Nemri and Kinnard (2020) compared four calibration strategies for the coupled GR4J–Cemaneige model across twelve snow-dominated basins of southern Quebec and showed that multi-objective calibration against both streamflow and measured snow water equivalent improves snow simulations, parameter identifiability, and parameter correlations with basin characteristics, yet leaves a large equifinal parameter ensemble that they diagnosed as reflecting structural non-identifiability and that still introduces non-negligible uncertainty into the simulated temperature sensitivity of spring peak flow under warming. It remains open whether snow-observation-inclusive calibration can deliver identifiable parameters and robust hydrological projections under transient climate-change scenarios, or whether structural model changes are ultimately required.

Background

In snow-dominated catchments, winter snow accumulation and spring melt dominate the annual streamflow regime and much of the flood risk, so projections of how warming changes streamflow depend on how well a model represents snow. The standard tools are conceptual hydrological models: lumped, low-dimensional representations of catchment behaviour whose free parameters must be estimated by calibration, i.e., by numerically searching for parameter values that make simulated streamflow match observations through an objective function such as the Nash–Sutcliffe efficiency. A widely used example is GR4J (Génie Rural à 4 paramètres Journalier), a daily lumped rainfall–runoff model with four free parameters for soil storage and routing, coupled with the Cemaneige snow module, a two-parameter temperature-index (degree-day) routine in which snowmelt is proportional to air temperature above a threshold. The coupled GR4J–Cemaneige model thus has only six free parameters.

Two long-standing problems complicate this practice. First, calibrating only against streamflow under-constrains the snow routine: many combinations of snow and rainfall–runoff parameters reproduce discharge almost equally well while simulating very different snowpacks, so the simulated snow water equivalent (SWE — the depth of liquid water contained in the snowpack) can be unrealistic even when the streamflow fit is good. Second, parameter equifinality — the existence of many parameter sets with near-identical performance, a hallmark of conceptual hydrological models reviewed by Beven (2024) — means any single optimal parameter set carries hidden uncertainty into applications such as climate impact studies. When parameters are structurally non-identifiable, i.e., their ambiguity stems from how the model's stores and fluxes interact rather than from data scarcity, recalibration against the same observations cannot remove it. Whether the residual equifinality of the coupled GR4J–Cemaneige model is structural in this sense or instead data-limited is unresolved.

Nemri and Kinnard (2020) studied exactly this configuration: GR4J–Cemaneige on twelve snow-dominated basins in southern Quebec, comparing four calibration strategies — local and global optimization against streamflow alone, separate calibration of snow parameters against snow-course SWE measurements, and multi-objective calibration that optimizes streamflow and SWE fit simultaneously, characterizing the frontier of trade-off (Pareto-optimal) parameter sets rather than a single optimum. Multi-objective calibration improved SWE simulations, parameter identifiability, and correlations between calibrated parameters and basin characteristics, but a large equifinal ensemble remained, which Nemri and Kinnard attributed to structural non-identifiability, and equifinality caused a small but non-negligible uncertainty in the simulated response of spring peak flow to warming temperatures. Earlier work on an alpine basin with the SWAT model (Tuo et al. 2018) had similarly found that multi-objective calibration including snow observations can reduce equifinality.

The study's discussion raised a chain of unresolved issues that define the open problem: whether the equifinality reduction obtained with snow observations is large enough that hydrological projections become robust under transient, time-evolving climate-change scenarios rather than the uniform warming perturbation used (a uniform perturbation shifts observed temperatures by a constant offset, whereas transient scenarios use climate-model output that evolves over the century, including changes in the fraction and timing of snow versus rain); whether structural model changes — for example explicit representation of rain-on-snow events, in which rainfall onto an existing snowpack accelerates melt, a process absent from Cemaneige — are ultimately required to obtain identifiable parameters and robust estimates of the temperature sensitivity of streamflow; and several adjacent questions (spatial representativeness of single snow-course transects in heterogeneous terrain, parameter regionalization from improved parameter–basin correlations, and spatial independence of neighbouring basins' parameters) that remain largely unaddressed.

Problem Statement

For the coupled conceptual hydrological model GR4J–Cemaneige in snow-dominated basins, determine both of the following. First, whether calibration strategy alone, specifically multi-objective calibration against both streamflow and in-situ snow water equivalent (SWE) observations, can deliver parameter sets that are identifiable; if a residual non-identifiability remains, determine whether it is structural and therefore requires structural model modification, or instead data-limited and therefore reducible by additional or better snow observations — a verdict of full identifiability, of structural non-identifiability, or of a data-limited residual all resolve this part. Second, whether the simulated hydrological response to warming — in particular the temperature sensitivity of spring peak flow — is robust under transient, time-evolving climate-change scenarios rather than under the uniform warming perturbation used; state and justify what robustness of that sensitivity is taken to mean (a named metric with a tolerance, or an explicit qualitative standard) before assessing it.

References

  1. Nemri, S. and Kinnard, C. (2020). Comparing calibration strategies of a conceptual snow hydrology model and their impact on model performance and parameter identifiability. Journal of Hydrology 582, 124474. DOI: 10.1016/j.jhydrol.2019.124474. https://doi.org/10.1016/j.jhydrol.2019.124474
  2. Ruelland, D. (2024). Potential of snow data to improve the consistency and robustness of a semi-distributed hydrological model using the SAFRAN input dataset. Journal of Hydrology 631, 130820. DOI: 10.1016/j.jhydrol.2024.130820. https://doi.org/10.1016/j.jhydrol.2024.130820
  3. Bérubé, S., Brissette, F. and Arsenault, R. (2022). Optimal Hydrological Model Calibration Strategy for Climate Change Impact Studies. Journal of Hydrologic Engineering 27(3), 04021053. DOI: 10.1061/(ASCE)HE.1943-5584.0002148. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002148
  4. Hundecha, Y., Arheimer, B., Berg, P., Capell, R., Musuuza, J., Pechlivanidis, I. and Photiadou, C. (2020). Effect of model calibration strategy on climate projections of hydrological indicators at a continental scale. Climatic Change 163(3), 1287–1306. DOI: 10.1007/s10584-020-02874-4. https://doi.org/10.1007/s10584-020-02874-4
  5. Tiwari, D., Trudel, M. and Leconte, R. (2024). On optimization of calibrations of a distributed hydrological model with spatially distributed information on snow. Hydrology and Earth System Sciences 28(5), 1127–1146. DOI: 10.5194/hess-28-1127-2024. https://doi.org/10.5194/hess-28-1127-2024
  6. Todorović, A., Grabs, T. and Teutschbein, C. (2026). Hydrological climate change impact assessment in high latitudes: are bucket-type models up to the task? Environmental Modelling & Software 201, 106964. DOI: 10.1016/j.envsoft.2026.106964. https://doi.org/10.1016/j.envsoft.2026.106964
  7. Wagener, P., Knoben, W. J. M., Schütze, N. and Spieler, D. (2026). Metrics that matter: objective functions and their impact on signature representation in conceptual hydrological models. Hydrology and Earth System Sciences 30(15), 4867–4888. DOI: 10.5194/hess-30-4867-2026. https://doi.org/10.5194/hess-30-4867-2026
  8. Beven, K. J. (2024). A short history of philosophies of hydrological model evaluation and hypothesis testing. WIREs Water 12(1), e1761. DOI: 10.1002/wat2.1761. https://doi.org/10.1002/wat2.1761
  9. Tuo, Y., Marcolini, G., Disse, M. and Chiogna, G. (2018). A multi-objective approach to improve SWAT model calibration in alpine catchments. Journal of Hydrology 559, 347–360. DOI: 10.1016/j.jhydrol.2018.02.055. https://doi.org/10.1016/j.jhydrol.2018.02.055
  10. Kinnard, C., Nemri, S. and Assani, A. (2024). Mechanisms of spring freshet generation in southern Quebec, Canada. Canadian Water Resources Journal 49(4), 421–440. DOI: 10.1080/07011784.2024.2375346. https://doi.org/10.1080/07011784.2024.2375346
  11. Shen, H., Tolson, B. A. and Mai, J. (2022). Time to Update the Split-Sample Approach in Hydrological Model Calibration. Water Resources Research 58(3), e2021WR031523. DOI: 10.1029/2021WR031523. https://doi.org/10.1029/2021WR031523