Our work is focused on the South Fork of the Flathead (SFF) River watershed basin which has an area of approximately 4340 km² and spans an elevation range from 922 to 2853 m above sea level (Fig. 1). The basin consists of forest and alpine areas with a dam-controlled reservoir covering about one fourth of the valley floor. Within the basin, there are four permanent automated weather stations, one of which is a Snow Telemetry (SNOTEL) site located at a relatively low elevation of 1326 m elevation (Emery Creek SNOTEL). SNOTEL sites are automated snowpack and climate monitoring stations operated by the Natural Resources Conservation Service which is part of the US Department of Agriculture. They provide hourly measurements of SWE, precipitation, temperature, and sometimes snow depth at remote locations in mountainous regions of the Western United States. Another SNOTEL site is located approximately 500 m west of the basin ridge line at 1841 m elevation close to the northern end of the basin (Noisy Basin SNOTEL). We include a ∼ 29 km² area around this SNOTEL site in our watershed model domain in order to have two sites with different elevations to compare our modeled SWE results against.

We use Alpine3D (Lehning et al., 2006) to model snowpack evolution physics over the SFF basin with an 800 by 800 m resolution. With this resolution the model elevation range is 944 to 2594 m above sea level. Alpine3D is a spatially distributed snow allocation and surface hydrology model developed by the WSL Institute for Snow and Avalanche Research. The model incorporates modules for resampling/filtering meteorological data (MeteoIO) (Bavay and Egger, 2014) and a physics based, finite element 1D snowpack evolution model (SNOWPACK) (Lehning et al., 1999) along with internal models for snow transport (SnowDrift), energy balance (EBalance), and runoff. SNOWPACK is a complex snow evolution model (Essery et al., 2013) that evaluates thermal conductivity based on the microstructural properties of snow (Lehning et al., 2002) instead of parametrizing conductivity as a function of snow density. This method of evaluating thermal conductivity allows for a potentially more accurate accounting of cold content within the snowpack than other models.

As part of the physics-based model structure of Alpine3D, cold content, liquid water content, and SWE of the full snowpack depth are calculated for each time step. Within the model, cold content (CC) is calculated for each layer by Eq. (1): 1CC=ciρsds(Ts-Tm), where ci is the specific heat of ice, ρs is the snow density, ds is depth of snow, and Ts and Tm are the snow and melting temperature of snow, respectively.

Model forcing parameters listed in Appendix Table A1 are derived from ERA5-Land reanalysis products (Muñoz-Sabater et al., 2021).

ERA5-Land (Muñoz-Sabater et al., 2021) is a global reanalysis product based on the land surface component of the fifth generation European ReAnalysis (ERA5) meteorological model provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) which is available globally on a 0.1° grid with hourly time steps from 1950 to 2–3 months prior to the present date. This data product provides a consistent source of surface climatic variables with high spatial and temporal resolution over a long duration. For this study we use the 2 m air temperature, 2 m dewpoint temperature, near surface soil temperature, directional 10 m wind components, downward surface solar radiation, and downward surface thermal radiation. Table A1 describes how each variable is used to calculate forcing parameters for Alpine3D model input.

Previous studies have used ERA5-Land data as meteorological forcing to run snowpack models (e.g. Zhou et al., 2025; Sourp et al., 2025). To the best of our knowledge there are no previously published examples of ERA5-Land being used to run Alpine3D or SNOWPACK.

Comparison of modeled max SWE and date of max SWE vs. SNOTEL measurements show reasonable agreement when ERA5-Land precipitation input is multiplied by a regional factor of 1.5 (Fig. A1 in the Appendix). This regional bias correction of precipitation is based on a simple regression of ERA5-Land and SNOTEL precipitation (Pan et al., 2003) which accounts for well-known uncertainty in land surface model precipitation values, especially in mountainous terrain (e.g. Cho et al., 2022; Pan et al., 2003; Raleigh et al., 2015).

Alpine3D does not output LW_bc for the snowpack, thus we calculate LW_bc using Eq. (2): 2LWbc=CCLf-SWESw-LWC, where CC is cold content (MJ m⁻²), SWE is snow water equivalent (kg m⁻²), Sw is the irreducible water saturation of the snowpack (percent by weight), LWC is liquid water content of the snowpack (kg m⁻²), and Lf is the latent heat of fusion for water (0.334 MJ kg⁻¹). Note that the units of LW_bc (kg m⁻²) can be expressed as millimeters of water equivalent (mm WE), which we use for our results.

Laboratory derived estimates of Sw range from 5 %–15 % by weight (e.g. Coléou and Lesaffre, 1998). We identify Sw in the model output as this is the minimum liquid water content within a zero-degree snowpack that allows for runoff. We calculate this for each grid point by determining the annual minimum of the liquid water content divided by SWE where (1) SWE is greater than zero, (2) cold content is zero, and (3) water flows from the base of the snowpack. This calculated value of Sw, which ranges between 0.1 % and 15.4 % over all years at all points, allows for spatial and temporal variation of irreducible water saturation without the magnitude of LW_bc falling below zero.

We examine trends in modeled SWE, cold content, and LW_bc over the 72 years of model time (water years 1951–2022). Each of these snowpack parameters varies throughout the year at each grid point, generally growing slowly in magnitude from late fall through mid-winter and reducing quickly in the late winter and spring. Since this evolution of accumulation and ablation is roughly consistent through time, we are able to analyze inter-annual variations in snow properties by date. We exclude 29 February from our analyses which is consistent with previous snow studies that assess seasonal snowpack on a specific date, usually early to mid-April in the Western United States (e.g. Bohr and Aguado, 2001; Hatchett and McEvoy, 2018; Pederson et al., 2011; Schmitt et al., 2024; Serreze et al., 1999).

Snowpack properties on any given day can vary greatly from year to year (e.g. Fig. 2a), resulting in low significance to a trend line fit to data. Therefore, to generate robust confidence intervals in our trend analysis, we use a modified bootstrap linear regression technique wherein we randomly omit a portion (20 %) of the data, compute a linear fit to the remaining data, and repeat the process 10 000 times for each day of the water year. There are approximately 20 billion random combinations of a 20/80 split for our time series data; we assume that 10 000 iterations are a representative sub-set of the full set of random combinations (e.g. Fig. 2a). Histograms of regression coefficients (slopes) for the linear fits reveal a near-Gaussian probability distribution of trends associated with the change in modeled snowpack properties on a single day of year (e.g. Fig. 2b). Trends and errors are then based on the evolution of the daily probability distributions throughout the water year.

This modified bootstrap approach allows us to constrain the upper and lower significance bounds for the full 72-year period more accurately than other slope estimation techniques such as the Theil-Sen estimator, which includes short time scales in the error calculation. Both methods give similar values for coefficient of change (less than 0.25 mm WE difference when applied to SWE data). Here we consider trends to be statistically significant only where the 2σ, 95 % bounds on the normal distribution of the regression coefficients do not include 0 mm WE per year.

Along with providing an analysis of the 72-year trend in average snowpack over the entire basin, we also analyzed the trends over 17 elevation bands of 100 m each to elucidate the effect of elevation on the snowpack properties. To aid in our analysis of the trends, we divide the snow season into four periods which are defined by inflection points in the SWE and LW_bc trend curves (see results). We call these periods Early Accumulation (19 November to 27 January), Core Accumulation (28 January to 8 March), Late Accumulation (9 March to 17 April), and Melt Onset (18 April to 7 June) (Table 1).

Snowpack properties from our model output show interannual variability greater than 60 % of mean basin values for each day from the beginning of Early Accumulation to through the end of Melt Onset (e.g. Fig. 2a). However, even with the large variance in the data, probability distribution functions of the modified bootstrap linear fits are robust, resulting in a near-Gaussian distribution of the calculated trends (e.g. Fig. 2b). The prevalence of large interannual variability resulting in near-normal distribution from Early Accumulation through Melt Onset is seen in SWE, CC, and LW_bc (Fig. 3). For modeled SWE outputs, these variations in magnitude are approximately commensurate with the mean magnitude of values whereas variations in magnitude are greater than the mean magnitude of CC and LW_bc daily values.

Trends in snowpack properties exhibit distinct seasonal patterns. Across the Early Accumulation Period, the magnitudes of SWE trends are negative, indicating diminishing snowpack over the 72 years (Fig. 3b). With changes amassing as the snowpack accumulates during winter, the trend magnitudes of SWE loss generally grows with time, reaching a rate of 1.4 ± 0.5 mm WE yr⁻¹ by the end of the period. The SWE loss is accompanied by a small reduction in CC of up to 0.050 ± 0.02 mm WE yr⁻¹ (Fig. 3d), and small but significant trends of decreasing LW_bc (Fig. 3f).

The Core Accumulation Period begins with held-over deficits in SWE, CC, and LW_bc. Trend magnitudes of SWE loss cease to increase over time, indicating no significant changes to the growth of SWE during the midwinter period. However, CC trends, which start the period as negative, become increasingly less negative early in the period. This indicates that the CC during the 72 years trended upward during much of February due to colder snowpack temperatures. The magnitude of LW_bc trends show slight decreases during early February but remain relatively unchanged during the mid-winter period. The trends of CC loss then increase in the Late Accumulation Period, likely reflecting greater surface temperatures and/or more liquid precipitation. As a result, LW_bc trend magnitudes decline sharply despite unchanged trends in SWE.

During the Melt Onset Period, SWE trends show rapidly decreasing values. This is consistent with earlier melt onset; the date of peak SWE shifted by 0.18 d earlier per year, equivalent to about two weeks earlier over 72 years (Fig. A2). The trends of CC approach zero by late May, reflecting no possible changes in the CC of an isothermal snowpack. Similarly, trends of LW_bc continues to decline as the snowpack ripens and becomes isothermal.

We find increased vulnerability to ROS flooding events at all elevations during all accumulation periods (Fig. 4a), with the largest trends occurring at the highest elevations (Fig. 4b) and the greatest risk of a total loss of LW_bc at relatively low elevations since the LW_bc magnitude is less at low elevations (Fig. 4c). Percent loss of LW_bc in the Early and Core Accumulation periods is approximately 20 % of the mean magnitude of LW_bc with the exception of the lowest elevation band. Late Accumulation percent loss of LW_bc ranges from about 42 % to 78 %, with the highest percent loss at the lowest elevations (Fig. 4a). Increased risk of ROS-induced runoff causing flooding, however, is greatest where the percent decrease in LW_bc is high and the mean magnitude SWE is also high. Our data show that this elevation range is between about 1600 m and 2300 m, where modeled LW_bc has decreased by 42 % to 58 % and over 75 % of total basin SWE typically exists (Fig. 4d).

Examination of mean LW_bc over the 72 model years reveals an increasing amount of interannual variability for mean LW_bc during the Late Accumulation period which is not apparent in the Early or Core Accumulation periods (Fig. 5a, b, c). Changes in interannual variability are especially striking when we compare the coefficient of variation (CV) for the first 36 model years (1950–1986) to the last 36 model years (1987–2022) over the three accumulation periods (Table 2). This comparison reveals that there is very little change in LW_bc interannual variability during the Early Accumulation and Core Accumulation periods (Fig. 5a, b), whereas the last 36 years of the Late Accumulation period (Fig. 5c) has nearly double the interannual variability (52.1 %) of the first 36 years (27.1 %).

There are other marked differences between the Late Accumulation snowpack LW_bc for the first 36 model years and last 36 model years. To highlight this, we examined the number of years with at least one day of zero LW_bc for each 100 m elevation band within the basin (Fig. 5d). During the first 36 model years, at the lowest elevations (900 to 1300 m) Late Accumulation LW_bc reached zero for at least one day between 25 % and 97 % of modeled years, between 1300 m and 2000 m spring LW_bc reached zero between 3 % and 9 % of the years. Only the year 1986 had zero LW_bc for at least one day above 2000 m elevation, the 1986 model run has zero LW_bc for the entire Late Accumulation period across all elevations. In contrast, the last 36 years of the model period has 2–5 years where LW_bc went to zero for at least one day at all elevations. Further, below 1300 m elevation LW_bc dropped to zero more than 50 % of years, between 1300 and 2100 m elevation 14 % to 44 % of the latter half of the years modeled had zero LW_bc, and 5 % to 11 % of years had zero LW_bc for at least one day for elevations above 2100 m.

Interpretation of the trends we identify in our analysis must accommodate the limitations of our modeling framework and assumptions. Our analysis addresses the total LW_bc of the full one-dimensional snowpack, calculated at points and distributed over the basin. However, prior studies have shown that during ROS events, initial water inputs to the snowpack often bypasses much of the snow by traveling along preferential flow paths, reaching the base and initiating runoff before the entire snowpack is saturated or “ripened” (Juras et al., 2017; Würzer et al., 2016). Runoff can therefore begin several hours before the bulk snowpack has received enough energy to become fully ripened. In our case, the 1D LW_bc can be interpreted either as the energy barrier associated with flow along preferential pathways, or as the integrated capacity of the full snowpack. The distinction is critical in hydrologic studies concerning the buffering effects on the specific timing of ROS runoff onset.

Trends of declining peak SWE in the mountain snowpack of the western US have been documented by numerous studies (e.g. Hamlet et al., 2005; Mote et al., 2005, 2018), most commonly based on 1 April values. However, LW_bc and trends therein depend on the interplay between SWE and CC and thus require more complex interpretation with regards to changes in potential runoff from ROS events.

High interannual variability is SWE is a well-established characteristic of the Western US mountain snowpack (e.g. Cayan, 1995; Musselman et al., 2021; Serreze et al., 1999; Zeng et al., 2018). Our results show an overall decline in LW_bc that is accompanied by increased interannual variability, especially in spring. Some years are characterized by shallow, warm snowpacks, while others resemble the colder, more persistent snowpacks that were common in the 1950s–1980s. Thus, despite a long-term trend toward greater ROS-induced runoff risk due to lowered LW_bc, individual years with relatively low susceptibility still occur late in the record. Overall trends need to be interpreted within the context of year-to-year variability.

The impact of changing LW_bc on the potential for ROS-induced runoff also shows strong seasonality. Our findings reveal a clear trend toward less snowpack during the Early Accumulation period, and thus reduced average flood hazard, consistent with prior work indicating that ROS risk declines with diminishing snowpack (McCabe et al., 2007; Musselman et al., 2018). Although the effects of reduced SWE and CC during the Early Accumulation period carry over to the Core Accumulation period, the latter shows no additional loss in LW_bc over our 72-year record. SWE exhibits no significant trend, and CC actually increases over much of the period, as does LW_bc early on. Had significant warming or rainfall increases occurred, we would expect declining CC and LWbc, which are not observed. This stability is remarkable compared to the substantial changes in snowpack properties during the early and late periods. Moreover, despite representing a relatively small share of the snowpack's energy balance, the CC appears to play a critical role in maintaining this resilience.

Although SWE in our basin peaks in later April or May, typical of the Northern US Rockies (e.g. Bohr and Aguado, 2001; Zanewich and Rood, 2025), March emerged in our analysis as the critical month with relatively sustained peak LW_bc. After March, the average potential for runoff from ROS events has increased as the CC has trended strongly downward and the number of days with a ripe snowpack has trended upward. While the largest changes in LW_bc were at high elevations, this is where the LW_bc is greatest and requires the most energy input from a ROS event to induce runoff. Low elevation areas of the basin, on the other hand, do not accumulate much SWE and never had much LW_bc against ROS flooding. Thus, it is the mid-to-high elevations that represent a “vulnerability zone,” where significant SWE volume, combined with marked LW_bc decline, creates conditions most conducive to ROS enhanced runoff. These areas contribute the bulk of basin SWE, making their increased susceptibility particularly important for downstream flood risk.

Quantifying the historical frequency, duration, and intensity of winter rainfall events in mountain basins remains challenging, particularly in basins lacking long-term instrumentation. While extreme weather events are already intensifying (e.g. Fischer and Knutti, 2016; Li et al., 2024) and are projected to further increase under a warming climate (Seneviratne et al., 2021; de Vries et al., 2024), the rarity and spatial variability of such events make them particularly difficult to quantify and project at the scale required for watershed hazard assessments (e.g. Broderick et al., 2019). Conceptually, a warming climate tends to (a) shift precipitation from snow to rain and (b) increase the magnitude of extreme precipitation events (Donat et al., 2013; Rahmstorf and Coumou, 2011). However, the detailed quantification of these metrics for a given basin, which is necessary for robust rain-on-snow (ROS) risk analysis, remains elusive.

Nevertheless, the relevance of our findings depends on whether the observed 72-year decline in snowpack LW_BC is meaningful relative to the size and frequency of winter rainfall events in this basin. This motivates a first-order assessment of snowpack LW_BC with precipitation. Over the study period, the 15 March snowpack LW_BC declined on the average trend line by 19 mm, from 46 mm in 1950 to 27 mm in 2022. Thus, a rainfall event of 27 mm would deplete all the 2022 snowpack LW_BC value, but only 60 % of the 1950 value which requires 46 mm. How frequent have such events been? Using the 49 years of existing precipitation records from the Noisy Basin SNOTEL site, March events with above-freezing air temperatures had recurrence intervals of approximately 2 years for 27 mm and 10 years for 46 mm. Many of these events were likely warm snowfalls rather than pure rain. Nevertheless, the decline in snowpack LW_BC along the trend line implies an impactful increase (fivefold in this exercise) in the frequency that the snowpack LW_bc could be fully depleted by a precipitation event. Importantly, this appraisal (1) is based on changes to the snowpack only, not precipitation; (2) assumes that all precipitation falls as rain, and; (3) applies only to the mean trend, noting that snowpack LW_BC exhibits substantial interannual variability.