| 15 Oct 2025
Can streamflow observations constrain snow mass reconstructions? Lessons from two synthetic numerical experiments
Abstract. Historical snow mass estimates are key to understanding snowmelt-driven streamflow and climate change impacts on snow water resources. However, snow mass observations are scarce, and SWE reconstructions rely largely on snow models forced with meteorological inputs. Ground-based and satellite observations are often used to constrain the typically high uncertainty of modeled snow mass reconstructions, but their constraining potential is limited in data-scarce regions and prior to the onset of satellite monitoring. Here, we suggest using streamflow information as an additional information source to better reconstruct snow mass. We introduce an inverse hydrological modeling framework that selects realistic snow mass realizations based on the accuracy of their streamflow response. Before real-world application, we test the framework in two synthetic experiments. Our results demonstrate that streamflow has the potential to constrain snow mass reconstructions, but that non-uniqueness in the snow-streamflow relationship and uncertainties in the inverse modelling chain can easily stand in the way. We also show that streamflow is most helpful in estimating catchment-aggregated properties of snow mass reconstructions, in particular catchment-aggregated melt rates. Future work should assess the potential of streamflow-constrained snow mass reconstruction under real-world conditions and investigate the added value of streamflow when combined with other snow data sources.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
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.
Summary:
The submitted manuscript investigates how streamflow observations can help reconstruct historical snow mass. Therefore, the authors formulate the problem as a Bayesian inversion (i.e. estimating the posterior distribution of SWE given streamflow observations). Two complementary numerical experiments are conducted: a fully synthetic (FS) case, in which the reference SWE is generated by the same model used in the ensemble, and a semi-synthetic (SS) case, where the reference SWE is taken from OSHD data. While the selection of the posterior ensemble was carried out using NSE between observed and modelled streamflow, the evaluation of how well the selected posterior SWE maps match with the SWEprior is performed using grid-based and catchment-aggregated snow metrics. The results demonstrate that streamflow does contain meaningful information about seasonal snow dynamics, can narrow the range of plausible SWE scenarios, and is especially useful for reconstructing catchment-aggregated melt. However, the study’s results also suggest that SWE scenarios with systematic biases can still produce excellent streamflow performance. Moreover, the authors state that there is a large degree of non-uniqueness in the SWE–streamflow relationship. The semi-synthetic experiment further highlights that realistic model and forcing uncertainties amplify this equifinality. For future work, the authors recommend incorporating complementary snow observations (e.g. snow depth, SCA) to reduce equifinality and improve SWE reconstruction.
Overall Feedback:
The manuscript is of high quality in both methodology and writing and will likely be a valuable contribution to the snow-hydrology community. The authors provide a clear motivation, a well-structured experimental design, and a thoughtful discussion of relevant uncertainties (e.g., performance metric choice, model structural limitations, and forcing errors). Overall, the work is comprehensive, clearly presented, and addresses a timely question within hydrologic modeling and cryospheric science. I suggest to return the manuscript to the authors for a minor revision. I would appreciate if the authors would address my comments below during this revision.
General Comments:
In my opinion, the manuscript could benefit from a deeper methodological integration and/or theoretical discussion of recurring spatial patterns of snow accumulation, which the authors also acknowledge in the introduction (L46–56). Numerous studies show that snow distribution is controlled by (relatively static) topographic controls (elevation gradients, wind exposure, canopy effects) and tends to vary primarily in magnitude rather than in relative spatial differences. This raises an important question for the inversion framework:
Can the recurring nature of snow distribution patterns be used to reduce the effective dimensionality of the prior space or to inform the posterior selection procedure?
I would encourage the authors to reflect on how recurring snow patterns could be incorporated into different parts of their framework, for example:
1. Method (Sect. 2.1): Dimensionality reduction of the prior (Could be discussed for future applications..)
Currently, the prior is defined through independent parameter ranges, which leads to a large prior state space. Considering the reoccurring behaviour of snow distribution, do the authors think that this creates an unnecessarily large prior space and hence potentially amplifies non-uniqueness? One possibility would be to represent SWE as a scaled version of a known distribution pattern (Pflug & Lundquist, 2020; Vögeli et al., 2016; Ylönen et al., 2025), e.g. HSWE(x,y,t) = α(t)⋅Hpattern(x,y)+ϵ(x,y,t)
2. Posterior ensemble selection (Sect. 2.4): Plausibility
Posterior filtering could penalize SWE fields that violate well-known topographic dependencies (e.g., monotonic elevation gradients), thereby favoring more physically meaningful inversions. Figure 4 and especially Figure 5 show that the NSE-selected posterior contains some of the best SWE simulations of the prior – even for the SS experiment. I wonder whether a second-stage selection step, based on physically realistic spatial patterns, could further refine the posterior and help exclude SWE fields that match streamflow but are unlikely given known snow distribution processes. Such plausibility-based filtering (e.g., constraining elevation–SWE relationships or enforcing typical accumulation gradients) may help reduce non-uniqueness and improve the interpretability of the resulting posterior ensemble.
3. Discussion (Section 4.2.):
It may be worthwhile to discuss whether, in real-world applications, the existence of spatial patterns may actually help reduce non-uniqueness compared to the synthetic inversion setups presented here.
Specific Comments:
References
Daudt, R. C., Wulf, H., Hafner, E. D., Bühler, Y., Schindler, K., & Wegner, J. D. (2023). Snow depth estimation at country-scale with high spatial and temporal resolution. ISPRS Journal of Photogrammetry and Remote Sensing, 197, 105–121. https://doi.org/10.1016/j.isprsjprs.2023.01.017
Pflug, J. M., & Lundquist, J. D. (2020). Inferring Distributed Snow Depth by Leveraging Snow Pattern Repeatability: Investigation Using 47 Lidar Observations in the Tuolumne Watershed, Sierra Nevada, California. Water Resources Research, 56(9). https://doi.org/10.1029/2020WR027243
Vögeli, C., Lehning, M., Wever, N., & Bavay, M. (2016). Scaling Precipitation Input to Spatially Distributed Hydrological Models by Measured Snow Distribution. Frontiers in Earth Science, 4.https://doi.org/10.3389/feart.2016.00108
Ylönen, M., Marttila, H., Kuzmin, A., Korpelainen, P., Kumpula, T., & Ala-aho, P. (2025). UAV LiDAR surveys and machine learning improves snow depth and water equivalent estimates in the boreal landscapes.https://doi.org/10.5194/egusphere-2025-1297
Zheng, Z., Molotch, N. P., Oroza, C. A., Conklin, M. H., & Bales, R. C. (2018). Spatial snow water equivalent estimation for mountainous areas using wireless-sensor networks and remote-sensing products. Remote Sensing of Environment, 215, 44–56. https://doi.org/10.1016/j.rse.2018.05.029