could the authors provide additional metrics, specifically for high-flow and low-flow conditions, based on Figure 4?
L446: The overlap ratio between the ASG-based graph and the flow-direction-based graph (FD) has been provided. Accordingly, the overlap ratio between the DTW-based graph (DTW) and the FD should be reported for comparison. The overlap ratio between the DTW-based graph (DTW) and the flow-direction-based graph (FD) should be quantified and reported.
L460: According to the setup (3 × 2 × 2 = 12 models + baseline = 13), only six models are presented, please clarify the rationale.

Citation: https://doi.org/10.5194/egusphere-2025-4171-RC2

Yueming Nan, Lizhi Tao, Dong Yang, Haibo Zou, Yufeng He, Zhichao Cui, and Yuanbo Luo

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Short summary

Reliable prediction of river flow is vital for water resources, flood prevention, and ecosystem protection. In this study we developed a new model that combines multiscale data analysis with advanced graph-based learning to better capture complex river behaviors. Compared with traditional methods, our model can more effectively capture flow variations across stations at different scales and shows stronger ability to generalize. Our findings support more informed water management.


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