Estimating the streamflow driven by snowmelt in rugged mountain watersheds is difficult. Challenges are associated with the limited observations of hydrologic and meteorological datasets and inadequate implementation of the snow hydrology models. This study aims to improve streamflow prediction during the snowmelt season using a snow hydrology model aided by field observations. When the point-based weather forcing data and in-situ snowpit measurements exist in or near a small-scale (2–3 km2) watershed, the hydrologic model demonstrated an improved streamflow prediction during the snowmelt period. A snow hydrology model was applied to the Senator Beck Basin (SBB) in Colorado to improve the streamflow prediction. A temperature index method was implemented in the hydrological model to accommodate the snowmelt routine, which releases water as a multiplication factor for a grid temperature surplus above the melting point. The temperature index was adjusted using in-situ snowpit observations collected in the SBB by the NASA SnowEx Year-1 campaign in February 2017. Using the determined temperature index and weather forcing data from the nearby USDA snow observation telemetry station, the Nash-Sutcliffe Efficiency of the simulated streamflow was elucidated with a value of 0.88 against the observed streamflow during April 1–22, 2017.

  • The temperature index snowmelt method with snowpit observations captures the streamflow.

  • Predictability of the streamflow requires weather station and snowpit observation.

  • A model application demonstrates spatio-temporal patterns of cold-region watersheds.

Monitoring global terrestrial snow and its release to supply freshwater has received increasing attention (Sturm et al. 1995). This release has primarily been driven by unprecedented climate change and its societal impacts on livelihoods in areas where snow and ice melt provide a significant amount of water resources (Barnett et al. 2005). However, it is challenging to measure terrestrial snow because it is located in difficult-to-reach areas with high altitudes and latitudes. Efforts have been devoted to resolving this observational challenge with remote sensing technologies to retrieve the snow water equivalent (SWE) and the timing of its melt on a global scale (Tedesco & Narvekar 2010; Anderson et al. 2014). Other contributions have been made by obtaining the best remote sensing methods for SWE, such as the National Aviation and Space Administration Cold Land Processes Field Experiment (NASA CLPX, Cline et al. 2009), the European Space Agency (ESA) Nordic Snow Radar Experiment (NoSREx) (Lemmetyinen et al. 2016), and the NASA SnowEx (Kim et al. 2017). Previous efforts (Simpson et al. 2004; Guan et al. 2013; Brown et al. 2014) have shown promise in improving streamflow estimation using remote sensing technologies. While various remote sensing technologies have been applied in the visible, infrared, microwave, and gamma spectra (Tuttle et al. 2017), it remains limited for obtaining sufficient validation for snow retrieval in alpine/high latitude areas, and its release to downstream watersheds is still difficult. Hydrologic modeling has been applied to resolve the issues of SWE remote sensing, but complexities in the simulation of snow hydrological processes, such as streamflow generation, persist (Anderson et al. 1955; Lehning et al. 2006; DeWalle & Rango 2008). While several well-represented snow hydrology models exist (CRHM, Pomeroy et al. 2007, CHM, Marsh et al. 2020; Boucher et al. 2020; Alvarado-Montero et al. 2022; Gan et al. 2022), the application of the sophisticated models is often challenging for streamflow prediction on a regional scale in the snowmelt-dominant watersheds because of the models' computational costs and incorrect estimation of the streamflow even with detailed simulation of the snowpack. It is interesting to see recent advancements in SWE data assimilation techniques (Dechant & Moradkhani 2011; Bergeron et al. 2016; Gichamo & Tarboton 2019). Various statistical methods were attempted using satellite remote sensing and input parameter calibration methods in the snowmelt-dominant watersheds. However, it is critical to have exact in-situ/remote sensing observations to improve the streamflow prediction due to snowmelt (Marsh & Woo 1984). In this paper, streamflow estimation was done using a simple but snow hydrology model in a high mountain watershed with a data-sparse environment.

Anderson (1976) pioneered the implementation of a snow hydrology model in Sierra Nevada, California, USA, adopting an energy-balance approach to simulate the snow physical properties of snow interacting with the ambient atmosphere. Tarboton & Luce (1996) developed the Utah-Energy-Balance (UEB) model, a physically distributed watershed hydrological model, in which snow is a hydrologic variable that plays a similar role to rainfall when released due to the physical temperature of the snowpack exceeding the melting point. Ferguson (1999) summarized snowmelt methods in a fully distributed manner by applying them to a small-scale watershed. Bartelt & Lehning (2002) implemented and applied the energy-balance method in an alpine watershed in Europe. Brauchli et al. (2017) recently conducted detailed numerical experiments on snowmelt runoff in the Swiss Alps using a high-resolution distributed snow hydrology model to evaluate the response of streamflow to snowmelt at sub-basin scales. Rajkumari et al. (2019) reported that spatially varying temperature indices are critical for controlling the snowmelt runoff processes in alpine watersheds. Follum et al. (2019) implemented more advanced temperature index methods for snowmelt-dominant watersheds. They also applied the temperature index model applications to the Senator Beck Basin by calibrating the snow-covered area (SCA) against the remotely retrieved SCA observations. While the temperature index method has been applied for a very long time since 1887 (Hock 2003), it is still limited in regards to showing the exact improvement in streamflow prediction, especially during the snow melt season. The challenges are primarily associated with relatively large time steps such as daily and an averaging effect to evaluate three water years of simulation time span. On the other hand, most community-based land models also have snow subroutines at large spatial scales, such as semi-continental scales (Andreadis & Lettenmaier 2006; Niu et al. 2011; Toure et al. 2018), where the models parameterize cold-region hydrological processes at a semi-continental (degree) scale and in a spatially distributed manner considering changes in the snow with elevation in the modeling domain. However, such models remain restricted for quantifying the streamflow driven by snowmelt on finer scales, such as grid resolutions of several meters. With the recent advancements in remote sensing technologies, it is essential to apply a simple but practical snowmelt method at small watershed scales, such as several square kilometers. A snow hydrology model supported by the snowmelt method can describe the cold-region hydrological process on a meter scale, including the streamflow and spatiotemporal pattern of the snow physical properties, such as the snowmelt rate, the water depth, and the SWE. In addition, the use of in-situ SWE observations in a basin can assist in determining the temperature index to improve the streamflow prediction in a small-scale watershed such as 2–3 km2 of the basin area.

When the snowpack temperature is above the freezing point, the released water is added to the water depth during the current time step in the overland and channel grid cells. The amount of released water is determined by the product of the temperature surplus above 0 °C and the temperature index. A series of sensitivity tests were conducted by varying the temperature indices to determine the temperature index. In-situ snowpit observations from the watershed were used to adjust the simulated SWE to the observed in-situ SWE. Although the snowpit measurements were spatiotemporally sparse, the temporally continuous and spatially distributed hydrologic simulations enabled the prediction of the in-situ SWE at the coincident time and collocated location of the snowpits. After fitting the temperature index based on the SWE sensitivity tests against the in-situ SWE observations, the streamflow was assessed against the measured streamflow at the outlet for evaluation. It is thus imperative to use in-situ observations to find the temperature index in the rugged alpine watershed, where hydrologic and meteorological observations are limited.

In response to the observational challenge of seasonal snow, snow observation telemetry (SNOTEL) was established in the western U.S. by the Natural Resources Conservation Service of the U.S. Department of Agriculture, where snowmelt is a primary component of freshwater resources, mainly in the western United States (Schaefer & Paetzold 2001). The SNOTEL was the first semi-continental scale of the observational network to measure SWE and other environmental variables, including air temperature, precipitation, and wind speed. However, it is still challenging to cover SWE observations for the entire U.S. on a continental scale and on a global scale as well. Thus, remote sensing efforts have recently been devoted to determining an optimal set of sensing techniques for monitoring global snow from space. For its first year of operation, NASA SnowEx was conducted in western Colorado during 2016–2017 at two sites: (1) Grand Mesa, Colorado, USA, a 3500-m plateau, and (2) Senator Beck Watershed, Colorado, USA, which is an alpine basin. Senator Beck was mainly selected to accommodate watershed-based research in an area where snowmelt predominantly contributes to freshwater generation. The Senator Beck Basin (SBB) is also maintained by the Colorado Avalanche Center (CAC), which continuously collects snow-related observations and performs several activities, including routine snowpit observations, weather station networks, and autonomous streamflow observations at the Senator Beck watershed outlet. Streamflow observations provide a critical opportunity to evaluate the improvement in streamflow prediction driven by snowmelt. NASA SnowEX also conducted in-situ snowpit observations throughout the basin in February 2017. With the given observations at the SBB, an application of the snow hydrology model is a prerequisite to demonstrate the utility of the in-situ SWE observations for the temperature index and an improvement in the streamflow prediction.

This study aims to answer two primary questions: (1) Can an adjusted range of the temperature index be obtained using simulated SWEs against in-situ SWE observations? (2) To what extent can streamflow prediction be improved if a hydrologic model is applied with the selected temperature index? Handling a geographic information system (GIS) dataset is a prerequisite for simulating the distributed hydrological model. Driving the hydrologic model with the preprocessed inputs and meteorological forcing produces hydrologic outputs, including the water depths, snowmelt rates, SWEs over the watershed, and streamflow at the channel outlet during the simulation period. By answering these two questions, another benefit can be obtained: elucidation of cold land hydrological processes in a regional-scale watershed. This information can benefit both watershed modelers and snow ecologists with springtime-streamflow generation and interpretation of the cold-region hydrological processes. A temporally discretized and spatially distributed SWE, snowmelt rate, and water depth analyses can be used to describe cold-region hydrological processes. Finally, the simulated streamflow at the Senator Beck Basin outlet was compared to the observed streamflow in order to confirm the improvement in streamflow prediction attributed to the updated SWE.

The remainder of this paper is organized as follows. Section 2 describes the temperature index method, a preprocessing of the input dataset, the study site, the Senator Beck watershed, and SNOTEL observations at the Red Mountain Pass, Colorado. Section 3.1 begins with the sensitivity tests of hydrologic simulations using various temperature indices. The simulated SWEs were collocated with in-situ observed snowpit SWEs to determine the temperature index. A streamflow comparison was then conducted to improve the streamflow prediction with the pre-determined temperature index in Section 3.2. The spatiotemporal patterns of the snowmelt rate, water depth, and SWE are also presented in Section 3.3. Section 4 concludes the paper by discussing the value of in-situ SWE observations when applying the distributed hydrological model in a snowmelt-dominant basin. The conclusions are supported by the inter-annual variability of snowmelt-driven streamflow in the 2016, 2017, and 2018 water years in the Senator Beck Basin. Section 4 also includes further recommendations for snowmelt schemes in the distributed hydrological model.

It is imperative to determine the streamflow peak during the snowmelt season, especially in poorly observed and hard-to-reach watersheds. Figure 1 illustrates how two primary parameters, the temperature index and the amount of snowfall in the snow hydrology model, can be adjusted to fit the streamflow during the snowmelt season, which features a sub-seasonal prediction of the streamflow driven by the preceding snowmelt. The key observation of SWE can be acquired either by the snowpits or the remote sensing observation. This article is based on the snowpit observation to determine a range of the temperature index and the amount of snowfall (Psnow), where remote sensing technology can provide better means to replace labor-intensive snowpit observations, especially in watersheds in high latitudes and altitudes. The temperature index method requires a single or several in-situ SWE observations and an autonomous weather station in a given watershed. The observed SWE can provide an upper and a lower limit of the temperature indices when applying the snow hydrology model at the same location as the snowpit observation and the weather station. This study focused on the use of the in-situ SWE observations and their applicability to find the temperature index. Instead of calibrating and validating a snow hydrology model, this study concentrates on the practical applicability of in-situ SWE measurements to streamflow predictability in snowmelt-dominant watersheds. Thus, this simplified case is extended to a realistic one in the SBB, where the Red Mountain SNOTEL observations provide precipitation and air temperature data. Over 10 locations of the snowpit samplings were provided by NASA SnowEx. The following sub-sections explain all of the components to support the streamflow predictability, including the snow hydrology model along with the temperature index method in Section 2.1, pre-processing of the watershed dataset in Section 2.2, and the meteorological observations provided by the nearby SNOTEL site in Section 2.3.
Figure 1

A schematic view of sub-seasonal prediction of streamflow by updating Mf (temperature index) and Psnow (the amount of winter snowfall) using simulated and observed SWE in the previous months in February and March to the spring streamflow in April and May.

Figure 1

A schematic view of sub-seasonal prediction of streamflow by updating Mf (temperature index) and Psnow (the amount of winter snowfall) using simulated and observed SWE in the previous months in February and March to the spring streamflow in April and May.

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TREX and implementation of the temperature index method

Two-dimensional Runoff and eXport (TREX), a physically distributed hydrological model, has been developed at Colorado State University since 2008 to accommodate regional distributed hydrologic models in a meter-scale (England et al. 2007; Velleux et al. 2008). TREX is written in the C programming language and was adopted from a previous CASC2D (Julien & Saghafian 1991; Julien & Rojas 2002) model written in Fortran 77. However, the CASC2D still did not have a snowmelt subroutine in 2003. The first author of this paper implemented a function to read snowfall from weather forcing, and modified precipitation function considering snowmelt for his master thesis (Kang 2005), where the streamflow was simulated by CASC2D and compared against the streamflow observations in sub-basins and outlet of the California Gulch Leadville, Colorado. The latest version of TREX is utilized in this paper to demonstrate the onset (the initial existence of peak) streamflow prediction generated by snowmelt in the SBB. The TREX is a regional watershed model with three main themes: (1) hydrology, (2) sediment transport, and (3) chemical transport. The primary driver of sediment and chemical transport is precipitable water governed by gravitational and frictional forces between a water body and the land surface upon arrival of the precipitation to Earth. By solving a free body diagram of a rigid water body, the overland and channel water flows were numerically determined at each time step to update the water depth based on its temporal change. Details of the governing equations to solve water depth at each time step in overland and channel are in Velleux (2005) and Velleux et al. (2006) from rainfall, interception, infiltration, overland flow, and channel flow. It notes that snowmelt is added to the rainfall sub-function forcing after calculating the temperature difference between the grid and air temperature of the grid cell multiplied by the temperature index. Specifically, the model is applied to cover the water year starting October 1, 2016, to September 30, 2017, while the focus is on the onset of the streamflow in March and April. But, spatio-temporal variations of the SWE, the water depth, and the infiltration are used from the simulation for the water year. The time step spans from 0.1 to 10 seconds, depending on the numerical load of the calculation. Previously, only rainfall-runoff processes were used in CASC2D and TREX. However, snowmelt plays the same role as rainfall when an existing snowpack begins to melt because of the phase change in the snowpack when the melting temperature is exceeded. In snowmelt-dominant basins, cold-region hydrological processes are essential for driving water flow from upstream to downstream. In this study, snowmelt release associated with the temperature rise was implemented in the model by introducing a temperature index.

When the snowpack temperature is above the freezing point, the released water is added to the water depth during the current time step in the overland and channel grid cells. The amount of released water is determined by the product of the temperature surplus above 0 °C and the temperature index. A series of sensitivity tests were conducted by varying the temperature indices to determine the temperature index. In-situ snowpit observations from the watershed were used to adjust the simulated SWE to the observed in-situ SWE. Although the snowpit measurements were spatiotemporally sparse, the temporally continuous and spatially distributed TREX simulations enabled the prediction of the in-situ SWE at the coincident time and collocated location of the snowpits. After fitting the temperature index based on the SWE sensitivity tests against the in-situ SWE observations, the streamflow was assessed against the measured streamflow at the outlet for evaluation. It is thus imperative to use in-situ observations to find a range of temperature indices in the rugged alpine watershed, where hydrologic and meteorological observations are limited.

The snowmelt rate was determined by the temperature index, which is an additional element of the derivative term of the water depth at the previous time step. This was done to update the water depth at the current time step.
formula
(1)
formula
(2)
where Wt is the water depth at time t, Rnet is the net rainfall rate [m/s], Infilt is the infiltration rate [m/s], and Smelt is the snowmelt rate [m/s], which is defined as
formula
(3)
formula
(4)
where Mf is the temperature index, Tgrid is the grid temperature, and Tc is the melting point (typically 0 °C). Tgrid is defined as the air temperature of the grid cell subtracted from the atmospheric lapse rate and multiplied by the elevation difference between the grid and the SNOTEL, which was 3,413.7 m in this study. Only the temperature index, Mf, is used to enhance the onset streamflow predictability. Instead of using a multi-parameter estimation method, this paper attempts to simplify the problems of the snowmelt-dominant watershed by focusing on Mf. This will allow more applicability to the water managers where snowmelt is the primary source of freshwater inputs to the downstream community (Peterson et al. 2013; Vano et al. 2014).

Snowpack accumulates when precipitation occurs, and the grid temperature is below the melting point. When the air temperature increases, the grid temperature also increases, considering an atmospheric adiabatic lapse rate of −0.0098 °C per meter. Here it would cause uncertainties in the streamflow prediction if the constant atmospheric adiabatic lapse rate is used. This is because the adiabatic lapse rate is a function of humidity or dryness of the air mass in a given elevation (Blandford et al. 2008). However, this paper focuses on predicting the streamflow using the limited parameter, the temperature index. The surplus of the grid temperature above 0 °C was used to determine the amount of water released from the snowpack by multiplying the temperature excess by the temperature index. The implementation of the temperature index method in the TREX modeling framework for interacting with functions to call (OverlandWaterRoute.c) and to be called (WaterTransport.c) is explained in the Supplementary Material.

Pre-processing of GIS dataset for TREX

Senator Beck Basin (SBB) is situated in the Ouray Ranger District of the Uncompahgre National Forest in southwestern Colorado at 37.9 ° N 107.7 ° W. The CAC maintains two study plots and a stream gauging station within the 719-acre (290 ha, 2.9 km2) Senator Beck Basin. The Senator Beck Basin Stream Gauge is located in a narrow bedrock gorge at the hydrological outlet of the Basin in the southeastern area of the watershed, with 3,362 m above sea level. An overall description of the SBB is shown in Figure 2.
Figure 2

Schematic view of the Senator Beck Basin with the snowpit observations sites (red circles), channel cells (blue squares), streamflow gauge (blue-filled square), and Red Mountain Pass SNOTEL (cyan triangle). The watershed covers an area of 2.9 km2. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Figure 2

Schematic view of the Senator Beck Basin with the snowpit observations sites (red circles), channel cells (blue squares), streamflow gauge (blue-filled square), and Red Mountain Pass SNOTEL (cyan triangle). The watershed covers an area of 2.9 km2. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

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Several input files from GIS software are required to drive the TREX model in the SBB, such as a digital elevation model (DEM, here 50 m), soil classification, and land-use grids for the boundary conditions of the modeling domain. The DEM was re-processed from a 30-m DEM provided by the CAC. First, a 30 meter-based hydrologic modeling application was attempted, but it was not successful owing to some glitches in the distributed hydrology model, TREX. Also, a 50-meter spatial resolution was sufficient, considering the relatively uniform land cover of the Senator Beck Basin. The mask file represented valid cells and calculated TREX hydrology based on the infiltration characteristics defined in the soil and land-use classifications. The temperature index method required weather forcing datasets, including air temperature and precipitation. A weather forcing dataset was obtained from a nearby SNOTEL station on the Red Mountain Pass (SNOTEL ID 713). Based on the atmospheric adiabatic lapse rate, the temporally interpolated air temperature was adjusted to the temperature in a grid cell by considering the elevation difference between the Red Mountain Pass SNOTEL and each grid cell.

Figure 3 shows the input dataset used for the model simulation by Geographic Information System pre-processing for the geospatial datasets, such as the initial SWE (on October 1, 2016), DEM, soil class, land class, channel links, and nodes. The initial SWE had a maximum value of 0.6 m at the headwaters of the watershed and gradually decreased with a decreasing elevation. The channel grid cells were identified from upstream to downstream using the GIS method to obtain the flow direction and accumulation from the DEM. The link represents each subsidiary upstream river stem, with nodes assigned consecutive numbers for each link of the river stem. As shown in the ‘link’ channel of Figure 3, 13 links are identified, with each link composed of each 50-m grid cell, i.e., the nodes. The channel file defines the channel characteristics of each node and link, such as the bottom width, side slope, bank height, Manning's n, sinuosity, and dead storage height. A rectangular channel geometry was adopted, and the channel cross-section area was increased downstream. The channel properties were used to solve a continuity equation for the open flow channel in order to determine the current water depth with the given channel geometry and water flow at the previous time step. Soil and land cover classifications were extracted from the United States Geological Survey (USGS, National Cooperative Soil Survey (see Data Availability Section]). Detailed soil properties, such as the hydraulic conductivity [m/s], capillary suction head [m], and the soil moisture deficit [m3/m3], governed the infiltration processes based on the Green-Ampt Law (Green & Ampt 1911). Manning's n was used to calculate the overland and channel flow velocities. The interception depth [mm] was used to determine the intercepted water from rainfall by vegetation classified as deciduous, evergreen, grassland, etc.
Figure 3

TREX model setup: (1) initial SWE on October 1, 2016, (2) digital elevation model, (3) soil classification map (see Table 1), (4) land class map (see Table 3), (5) channel links, and (6) channel nodes indicating the streamflow gauge at the outlet (blue dot). Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Figure 3

TREX model setup: (1) initial SWE on October 1, 2016, (2) digital elevation model, (3) soil classification map (see Table 1), (4) land class map (see Table 3), (5) channel links, and (6) channel nodes indicating the streamflow gauge at the outlet (blue dot). Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

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Table 1

Soil infiltration properties used for TREX

NameHydraulic Conductivity [m/s]Capillary Suction Head [m]Soil Moisture Deficit [ ]
Rock outcrop1  0.22 0.029 
Rubble land  0.14 0.029 
Unlocated  0.17 0.029 
Needleton  0.22 0.029 
Unlocated  0.18 0.029 
Cryorthents  0.22 0.029 
Whitecross  0.15 0.029 
Unlocated  0.22 0.029 
Rock outcrp2  0.14 0.029 
10 Whitecross very stony  0.17 0.029 
NameHydraulic Conductivity [m/s]Capillary Suction Head [m]Soil Moisture Deficit [ ]
Rock outcrop1  0.22 0.029 
Rubble land  0.14 0.029 
Unlocated  0.17 0.029 
Needleton  0.22 0.029 
Unlocated  0.18 0.029 
Cryorthents  0.22 0.029 
Whitecross  0.15 0.029 
Unlocated  0.22 0.029 
Rock outcrp2  0.14 0.029 
10 Whitecross very stony  0.17 0.029 

The streamflow gauge maintained by the CAC was located in the outlet channel cell at the same latitude and longitude. The gauge grid was located in the thirty-first row and fifty-second column within the 38 rows and 54 columns of the modeling grids; thus, it was located in the lower right corner. The NASA SnowEx field crew acquired 40 snowpit observations from the basin during February 2017, as indicated by the red dots in Figure 2. The snowpit observations presented in Figure 2 were collected by the SnowEx Year 1 team (Elder et al. 2018). Between the two SnowEx Year 1 sites, SBB was sampled from 40 snowpits during February 2017. Snowpit extraction includes the physical multi-layered snow properties, such as the temperature, stratigraphy, grain size, grain type, wetness, depth, density, and SWE. Each snowpit contains site information, including the location of the UTM and time stamp. The SWE simulated by the snow hydrology model was validated against the snowpit observations. The exact time and location are based on the simulation time and collocated modeling grid cell.

These snowpit observations were used to adjust the temperature indices based on the sensitivity tests of the TREX. The weather forcing dataset containing the air temperature and winter precipitation data was obtained from the Red Mountain Pass SNOTEL, just south of the watershed. As SNOTEL measures the mass of the snowpack above a snow pillow, the measured precipitation at SNOTEL only considers the amount of snowfall. Therefore, the hourly air temperature and winter precipitation data were used to drive the TREX from October 1, 2016, to September 30, 2017. The air temperature at the Red Mountain SNOTEL was adjusted with an atmospheric adiabatic lapse rate of −0.0098 °C per meter, depending on the difference in elevation between the SNOTEL (3,413 m) and each modeling grid.

Weather forcing dataset: SNOTEL Red Mountain Pass

Figure 4 shows the monthly precipitation and air temperature data measured at the Red Mountain Pass SNOTEL Station (SNOTEL 713). The raw dataset at the Red Mountain Pass SNOTEL was measured hourly using a routine quality control conducted by the US Department of Agriculture. This station is located at 3,413-meter high and is just outside the SBB. The amount of winter precipitation increased slightly after October and peaked in January. The accumulated snowfall from October to March was then released into the surface water when the air temperature exceeded the melting point in April. Spatial interpolation of the air temperature was performed with an adiabatic lapse rate, −0.0098 °C/m, using an elevation difference between the SNOTEL and a modeling grid cell. The precipitation measured at the SNOTEL was equivalently applied to all grid cells without any modification. The area of the watershed is 2.9 km2, which is small enough to consider a constant precipitation rate at each time step with 50 meter spatial grid resolution.
Figure 4

Precipitation and air temperature at the Red Mountain SNOTEL site in Water Year 2017.

Figure 4

Precipitation and air temperature at the Red Mountain SNOTEL site in Water Year 2017.

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This section first compares the point-based SWE simulations to the in-situ snowpit observations in order to obtain a range of the temperature index to enhance the streamflow predictability. The streamflow estimations were improved by a determined range of the temperature index. The other watershed representations describe the simulated spatiotemporal changes in the SWE, snowmelt rate, and water depth to achieve a better understanding of the cold land hydrological processes in the SBB.

SWE on the Senator Beck Basin

The constant temperature index (3.52 × 10−7 m/s) within a range of the temperature index was used for the TREX simulation, as shown in Figure 5. SWE is simulated at 38 rows and 54 columns of the 50 meter resolution grids. The SWE is calculated in the grid cell when the snowfall occurs and is subtracted by the melt when the grid temperature is above 0 °C. The simulated SWE is compared against the NASA SnowEx 2017 snowpit observations at a given location and time in February 2017. Additional numerical experiments with time-varying temperature indices do not improve streamflow prediction in the spring-time melt season for this small-scale watershed with 2.9 km2. It is because the streamflow response in this small watershed is negligibly impacted by sub-daily variations in the temperature index. Instead, the constant temperature index, if it is properly adjusted with the in-situ snowpit observations, enhances the onset streamflow prediction. Figure 5 presents the evolution of the simulated point-based SWE against each in-situ snowpit observation with the co-located modeling grid cell simultaneously. The ancillary snowpit information, such as the elevation, sampling date/time, and snowpit ID provided by the SnowEx field crew, is displayed in each figure (Elder et al. 2018), and the approximate position of the snowpit within the watershed is shown in the small inset at the lower-right of each figure. With given weather forcing from the Red Mountain SNOTEL, any SWE simulations can be obtained with arbitrary temperature indices. However, spatially distributed snowpit observations provide criteria to constrain the range of the temperature indices. With the given ranges of temperature indices, the observed SWE can be within the zone of the simulated SWEs covering the watershed. The determined temperature index ( m/s) placed the simulated SWE between two other simulated SWEs by the small (0.5×) and large (1.5×) temperature indices in February 2017. The 50% uncertainty interval was obtained from the remote sensing retrieval study of SWE (Foster et al. 2005). Here, it notes that m/s (equivalently 30.4 mm day−1 °C−1) is relatively high based on Table 1 (Hock 2003). This high value of the temperature index can be explained by the fact that TREX does not consider the sub-surface flow (baseflow). Thus more melt-water is needed to supply the surface runoff, and the absence of the baseflow implementation can explain the large difference from April 22 to May 1 in the low flow regimes. It also notes that m/s is not the best temperature index and 1.5 and 0.5 multiplications to the temperature index suggest a range of the temperature index to ensure the streamflow predictability. It would be worthwhile to consider varying temperature indices within the watershed, but the size of the SBB is 2.9 km2 which is quite small to apply the varying temperature index for the best streamflow prediction. At the large temperature index, the lower SWE was observed in the simulation, and the simulated SWE was higher at smaller temperature indices. Thus, the sensitivity test confirms the utility of using in-situ snowpit observations in February 2017 to adjust the temperature indices valid at 10 locations throughout the SBB.
Figure 5

SWE sensitivity experiments in the water year 2017 using 0.5, and 1.5 multipliers of the temperature indices (Mf or Atindex), which was upper- and lower-boundary for in-situ snowpit SWEs at ten different locations. Another SWE simulation is added with the varying temperature indices. The inserts indicate the approximate position of the snowpit within the SBB. The snowpit ID, elevation, and sampling time are located at the top of each chart.

Figure 5

SWE sensitivity experiments in the water year 2017 using 0.5, and 1.5 multipliers of the temperature indices (Mf or Atindex), which was upper- and lower-boundary for in-situ snowpit SWEs at ten different locations. Another SWE simulation is added with the varying temperature indices. The inserts indicate the approximate position of the snowpit within the SBB. The snowpit ID, elevation, and sampling time are located at the top of each chart.

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Another TREX simulation is made by adjusting the temperature index varying with elevation. A linear curve is produced from the temperature index values to fit the ten snowpit observations in Figure 5. With the varying temperature indices (where , is the multiplication factor to the existing temperature index), SWE simulation is included in Figure 5, and the streamflow simulation is also shown in Figure 6. This reduces a SWE bias (bias values shown in Table 2) with 6.7% against the constant temperature index, but the streamflow prediction only shows 0.4 NSE shown in Table 4. It would be desirable to consider different temperature indices depending on the land cover, such as Bare, Deciduous, Evergreen, and Merbeceous, as shown in Table 3 (Leavesley 1989; Follum et al. 2019). Also, a streamflow calibration needs other considerations, such as soil depth and soil infiltration properties, to fit the historical streamflow observations (Gao et al. 2010).
Table 2

SWE biases with the constant temperature index and varying indices in [mm]

L40L37L38L34L35L39L37L36M22M30Sum
Bias with a constant temperature index 170 18 32 160 50 344 87 108 175 1,148 
Bias with varying temperature indices 130 36 33 44 171 11 302 52 131 161 1,071 
L40L37L38L34L35L39L37L36M22M30Sum
Bias with a constant temperature index 170 18 32 160 50 344 87 108 175 1,148 
Bias with varying temperature indices 130 36 33 44 171 11 302 52 131 161 1,071 
Table 3

Manning's n from landuse dataset for TREX

NameManning's nInterception depth [mm]
Bare 0.1825 
Deciduous 0.0678 0.5 
Evergreen 0.368 
Merbaceuous 0.086 
NameManning's nInterception depth [mm]
Bare 0.1825 
Deciduous 0.0678 0.5 
Evergreen 0.368 
Merbaceuous 0.086 
Figure 6

Sensitivity experiments of the simulated streamflow with changes in the temperature index.

Figure 6

Sensitivity experiments of the simulated streamflow with changes in the temperature index.

Close modal

The trial-and-error method was attempted to fit the temperature index by comparing the simulated and observed SWE values over the basin. Conducting several sensitivity test trials allowed us and hydrologic modelers to determine the exact temperature index by comparing the simulated SWEs against the SWEs observed from the snowpits. The poor predictability of the SWE at high altitudes could be explained by the limited accessibility to deep snow if the snowpit crews sampled low-lying snowpits for safety. However, the hydrological model represented the overall values of the SWE based on the spatial resolution assigned for the model simulation, which was 50 m for the TREX simulation. Thus, the snowpit observations are likely to fit the upper limit (0.5 × the temperature index) of the SWE simulation at snowpit ID M22. In conclusion, the SWE sensitivity tests demonstrated that a precise SWE estimation is a prerequisite for predicting streamflow during the melt season.

Streamflow

Hydrological sensitivity simulations demonstrated that streamflow is subject to changes in the temperature indices where the robustness of the selected temperature index is shown (Figure 6 and Table 4). Figure 5 shows that the temperature index was determined by comparing the simulated and observed SWEs from in-situ snowpit measurements. Subsequently, the determined temperature index was used to simulate the streamflow against the observed streamflow. The observed streamflow was obtained from the CAC, which autonomously collected hourly streamflow observations. This study focuses on the snowmelt period, where the most streamflow is only driven by the meltwater. However, the simulations in late May underestimate the observed streamflow regardless of perturbations. This is due to uncertainties associated with the precipitation forcing from the SNOTEL (Figure 4), where the winter precipitation is obtained by using snow pillow observations. Then, the rainfall observation can be missed and cause the underestimation of the rainfall-runoff in the hydrologic simulation, especially with rain on snow (McCabe et al. 2007). This selection was reasonable in this 50-meter spatial resolution application with varying time steps under 1.0 minutes. The Nash Sutcliffe efficiency (NSE) was 0.88 from April 1–22 (with the temperature index, m/s), while that from May 4 to 9, during peak flow driven by snowmelt, it was 0.87. The discrepancy between the observation and simulation from April 23 to May 3 can be explained by an overestimated overland flow velocity after the peak flow was reached. However, the increasing phase of the streamflow was captured well by the simulation. The streamflow was amplified as the temperature index increased by 1.2 and 1.5 times. The attenuated temperature indices also controlled the decreasing trend of streamflow with the given temperature index multiplied by 0.8 and 0.5. However, the decreasing streamflow in April returned at the end of May owing to the late melting of the remaining snow caused by the low-temperature indices. As shown in Figure 5, the SWE sensitivity tests indicate that the observed snowpit SWE was lower than the simulated SWE when the temperature index was multiplied by 0.5 and larger when the temperature index was multiplied by 1.5. The simulated SWE was inversely related to the temperature index because a higher temperature index led to a decreased SWE associated with more melting. It also notes that this study is aimed at estimating the snowmelt-driven streamflow during an onset of the snowmelt. Another simulation is conducted using the determined temperature index from Figure 5, consisting of 10 data points. A scatter plot is created where the x-axis is the elevation of the snowpits and y axis is the temperature index values to fit the in-situ SWE observation. Even with the slight improvement of the SWE estimation, it does not lead to the enhancement of streamflow predictability. The sensitivity tests shown in Figures 5 and 6 confirm that determining the temperature index and SWE amount over the watershed was critical for predicting the streamflow in snowmelt-dominant watersheds during the melt season.

Table 4

NSE and Root Mean Squared Error (RMSE) of streamflows with varying temperature indices

NSERMSE
Temp. index × 1.0 0.88 0.017 
Temp. index × 1.5 −0.0029 0.081 
Temp. index × 1.2 −0.33 0.034 
Temp. index × 0.8 0.45 0.042 
Temp. index × 0.5 −0.47 0.063 
Varying Temp. index 0.40 0.051 
NSERMSE
Temp. index × 1.0 0.88 0.017 
Temp. index × 1.5 −0.0029 0.081 
Temp. index × 1.2 −0.33 0.034 
Temp. index × 0.8 0.45 0.042 
Temp. index × 0.5 −0.47 0.063 
Varying Temp. index 0.40 0.051 

Spatio-temporal changes in the SWE, snowmelt rate, and water depth

Figures 7,89 show the temporal snapshots of the SWE [m], snowmelt rate [mm/hr], and water depth [m] over the SBB. The SWEs in Figure 7 are dynamically linked to both the observed and simulated streamflows. The spontaneous timing of the streamflow is indicated by the blue dot in the upper panel of each figure. The air temperature [°C] was used to support the snowmelt rate and the water depth simulations in Figures 8 and 9 instead of the streamflow. Another y-axis of streamflow/air temperature in the upper panel includes the snowfall [mm/hour].
Figure 7

Seasonal change of the SWE [m] associated with streamflow responses at 15:00 on April 5, 15, 20, and May 3, 2017. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Figure 7

Seasonal change of the SWE [m] associated with streamflow responses at 15:00 on April 5, 15, 20, and May 3, 2017. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Close modal
Figure 8

Diurnal change of the snowmelt rate [mm/hour] at 7:00, 9:00, 13:00, and 16:00 on April 16, 2017. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Figure 8

Diurnal change of the snowmelt rate [mm/hour] at 7:00, 9:00, 13:00, and 16:00 on April 16, 2017. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Close modal
Figure 9

Diurnal change of the water depth [m] at 7:00, 9:00, 13:00, and 16:00 on April 16, 2017. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Figure 9

Diurnal change of the water depth [m] at 7:00, 9:00, 13:00, and 16:00 on April 16, 2017. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.180.

Close modal

On April 5, the simulated SWE distributed over the watershed was up to 1.5 m SWE [m] primarily as a function of elevation. The disappearance of the SWE leading to the middle basin from the outlet on April 15 can be explained by the increase in streamflow from April 5. The SWE in the upper basin remained until April 20, whereas the streamflow was slightly attenuated after a local peak. From April 20 to May 3, the streamflow returned to a decreasing trend. The SWE recovered over three-quarters of the upper basin, indicating that continuous snowfall (shown in the upper panel) and low air temperature below the freezing point was assumed to be maintained between April 20 and May 3. It should be noted that the SWE decreased until April 20, even after the local streamflow peaked on April 15. The streamflow continued to decrease from April 20 to May 3, indicating a possible decrease in the air temperature and attenuated meltwater between April 20 and May 3. This simulated spatial distribution of the SWE, along with the streamflow, shows the time delay in the streamflow response to the melting SWE covering the watershed.

Figure 8 shows the diurnal changes in the snowmelt rates [mm/h] associated with the air temperature change and the initial existence of the SWE in the basin on April 16. At 7:00 AM, snowmelt occurred downstream because of the high air temperatures at the low elevations. The snowmelt rate expanded upstream at 9:00 AM, with the weakened snowmelt in the highest headwaters. At 1:00 PM, only the snowmelt rate in the upstream region remained constant. This snowmelt change indicates that the snow disappeared in the mid and downstream watersheds after 1:00 PM due to the high air temperature of approximately 10 °C. The snowmelt rate at 4:00 PM indicated that snowmelt did not occur in the headwaters because of the decreased air temperature associated with the highest elevations. The daytime changes in the snowmelt rate on April 16 explain why seasonal snow in the basin was affected by the strong diurnal air temperature cycle and the existence of the SWE.

Figure 9 presents the diurnal changes in water depth [m] due to snowmelt on April 16. At 7:00 AM, a high volume of water (up to 0.8 m) in the channel existed downstream, near the outlet. At 9:00 AM, the entire watershed became wet because of the snowmelt, and the lowest basin became dry except for the channel cells. Figure 8 also confirms that snowmelt occurred throughout the watershed, excluding the lowest basin because the SWE had disappeared to melt. Water vanished from the mid- and downstream overland areas at 1:00 PM owing to the lack of snow in the lower basin. The water disappeared from the headwaters at 4:00 PM, but it remained in the middle basin. Additionally, a high channel water depth continued with a 0.8 m water depth at the outlet. The diurnal change in water depth exhibits a delayed response of the water depth to the snowmelt, which is associated with the existence of SWE and the air temperature change.

The study also evaluated several uncertainty sources that impacted simulated streamflow driven by snow melt. Simulated streamflow using temporal variations in temperature index, including the sine function of the simulated time, but it was found that a negligible improvement was made. Other considerations, such as slope and aspect, also did not have noticeable consequences in the streamflow generation. Although an improvement in the SWE estimation is expected, the streamflow is not directly affected by the temporal variations in the temperature index. However, as the additional simulation with the varying temperature indices with elevation suggested, a consideration of the land cover to the temperature index might reduce the SWE uncertainties and improve the streamflow prediction.

This section covers the interannual variability during the water years 2016 and 2018 and compares them with the water year 2017. The comparison of the streamflow demonstrates the importance of the in-situ snowpits observations for streamflow prediction.

Figure 10 shows the simulated and observed streamflow and SWEs in the water years 2016, 2017, and 2018. Here, the observed SWE is separately extracted from the Colorado Avalanche Center, where the sampling site is called SASP (Swamp Angel Study Plot, 37.91° N, −107.71° W), along with the co-located simulated SWEs. To show an improvement of the streamflow predictability, a baseline simulation is included in the water year 2017 with the temperature index of 2.31 × 10−8 m/s. The temperature index is a moderated (2 times) value from Bhuiyan et al. (2017). It indicates that the baseline simulated SWE is overestimated compared to the observed one, and thus the streamflow is not generated during a snowmelt-season. The weather forcing is again extracted from the Red Mountain SNOTEL to cover the entire three years. The given temperature index determined in the water year 2017 is equally applied to the other two years to evaluate streamflow responses. In the water year 2016, the simulated SWE underestimates the observed SWE. After two months, the simulated streamflow in April and May is highly underestimated compared to the observed one. On the other hand, in the water year 2018, the simulated SWE in December and January was much higher than the simulated SWE. The simulated streamflow in April and May is thus amplified compared to the observed streamflow. In the water year 2017 where the temperature index is selected using in-situ SnowEx snowpits, the simulated SWE is predicted well against the observed SWE from December to February. Following this, the streamflow in April and early May is also well captured against the observed streamflow. Figure 10 demonstrates the importance of predicting SWE to correctly simulate the streamflow with two months of temporal delay.
Figure 10

Simulated and observed streamflows and SWEs in the water years 2016, 2017, and 2018 along with SWE. The water year 2016 includes the baseline SWE and streamflow simulations, where Mf is the temperature index. The inset (a, b, and c) figure within the large one shows the SWE simulations and observations, which is preceded by a few months to the streamflow generation due to snowmelt. The location of the pit in the SBB is also shown in the smallest figure.

Figure 10

Simulated and observed streamflows and SWEs in the water years 2016, 2017, and 2018 along with SWE. The water year 2016 includes the baseline SWE and streamflow simulations, where Mf is the temperature index. The inset (a, b, and c) figure within the large one shows the SWE simulations and observations, which is preceded by a few months to the streamflow generation due to snowmelt. The location of the pit in the SBB is also shown in the smallest figure.

Close modal

It also notes that the constant lapse rate (–0.098 °C per meter) might overestimate the temperature index. This is because the lapse rate is likely to decrease in dry climate such as in the alpine watershed (Blandford et al. 2008). Another point which needs to be addressed is a constant temperature index. As summarized and implemented in Hock (2003) and Follum et al. (2019), varying temperature index would be desirable to realistically simulate water mass and energy balance in the watershed. However, it would be worthy to address later the changing adiabatic lapse rate and the temperature index and their contributions to the streamflow generation.

This SWE prediction shows a prototype example of the sub-seasonal prediction of the streamflow in the snowmelt-dominant watershed in the western parts of North America (Qin et al. 2020). Another implication of this study is that it evaluated the spatio-temporal behavior of cold region hydrological processes at a regional scale (2–3 km2) and two temporal scales for a streamflow within two months and a surface mass and energy balance with one water year. Previous research (Matheussen et al. 2000; Anderson, 1976) has shown a robust estimation of the streamflow driven by snowmelt, but its spatial scale is semi-continental not capturing SWE mass and energy balance in the model. Reversely, even with a detailed interpretation of the snow physical properties (Tarboton & Luce 1996; Hedrick et al. 2018), the SWE evaluations could not reach the streamflow estimation which has broad implications for the public where snowmelt is a primary source of freshwater.

This study demonstrates an improvement in snowmelt-driven streamflow prediction using the available weather forcing dataset and in-situ snowpit measurements from an alpine watershed. In the discussion, the interannual variability is demonstrated for the importance of the selection of the temperature index to predict streamflow in the water years 2016, 2017, and 2018. This study explored the sub-seasonal predictability of streamflow in a snowmelt-dominant basin. If peak SWE observations are available, it allows for a better estimation of the springtime streamflow. While this study used snowpit observations, advanced remote sensing technologies will improve the predictability of the springtime streamflow in the alpine watersheds. As shown in Figures 1 and 2, the laborious snowpit observations can be replaced with remote sensing retrievals of SWE. In case the SWE observation exists from January to March, the adjusted temperature index and the amount of snowfall lead to an improvement of the streamflow prediction in the following months in April and May. Below are the point-by-point conclusions of this study.

  • The application of the distributed hydrology model driven by the weather forcing observations successfully captured the streamflow primarily attributed to the snowmelt with 0.88 NSE of the streamflow prediction for April 1–22, 2017 in the Senator Beck Basin, Colorado, USA.

  • The temperature index method in the distributed hydrology model plays a principal role in simulating the streamflow response associated with the air temperature change and the spatial distribution of the SWE over the basin.

  • The temperature index can be determined by the sensitivity tests of the distributed hydrologic model for SWE simulations against the in-situ snowpit observations. The in-situ SWE observations are within the upper and lower bounds of the simulated SWEs with 0.5 times lower and 1.5 times higher temperature indices.

  • The temperature index value () determined by comparisons between simulated and observed SWEs during the snow peak season is not a definite number. Instead, it provides a range of temperature indices to achieve a high predictability of the streamflow during the on-set of the snowmelt season, which is a few months later to the snow peak season.

  • Spatio-temporal evaluations of the SWE, snowmelt rate, and water depth demonstrate the cold land hydrological processes associated with the existence of SWE and air temperature variations over the watershed toward streamflow response at the outlet.

  • The interannual streamflow responses with the same temperature index during the water years 2016, 2017, and 2018 demonstrated that SWE prediction is a key to estimating the streamflow with two months of time delay between SWE and the streamflow.

The water resources of the western U.S. and Canada highly are highly dependent on the seasonal snow in the mountains. This solid state of the water provides freshwater for metropolitan cities and agricultural farmlands. The estimation of cold-water storage is subject to the prediction of the mountain snowpack. This challenge of limited water resources is not constrained to western North America but also affects high-mountains in Asia (Rowan et al. 2018), the Andes Mountains (Ragettli et al. 2016), the Swiss Alps (Seidel et al. 1998), and the Iranian Mountains (Ashraf Vaghefi et al. 2014). The implemented temperature index method using the available in-situ snowpit monitoring is promising for enhancing the estimation of the streamflow associated with snowmelt runoff in mountain watersheds worldwide. In general, extensive in-situ hydrological and meteorological observations are difficult to obtain but, remote sensing has potential to obtain SWE from space if the retrieval algorithm is mature. The temperature index method is straightforwardly applicable to areas with environmental settings similar to those of western North America with the minimum observations such as a point-based weather station and several in-situ SWE observations.

With more temporally available and spatially interpolated weather forcing datasets, extended hydrologic modeling studies can be pursued to implement an energy balance method into the snow hydrology model (Cline et al. 1998; Bartelt & Lehning 2002; Dingman 2015). The energy balance method requires other ancillary weather datasets as well, including short-, and longwave radiations, wind speed, and relative humidity. This application will lead to a realistic representation of the snowpack in the watershed. Several sample-modeling grid cells can be tested using the energy balance approach and validated with the simulated snowpack against the one using the simple temperature index method. In addition, in-situ snowpit or remotely retrieved snow observations can calibrate parameters in the energy balance method. Van Pelt et al. (2012) extended a possibility to calibrate parameters of the snow energy balance approach to estimate SWE and glacier in near arctic glaciers. The energy balance and the temperature index methods can be applied to investigate streamflow for water resource management and the physical properties of snow, respectively. State-of-the-art remote sensing observations, such as microwave and optical sensing, can support the in-situ snowpit observations and increase the use of the spatially distributed snow hydrological models. Optical airborne LiDAR sensing (Painter et al. 2016) can be compared with snow depth simulations too. The SWE retrieval using the microwave volume scattering method (Tsang et al. 2017) can be used to assess the simulated SWE in a watershed. More flexible hydrological modeling is possible with available measurements from snowpits and weather stations, and remote sensing observations. The upcoming NASA SnowEx campaign offers potential opportunities to apply the temperature index method for improving streamflow prediction under different seasonal snow conditions (Sturm et al. 1995). This study explored the utilization of the weather and in-situ snowpit measurements for enhanced streamflow predictability using a snow hydrology model in an alpine watershed.

This research was supported by the first author's NASA grant, 80NSSC18K1136. Thanks to John Choi for resolving initial bugs to compile the TREX source codes. Special thanks to Jeff Derry at the Colorado Avalanche Center for providing with hourly streamflow dataset at the Senator Beck Basin.

All relevant data are included in the paper or its Supplementary Information. The source code of the TREX is publicly available at https://www.engr.colostate.edu/~pierre/ce_old/Projects/TREX%20Web%20Pages/TREXHome.html. Land cover data is from U.S. Geological Survey, 2021, USGS Land Cover Data Download, accessed 24 January 2021, at URL https://www.usgs.gov/core-science-systems/scienceanalytics-and-synthesis/gap/science/land-cover-data-download?qt-science_center_objects=0#qtscience_center_objects. Soil classification is from Soil Survey Staff, Natural Resources Conservation Service, United States Department of Agriculture. Soil Series Classification Database. Available online. They were accessed on 24 January 2021. Senator Beck's streamflow data is from the Colorado Avalanche Center (CAC) at URL https://snowstudies.org/sb-stream-gauge/ (accessed on 24 January 2021). The 10-meter digital elevation model processed by CAC is resampled to 50 meter DEM for the TREX application.

The authors declare there is no conflict.

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