the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Jan 2026
Propagating Meteorological Uncertainty in Physically Based Mountain Snow Simulations
Abstract. Snow estimation in mountainous regions is uncertain because meteorology varies with topography, in situ observations are sparse and biased, and snow models have structural and scale limitations. Probabilistic methods are increasingly recognized as essential for quantifying and propagating these uncertainties in hydrological assessment. This study generates meteorological forcing ensembles designed for mountainous terrain and applies them for probabilistic, physically based snow modeling. Precipitation from global station datasets is corrected for wind induced undercatch using standardized transfer functions. Using the Geospatial Probabilistic Estimation Package (GPEP), we generate station based meteorological ensembles that combine static topographic predictors with dynamic atmospheric predictors from reanalyses. Deterministic fields are estimated with locally weighted regression and random forests, and spatially correlated random fields are used to sample residuals and produce skillful, reliable ensembles. The resulting ensembles drive the SUMMA energy-balance snow model in three contrasting basins: the Chena (Interior Alaska), Bow (Canadian Rockies), and Tuolumne (Sierra Nevada). Undercatch correction improves cold-season precipitation, dynamic predictors enhance regression skill, and random forests outperform locally weighted regression. Ensemble verification yields positive Brier Skill Scores, and ensemble-forced SUMMA simulations reproduce observed snow water equivalent with credible magnitude, timing, and uncertainty estimates. This structured approach advances probabilistic estimation of mountain snow by explicitly representing forcing uncertainty in complex terrain, supporting modeling, data assimilation, and water resource management applications.
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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.
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Preprint
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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.
- Preprint
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Supplement
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- Final revised paper
Journal article(s) based on this preprint
Improving mountain snow prediction requires better representation of meteorological uncertainty. This study generates meteorological ensembles accounting for topography, gauge undercatch, and large-scale atmospheric patterns. Driving a physics-based snow model calibrated using a Large Sample Emulator with these ensembles propagates forcing uncertainty into snow accumulation and melt, producing probablistic estimates for data assimilation and hydrological forecasting.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-6066', Anonymous Referee #1, 09 Mar 2026
Summary
Casson et al. develop and demonstrate a framework for including uncertainty in meteorological forcing data through probabilistic snow model simulations with SUMMA in three contrasting study basins (Chena, Alaska; Bow, Alberta; Tuolumne, California). The framework first applies undercatch corrections to station precipitation data using different WMO equations for the study basins. Next, two approaches are developed (locally weighted regressions, LWR; random forests, RF) in terms of static and dynamic predictors, where it is found that RF generally improves KGE scores relative to LWR and dynamic predictors provide a modest enhancement. The SUMMA model is calibrated using a large sample emulator (LSE), and then applied with 50 RF-generated ensembles and two benchmark forcing datasets (ERA5 and CaSR). The paper reports that the probabilistic ensemble from the RF approach generates realistic SWE time series and improved metrics relative to the two deterministic approaches. The authors conclude that the framework provides a scalable approach to improve how forcing uncertainty is represented in distributed SWE simulations.
Recommendation
In my opinion, this is a potentially impactful and useful study that is within the journal’s scope. This paper provides multiple novel contributions and innovations, including the LSE for parameter identification, the demonstration of RF as an effective non-linear approach for determining meteorological fields, and the probabilistic ensemble-based application across GRUs in multiple snow climates. The methods are generally thoroughly described, which justifies the use of multiple appendices. I appreciate the authors’ embrace of FAIR principles and open-source frameworks, which should increase the potential usage by others in the community. Below, I offer several recommendations to improve the manuscript prior to publication.
Main Comments
- While the paper’s organization is generally logical and effective, I think that there may be a need to improve the organization of Section 4 (methods). It seems that there is an opportunity to align the subsections here based on the methodology chart from Figure 3. In the current version, these are somewhat similar, but not exactly in alignment. This makes it a little hard to map the different components of the figure to the text in section 4. Additionally, it would help to refer back to Figure 3 as the seven components are described in the section 4 subsections.
- A limitation in the SWE evaluations is the spatial scale mismatch between observations and GRU estimates, which is noted by the authors (e.g., L. 558-559, 634-640, Fig. 14). It seems that there is a missed opportunity to conduct some spatial evaluation with remotely sensed snow data, such as MODIS-based snow cover metrics (e.g., Crumley et al., 2020) or lidar-based SWE. The authors indicate they do not pursue these given inconsistent availability across their study sites (e.g., L. 206-207). I would argue that this type of evaluation could be instructive, even if it is only done over a subset of the study basins/years.
- The paper states that the RF ensemble improves the timing and magnitude of melt (e.g., L. 559-560, 600), but I am not convinced. First, there is a potential issue with some ensemble members where the snowpack does not completely melt over summer in the Tuolumne basin following large snow years like 2011 and 2017 (see bottom three panels of Fig. 12). The observational SWE data are unable to evaluate this aspect, and this points to another case where some type of spatial snow data (e.g., MODIS snow disappearance) could be helpful. Second, it would be more convincing if metrics were directly evaluated that isolated the melt timing and magnitude. Currently the paper focuses on SWE time series, which combines the effects of accumulation and melt, which makes it harder to understand how well these two processes are represented.
Specific Comments
- L. 38: Consider also citing Günther et al. (2019) here, as they compared multiple sources of uncertainty for a physical snow model.
- L. 49-51: You might also note here that the airborne and terrestrial lidar provide high spatial resolution.
- L. 59: Suggest adding “lumped” to “conceptual degree-day models”.
- L. 207: Add “across study basins” at the end of this sentence.
- L. 209: Should read “Sun et al. (2019)”.
- L 212-214: Is this the same as ERA5-Land? Please clarify.
- L. 246-251: I think this text should state more directly the types of gauges and corrections used for the study basins. This is implicit in Figure 4, but seems like it should be referenced more explicitly.
- L. 334: This seems like a logical place to reference Appendix C.
- L. 379: It would help to have a brief summary of the key model decisions to understand how SUMMA was setup here.
- L. 380-385: What is a single GRU and how is this different than an HRU? I read this part multiple times and the differences remain unclear to me.
- L. 432: Need to define the N_theta and N_atts variables.
- L. 423-442: I find the large sample emulator to be an innovative and appealing approach but I wonder about how accurate it is in predicting SUMMA skill in this multi-dimensional parameter space. Have the authors checked and verified that the predicted skill (from the emulator) matches evaluations with actual SUMMA runs with the final/optimal parameter sets?
- L. 443-452: I think some clarification is needed here in terms of the model calibration. Specifically, were the parameters derived by SUMMA simulations driven just by station observations? If not, how where did the additional meteorological data come from? Is it possible the optimized parameters favored the RF ensemble in some way over the two deterministic runs?
- L. 480: Replace “This” with “These”.
- L. 503-504 and Fig. 7: It might help to add markers (asterisks) above the predictors in Fig. 7 to denote which were retained.
- L. 510-518: Given the limited number of study basins, variables, and models, I wonder about how much can really be generalized here. You might rephrase the language to not use words like “tends”.
- L. 526: Suggest being more quantitative to clarify what “Most stations” means (e.g., include a percentage).
- L. 548-560: Here and elsewhere, it would be helpful to have a sense of how large the GRUs are in terms of area for the comparisons against the SWE observations.
- L. 562: Suggest moving this sentence to the caption of Fig. 13 as it would be helpful there for interpretation of the figure.
Figures and Tables
- Multiple figures (e.g., Fig. 5, 8, 10) include colors that are not accessible for someone with red-green color deficiency. Please check all figures and fix the color schemes.
- Figure 2: I am confused by the legend for the Tuolumne Snow Stations, which indicate they are either NOAA-NOHRSC or US NRCS. My understanding is that many/most of the snow stations in the Tuolumne are part of the CA Department of Water Resources cooperative snow network. Please double check and correct as necessary.
- Figure 4: This is not referenced directly in the text. Please do so.
- Figure 5: This is not referenced directly in the text. Please do so.
- Figure 6: It is unclear what the boxplots and area time series are summarizing. Is this GRUs or year or both? Please clarify.
- Figure 9: What does the background map represent? Elevation? Please explain in the caption and/or add a colorbar.
- Figure 14: Please state/clarify the study basin. Also, provide the area of the GRU, as this is important context.
References
Günther, D., Marke, T., Essery, R., and Strasser, U.: Uncertainties in Snowpack Simulations—Assessing the Impact of Model Structure, Parameter Choice, and Forcing Data Error on Point‐Scale Energy Balance Snow Model Performance, Water Resources Research, 55, 2779–2800, https://doi.org/10.1029/2018WR023403, 2019.
Citation: https://doi.org/10.5194/egusphere-2025-6066-RC1 - AC1: 'Reply on RC1', David Casson, 25 Mar 2026
-
RC2: 'Comment on egusphere-2025-6066', Anonymous Referee #2, 14 Mar 2026
Review of Propagating Meteorological Uncertainty in Physically Based Mountain Snow Simulations by Casson and co-authors for EGUSphere
Summary
The authors present a framework to quantify and propagate uncertainty in meteorological forcing through physically based snow modeling in mountainous terrain. It generates probabilistic meteorological forcing ensembles by combining station observations, topographic predictors, and atmospheric reanalysis with both regression and machine-learning methods to estimate spatial fields and their uncertainty. Precipitation observations are corrected for wind-induced gauge undercatch, and spatially correlated random fields are used to produce ensembles of meteorological inputs. These ensembles drive the energy-balance snow model SUMMA in three contrasting basins: the Chena (Alaska), Bow (Canadian Rockies), and Tuolumne (Sierra Nevada); basins that are generally well known in the North American snow hydrology community.
Results show that precip undercatch correction improves winter precipitation estimates, dynamic predictors such as reanalysis enhance regression skill, and Random Forest methods outperform regression in generating meteo fields. Ensemble verification shows positive probabilistic skill. When forced by the ensemble, snow simulations reproduce observed SWE in realistic ways: timing, magnitude, and uncertainty ranges seem reasonable. Overall, the study demonstrates a reproducible and transferable approach for explicitly representing meteorological forcing uncertainty in mountain snow simulations to support hydrologic modeling and water-resource decision making.
I commend the authors on a compelling demonstration of best practices in hydrological modeling, reproducibility, and uncertainty characterization. I believe this paper will serve as a guide for many early-career hydrologists seeking practical examples of rigorous modeling workflows and code development. The use of FAIR principles and Snakemake-based workflows is particularly notable and valuable for the community. The paper is clearly within the scope of the journal and will likely be well cited in the hydrological modeling literature, and potentially beyond in other environmental modeling disciplines.
Main Comments
Interpretation of Figure 13 – I found these results particularly interesting. Could the authors expand on the implications of the results shown in Figure 13? Specifically, what do the cross-site differences in S-bias & S-pattern relationships reveal about the relative strengths and limitations of the different forcing datasets?
Treatment of precipitation phase: There was surprisingly little discussion of how precipitation phase is treated in the model and how the calibration and ensemble framework may influence the impacts of precipitation phase errors on snow simulations. Could the authors expand on this aspect?
I would be interested to know whether there is a metric that could evaluate the relative uncertainty of the ensemble during precipitation events when air temperatures fall within the model’s specified snow–rain transition range. In other words, is there a way to quantify how the different forcing-generation methods influence the model’s treatment of precipitation phase and the resulting uncertainty in snow accumulation?
Representation of preferential snow accumulation areas: While the study focuses on GRUs and GRU-averaged snowpack metrics, it would be helpful if the authors could comment on the potential importance of resolving landscape units that exhibit preferential snow accumulation and harbor deep, persistent snowpack. These areas may provide critical surface and groundwater inputs and support important ecological functions. Such regions may also be the least likely to have in situ observations for either forcing or validation.
These landscape units may disproportionately contribute to basin water inputs and may either be more resilient to warming (snowpack refugia) or particularly susceptible to change. The manuscript clearly highlights the need to better resolve slope-scale wind effects from the perspective of gauge collection efficiency, but what about the potential to improve resolution of slope-scale orographic dynamics (e.g., the improvement of high-resolution reanalysis products that can capture precipitation banding from orography and atmospheric rivers, e.g.) in locations where precipitation gauges are absent?
Detailed Comments
Lines 253-254: Typo: "where data were co-located measurements"
Line 410: Replace with "Meteorology”?
Lines 458-459: It may be helpful to mention that snow pillows also record conditions in the absence of overhead forest canopy, which may influence the representativeness of comparisons with spatially averaged model outputs.
Citation: https://doi.org/10.5194/egusphere-2025-6066-RC2 - AC2: 'Reply on RC2', David Casson, 25 Mar 2026
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-6066', Anonymous Referee #1, 09 Mar 2026
Summary
Casson et al. develop and demonstrate a framework for including uncertainty in meteorological forcing data through probabilistic snow model simulations with SUMMA in three contrasting study basins (Chena, Alaska; Bow, Alberta; Tuolumne, California). The framework first applies undercatch corrections to station precipitation data using different WMO equations for the study basins. Next, two approaches are developed (locally weighted regressions, LWR; random forests, RF) in terms of static and dynamic predictors, where it is found that RF generally improves KGE scores relative to LWR and dynamic predictors provide a modest enhancement. The SUMMA model is calibrated using a large sample emulator (LSE), and then applied with 50 RF-generated ensembles and two benchmark forcing datasets (ERA5 and CaSR). The paper reports that the probabilistic ensemble from the RF approach generates realistic SWE time series and improved metrics relative to the two deterministic approaches. The authors conclude that the framework provides a scalable approach to improve how forcing uncertainty is represented in distributed SWE simulations.
Recommendation
In my opinion, this is a potentially impactful and useful study that is within the journal’s scope. This paper provides multiple novel contributions and innovations, including the LSE for parameter identification, the demonstration of RF as an effective non-linear approach for determining meteorological fields, and the probabilistic ensemble-based application across GRUs in multiple snow climates. The methods are generally thoroughly described, which justifies the use of multiple appendices. I appreciate the authors’ embrace of FAIR principles and open-source frameworks, which should increase the potential usage by others in the community. Below, I offer several recommendations to improve the manuscript prior to publication.
Main Comments
- While the paper’s organization is generally logical and effective, I think that there may be a need to improve the organization of Section 4 (methods). It seems that there is an opportunity to align the subsections here based on the methodology chart from Figure 3. In the current version, these are somewhat similar, but not exactly in alignment. This makes it a little hard to map the different components of the figure to the text in section 4. Additionally, it would help to refer back to Figure 3 as the seven components are described in the section 4 subsections.
- A limitation in the SWE evaluations is the spatial scale mismatch between observations and GRU estimates, which is noted by the authors (e.g., L. 558-559, 634-640, Fig. 14). It seems that there is a missed opportunity to conduct some spatial evaluation with remotely sensed snow data, such as MODIS-based snow cover metrics (e.g., Crumley et al., 2020) or lidar-based SWE. The authors indicate they do not pursue these given inconsistent availability across their study sites (e.g., L. 206-207). I would argue that this type of evaluation could be instructive, even if it is only done over a subset of the study basins/years.
- The paper states that the RF ensemble improves the timing and magnitude of melt (e.g., L. 559-560, 600), but I am not convinced. First, there is a potential issue with some ensemble members where the snowpack does not completely melt over summer in the Tuolumne basin following large snow years like 2011 and 2017 (see bottom three panels of Fig. 12). The observational SWE data are unable to evaluate this aspect, and this points to another case where some type of spatial snow data (e.g., MODIS snow disappearance) could be helpful. Second, it would be more convincing if metrics were directly evaluated that isolated the melt timing and magnitude. Currently the paper focuses on SWE time series, which combines the effects of accumulation and melt, which makes it harder to understand how well these two processes are represented.
Specific Comments
- L. 38: Consider also citing Günther et al. (2019) here, as they compared multiple sources of uncertainty for a physical snow model.
- L. 49-51: You might also note here that the airborne and terrestrial lidar provide high spatial resolution.
- L. 59: Suggest adding “lumped” to “conceptual degree-day models”.
- L. 207: Add “across study basins” at the end of this sentence.
- L. 209: Should read “Sun et al. (2019)”.
- L 212-214: Is this the same as ERA5-Land? Please clarify.
- L. 246-251: I think this text should state more directly the types of gauges and corrections used for the study basins. This is implicit in Figure 4, but seems like it should be referenced more explicitly.
- L. 334: This seems like a logical place to reference Appendix C.
- L. 379: It would help to have a brief summary of the key model decisions to understand how SUMMA was setup here.
- L. 380-385: What is a single GRU and how is this different than an HRU? I read this part multiple times and the differences remain unclear to me.
- L. 432: Need to define the N_theta and N_atts variables.
- L. 423-442: I find the large sample emulator to be an innovative and appealing approach but I wonder about how accurate it is in predicting SUMMA skill in this multi-dimensional parameter space. Have the authors checked and verified that the predicted skill (from the emulator) matches evaluations with actual SUMMA runs with the final/optimal parameter sets?
- L. 443-452: I think some clarification is needed here in terms of the model calibration. Specifically, were the parameters derived by SUMMA simulations driven just by station observations? If not, how where did the additional meteorological data come from? Is it possible the optimized parameters favored the RF ensemble in some way over the two deterministic runs?
- L. 480: Replace “This” with “These”.
- L. 503-504 and Fig. 7: It might help to add markers (asterisks) above the predictors in Fig. 7 to denote which were retained.
- L. 510-518: Given the limited number of study basins, variables, and models, I wonder about how much can really be generalized here. You might rephrase the language to not use words like “tends”.
- L. 526: Suggest being more quantitative to clarify what “Most stations” means (e.g., include a percentage).
- L. 548-560: Here and elsewhere, it would be helpful to have a sense of how large the GRUs are in terms of area for the comparisons against the SWE observations.
- L. 562: Suggest moving this sentence to the caption of Fig. 13 as it would be helpful there for interpretation of the figure.
Figures and Tables
- Multiple figures (e.g., Fig. 5, 8, 10) include colors that are not accessible for someone with red-green color deficiency. Please check all figures and fix the color schemes.
- Figure 2: I am confused by the legend for the Tuolumne Snow Stations, which indicate they are either NOAA-NOHRSC or US NRCS. My understanding is that many/most of the snow stations in the Tuolumne are part of the CA Department of Water Resources cooperative snow network. Please double check and correct as necessary.
- Figure 4: This is not referenced directly in the text. Please do so.
- Figure 5: This is not referenced directly in the text. Please do so.
- Figure 6: It is unclear what the boxplots and area time series are summarizing. Is this GRUs or year or both? Please clarify.
- Figure 9: What does the background map represent? Elevation? Please explain in the caption and/or add a colorbar.
- Figure 14: Please state/clarify the study basin. Also, provide the area of the GRU, as this is important context.
References
Günther, D., Marke, T., Essery, R., and Strasser, U.: Uncertainties in Snowpack Simulations—Assessing the Impact of Model Structure, Parameter Choice, and Forcing Data Error on Point‐Scale Energy Balance Snow Model Performance, Water Resources Research, 55, 2779–2800, https://doi.org/10.1029/2018WR023403, 2019.
Citation: https://doi.org/10.5194/egusphere-2025-6066-RC1 - AC1: 'Reply on RC1', David Casson, 25 Mar 2026
-
RC2: 'Comment on egusphere-2025-6066', Anonymous Referee #2, 14 Mar 2026
Review of Propagating Meteorological Uncertainty in Physically Based Mountain Snow Simulations by Casson and co-authors for EGUSphere
Summary
The authors present a framework to quantify and propagate uncertainty in meteorological forcing through physically based snow modeling in mountainous terrain. It generates probabilistic meteorological forcing ensembles by combining station observations, topographic predictors, and atmospheric reanalysis with both regression and machine-learning methods to estimate spatial fields and their uncertainty. Precipitation observations are corrected for wind-induced gauge undercatch, and spatially correlated random fields are used to produce ensembles of meteorological inputs. These ensembles drive the energy-balance snow model SUMMA in three contrasting basins: the Chena (Alaska), Bow (Canadian Rockies), and Tuolumne (Sierra Nevada); basins that are generally well known in the North American snow hydrology community.
Results show that precip undercatch correction improves winter precipitation estimates, dynamic predictors such as reanalysis enhance regression skill, and Random Forest methods outperform regression in generating meteo fields. Ensemble verification shows positive probabilistic skill. When forced by the ensemble, snow simulations reproduce observed SWE in realistic ways: timing, magnitude, and uncertainty ranges seem reasonable. Overall, the study demonstrates a reproducible and transferable approach for explicitly representing meteorological forcing uncertainty in mountain snow simulations to support hydrologic modeling and water-resource decision making.
I commend the authors on a compelling demonstration of best practices in hydrological modeling, reproducibility, and uncertainty characterization. I believe this paper will serve as a guide for many early-career hydrologists seeking practical examples of rigorous modeling workflows and code development. The use of FAIR principles and Snakemake-based workflows is particularly notable and valuable for the community. The paper is clearly within the scope of the journal and will likely be well cited in the hydrological modeling literature, and potentially beyond in other environmental modeling disciplines.
Main Comments
Interpretation of Figure 13 – I found these results particularly interesting. Could the authors expand on the implications of the results shown in Figure 13? Specifically, what do the cross-site differences in S-bias & S-pattern relationships reveal about the relative strengths and limitations of the different forcing datasets?
Treatment of precipitation phase: There was surprisingly little discussion of how precipitation phase is treated in the model and how the calibration and ensemble framework may influence the impacts of precipitation phase errors on snow simulations. Could the authors expand on this aspect?
I would be interested to know whether there is a metric that could evaluate the relative uncertainty of the ensemble during precipitation events when air temperatures fall within the model’s specified snow–rain transition range. In other words, is there a way to quantify how the different forcing-generation methods influence the model’s treatment of precipitation phase and the resulting uncertainty in snow accumulation?
Representation of preferential snow accumulation areas: While the study focuses on GRUs and GRU-averaged snowpack metrics, it would be helpful if the authors could comment on the potential importance of resolving landscape units that exhibit preferential snow accumulation and harbor deep, persistent snowpack. These areas may provide critical surface and groundwater inputs and support important ecological functions. Such regions may also be the least likely to have in situ observations for either forcing or validation.
These landscape units may disproportionately contribute to basin water inputs and may either be more resilient to warming (snowpack refugia) or particularly susceptible to change. The manuscript clearly highlights the need to better resolve slope-scale wind effects from the perspective of gauge collection efficiency, but what about the potential to improve resolution of slope-scale orographic dynamics (e.g., the improvement of high-resolution reanalysis products that can capture precipitation banding from orography and atmospheric rivers, e.g.) in locations where precipitation gauges are absent?
Detailed Comments
Lines 253-254: Typo: "where data were co-located measurements"
Line 410: Replace with "Meteorology”?
Lines 458-459: It may be helpful to mention that snow pillows also record conditions in the absence of overhead forest canopy, which may influence the representativeness of comparisons with spatially averaged model outputs.
Citation: https://doi.org/10.5194/egusphere-2025-6066-RC2 - AC2: 'Reply on RC2', David Casson, 25 Mar 2026
Peer review completion
Journal article(s) based on this preprint
Improving mountain snow prediction requires better representation of meteorological uncertainty. This study generates meteorological ensembles accounting for topography, gauge undercatch, and large-scale atmospheric patterns. Driving a physics-based snow model calibrated using a Large Sample Emulator with these ensembles propagates forcing uncertainty into snow accumulation and melt, producing probablistic estimates for data assimilation and hydrological forecasting.
Data sets
SUMMA Model and GPEP Input Files for Chena, Bow and Tuolumne David R. Casson https://doi.org/10.5281/zenodo.17740655
Ensemble Meteorological Forcing for Chena, Bow, Tuolumne David R. Casson https://doi.org/10.20383/103.01532
Model code and software
GPEP Snakemake David R. Casson https://doi.org/10.5281/zenodo.17727620
GPEP to SUMMA Snakemake David R. Casson https://doi.org/10.5281/zenodo.17727624
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David R. Casson
Guoqiang Tang
Nicolás Vásquez
Andrew W. Wood
Martyn P. Clark
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(34368 KB) - Metadata XML
-
Supplement
(188 KB) - BibTeX
- EndNote
- Final revised paper