Process diagnostics of snowmelt runoff in global hydrological models: Part I &ndash; Model evaluation from the perspective of robustness

Lei, Xiangyong; Lin, Haomei; Zheng, Kaihao; Lin, Peirong

doi:10.5194/egusphere-2025-6071

Preprints

https://doi.org/10.5194/egusphere-2025-6071

Preprints

20 Jan 2026

| 20 Jan 2026

Process diagnostics of snowmelt runoff in global hydrological models: Part I – Model evaluation from the perspective of robustness

Xiangyong Lei, Haomei Lin, Kaihao Zheng, and Peirong Lin

Abstract. Accurate simulation of snowmelt runoff (SMR) is critical for water resource management. However, despite the abundance of global hydrological models, little is known about their SMR performance. This study first presents a comprehensive evaluation of SMR across 15 state-of-the-art large-scale models and runoff products by focusing on their biases in first-order indices, i.e., the total volume (Q_sum), peak flow (Q_max), and centroid timing (CTQ) of runoff in the snowmelt period. Then by introducing 1,513 snow-dominated basins with increasing basin complexities, we further proposed a novel model robustness metric to quantify how the model performance changes with basin complexity. Our results reveal that (1) most models exhibit underestimated Q_sum and Q_max and predict CTQ too early. These biases are particularly pronounced in regions such as the western United States, northern Europe, and northeastern China. (2) Model biases systematically increase with basin complexity, with CTQ exhibiting the strongest sensitivity to increasing mean elevation and topographic variability, while that of Q_sum and Q_max is mainly shaped by mean elevation and the diversity of vegetation types in the basin. (3) The robustness assessment further shows that observation-constrained runoff products exhibit the most outstanding performance, followed by the ISIMIP3a and ISIMIP2a models. Overall, global hydrological models exhibit stronger performance in simulating SMR than land surface models. Notably, land surface models perform substantially better for CTQ than for Q_sum or Q_max, highlighting their structural advantage in capturing melt timing relative to runoff magnitude. This study provides a benchmark for SMR evaluation and a new framework for assessing model performance under basin complexity, offering crucial insights for future model development and uncertainty reduction.

Received: 05 Dec 2025 – Discussion started: 20 Jan 2026

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Preprint (PDF, 2536 KB)

Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
Preprint (2536 KB)

Download & links

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

Journal article(s) based on this preprint

21 Aug 2026

Process diagnostics of snowmelt runoff in global hydrological and land surface models – Part 1: A systematic evaluation across basins of increasing complexity

Xiangyong Lei, Haomei Lin, Kaihao Zheng, and Peirong Lin

Hydrol. Earth Syst. Sci., 30, 5343–5372, https://doi.org/10.5194/hess-30-5343-2026,https://doi.org/10.5194/hess-30-5343-2026, 2026

Short summary

Xiangyong Lei, Haomei Lin, Kaihao Zheng, and Peirong Lin

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-6071', Anonymous Referee #1, 15 Mar 2026
Overall, this manuscript presents a substantial amount of analysis on snowmelt runoff characteristics across a large sample of basins and multiple models/products, and the overall writing and presentation are generally clear. The topic is relevant and the study has clear value for large-scale model evaluation in cold-region hydrology. In particular, the authors made considerable efforts in constructing the intercomparison framework and diagnosing runoff volume, peak, and timing during snowmelt periods. However, several issues remain insufficiently addressed, especially regarding the parameter calibration and the formulation and interpretation of the newly proposed RI metric. My detailed comments are as below.
Major comments:
A major concern is the issue of parameter calibration. It is well accepted in hydrological modeling that calibration can strongly affect model performance, especially that hydrological models typically involve many empirical assumptions, conceptual runoff generation schemes, or regionally variable parameterizations. In practice, model performance may differ substantially before and after calibration, and parameter values can also vary greatly across climatic and physiographic conditions. However, the models included in this study do not appear to have a consistent calibration status: some are calibrated, some are uncalibrated, and some may be only partially calibrated. This compromises the comparability of the intercomparison and makes it difficult to attribute performance differences purely to model structure or process representation. This problem seems inevitable since the study uses existing model outputs rather than builds its own modeling frameworks. However, this problem should be emphasized in the manuscript (in many places) and its impact on the results should be thoroughly discussed.

The explanation of the proposed RI in Section 2.2.4 should be strengthened. First, the manuscript does not clearly define the “complexity level/group” used in the RI calculation, including how basins were grouped along the CI gradient and how the corresponding CI values for each group were assigned. Second, the rationale for combining normalized SMAB and normalized slope into a single Euclidean-distance-based metric is not sufficiently justified. At present, it remains unclear how reliable RI is as an integrated measure of model robustness, and whether it can meaningfully balance overall bias against sensitivity to increasing basin complexity. Since RI appears to be a newly proposed metric in this study, the manuscript should provide stronger justification of its formulation, interpretation, and practical usefulness.

I recommend that the authors moderate the novelty claims related to the evaluation framework. The volume/peak/timing analysis adopted here is useful and appropriate for process-based diagnosis, and I do not object to its use in this study. However, similar types of diagnostics have already been widely used in hydrological model evaluation, including in snow-related runoff studies. Therefore, some statements currently appear overstated. For example, the conclusion states that “This framework advances model intercomparison by moving beyond average bias evaluation,” but many previous studies have gone well beyond average bias and have used multiple performance metrics and more process-oriented diagnostics. I suggest rephrasing such statements to avoid overstating methodological novelty. More generally, the manuscript would benefit from another careful round of language revision, as several statements appear stronger than the evidence supports.

I also suggest revising the title of Part I. At present, the emphasis on “robustness” seems somewhat overstated, as the current emphasis on robustness may not fully reflect the primary contribution of the manuscript. The paper is fundamentally a global-scale evaluation of snowmelt runoff performance across large-scale hydrological models, and the title would be more accurate if it reflected this primary focus more directly.

Other:
In the abstract, “little is known about their SMR performance” appears overstated. In addition, “ISIMIP3a and ISIMIP2a” are mentioned without sufficient explanation, and I suggest simplifying or removing these terms in the abstract.

In the second paragraph of the Introduction, the statement that SMR-related simulations remain unsatisfactory should be qualified more carefully. Snow-related runoff can in some cases be easier to simulate because of its strong seasonality and regular hydrological response, whereas runoff simulation in arid regions is often more difficult.

Since the gridded runoff is at 0.5° resolution while the MERIT basins are much finer, the manuscript should discuss the possible impact of this scale mismatch on routing and the resulting evaluation.

The residual water-balance estimate is acceptable as a pragmatic screening proxy for identifying snowmelt-dominated basins, but it should not be interpreted as a rigorous quantification of snowmelt runoff contribution, because changes in catchment storage, delayed groundwater release, and rainfall–snowmelt interactions are not explicitly accounted for.

ERA5 SWE is used to define snow periods, but the manuscript should discuss the reliability and possible limitations of ERA5 SWE for this purpose, especially in complex terrain.

The description of the observed discharge data source needs clarification. The manuscript states that discharge data are obtained from GSHA, but it is not clear whether GSHA directly provides the daily discharge time series used here. Please clarify this point.
Citation: https://doi.org/10.5194/egusphere-2025-6071-RC1
- AC1: 'Reply on RC1', Peirong Lin, 13 May 2026
  
  Thank you for taking time and offering very constructive comments for us to improve the quality of the manuscript. We have carefully addressed every comment you raised, and please see attached for our responses.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6071-AC1
RC2:
'Comment on egusphere-2025-6071', Anonymous Referee #2, 16 Mar 2026
This study presents a large-scale evaluation of snowmelt runoff (SMR) simulation across 15 global hydrological models and runoff products using 1,513 snow-dominated basins worldwide. The authors evaluate three key hydrograph characteristics: total runoff (Qsum), peak flow (Qmax), and centroid timing (CTQ), and introduces a new robustness index to quantify how model performance degrades with increasing basin complexity. The results show that most models underestimate runoff magnitude and predict earlier snowmelt timing, and that model performance degrades as basin complexity increases. Overall, the manuscript is well written and provides a valuable large sample diagnostic of model performance. The concept of evaluating model robustness across environmental complexity gradients is particularly interesting and could offer useful insights for model development. However, several issues need clarification before the manuscript is suitable for publication.
Major comments:
The robustness metric is central to the manuscript but requires further justification and interpretation. The index combines the Stratified Mean Absolute Bias (SMAB) and the slope of bias vs. complexity into a Euclidean distance metric. Why was Euclidean distance selected as the combination method? Though the authors mentioned it was done in prior studies, it would be more helpful for readers if some justification can be added here. Also, is the robustness index comparable across different runoff metrics (Qsum, Qmax, CTQ)?

The basin complexity index is defined as the sum of normalized DEM, DEMstd, LAI, and PFTh. While this approach is straightforward, the four variables may not contribute equally to hydrological complexity. Some factors, like elevation and topographic variability, may already be strongly correlated. It would be better if the authors can discuss why these four metrics are selected and whether dependencies among these variables influence the analysis.

In this study, all runoff outputs are routed using RAPID to ensure comparability. However, the manuscript assumes that routing effects are minimal because long-term mean metrics are used. This assumption needs more justification because routing parameters can influence peak flow magnitude and CTQ. The authors should either provide a short sensitivity analysis, or cite studies showing that routing effects are negligible at the spatial scale considered.

Page 19, lines 340: what’s the potential reason that ISIMIP 3a outperforms ISIMIP 2a in simulating Qsum and Qmax, is it because of the forcing data?

The manuscript concludes that GHMs outperform LSMs for Qsum and Qmax, while LSMs perform better for CTQ. This is an interesting finding, but the discussion remains somewhat speculative. The authors attribute the differences to energy-balance representations and runoff parameterizations, but more concrete explanations or references would strengthen this argument. In addition, some differences could result from calibration, forcing datasets, and resolution differences. These factors should be discussed more carefully.

Minor comments:
The snowmelt period is defined as the interval between maximum SWE and when SWE falls below 1 mm. This definition may not capture multi-peak melt seasons or rain-on-snow events. A brief discussion of limitations would be helpful.

ERA5 SWE is used to define snowmelt timing. However, ERA5 has known biases in mountainous regions. The manuscript should briefly discuss how this may affect the analysis.

“Stern conditions” is not commonly used in scientific literature, especially in hydrology or Earth system science papers. It’s a bit awkward in this context. Do you mean “challenging conditions” or “complex environmental conditions”?

Page 18, in the title of Figure 6, change “blue circles denote GHMs, yellow squares denote LSMs, green triangles denote DGVMS, and grey diamonds denote data products.” to “circle denote GHMs, squares denote LSMs, triangles denote DGVMS, and diamonds denote data products.” Because shapes represent model types and colors shows the robustness.
Citation: https://doi.org/10.5194/egusphere-2025-6071-RC2
- AC2: 'Reply on RC2', Peirong Lin, 13 May 2026
  
  Thank you for taking time and offering very constructive comments for us to improve the quality of the manuscript. We have carefully addressed every comment you raised, and please see attached for our responses.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6071-AC2

Peer review completion

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

ED: Publish subject to revisions (further review by editor and referees) (23 May 2026) by Xing Yuan

AR by Peirong Lin on behalf of the Authors (25 Jun 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (29 Jun 2026) by Xing Yuan

RR by Anonymous Referee #2 (14 Jul 2026)

RR by Anonymous Referee #1 (01 Aug 2026)

ED: Publish as is (01 Aug 2026) by Xing Yuan

AR by Peirong Lin on behalf of the Authors (08 Aug 2026)

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-6071', Anonymous Referee #1, 15 Mar 2026
Overall, this manuscript presents a substantial amount of analysis on snowmelt runoff characteristics across a large sample of basins and multiple models/products, and the overall writing and presentation are generally clear. The topic is relevant and the study has clear value for large-scale model evaluation in cold-region hydrology. In particular, the authors made considerable efforts in constructing the intercomparison framework and diagnosing runoff volume, peak, and timing during snowmelt periods. However, several issues remain insufficiently addressed, especially regarding the parameter calibration and the formulation and interpretation of the newly proposed RI metric. My detailed comments are as below.
Major comments:
A major concern is the issue of parameter calibration. It is well accepted in hydrological modeling that calibration can strongly affect model performance, especially that hydrological models typically involve many empirical assumptions, conceptual runoff generation schemes, or regionally variable parameterizations. In practice, model performance may differ substantially before and after calibration, and parameter values can also vary greatly across climatic and physiographic conditions. However, the models included in this study do not appear to have a consistent calibration status: some are calibrated, some are uncalibrated, and some may be only partially calibrated. This compromises the comparability of the intercomparison and makes it difficult to attribute performance differences purely to model structure or process representation. This problem seems inevitable since the study uses existing model outputs rather than builds its own modeling frameworks. However, this problem should be emphasized in the manuscript (in many places) and its impact on the results should be thoroughly discussed.

The explanation of the proposed RI in Section 2.2.4 should be strengthened. First, the manuscript does not clearly define the “complexity level/group” used in the RI calculation, including how basins were grouped along the CI gradient and how the corresponding CI values for each group were assigned. Second, the rationale for combining normalized SMAB and normalized slope into a single Euclidean-distance-based metric is not sufficiently justified. At present, it remains unclear how reliable RI is as an integrated measure of model robustness, and whether it can meaningfully balance overall bias against sensitivity to increasing basin complexity. Since RI appears to be a newly proposed metric in this study, the manuscript should provide stronger justification of its formulation, interpretation, and practical usefulness.

I recommend that the authors moderate the novelty claims related to the evaluation framework. The volume/peak/timing analysis adopted here is useful and appropriate for process-based diagnosis, and I do not object to its use in this study. However, similar types of diagnostics have already been widely used in hydrological model evaluation, including in snow-related runoff studies. Therefore, some statements currently appear overstated. For example, the conclusion states that “This framework advances model intercomparison by moving beyond average bias evaluation,” but many previous studies have gone well beyond average bias and have used multiple performance metrics and more process-oriented diagnostics. I suggest rephrasing such statements to avoid overstating methodological novelty. More generally, the manuscript would benefit from another careful round of language revision, as several statements appear stronger than the evidence supports.

I also suggest revising the title of Part I. At present, the emphasis on “robustness” seems somewhat overstated, as the current emphasis on robustness may not fully reflect the primary contribution of the manuscript. The paper is fundamentally a global-scale evaluation of snowmelt runoff performance across large-scale hydrological models, and the title would be more accurate if it reflected this primary focus more directly.

Other:
In the abstract, “little is known about their SMR performance” appears overstated. In addition, “ISIMIP3a and ISIMIP2a” are mentioned without sufficient explanation, and I suggest simplifying or removing these terms in the abstract.

In the second paragraph of the Introduction, the statement that SMR-related simulations remain unsatisfactory should be qualified more carefully. Snow-related runoff can in some cases be easier to simulate because of its strong seasonality and regular hydrological response, whereas runoff simulation in arid regions is often more difficult.

Since the gridded runoff is at 0.5° resolution while the MERIT basins are much finer, the manuscript should discuss the possible impact of this scale mismatch on routing and the resulting evaluation.

The residual water-balance estimate is acceptable as a pragmatic screening proxy for identifying snowmelt-dominated basins, but it should not be interpreted as a rigorous quantification of snowmelt runoff contribution, because changes in catchment storage, delayed groundwater release, and rainfall–snowmelt interactions are not explicitly accounted for.

ERA5 SWE is used to define snow periods, but the manuscript should discuss the reliability and possible limitations of ERA5 SWE for this purpose, especially in complex terrain.

The description of the observed discharge data source needs clarification. The manuscript states that discharge data are obtained from GSHA, but it is not clear whether GSHA directly provides the daily discharge time series used here. Please clarify this point.
Citation: https://doi.org/10.5194/egusphere-2025-6071-RC1
- AC1: 'Reply on RC1', Peirong Lin, 13 May 2026
  
  Thank you for taking time and offering very constructive comments for us to improve the quality of the manuscript. We have carefully addressed every comment you raised, and please see attached for our responses.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6071-AC1
RC2:
'Comment on egusphere-2025-6071', Anonymous Referee #2, 16 Mar 2026
This study presents a large-scale evaluation of snowmelt runoff (SMR) simulation across 15 global hydrological models and runoff products using 1,513 snow-dominated basins worldwide. The authors evaluate three key hydrograph characteristics: total runoff (Qsum), peak flow (Qmax), and centroid timing (CTQ), and introduces a new robustness index to quantify how model performance degrades with increasing basin complexity. The results show that most models underestimate runoff magnitude and predict earlier snowmelt timing, and that model performance degrades as basin complexity increases. Overall, the manuscript is well written and provides a valuable large sample diagnostic of model performance. The concept of evaluating model robustness across environmental complexity gradients is particularly interesting and could offer useful insights for model development. However, several issues need clarification before the manuscript is suitable for publication.
Major comments:
The robustness metric is central to the manuscript but requires further justification and interpretation. The index combines the Stratified Mean Absolute Bias (SMAB) and the slope of bias vs. complexity into a Euclidean distance metric. Why was Euclidean distance selected as the combination method? Though the authors mentioned it was done in prior studies, it would be more helpful for readers if some justification can be added here. Also, is the robustness index comparable across different runoff metrics (Qsum, Qmax, CTQ)?

The basin complexity index is defined as the sum of normalized DEM, DEMstd, LAI, and PFTh. While this approach is straightforward, the four variables may not contribute equally to hydrological complexity. Some factors, like elevation and topographic variability, may already be strongly correlated. It would be better if the authors can discuss why these four metrics are selected and whether dependencies among these variables influence the analysis.

In this study, all runoff outputs are routed using RAPID to ensure comparability. However, the manuscript assumes that routing effects are minimal because long-term mean metrics are used. This assumption needs more justification because routing parameters can influence peak flow magnitude and CTQ. The authors should either provide a short sensitivity analysis, or cite studies showing that routing effects are negligible at the spatial scale considered.

Page 19, lines 340: what’s the potential reason that ISIMIP 3a outperforms ISIMIP 2a in simulating Qsum and Qmax, is it because of the forcing data?

The manuscript concludes that GHMs outperform LSMs for Qsum and Qmax, while LSMs perform better for CTQ. This is an interesting finding, but the discussion remains somewhat speculative. The authors attribute the differences to energy-balance representations and runoff parameterizations, but more concrete explanations or references would strengthen this argument. In addition, some differences could result from calibration, forcing datasets, and resolution differences. These factors should be discussed more carefully.

Minor comments:
The snowmelt period is defined as the interval between maximum SWE and when SWE falls below 1 mm. This definition may not capture multi-peak melt seasons or rain-on-snow events. A brief discussion of limitations would be helpful.

ERA5 SWE is used to define snowmelt timing. However, ERA5 has known biases in mountainous regions. The manuscript should briefly discuss how this may affect the analysis.

“Stern conditions” is not commonly used in scientific literature, especially in hydrology or Earth system science papers. It’s a bit awkward in this context. Do you mean “challenging conditions” or “complex environmental conditions”?

Page 18, in the title of Figure 6, change “blue circles denote GHMs, yellow squares denote LSMs, green triangles denote DGVMS, and grey diamonds denote data products.” to “circle denote GHMs, squares denote LSMs, triangles denote DGVMS, and diamonds denote data products.” Because shapes represent model types and colors shows the robustness.
Citation: https://doi.org/10.5194/egusphere-2025-6071-RC2
- AC2: 'Reply on RC2', Peirong Lin, 13 May 2026
  
  Thank you for taking time and offering very constructive comments for us to improve the quality of the manuscript. We have carefully addressed every comment you raised, and please see attached for our responses.
  
  Citation: https://doi.org/10.5194/egusphere-2025-6071-AC2

Peer review completion

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

ED: Publish subject to revisions (further review by editor and referees) (23 May 2026) by Xing Yuan

AR by Peirong Lin on behalf of the Authors (25 Jun 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (29 Jun 2026) by Xing Yuan

RR by Anonymous Referee #2 (14 Jul 2026)

RR by Anonymous Referee #1 (01 Aug 2026)

ED: Publish as is (01 Aug 2026) by Xing Yuan

AR by Peirong Lin on behalf of the Authors (08 Aug 2026)

Journal article(s) based on this preprint

21 Aug 2026

Process diagnostics of snowmelt runoff in global hydrological and land surface models – Part 1: A systematic evaluation across basins of increasing complexity

Xiangyong Lei, Haomei Lin, Kaihao Zheng, and Peirong Lin

Hydrol. Earth Syst. Sci., 30, 5343–5372, https://doi.org/10.5194/hess-30-5343-2026,https://doi.org/10.5194/hess-30-5343-2026, 2026

Short summary

Xiangyong Lei, Haomei Lin, Kaihao Zheng, and Peirong Lin

Viewed

Total article views: 2,258 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	BibTeX	EndNote
1,384	759	115	2,258	110	197

HTML: 1,384
PDF: 759
XML: 115
Total: 2,258
BibTeX: 110
EndNote: 197

Views and downloads (calculated since 20 Jan 2026)

Month	HTML	PDF	XML	Total
Jan 2026	685	330	54	1,069
Feb 2026	202	171	14	387
Mar 2026	332	160	28	520
Apr 2026	44	25	6	75
May 2026	63	36	6	105
Jun 2026	11	7	1	19
Jul 2026	15	10	2	27
Aug 2026	26	11	1	38
Sep 2026	6	9	3	18

Cumulative views and downloads (calculated since 20 Jan 2026)

Month	HTML	PDF	XML	Total
Jan 2026	685	330	54	1,069
Feb 2026	202	171	14	387
Mar 2026	332	160	28	520
Apr 2026	44	25	6	75
May 2026	63	36	6	105
Jun 2026	11	7	1	19
Jul 2026	15	10	2	27
Aug 2026	26	11	1	38
Sep 2026	6	9	3	18

Viewed (geographical distribution)

Total article views: 2,224 (including HTML, PDF, and XML) Thereof 2,224 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 11 Sep 2026

Download

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

Preprint (2536 KB)
Metadata XML

Short summary

Snowmelt runoff (SMR) is a critical freshwater resource. This study conducts the first comprehensive assessment of SMR, specifically its volume, peak, and timing, across tens of large-scale models and thousand of basins. We also test the models by assessing their performance drop as basins become more and more complex. Our results highlight the systematic biases and certain model categories with stronger robustness in stern conditions, paving the way for process diagnosis for SMR in models.


Total:	0
HTML:	0
PDF:	0
XML:	0