Quantifying Snowmelt-Driven Runoff and Estimating the Regional Water Balance of the Smith River Watershed, Montana, USA

Cooverji, Farhaan; Cho, Eunsang; Li, Bailing; Vuyovich, Carrie; Jacobs, Jennifer M.; Cho, Eunsaem; Sproles, Eric A.; Tuttle, Samuel E.

doi:10.5194/egusphere-2026-4186

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https://doi.org/10.5194/egusphere-2026-4186

Preprints

24 Aug 2026

| 24 Aug 2026

Quantifying Snowmelt-Driven Runoff and Estimating the Regional Water Balance of the Smith River Watershed, Montana, USA

Farhaan Cooverji, Eunsang Cho, Bailing Li, Carrie Vuyovich, Jennifer M. Jacobs, Eunsaem Cho, Eric A. Sproles, and Samuel E. Tuttle

Abstract. Seasonal snowpacks in snow-dominated watersheds across the western United States play a critical role in sustaining regional water resources by delaying runoff and regulating streamflow. Understanding snowmelt contribution to runoff is essential for quantifying regional water resources. While prior studies have utilized proportional approaches to estimate this contribution, a lack of incorporating the physical processes simulating snowpack evolution yields some uncertainty regarding the fate of deposited snow. This study explored water balance approaches and estimates snowmelt-induced runoff in the Smith River Watershed (SRW) located in Montana for a five-year period between the water years of 2017 and 2021. Annual watershed-averaged water balance analyses were carried out using a Noah Multiparameterization land surface model (LSM) dataset and hybrid observation-model-based approaches. While the hybrid approach provides more accurate estimates for water budget variables, the LSM-based approach was more suitable for the annual water balance analysis due to its ability to close the water budget and simulate relevant hydrological processes. The analysis also revealed that underestimations of evapotranspiration and sublimation in Noah-MP result in an overestimation of runoff. Snow-induced runoff was quantified by separating rain- and snow-generated surface and subsurface runoff using outputs from the Noah-MP dataset and hybrid mass balance approaches. The analysis yielded a value of ~32 % (85 mm) of runoff originating from snowmelt during the study period—substantially lower than previous regional estimates (~65 %) within the SRW reported in the literature. The study’s results highlight the value of utilizing land surface models to accurately quantify snowmelt contributions to runoff in mountain watersheds, and underscore the importance of continued refinement of multi-method approaches for representing watershed hydrology and supporting water resource management in snow-dominated regions of the western United States.

Received: 19 Jul 2026 – Discussion started: 24 Aug 2026

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Farhaan Cooverji, Eunsang Cho, Bailing Li, Carrie Vuyovich, Jennifer M. Jacobs, Eunsaem Cho, Eric A. Sproles, and Samuel E. Tuttle

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-4186', Anonymous Referee #1, 05 Oct 2026
In this paper, the authors explore different approaches to estimate the annual water balance of the Smith River Watershed (SRW), located in the headwaters of the Missouri River basin (Montana, USA), and quantify the contribution of snowmelt to runoff during the period WY 2017-WY 2021. To this end, the authors first examine an annual water balance obtained entirely from the Western Land Data Assimilation System (WLDAS; Erlingis et al. 2021) – which is based on the Noah land surface model with Multiple Parameterization options (Noah-MP; Niu et al. 2011) forced with NLDAS-2 – and then contrast it against two hybrid configurations: (i) an irrigation-adjusted version of the WLDAS water balance that incorporates consumptive use from LANID, and (ii) a multi-source water balance that combines PRISM precipitation, OpenET evapotranspiration, SnowModel sublimation, USGS streamflow, and groundwater and soil moisture storage changes from WLDAS. Snowmelt-induced surface and subsurface runoff are subsequently quantified at the grid-cell scale by adapting the snowmelt tracking algorithm of Li et al. (2017) to account for groundwater as a distinct component of subsurface storage. The results show that the WLDAS-based water balance yields very small annual residuals, although it underestimates ET and sublimation – and therefore overestimates runoff – when compared to the other datasets. Further, sublimation estimates differ greatly among WLDAS, SnowModel and SNODAS (~3%, ~17% and ~43% of annual snowfall, respectively). Finally, the authors estimate that ~32% (85 mm) of total runoff originates from snowmelt, which is substantially lower than the ~65% previously reported by Li et al. (2017) for the region.
This is a relevant topic for the snow hydrology and water resources communities, and the attempt to incorporate groundwater storage into the tracking of snowmelt-induced runoff is a valuable extension of previous work. However, I have important concerns regarding the formulation of the water balance equations, the level of reliability that the authors assign to the datasets used to construct the hybrid water balances (most of which come from process-based models), and the way the methods and results are presented. In particular, much of the methodological information is currently located in the Results section, which makes the study very hard to follow and, more importantly, hard to reproduce. I strongly recommend the authors to address these issues before this manuscript can be considered suitable for publication in HESS.
Major comments
Water balance equation (L230): since WLDAS comes from Noah-MP, I think that the water balance equation should consider changes in canopy storage and SWE. The same comment applies to the hybrid water balances (L262), which use groundwater and soil moisture storage from WLDAS, and to the annual water balance presented in Table 2 (L339), where interannual variations in SWE and canopy storage should be included. Additionally, I think that Section 4.1.2 would tremendously benefit from a diagram that explains how the different datasets combine in the hybrid water balance approach.

Reliability of datasets (L345-348): I do not think that the datasets used to construct the hybrid water balances are necessarily reliable, since these involve the use of process-based models that carry uncertainties in input forcing data, structural uncertainties (i.e., model equations and parameterizations used) and parametric uncertainties. To assess the reliability of these products (e.g., SNODAS, SnowModel), I think you should contrast model simulations against in situ observations and/or satellite remote sensing (SRS) products.

Section 5.2: In its current form, this section is very hard to follow. Additionally, the results from the three water balances (i.e., WLDAS-based, irrigation-adjusted and multi-source) should be included in a single figure/table to effectively make the point regarding possible differences among water balance approaches.

Minor comments
L24: The right name of the model is Noah Land Surface Model with Multiple Parameterization options (Noah-MP; Niu et al. 2011). Please correct here and everywhere else in the manuscript.

L27-28: Isn't this result obvious considering that, in the long term and at the annual time scale, it is expected that P = Q + ET?

L28-30: This sentence should be earlier in the abstract (i.e., before describing the results).

L58: 'its headwaters is critical since these headwater catchments'. This reads awkward. Please revise.

L63-64: This description – which refers to regional water balance approaches based on “measurable components” – contradicts L71, which mentions LSMs (whose outputs are not necessarily contrasted with measurements) as another regional water balance approach.

L76: This is not the right name of the model. Please revise and correct (see minor comment 1).

L85-93: I suggest citing these studies in chronological order.

L99-100: 'constrained by isotope data'. Li et al. (2017) did not constrain the method with isotope data: they simply validated the snowmelt tracking algorithm by comparing them against isotope data. Please revise.

L106: Although this is true, it should be noted that VIC produces baseflow anyway, which is released from the third soil layer.

Figure 1: I think that the resolution of the figure should be improved considerably. Please include the location of the two stream gages mentioned in section 3.6.

L144: Please spell out the model's name correctly before including the acronym (i.e., 'Noah Land Surface Model with Multiple Parameterization options').

L150: I suggest describing the meteorological datasets before the hydrological datasets.

L164: Please spell out all these acronyms (METRIC, geeSEBAL, DisALEXI, SSEBop, PT-JPL and SIMS) the first time they are used, and include appropriate references.

L166: Citation missing (the same applies to L207).

Section 3.4: For the data extracted from model simulations, I think that it would be useful to have a summary table with model names, references, parameterizations used (especially for modular platforms like Noah-MP), parameters calibrated (if any) and calibration procedure (objective function, calibration period, optimization algorithm). Please specify whether (and which) a spin-up period was considered in the final model runs. All this information is critical to judge the credibility of your water balance results.

L184: But you are also using sublimation from WLDAS. Are you combining them somehow? Please clarify.

L190-191: 'to evaluate the estimated sublimation by WLDAS and SNODAS'. I think that a better word for what you did is 'contrast' since, in my opinion, model evaluations should be performed using reference observational (in situ or remotely sensed) datasets.

L210: But this variable (ETa) is also obtained from WLDAS. Please clarify.

Table 1: Please switch 'Spatial resolution' to 'Horizontal resolution'. Also, you are including the period, NOT the temporal resolution. Please add the temporal resolution (e.g., daily, monthly) in a separate column. I also suggest adding a column with the variables used from each dataset, and spelling out the acronyms of the dataset names in the first column.

L227: 'The extracted data'. Extracted from Noah-MP? Please clarify.

L231: By definition, ET is the sum of ALL evaporative fluxes that go to the atmosphere (including sublimation).

L243: Why are you considering two sublimation values (SNODAS and SnowModel)?

L248: At this point, I forgot whether OpenET has some overlap with WLDAS. Please clarify (the diagram suggested in major comment 1 could also help here).

L287-292: If these are exactly the same equations used by Li et al. (2017), I think it should be mentioned here.

L293 (Eq. 7): I think that this equation is missing the time step (Δt).

L295: Does ETsnow,t include sublimation?

L297-298 (Eq. 8): I think that the time step is also missing in this equation.

L307: Do you really need such a long spin-up period (WY 1980 to WY 2016)?

L311 (Eq. 10): Why did you use the value of fWS,snow at time step t-1 and NOT t?

L339: I presume that ET excludes sublimation here, right? Please clarify this point throughout the manuscript.

L345-350: All this information should be in the Methods section. Additionally, the explanation on the use of LANID CU values (L348-350) is extremely hard to follow, and I do not think I could replicate the methodology with it.

L354-363: This text should be in the Methods section.

L364-365: What do you mean with 'well-established'? Please see major comment 2. I think that 'widely used' would be a better adjective for these datasets. Also, this text should be in the Methods section.

L373-375: Higher resolution does not necessarily imply more realistic results. I do not believe this statement unless you show a comparison against in situ SWE or snow depth measurements.

L394-395: I strongly advise showing these differences graphically.

L395-399: Where (i.e., figure/table) should I be looking if I wanted to verify these points.

Section 5.3: I think you should show, for a sample of grid cells within the domain, whether the unknown fraction of subsurface water origin goes to zero.

L409-411: This text should be in the Methods section.

L415-416: This text should be in the Methods section.

L416-419: There is a lot of redundant information in this sentence. Please revise.

L426-427: I do not see this one-month lag. Indeed, I see snow subsurface runoff highly correlated with total snowmelt runoff in Figure 6. Instead, what I see is a one-month delay between snow subsurface runoff and snow surface runoff. Is this what you wanted to say?

L433-441: Overall, it is hard to visualize the connections with topography. I suggest correlating the variables analyzed with elevation.

L445: 'due to forested landcover'. Same comment here. You could correlate the variables analyzed against forest fraction to make this point?

Figure 7: I suggest using the same ranges in the colorbars within the same column.

L461-463: I think that this paper (Hedrick et al. 2020) should be mentioned in the Introduction.

L467-469: Why are you contrasting your results with those obtained for the Tuolumne basin? Did Hedrick et al. (2020) use the same methodology? I think that the presentation of this comparison needs some context.

L474-477: This study (Denver et al. 2025) should be mentioned in the Introduction as well.

L478: Can these differences be explained by methodological differences? Even if the numerical models were the same, differences may be attributed to parameter values.

L485-486: This study (Dozier and Melack 1989) should also be mentioned in the Introduction.

L496: 'the water balance closure'. Here and everywhere else: please specify what you mean with 'water balance closure'. Do you mean that the mean interannual change in catchment water storage is zero? Does it make sense to examine water balance closure at the annual scale only for a 5-year period?

L500: 'to maintain low annual residual storage differences'. Why do you want to maintain low annual differences in storage? Note that the time that every catchment takes to reach dS/dt = 0 depends on a specific combination of climatic and physiographic properties (Han et al. 2020).

L505: 'SnowModel's robust snowpack sublimation processes'. How do you know that this is comparatively more robust?

L521-523: I recommend the authors be more cautious with statements like this. Even if a numerical snow model includes detailed process representations, there are large uncertainties associated with parameters that are many times hard coded.

L539-542: I think that the difference in period (1950-2005 in Li et al. 2017 versus WY 2017-WY 2021 in this study) is not minor at all. Were your five years wetter or drier than an average climatological WY? How about model parameters? Note that the choice of model parameters can have a large effect on the partitioning of precipitation into ET and runoff (e.g., Mendoza et al. 2015, 2016).

L555: Please insert specific citations for the Rio Grande and Lower Colorado basins.

L564: I think you should include parameter estimation here.

Some suggested edits
L24 and L76: 'Noah Multiparameterization' -> 'Noah Land Surface Model with Multiple Parameterization options (Noah-MP)'.

L55: 'As evidenced by the 2019 flood events alone, these flood events' -> 'The 2019 flood events'.

L233-234: 'the Sub variable values were subtracted from each year's ET and presented as a separate variable' -> 'the Sub variable values were subtracted from each year's ET, such that ET represents all evaporative fluxes except sublimation'.

L319: 'reginal' -> 'regional'.

L453: 'are depicted are percentages' -> 'are depicted as percentages'.

L533: 'Monthly' should not be capitalized.

L551: 'appears to underestimate' or 'underestimates'? Please be specific.

References
Erlingis, J. M., and Coauthors, 2021: A high-resolution land data assimilation system optimized for the Western United States. J. Am. Water Resour. Assoc., 57, 692-710, doi:10.1111/1752-1688.12910.
Han, J., Y. Yang, M. L. Roderick, T. R. McVicar, D. Yang, S. Zhang, and H. E. Beck, 2020: Assessing the steady-state assumption in water balance calculation across global catchments. Water Resour. Res., 56, e2020WR027392, doi:10.1029/2020WR027392.
Li, D., M. L. Wrzesien, M. Durand, J. Adam, and D. P. Lettenmaier, 2017: How much runoff originates as snow in the western United States, and how will that change in the future? Geophys. Res. Lett., 44, 6163-6172, doi:10.1002/2017GL073551.
Mendoza, P. A., M. P. Clark, N. Mizukami, A. J. Newman, M. Barlage, E. D. Gutmann, R. M. Rasmussen, B. Rajagopalan, L. D. Brekke, and J. R. Arnold, 2015: Effects of hydrologic model choice and calibration on the portrayal of climate change impacts. J. Hydrometeorol., 16, 762-780, doi:10.1175/JHM-D-14-0104.1.
--, M. P. Clark, N. Mizukami, E. D. Gutmann, J. R. Arnold, L. D. Brekke, and B. Rajagopalan, 2016: How do hydrologic modeling decisions affect the portrayal of climate change impacts? Hydrol. Process., 30, 1071-1095, doi:10.1002/hyp.10684.
Niu, G.-Y., and Coauthors, 2011: The community Noah land surface model with multiparameterization options (Noah-MP): 1. Model description and evaluation with local-scale measurements. J. Geophys. Res., 116, D12109, doi:10.1029/2010JD015139.
Citation: https://doi.org/10.5194/egusphere-2026-4186-RC1
RC2:
'Comment on egusphere-2026-4186', Anonymous Referee #2, 11 Oct 2026
General Comments
This study quantifies snowmelt-driven runoff in the Smith River Watershed (SRW) using outputs from the Noah-MP land surface model through WLDAS. The authors evaluate the regional water balance using several model products and observational datasets, and further estimate snowmelt-induced surface and subsurface runoff based on the method of Li et al. (2017), with groundwater storage included.
The study is interesting, fits well within the scope of HESS, and provides a comprehensive assessment of the regional water balance and snowmelt contributions to runoff by integrating multiple datasets and extending the method of Li et al. (2017). However, I have several major concerns regarding the Noah-MP model configuration, calibration and evaluation, meteorological forcing, and the reliability of the resulting snowmelt runoff estimates. These issues should be addressed before the manuscript can be considered for publication.
Major Comments
The Noah-MP parameterization schemes used in WLDAS (Section 3.1) are not sufficiently described. Noah-MP provides multiple options for hydrological processes, including runoff generation, precipitation phase partitioning, snow processes, frozen soil, and vegetation dynamics (Niu et al., 2021). Since these choices can affect the simulated water balance and snowmelt-driven runoff, the authors should explicitly describe the schemes adopted in this study.

Was the Noah-MP configuration used by WLDAS calibrated specifically for the SRW? The study appears to use existing WLDAS outputs without basin-specific calibration. However, simulated runoff is substantially higher than observed USGS streamflow (approximately 267 versus 69 mm/year on average, Table 3, without accounting for irrigation), raising concerns about the reliability of the estimated snowmelt contributions. I would encourage the authors to recalibrate or further constrain Noah-MP using available observations, particularly streamflow and snow data, and reassess the resulting snowmelt contributions.

The study uses WLDAS outputs driven by NLDAS-2 meteorological forcing, while PRISM precipitation appears to agree better with station observations. Why was bias-corrected precipitation and temperature forcing not considered? Given the substantial precipitation differences and their influence on snow accumulation and runoff generation, I suggest considering rerunning Noah-MP with bias-corrected forcing, for example, with corrections informed by PRISM and station observations.

For a snow-influenced watershed, I would expect a more comprehensive evaluation of snow accumulation and melting processes. The study compares sublimation estimates from WLDAS, SNODAS, and SnowModel but does not sufficiently evaluate their SWE estimates. I suggest comparing SWE time series from these products against available observations or SNOTEL or other independent SWE datasets to assess the reliability of simulated snow accumulation and melting processes.

The authors emphasize the small residuals in the WLDAS-based water balance (Line 496). However, good water balance closure does not necessarily indicate accurate simulation of individual hydrological components, particularly given the substantial runoff overestimation. Furthermore, the irrigation adjustment in Table 4 appears to redistribute runoff into runoff and irrigation consumption without changing the overall water balance residual. Please clarify the physical interpretation of this adjustment and its implications for model evaluation.

Lines 415–419 indicate that approximately 15–17% of subsurface water remains of unknown origin after the spin-up period. How does this uncertainty affect the estimated 32% snowmelt contribution to runoff? I suggest quantifying its potential influence and discussing the robustness of the main conclusions.

Minor Comments
Figure 1(a): Consider using more contrasting colors for the land-cover classes to improve their visual distinction.

Line 231 and Eqs. (2)–(9): Please explicitly indicate the units of the water balance variables and clarify the units used in the equations where appropriate.

Line 296: The statement "Dividing Equation (7) with the total quantity of each variable" is unclear. Please explain the mathematical derivation of Eq. (8) from Eq. (7) more explicitly, including the assumptions involved.

Tables 2 and 4: Several columns contain identical values, including P, ET, Sub, ΔGW, and ΔSM. Consider simplifying Table 4 or highlighting only the differences to avoid unnecessary repetition.

Line 426: The authors discuss the lagged runoff response to snowmelt, but Figure 6 presents snowfall rather than snowmelt. Please clarify whether the reported lag is relative to snowfall or actual snowmelt.

Figure 6: The legend labels the dark-blue line as "Total snow runoff", whereas the caption describes it as "total monthly runoff". Please clarify which variable is shown and correct the legend or caption accordingly. If the line represents snow-generated runoff, it should be consistent with the sum of snow-generated surface and subsurface runoff.

Line 499: Noah-MP underestimates ET and sublimation while overestimating runoff. Please clarify how these biases may affect the estimated snowmelt contribution to runoff.
Citation: https://doi.org/10.5194/egusphere-2026-4186-RC2

Farhaan Cooverji, Eunsang Cho, Bailing Li, Carrie Vuyovich, Jennifer M. Jacobs, Eunsaem Cho, Eric A. Sproles, and Samuel E. Tuttle

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Short summary

Quantifying how much snowmelt feeds mountain rivers is hard. In a Missouri Headwater watershed, we estimated the region's water cycle, focusing on snowmelt generation. Well-validated hydrological data were more accurate individually, but the land surface model better balanced the annual water budget. It also underestimates evaporation and sublimation, inflating runoff estimates. This approach shows snowmelt supplies only about 32 % of runoff, well below earlier estimates near 65 %.


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