Abstract
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.
HIGHLIGHTS
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.
INTRODUCTION
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 Center for Snow Avalanche Studies (CSAS) <snowstudies.org>, 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.
METHODS AND MATERIALS
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.
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
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.
. | Name . | Hydraulic Conductivity [m/s] . | Capillary Suction Head [m] . | Soil Moisture Deficit [ ] . |
---|---|---|---|---|
1 | Rock outcrop1 | 0.22 | 0.029 | |
2 | Rubble land | 0.14 | 0.029 | |
3 | Unlocated | 0.17 | 0.029 | |
4 | Needleton | 0.22 | 0.029 | |
5 | Unlocated | 0.18 | 0.029 | |
6 | Cryorthents | 0.22 | 0.029 | |
7 | Whitecross | 0.15 | 0.029 | |
8 | Unlocated | 0.22 | 0.029 | |
9 | Rock outcrp2 | 0.14 | 0.029 | |
10 | Whitecross very stony | 0.17 | 0.029 |
. | Name . | Hydraulic Conductivity [m/s] . | Capillary Suction Head [m] . | Soil Moisture Deficit [ ] . |
---|---|---|---|---|
1 | Rock outcrop1 | 0.22 | 0.029 | |
2 | Rubble land | 0.14 | 0.029 | |
3 | Unlocated | 0.17 | 0.029 | |
4 | Needleton | 0.22 | 0.029 | |
5 | Unlocated | 0.18 | 0.029 | |
6 | Cryorthents | 0.22 | 0.029 | |
7 | Whitecross | 0.15 | 0.029 | |
8 | Unlocated | 0.22 | 0.029 | |
9 | 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
RESULTS
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
. | L40 . | L37 . | L38 . | L34 . | L35 . | L39 . | L37 . | L36 . | M22 . | M30 . | Sum . |
---|---|---|---|---|---|---|---|---|---|---|---|
Bias with a constant temperature index | 170 | 18 | 4 | 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 |
. | L40 . | L37 . | L38 . | L34 . | L35 . | L39 . | L37 . | L36 . | M22 . | M30 . | Sum . |
---|---|---|---|---|---|---|---|---|---|---|---|
Bias with a constant temperature index | 170 | 18 | 4 | 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 |
. | Name . | Manning's n . | Interception depth [mm] . |
---|---|---|---|
1 | Bare | 0.1825 | 0 |
2 | Deciduous | 0.0678 | 0.5 |
3 | Evergreen | 0.368 | 1 |
4 | Merbaceuous | 0.086 | 1 |
. | Name . | Manning's n . | Interception depth [mm] . |
---|---|---|---|
1 | Bare | 0.1825 | 0 |
2 | Deciduous | 0.0678 | 0.5 |
3 | Evergreen | 0.368 | 1 |
4 | Merbaceuous | 0.086 | 1 |
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.
. | NSE . | RMSE . |
---|---|---|
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 |
. | NSE . | RMSE . |
---|---|---|
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
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.
DISCUSSION
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.
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.
CONCLUSION
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.
ACKNOWLEDGEMENTS
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 Center for Snow Avalanche Studies (CSAS) for providing with hourly streamflow dataset at the Senator Beck Basin.
DATA AVAILABILITY STATEMENT
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 Center for Snow Avalanche Studies (CSAS) 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.
CONFLICT OF INTEREST
The authors declare there is no conflict.