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  • View in gallery

    Land-cover distribution and observation sites in the RME watershed.

  • View in gallery

    Modeled and observed (a) streamflow for WYs 1984–2008 and (b) groundwater depth for WYs 2006–08 [light gray vertical lines in (b) demarcate period from 1 to 13 Apr in WY 2006].

  • View in gallery

    Streamflow time series for WY 2006 during melt season. Also illustrated is the DPT hour (after noon) for every day. Times in black indicate peak hour for days with distinct diurnal signal. Times in gray boxes indicate peak hour for days with multiple peaks. All times are with respect to the local noon. Note that negative value means time before noon, for example, −2 means 1000 local time (LT).

  • View in gallery

    Comparison of simulated and observed streamflow during the melt season for (a) a very wet, warm snow season (WY 1996) and (b) a dry, cool snow season (WY 1999). See Reba et al. (2011b) for details on conditions during WYs 1996 and 1999.

  • View in gallery

    Schematic of observed and modeled daily streamflow hydrographs with (a) identical observed and modeled daily peak hour (here observed peak hour = modeled absolute peak hour = modeled Q1% peak hour) and (b) different observed and modeled peak hour with very small variations near the top 1% peak discharge (here observed peak hour = modeled absolute peak hour − 1 = modeled Q1% peak hour).

  • View in gallery

    Observed and modeled daily peak time for 24 WYs ranging from WYs 1984 to 2008 (WY 1992 was excluded). The x axis represents WY day, and the y axis indicates the daily peak time hour with respect to local noon. Note that negative value means time before noon, for example, −4 means 0800 LT.

  • View in gallery

    Modeled daily total melt and streamflow during melt period in WY 2006.

  • View in gallery

    Results of peak hour variation after discounting different processes for 24 WYs: P1234 is the original modeled peak hour; P1 is the peak hour of melt flux when translation time through snowpack is not accounted for, P12 is the peak hour from translated liquid water flux, and P123 is based on the original model but assuming translation in the river does not happen. Detailed explanations of the four experiments are presented in section 3a.

  • View in gallery

    Peak time and delay caused by different factors in WY 2006 (P1 is peak hour from melt flux when translation time through snowpack is not accounted for, P12P1 is peak hour delay caused by snow translation process, P123P12 is peak hour delay caused by ground translation process, and P1234P123 is peak hour delay caused by in channel translation process).

  • View in gallery

    (a) Peak time and delay caused by ground translation process (P123P12) in WY 1984. (b) Original melt, melt after translation through snowpack, and streamflow time series for WY 1984.

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Assessment of the Timing of Daily Peak Streamflow during the Melt Season in a Snow-Dominated Watershed

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  • 1 Nicholas School of the Environment, Duke University, Durham, North Carolina
  • | 2 Northwest Watershed Research Center, Agricultural Research Service, USDA, Boise, Idaho
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Abstract

Previous studies have shown that gauge-observed daily streamflow peak times (DPTs) during spring snowmelt can exhibit distinct temporal shifts through the season. These shifts have been attributed to three processes: 1) melt flux translation through the snowpack or percolation, 2) surface and subsurface flow of melt from the base of snowpacks to streams, and 3) translation of water flux in the streams to stream gauging stations. The goal of this study is to evaluate and quantify how these processes affect observed DPTs variations at the Reynolds Mountain East (RME) research catchment in southwest Idaho, United States. To accomplish this goal, DPTs were simulated for the RME catchment over a period of 25 water years using a modified snowmelt model, iSnobal, and a hydrology model, the Penn State Integrated Hydrologic Model (PIHM). The influence of each controlling process was then evaluated by simulating the DPT with and without the process under consideration. Both intra- and interseasonal variability in DPTs were evaluated. Results indicate that the magnitude of DPTs is dominantly influenced by subsurface flow, whereas the temporal shifts within a season are primarily controlled by percolation through snow. In addition to the three processes previously identified in the literature, processes governing the snowpack ripening time are identified as additionally influencing DPT variability. Results also indicate that the relative dominance of each control varies through the melt season and between wet and dry years. The results could be used for supporting DPTs prediction efforts and for prioritization of observables for DPT determination.

Current affiliation: WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland.

Corresponding author address: Mukesh Kumar, Nicholas School of the Environment, Duke University, 450 Research Dr., LSRC A207A, Durham, NC 27708. E-mail: mukesh.kumar@duke.edu

Abstract

Previous studies have shown that gauge-observed daily streamflow peak times (DPTs) during spring snowmelt can exhibit distinct temporal shifts through the season. These shifts have been attributed to three processes: 1) melt flux translation through the snowpack or percolation, 2) surface and subsurface flow of melt from the base of snowpacks to streams, and 3) translation of water flux in the streams to stream gauging stations. The goal of this study is to evaluate and quantify how these processes affect observed DPTs variations at the Reynolds Mountain East (RME) research catchment in southwest Idaho, United States. To accomplish this goal, DPTs were simulated for the RME catchment over a period of 25 water years using a modified snowmelt model, iSnobal, and a hydrology model, the Penn State Integrated Hydrologic Model (PIHM). The influence of each controlling process was then evaluated by simulating the DPT with and without the process under consideration. Both intra- and interseasonal variability in DPTs were evaluated. Results indicate that the magnitude of DPTs is dominantly influenced by subsurface flow, whereas the temporal shifts within a season are primarily controlled by percolation through snow. In addition to the three processes previously identified in the literature, processes governing the snowpack ripening time are identified as additionally influencing DPT variability. Results also indicate that the relative dominance of each control varies through the melt season and between wet and dry years. The results could be used for supporting DPTs prediction efforts and for prioritization of observables for DPT determination.

Current affiliation: WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland.

Corresponding author address: Mukesh Kumar, Nicholas School of the Environment, Duke University, 450 Research Dr., LSRC A207A, Durham, NC 27708. E-mail: mukesh.kumar@duke.edu

1. Introduction

Snowmelt is the major source of groundwater recharge and streamflow in mountainous areas throughout the western United States. More than 50%–70% of the western U.S. water supply originates in snow-fed upland watersheds (Barnett et al. 2005; Carroll et al. 2006; DeWalle and Rango 2008). Accurate quantification of the variability of streamflow from these watersheds can be crucial for both stream ecology and sustainable management of water supply resources.

Streamflow variability in the western United States exhibits spatial and temporal dependencies. This study examines the temporal dependencies, in particular, those that occur at subdaily time scales (Lowry et al. 2010; Lundquist and Cayan 2002; Lundquist and Dettinger 2005; Tobin et al. 2013). Subdaily streamflow variations are important for fluvial processes and aquatic ecology as well as reservoir operations aimed at reducing the magnitude of high flows (Graf 1999; Poff et al. 1997) and modulating downstream aquatic communities (Bain et al. 1988) and water quality variables such as stream temperature (Neumann et al. 2003) and dissolved oxygen. The diurnal variations in streamflow are mainly introduced by ice or snowmelt and evapotranspiration and have been the focus of many studies (Caine 1992; Gribovszki et al. 2008, 2010; Johnson et al. 2013; Loheide 2008; Loheide and Lundquist 2009; Lundquist and Dettinger 2005; Soylu et al. 2012). We focus on assessing the intra- and interseasonal variations in daily streamflow peak times (DPTs) during the melt season and identifying the process dependencies of these variations. DPT is defined as the hour when streamflow is the maximum within a day, and melt season is considered to span from the first to last day that shows a melt-affected diurnal signal (characterized by a rapid increase followed by a gradual decrease in daily hydrograph; Lundquist and Cayan 2002).

DPTs during the snowmelt season can demonstrate varied shifts. As the melt season progresses, DPTs may occur earlier in the diurnal cycle (Caine 1992; Jordan 1983a,b), later (Grover and Harrington 1943; Lundquist and Cayan 2002), or have no significant temporal shift (Lundquist et al. 2005). Earlier/later DPTs indicate shorter/longer time intervals between peak melt pulse and peak subdaily streamflow. These disparate shifts have been attributed to a combination of three primary controls: 1) the percolation of liquid water through the snowpack (Ambach et al. 1981; Caine 1992; Colbeck and Davidson 1973; Dunne et al. 1976; Jordan 1983a; Pfeffer et al. 1990), 2) the translation of meltwater from the base of snowpack to the river channel (Caine 1992; Dunne and Black 1971; Flerchinger et al. 1992; Kobayashi 1986; Maulé and Stein 1990), and 3) the translation of water flux in the river channel to the stream gauging station (Lundquist and Dettinger 2005). These three controls affect the time difference between the peak melt pulse at the snowpack surface due to energy inputs and peak subdaily streamflow at the stream gauging station; for example, peak melt pulse typically occurs in the early afternoon, while peak subdaily streamflow generally occurs late at night or even the following morning (Lundquist and Dettinger 2005).

The first control affects the DPTs during the melt season by altering percolation time of liquid water through the snowpack as the melt season progresses. During spring melt when snow cover densities exhibit low variability, liquid water translation times are generally longer through thicker snowpacks than thinner ones. At the beginning of the melt season when snowpack is generally thicker, the translation time is longer. Refreezing of meltwater may further contribute to slow effective percolation velocity early in the melt season (Colbeck and Davidson 1973; Colbeck 1975; Pfeffer et al. 1990). In contrast, the percolation time is reduced during the late melting season as the snowpack thins (Caine 1992; Jordan 1983a,b; Kobayashi and Motoyama 1985). Percolation rates may also be affected by the evolution of preferential flow paths in the snowpacks during the melt season (Marsh and Woo 1985; Marsh and Pomeroy 1996).

The second control on shifts in the timing of DPTs is associated with the time difference between surface water input from the base of the snow cover and the melt response signal in the stream. In larger watersheds that span over a wide range of elevations, streamflow response time will increase during the melt season as the snow line retreats to higher elevations. This results in a shift of DPTs to later in the day (Caprio 1966; Lundquist and Cayan 2002; Lundquist and Dettinger 2005; Lundquist et al. 2004, 2005). In watersheds with fractured basalt in the subsurface, DPTs have been reported to vary nonmonotonically depending on the snow distribution and distance of residual snow cover from the stream gauging station (Flerchinger et al. 1992). In some large watersheds with a highly heterogeneous snow cover distribution, the delaying effect of retreating snow line may offset the effect of percolation time change within the snowpack, resulting in an essentially unchanged DPTs through the melt season (Lundquist et al. 2005).

The third control on changes in DPTs during the melt season is caused by differences in daily average flow velocity in the stream channel. Flow velocity varies with streamflow volume, with higher velocities around the streamflow peak and lower velocities late in the melt period (Lundquist and Dettinger 2005).

As the snow cover amount and properties vary interseasonally, the effects of each aforementioned control on DPTs is expected to change from one year to the next. Using 5 years of data in Martinelli snowpatch (0.08 km2 area), Caine (1992) suggested that the DPT occurred later in the day during years with larger basin-scale snow depth. Similar conclusions were also drawn by Lundquist and Dettinger (2005) based on data from Marble Fork watershed.

The primary purpose of this paper is to evaluate the role of the process controls on both intra- and interseasonal variations in DPTs. Lundquist et al. (2005) assessed the impacts of percolation time through the snowpack and the travel time of meltwater in the river channel on DPT shifts while assuming that travel times between the base of the snowpack and the stream were negligible [see paragraph 19 of Lundquist et al. (2005)]. However, this assumption cannot be universally applied, especially in watersheds where streamflow has a large groundwater contribution. To explore the impact of percolation of liquid water through the snow cover and translation of water from the base of the snow cover to the stream and to evaluate the role of these and any additional processes that may determine DPT variation, we couple a snowmelt model, ISNOBAL, with a hydrology model, Penn State Integrated Hydrologic Model (PIHM), to simulate the DPTs. The intra- and interseasonal variations in both observed and modeled DPTs are identified, and the capability of the coupled ISNOBAL–PIHM to estimate DPTs and its variations during the melt season is evaluated. Through a series of process-unmixing experiments, the coupled modeling system is then used to isolate the role of individual processes in determining DPTs. Aside from the three previously reported controls, the physically based coupled modeling framework allows us to also assess the roles of additional processes on observed DPT variations. These experiments were used to answer the following two questions: 1) How do DPTs vary intraseasonally and what processes are critical to determine the magnitude of those variations? and 2) How do DPTs vary interseasonally and what are the processes that control that variation?

This paper is organized as follows. Section 2 presents the study area, the modeling methodology, and related calibration and validation details of the linked model (ISNOBAL–PIHM). Section 3 describes the design of process-unmixing experiments and the information obtained from these experiments. Section 4 describes the results from the process-unmixing experiments and discusses process-dependent controls on intra- and interseasonal variations of DPTs. Section 5 summarizes the results and takeaways from this study.

2. Setting and model details

a. Study area and relevant datasets

Reynolds Mountain East (RME), a snow-dominated headwater catchment within the Reynolds Creek Experimental Watershed (RCEW; Marks 2001), was selected for this study (Fig. 1). Elevations in RME (0.38 km2) range from 2028 to 2137 m above mean sea level. Hillslope angles range from 0° to 21.4°. Soil texture in the watershed ranges from loam to clay, with variably fractured and altered basalt underneath. The watershed is covered by dense willows and aspen near the riparian zone and mixture of sparse Douglas fir, Vaseyana sagebrush, scattered dry meadow, and aspen patches farther away from the stream (Grant et al. 2004; Reba et al. 2011a). Based on the 25-water-year (WY)1 dataset presented in Reba et al. (2011a) (and discussed further below), the monthly average temperature in the watershed ranges from −4°C in December to 17°C in July. Over 70% of the precipitation occurs in the form of snow during the winter months, with July–September being typically very dry. WY precipitation at the snow pillow site (filled circle in Fig. 1) varies from 584 to 1537 mm with a WY average of 967 mm. In contrast, WY precipitation at the exposed site, which is only around 350 m away and is located in an exposed area within a sagebrush community (filled triangle in Fig. 1), varies from 454 to 1201 mm with a WY average of 779 mm (Marks and Winstral 2001). The differences in precipitation are due to complex snow accumulation patterns produced by wind scour and drifting. Heterogeneity in mass and energy inputs in this watershed produce spatial–temporal differences in melt production with exposed areas producing a greater proportion of early spring melt and sheltered regions contributing higher percentages in late spring (Marks et al. 2002).

Fig. 1.
Fig. 1.

Land-cover distribution and observation sites in the RME watershed.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

The aforementioned 25-WY (1984–2008) hydroclimatic dataset (Reba et al. 2011a) was used to evaluate DPT variations. Relevant datasets were hourly streamflow at the basin outlet (WYs 1984–2008), hourly groundwater at three wells (WYs 2006–08), and hourly soil moisture at one site (WYs 2005–08). Streamflow from the RME watershed ranges from 125 mm in the driest WY to 1106 mm in the wettest WY, with an average of 518 mm for the 25-WY period. The runoff ratio varies from 0.24 to 0.90, with an average runoff ratio of 0.61 for the 25-WY simulation period. The three years containing fine temporal groundwater and soil moisture data encompass a wide range of hydroclimatic conditions, with 2006 and 2007 WYs being among the wettest and driest five WYs, respectively, over the 25-WY dataset (Reba et al. 2011a). WY 2008 was an average year with precipitation of 856 mm at the exposed site and 996 mm at the sheltered site. All relevant topographic, physiographic, and hydroclimatic datasets for WYs 1984 to 2008 are obtainable from the Northwest Watershed Research Center, USDA (ftp://ftp.nwrc.ars.usda.gov/public/RME_25yr_database). Detailed descriptions of these datasets can be found in Hanson et al. (2001).

b. Modeling methodology

For this analysis, ISNOBAL was coupled to PIHM, simulating snow accumulation, melt, and hydrologic processes across the RME watershed for the 25-WY simulation period. ISNOBAL is a grid-based two-layer energy- and mass-balance snow model (Marks et al. 1999), forced with distributed fields of precipitation, air temperature, net shortwave radiation, downwelling thermal radiation, wind speed, and relative humidity. ISNOBAL simulates snow states including snow temperature, density, and snow water equivalent for each layer at every time step. Snowmelt is initiated with additional energy input once snow temperature in either of the two layers reaches 0°C. Melt water is retained in the snowpack by capillary forces (surface tension) until threshold saturation levels are reached. At this point, surface tension can no longer retain any additional liquid water against gravity and any additional energy input results in meltwater percolating downward. ISNOBAL delivers excess meltwater, or rain on bare ground to the soil surface as surface water input (SWI) for each hourly time step, assuming zero lag time. ISNOBAL has been previously applied across sites with varying snow and climate conditions in the United States (Garen and Marks 2005; Link and Marks 1999; Reba et al. 2011b; Winstral et al. 2009). In this work, a lag function was incorporated in ISNOBAL to delay the SWI fluxes using (Anderson 1976; Flerchinger 2000)
e1
where L is the SWI delay time (h); C2 is an empirical coefficient with the value 0.01 m−1; W is the depth of the SWI flux (m); and is the maximum lag time (h), calculated as
e2
where C1 is the maximum allowable lag obtained from best fit of experimental data (Anderson 1976), C1 = 10 h; ds is snow cover depth (m); and ρs is snow cover density (kg m−3).

Even though this “lag and route” approach calculates the percolation time of excess liquid water without accounting for the preferential flow paths (Marsh and Woo 1985; Marsh and Pomeroy 1996) and an explicit distinction of the snowpack into unsaturated and saturated layers (Gray et al. 1985), it has been shown to be effective in simulating hourly outflow from the bottom of snowpack (Barry et al. 1990). Equation (1) suggests that for a ripe snowpack with a density of 480 kg m−3, depth of 0.90 m, and melt rate of 1.2 mm h−1, the liquid water flux lag time at a point would be around 3.5 h. This propagation time is similar to the one obtained using the equations presented in Lundquist and Dettinger (2005), which calculates a translation time of 3.7 h. Dunne et al. (1976) reported the observed shift in lag time in the range of 0.5–7.9 h from plots sampled at a range of aspects, vegetation cover, snow depth, and density. After accounting for the delay in SWI flux translation through snowpacks, the resulting adjusted SWI is input to PIHM (Kumar 2009; Kumar et al. 2009; Qu and Duffy 2007).

PIHM is a physics-based distributed hydrologic model, which employs a semidiscrete finite volume formulation to simulate a range of processes, including snowmelt, evapotranspiration [Penman–Monteith equation (Allen et al. 1998)], interception [Rutter model (Rutter et al. 1971)], overland flow [2D diffusion wave equation (Gottardi and Venutelli 1993)], unsaturated zone infiltration [1D approximation of Richards’s equation (Richards 1931)], groundwater flow (3D, Richards’s equation), and streamflow [1D diffusive wave equation (Strelkoff 1970)]. It is to be noted that one-way linking between ISNOBAL and PIHM involved deactivating the temperature index snowmelt utility in PIHM and replacing it with the physically based snowmelt SWI output from ISNOBAL. Additionally, simulated ground evaporation in PIHM is shut off at locations shielded by accumulated snow, but evapotranspiration from protruding vegetation still occurs. Energy exchanges at snow-free locations remain the same. Both ISNOBAL and PIHM are set to run at an hourly time step; however, the spatial resolution of ISNOBAL and PIHM are different. ISNOBAL was run on a total of 3978 10 m × 10 m structured grids in the model domain, while PIHM has 101 unstructured triangular grids in the same domain. SWI for each triangle grid contains the sum of SWI output from ISNOBAL structured grids, which has the centroid within the triangle. PIHM has been previously applied across watersheds with different scales and climate conditions (Chen et al 2015; Kumar and Duffy 2015; Shi et al. 2014; Yu et al. 2014). The linked framework has been previously used in Kumar et al. (2013) and Wang et al. (2013) to model relevant hydrologic states and fluxes in RME.

c. Model calibration and validation

1) Model calibration

Model calibration is performed only in PIHM. Though ISNOBAL is uncalibrated, the terrain-based wind redistribution parameters tuned to topographic and vegetation structure of the RME catchment as presented by Winstral et al. (2009) were used for the ISNOBAL simulation. The ability of the model to simulate snow distribution and total melt and surface water output has already been demonstrated in Winstral and Marks (2002). Reba et al. (2011b) showed that for an uncalibrated ISNOBAL simulation, the average Nash–Sutcliffe model efficiency (NSE) over the 25-WY period for predicted versus measured SWE at the snow pillow was 0.90, with a range of values between 0.74 and 0.98. Calibration of parameters for PIHM simulations involved nudging of hydrogeological parameters uniformly across the model domain (Refsgaard 1997) to match the baseflow magnitude, groundwater head distribution, and decay rate of the hydrograph during the recession period. Calibration experiments were performed for two periods: 1) a dry period with no appreciable antecedent recharge (10–25 October 2005) and 2) a wet and cold period with peak streamflow response (caused by rainfall event) and negligible evapotranspiration (from 30 December 2005 to 30 January 2006). Streamflow during the first calibration period was assumed to be predominantly base flow and controlled by subsurface properties. It was assumed that streamflow during the second calibration period was controlled by both surface and subsurface properties. This strategy ensured that calibration of the coupled snow and hydrology model did not depend on the ISNOBAL SWI output. Hydrogeological parameters that were adjusted during the calibration procedure included soil drainage parameters, such as van Genuchten coefficients (Van Genuchten 1980), porosity, and conductivity of the top soil and the underlying subsurface. More details about the calibration methodology are presented in Kumar et al. (2013). It is to be noted that parameter optimization did not include matching the magnitude or timing of streamflow peak response at either daily or seasonal scales.

2) Model validation

(i) Streamflow, groundwater, and soil moisture validation

Results of streamflow validation for the simulation period 1984–2008 (Fig. 2a) showed NSE of 0.86 and coefficient of determination r2 of 0.93 for hourly data, 0.88 and 0.94 for daily data, 0.86 and 0.96 for monthly data, and 0.86 and 0.96 for yearly data. The simulated and observed annual runoff means during WYs 1984–2008 were 528 and 468 mm, respectively.

Fig. 2.
Fig. 2.

Modeled and observed (a) streamflow for WYs 1984–2008 and (b) groundwater depth for WYs 2006–08 [light gray vertical lines in (b) demarcate period from 1 to 13 Apr in WY 2006].

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

Groundwater table dynamics validation for the period WY 2006–08 is presented in Fig. 2b. Though the observed groundwater responses at wells 1 and 2 were unusually steep, for example, varying by as much as 7.5 m in a matter of 3 h, the model was able to capture the general shape and structure of these dynamics across all years where groundwater height data were available [see Kumar et al. (2013) for details]. Figure 2b shows that the model captures the slower dynamics equally well. More detailed characterization of the subsurface, finer spatial data and model grid resolution, and an automated calibration strategy may possibly help resolve the discrepancies. It is possible that the simple representation of macroporous flow behavior in the subsurface is not adequate for highly transient subsurface flow systems.

Comparisons between observed soil moisture at multiple locations has already been shown in Fig. 2 of Kumar et al. (2013), where the simulated top soil saturation magnitude and timing reasonably matches the observation. Even though hourly soil moisture data exist for the snow pillow site from WYs 2005 to 2008, out of 67 melt days during this period only 6 exhibited a peak signal. On these 6 days, average error between peak hour in the observed soil moisture data and the modeled lagged SWI flux was within an hour. On the rest of the 61 days, soil is either completely saturated during the day or it saturates well before the melt peak is reached. Despite using a nonlocalized calibration approach, model predictions for streamflow, groundwater table, and soil moisture variations can be considered adequate and underscore the potential of the coupled ISNOBAL–PIHM system for simulating hydrologic responses and understanding the role of process controls on DPTs.

(ii) DPT validation

In this study, melt season DPTs were calculated from simulated streamflow and compared to observed DPTs for WYs 1984–2008. Days without a melt-affected (diurnal) signal were excluded from the analysis (i.e., the hydrograph showed monotonic variations within a day). Figure 3 shows the typical streamflow diurnal signals during the melt season and corresponding DPTs. Performance of the linked model was evaluated based on the following two metrics: 1) presence/absence of an observed diurnal signal in simulation results and 2) DPT simulation.

Fig. 3.
Fig. 3.

Streamflow time series for WY 2006 during melt season. Also illustrated is the DPT hour (after noon) for every day. Times in black indicate peak hour for days with distinct diurnal signal. Times in gray boxes indicate peak hour for days with multiple peaks. All times are with respect to the local noon. Note that negative value means time before noon, for example, −2 means 1000 local time (LT).

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

A. Presence/absence of an observed diurnal signal in simulation results

For the 25-WY simulation period, a total of 811 and 595 days showed melt-affected signal in observed and simulated streamflow, respectively, with 519 days (64% of observed melt-affected days) showing melt-affected signal in both observed and simulated streamflow. For the wettest 5 years, which is defined as the 5 years with the largest precipitation amount before the melt-out date at the snow pillow site, a total of 195 and 169 days showed melt-affected signal in observed and simulated streamflow, respectively, with 150 days (77% of observed melt-affected days) showing melt-affected signal in both observed and simulated streamflow data. In contrast, for the driest 5 years, which is defined as the 5 years with the smallest precipitation amount before the melt-out date at the snow pillow site, a total of 124 and 57 days showed melt-affected signal in observed and simulated streamflow, respectively, with 56 days (45% of observed melt-affected days) showing melt-affected signal in both observed and simulated streamflow. The results indicate that the model could capture the days with diurnal signal much more accurately in wet years than in dry years.

The observed disparity in accuracy between wet and dry years is largely due to the effectiveness of the model during the early melt period. Isolating the first 5 days of the season with melt-affected diurnal signals in observed streamflow, modeled streamflow similarly exhibits a diurnal signal on 88% of the days in the wettest 5 years and only 52% of the days in the driest 5 years. The inability of the model to capture melt-affected streamflow in early spring, especially during dry years, is highlighted in Fig. 4. The streamflow simulation is fairly accurate throughout the melt season for a very wet, warm snow season (WY 1996, Fig. 4a). In contrast, Fig. 4b shows that, for a dry, cool snow season (WY 1999), the model underestimates streamflow early in the melt season and overestimates streamflow later in the melt season. One possible reason could be that PIHM did not simulate soil temperature, and hence the consequent reduction in infiltration capacity under frozen/near-frozen soil conditions was not accounted for (Burt and Williams 1976; Flerchinger et al. 2006; Horiguchi and Miller 1983; Watanabe and Flury 2008). As a result, instead of surface runoff during the cool WY 1999 snow season, the model overestimated recharge to the subsurface, thus missing the melt-affected streamflow in early spring. These conclusions are consistent with reported cold snow and soil temperatures during the WY 1999 snow season (see Reba et al. 2011b).

Fig. 4.
Fig. 4.

Comparison of simulated and observed streamflow during the melt season for (a) a very wet, warm snow season (WY 1996) and (b) a dry, cool snow season (WY 1999). See Reba et al. (2011b) for details on conditions during WYs 1996 and 1999.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

B. DPT magnitude

The DPTs were compared for the days when both observed and simulated data showed a melt-affected signal. Since both observed and modeled daily hydrographs may often consist of almost flat and slightly noisy high-flow periods lasting few hours (<4 h) with very small hour-to-hour variations, comparison of modeled and observed absolute DPTs can sometimes be muddled by noise (Fig. 5). Hence, comparisons were also performed against “modeled Q1% peak hour,” which is defined as the closest hour to the observed DPTs in which the modeled streamflow is within the top 1% of the modeled daily streamflow range. An identical observed DPT and modeled Q1% peak hour indicates that the top 1% of modeled daily streamflow occurred within the same hour as the observed daily peak. In contrast, a larger difference between modeled DPT and modeled Q1% DPT indicates a longer period of relatively flat (and possibly noisy) hydrograph near the peak.

Fig. 5.
Fig. 5.

Schematic of observed and modeled daily streamflow hydrographs with (a) identical observed and modeled daily peak hour (here observed peak hour = modeled absolute peak hour = modeled Q1% peak hour) and (b) different observed and modeled peak hour with very small variations near the top 1% peak discharge (here observed peak hour = modeled absolute peak hour − 1 = modeled Q1% peak hour).

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

DPTs in all the figures presented here are with respect to the local noon, that is, 9 indicates 9 h after noon, which is 2100 local time (LT). DPT simulation results for the 24 WYs are shown in Fig. 6. WY 1992 is not shown here since the model could not capture the diurnal signal exhibited on any of the 5 days with an observed diurnal signal during this extremely dry year. The r2 value between modeled and observed DPTs for the 519 days with diurnal signal in both simulated and observed streamflows was 0.58, while r2 between Q1% DPTs and observed DPTs was 0.74. However, 130 of these days had multimodal peaks because of rain or snow events that interfered with the diurnal variation in energy forcing to the snowpack. For days with unimodal peak, r2 between modeled and observed DPTs was 0.61 and between Q1% DPTs and observed DPTs was 0.80.

Fig. 6.
Fig. 6.

Observed and modeled daily peak time for 24 WYs ranging from WYs 1984 to 2008 (WY 1992 was excluded). The x axis represents WY day, and the y axis indicates the daily peak time hour with respect to local noon. Note that negative value means time before noon, for example, −4 means 0800 LT.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

Figure 6 shows that both modeled and Q1% DPTs appear to follow the seasonal variations exhibited by the observed data. The mean and variance of observed, modeled, and Q1% DPTs were (5.8, 7.4), (5.6, 9.3), and (6.0, 7.7) h, respectively. Further analyses indicated that, of the number of days considered in Fig. 6, years with more than 80% of days with |(observed DPT − modeled absolute DPT)| and |(observed DPT − modeled Q1% DPT)| being smaller than or equal to 1 h are 6 and 14 years, respectively. For the 24 years under consideration, more than 59% of days had a difference between observed and modeled DPTs of less than 1 h, and more than 78% of days had this difference in the range less than 2 h. The corresponding numbers for the difference between Q1% modeled and observed DPTs were 76% and 88%, respectively.

Presented results indicate that the simulated hour of peak discharge, especially the hour of the Q1% peak, closely matched the hour of observed daily streamflow peak during the snowmelt season, especially in wetter years. However, ISNOBAL–PIHM was not as successful in capturing diurnal variations in streamflow, especially early in the melt season during drier years.

3. Experiment design and details

a. Daily peak time and melt season duration

The initial day of the melt period, identified by the melt-induced signal in streamflow, does not always mean that snowmelt begins on this given day. For example, analysis of the simulated daily SWI volume for WY 2006 indicates 12 days of melt before a melt-affected streamflow signal was registered. Furthermore, it also does not mean that the SWI volume on this day is necessarily larger than that on the previous days. For example, on the previous and following 5 days of initiation of the melt period (13 April, day 195 of WY 2006), simulated melt amount only differed marginally (Fig. 7). Simulation results suggest that the melt-affected diurnal signal in this year was expressed only after groundwater table was shallow enough for it to substantially contribute to streamflow. Before this, most of the melt recharges the subsurface moisture deficit and groundwater. This explanation is supported by the observed groundwater table and streamflow data for WY 2006 (see Figs. 2, 3) where the melt-affected signal in streamflow starts on 13 April (WY day 195), only after the observed groundwater levels in wells 1 and 2 have become shallow enough after undergoing gradual increase from 1 to 13 April (this time interval is highlighted by two circular dots in well 1 and 2 groundwater series in Fig. 2) in response to melt recharge. Groundwater control on diurnal streamflow response is further evident from diurnal streamflow fluctuations that are much smaller (both in terms of volume and amplitude) than melt (see Fig. 7). It is clear in Fig. 7 that before WY day 195, the magnitude of SWI is comparable to that after day 200; however, SWI at the beginning of the melt season (before WY day 195) does not lead to substantial streamflow as it does later in the melt season (e.g., after WY day 200). Also, the observed streamflow magnitude on the first melt-affected day is small and increases in subsequent days (concomitantly with the increase in groundwater height) even though a similar increasing trend in melt and SWI does not exist. This indicates a large groundwater contribution to streamflow response (Bengtsson 1982). In fact, simulation results suggest that the groundwater contribution to streamflow is close to 100% during the melt season in the RME watershed. This indicates that DPTs analyzed in this watershed are dominantly controlled by subsurface flow processes, including infiltration of SWI into the upper unsaturated zone and its translation to groundwater.

Fig. 7.
Fig. 7.

Modeled daily total melt and streamflow during melt period in WY 2006.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

b. Isolating the relative role of individual process controls on DPTs through process-unmixing experiments

The variation of DPTs within a melt season has been previously attributed to three processes (see section 1 for detailed discussion). We hypothesize that the time for snow cover ripening may also contribute to intraseasonal variations in DPTs. Therefore, in the ensuing analyses, we consider the role of the following four processes on DPT variations: 1) net incoming energy (turbulent heat + radiation + advection) to the snowpack and snowpack properties (depth + temperature + moisture content), which determines the snowpack ripening time; 2) percolation rate of liquid water flux through the ripened snowpack; 3) translation of meltwater output from the bottom of the snowpack (SWI) to the stream channel through surface and/or subsurface pathways; and 4) translation of water in the river channel to the streamflow gauge. Notably, many other factors, such as snowpack and its distribution and watershed properties, may also affect the peak time, but they do so by indirectly influencing the aforementioned four processes. The scope of this paper is restricted to assessing the influence of the four basic processes on DPTs.

To isolate the influence of each process on the timing of daily peak streamflow, DPTs are evaluated with and without the process under consideration. DPTs from different processes and relations between them are listed in Table 1. It is to be noted that the peak time delay (P12P1) caused by translation within a snowpack is not equivalent to the average translation time through the snowpack. Instead, (P12P1) represents the time difference between instances that receive the largest water flux in the two simulations and hence is a function of both melt flux amount and the time of translation. For example, between two cases with identical spatial distribution of percolation times through the snowpack in a watershed, if melt contributions from thinner snow (with relatively shorter percolation times) are larger than that from deeper snow, then (P12P1) will be smaller. Conversely, if melt contributions are mostly from deeper snowpacks through which the translation time is relatively longer, (P12P1) can be expected to be larger. Similarly, (P123P12) expresses the contribution from surface/subsurface flow processes in delaying the peak time.

Table 1.

Description of processes considered and process-unmixing approach.

Table 1.

4. Results and discussion

The results are presented thematically following the two questions outlined in section 1.

a. How do DPTs vary intraseasonally and what are the key processes that determine its magnitude and variations?

1) Intraseasonal DPT variations

Within each melt season, DPTs generally exhibited a shift to earlier in the diurnal cycle as the melt season progressed, that is, DPT on the last day of the melt season was earlier than that on the start day. The change in DPTs from the start to end of the melt season across the 25-WY period was from 10 to 1 h in the observed data, from 12 to 1 h in the ISNOBAL–PIHM results, and from 11 to 1 h in Q1% modeled results. The shift of DPTs to earlier in the day was often obscured by abrupt nonmonotonic day-to-day variations. For example, in WY 1993 (Fig. 6), the observed DPTs shifted from hour 12 to 3 (2400–1500 LT) between WY days 207 and 215, abruptly shifting to hour 11 (2300 LT) on WY day 217 (identified by an arrow in Fig. 6) and then gradually shifted earlier again to hour 4 (1600 LT) by WY day 232. During the simulation period, abrupt shifts (≥2 h) in DPTs were observed on 40 days in the observation data, with a maximum shift equal to 8 h. Comparatively, abrupt shifts occurred on 43 days in the modeled streamflow and on 36 days in Q1% modeled results, with a maximum shift time of 5 and 6 h, respectively.

2) Influence of physical controls on intraseasonal peak time and its variations

Using the strategy detailed in section 3b, the time of peak streamflow (e.g., P1, P12, and P123) was obtained after discounting the effect of individual process controls. Results (Fig. 8) suggest that discounting the role of individual processes affects both the timing of daily simulated peak streamflow and its variation during the season. The daily peak time was earlier, as expected, as increasing number of process controls were discounted, that is, P1 < P12 < P123 < P1234. In addition, the difference between P1, P12, P123, and P1234 was much larger in the beginning of the season than at the end for each year. However, the relative contribution of each process control was observed to vary from day to day. In the next section, we evaluate the role of each process control on the intraseasonal timing and variation of DPTs.

Fig. 8.
Fig. 8.

Results of peak hour variation after discounting different processes for 24 WYs: P1234 is the original modeled peak hour; P1 is the peak hour of melt flux when translation time through snowpack is not accounted for, P12 is the peak hour from translated liquid water flux, and P123 is based on the original model but assuming translation in the river does not happen. Detailed explanations of the four experiments are presented in section 3a.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

(i) Role of net incoming energy and evolving snowpack properties

Increasing energy inputs and concomitant changes in snowpack properties are expected to result in decreasing DPTs. This is because as net energy input increases, snow cover ripening may occur earlier during the day. In addition, changing snowpack properties such as increasing snowpack temperature and liquid water content and decreasing depth would require less energy to ripen the snowpack, leading to earlier melt. The average P1 difference from the start to end of the snow season during the simulation period was 1.1 h. While in some years P1 at the start of the season was up to 10 h later than that at the end, other years showed no differences. Since a shift in P1 is a compound effect of both increasing incoming energy and changing snowpack properties, two additional ISNOBAL experiments were performed to assess influences of the two factors.

To evaluate the influence of increasing net energy input on the DPTs, ISNOBAL snow states for each day within the melt season were fixed to conditions on the first day of melt. With fixed snow states and varying net energy input, the average P1 difference from start to end of the season during the simulation period was around 0.3 h. Similarly, to evaluate the influence of changing snowpack properties on the DPTs, ISNOBAL incoming energy for each day within the melt season was fixed to conditions on the first day of melt. With fixed incoming energy and varying snowpack properties, the average P1 difference from start to end of the season during the simulation period was around 0.7 h. The results from the two additional experiments indicate that evolving snowpack properties play a more important role than the incoming energy in the melt timing. In reality, the variation of P1 (shown in Fig. 8) during the melt season is not monotonic, as it is dependent on net energy fluxes and snowpack properties, which exhibit strong variability. Sudden decreases in temperature or radiation, or new snow events, which increase albedo and snow depth, can lower the net energy inputs and modulate temperature of the snowpack. In fact, all 95 days showing a delayed streamflow peak time in P1 had either large decreases in temperature or radiation relative to the prior day. Of these 95 days, 55% showed a concomitant increase in P1234. In summary, an increasing trend in radiation and temperature, with concomitant increase in snowpack temperature and moisture content and decrease in snowpack depth during the melt season, generally leads to a decreasing trend in P1. However, the isolated impact of net energy input is only marginal. Sudden decreases in radiation or temperature (e.g., due to cloudiness) and precipitation events may lead to an abrupt P1 increase. Changes in P1234 could mirror changes in P1. Evaluation of the isolated impact of cloud and/or precipitation on P1234 is reserved for future study.

(ii) Role of snow percolation process

Delay in the DPTs (i.e., the time difference in DPTs if a process’ contribution is considered or not) caused by the process of snow percolation (P12P1) is also expected to decrease as the melt season progresses because of decreasing snow depth and increasing liquid water content. This is evident in Figs. 8 and 9, where the difference between P12 and P1 is generally larger in the beginning than the end of the melt season for all years. The average (P12P1) at the start and end of the melt season over all years is 2.7 and 0.2 h, respectively. However, the delay from translation of meltwater through the snowpack showed a nonmonotonic decrease and could vary significantly from day to day. One example of such day-to-day variance could be seen on WY days 196 and 197 in WY 2006 (Fig. 9). On WY day 196, P1-forced DPT was determined by an intense rain event occurring late in the day at 1800 LT. This intense rain event resulted not only in accelerated melt, but translation of rainwater through the snowpack, leading to a reduction in snow translation delay (P12P1) of 3 h [based on Eq. (1)]. The following day (WY day 197), where melt was forced primarily by diurnal energy fluxes, the snow translation delay was 6 h. The difference in the time of meltwater translation through the snow between WY days 196 and 197 was mainly caused by the intense rain event on WY day 196 that increased the percolation flux. Our analysis shows that a decreasing trend in snow depth during the melt season generally leads to a decreasing trend in (P12P1). However, timing of rain-on-snow events during the day may interfere with this trend and can lead to an abrupt increase in (P12P1).

Fig. 9.
Fig. 9.

Peak time and delay caused by different factors in WY 2006 (P1 is peak hour from melt flux when translation time through snowpack is not accounted for, P12P1 is peak hour delay caused by snow translation process, P123P12 is peak hour delay caused by ground translation process, and P1234P123 is peak hour delay caused by in channel translation process).

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

(iii) Role of surface/subsurface flow

The streamflow in RME watershed is controlled primarily by subsurface processes (see section 3a). As the melt season progresses, soil moisture storages become increasingly saturated, water-table height increases, and the contributions of subsurface processes to discharge increase. Since the subsurface hydrologic conductivity in the watershed decreases with depth, net increase in water-table height during the melt season leads to a consequent increase in effective hydraulic conductivity of the watershed (Wildenschild and Jensen 1999; Yeh and Harvey 1990; Quinton and Marsh 1998; Quinton and Gray 2003). Though the groundwater table during the melt period generally reduced after the peak melt, it still remained higher than its level at the beginning of melt season. In fact, the average difference in groundwater table between the beginning and end of the melt season across the simulation years was 2.1 m. As a result, the delay in timing of peak streamflow caused by subsurface flow (P123P12) is expected to decrease. This is evident in Fig. 8, where the difference between P123 and P12 is generally larger in the beginning than the end of the melt season. Average (P123P12) at the start and end of melt season over all years was 4.0 and 1.6 h, respectively. However, (P123P12) does not decrease monotonically during the melt season. A closer look at the melt flux peak and corresponding streamflow suggested that mild increases in (P123P12) on consecutive days were often observed, mostly because of a flat hydrograph around the peak (see section 4a). However, on certain days, (P123P12) exhibited jumps as large as 5 h (an abrupt increase during WY 1984 is highlighted in Fig. 10). Interestingly, the abrupt jump identified in WY 1984 occurred on days with very small differences in melt and groundwater distributions. Further investigation of WY 1984 melt flux and streamflow on WY day 236 revealed that both the original melt flux and translation of meltwater through the snow were trimodal on this day, with the middle peak being the largest. However, daily streamflow showed only two peaks due to dry antecedent groundwater conditions early in the day. Because of the multiple melt recharge pulses during the day, the difference in the hour of peak streamflow for days with multimodal melt flux could not be compared to days with a single peak. Variations in (P123P12) were also affected by dynamic changes in subsurface moisture and its distribution, which influenced infiltration capacity and drainage pathways. Our analysis shows an increasing trend in effective hydraulic conductivity due to a rising groundwater table during the melt season, which generally leads to a decreasing trend in (P123P12). However, days with a multimodal melt flux can exhibit abrupt jumps in (P123P12) because of dynamic changes in losses and subsurface storage.

Fig. 10.
Fig. 10.

(a) Peak time and delay caused by ground translation process (P123P12) in WY 1984. (b) Original melt, melt after translation through snowpack, and streamflow time series for WY 1984.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0152.1

(iv) Role of stream channel translation

Impacts of stream channel translation on DPTs during melt season were generally within an hour because of the small size of the RME catchment (0.4 km2) and the limited stream channel (<500 m). This is illustrated by Fig. 8, which shows that P123 and P1234 overlap each other on most of the days during the melt season. Resolving DPTs at finer time steps might reveal contributions from this process to be on the order of minutes for days with overlapping P123 and P1234; however, to maintain consistency in the analyses given that the temporal resolution of the observation data is an hour, only hourly difference in P123 and P1234 is reported here.

(v) Relative role of each process in delaying the time of peak streamflow

Among the above four processes, P1 controls the timing of melt flux while the other three processes contribute to the delay in the translation of meltwater from the snow through the soil and groundwater to the stream channel and finally to the stream gauge. The peak streamflow timing delays attributable to each process are taken as differences in simulated peak flows before and after including each process in the simulations. Average delays due to percolation of flow through the snowpack (P2), flow through the subsurface (P3), and flow in the stream channel (P4) were 1.7, 2.3, and 0.2 h, respectively. The average delay values indicate that subsurface translation played the dominant role in delaying the peak times, with snow percolation being the secondmost important factor. The influence of stream translation process on the streamflow DPTs was negligible compared to the other two factors, which is consistent with the findings in Lundquist et al. (2005).

As noted in the previous sections, the delay effect caused by the percolation and subsurface processes was generally larger in the beginning of the melt season than the end. To identify the relative contribution from each process at different times during the melt season, the melt period was evenly divided into three periods: 1) the early melt period (deep snowpack + deep groundwater table), 2) the rapid melt period (rapidly reducing snowpack + rapidly increasing groundwater table), and 3) the late melt period (thin snowpack + shallow groundwater table). Average timing delay for DPTs during the three intervals as caused by each process was calculated and compared. Results indicate that the relative importance of individual processes change during the melt season.

During the early melt period in the wettest 5 years, average delay caused by snow translation and subsurface flow was 3.4 and 2.3 h, respectively. During this period, translation through snow was the dominant control in determining DPTs. In the rapid melt period, delays caused by translation through snow and subsurface processes were 1.3 and 2.2 h, respectively. During this period, subsurface processes became the dominant factor. In the late melt period, translations through snow and the subsurface contributed evenly to the delay in DPTs, with delay time being 1.2 h for both.

For the driest 5 years, subsurface processes were the dominant factor for delay throughout the melt season. Average delay caused by translation through the subsurface for the early melt period, rapid melt period, and late melt period were 7.8, 4.7, and 2.7 h, respectively, while corresponding delays caused by snow translation were only 1.3, 0.7, and 0.6 h, respectively. The contribution to DPT from translation through snow was generally larger in the early melt period, while the contribution from the subsurface process was much more prominent in the later periods when most of the snow had ablated. The importance or controlling influence of a process on changes to DPT during particular times of the melt season does not always mean that it is also the main determinant on seasonal DPT variations, especially the seasonal decreasing trend. Our analysis indicates that while subsurface flow processes were more dominant in determining the actual streamflow peak time, the decreasing trend in DPT was controlled primarily by the snow translation process. Variations in net energy input, on the other hand, mainly affected day-to-day variations in DPT during the melt season.

b. How do DPTs vary interseasonally and what are the processes that control this variation?

1) Interseasonal DPT variations

Seasonal average DPTs (for days exhibiting melt-affected signal) showed significant variations among years, ranging from 4.0 to 7.1 h after local noon in the observed data, 3.2 to 7.6 h in the modeled absolute DPTs, and 4.4 to 7.4 h in Q1% modeled results. These variations are likely the result of interaction among the controlling processes identified in section 3b.

It is important to recognize that the differences in seasonal average DPT among individual years are also influenced by the variations in the number and timing of melt days between different years, which in turn are controlled by the peak SWE, soil temperature, abrupt changes in meteorological conditions, and water-table depth. Initiation of the melt season varied by as many as 28 days (earliest start WY day = 183, latest start WY day = 211) in the observed data and 40 days in modeled streamflow results (earliest start WY day = 184, latest start WY day = 224). Similarly, the number of days with a diurnal melt signal ranged from 13 to 54 days in observed data and 6 to 38 days in modeled DPT results. Depending on the timing of melt-affected days during the melt season, the process controls that determined DPTs such as energy input to the snow, its depth, and melt recharge into the soil may vary, thus resulting in interseasonal variations in DPTs.

Interseasonal variations also occurred in seasonal shifts in DPTs. Seasonal DPT shift, defined as the difference in daily peak time between the first third and the last third of the melt season, averaged 2.4 h (range of 1–5 h) in the observed data, 3.6 h (range of 1–9.8 h) in the modeled data, and 3.1 h (range of 0.8–6.3 h) in Q1% modeled results, among the years of study. The average peak hour difference between the first and last days of the melt season for the three streamflow series was found to be 4.1, 5.5, and 4.1 h, respectively. This difference ranged from 10 (early season) to 1 h (late season) in observed data, 12 to 1 h in modeled results, and 11 to 1 h in Q1% modeled results.

2) Influence of physical controls on interseasonal peak time and its variations

Analyses of the relative role of each process control on average DPT delay for the entire simulation period [see section 4a(2)(v)] demonstrated that subsurface translation played the most dominant role on the average DPT, followed by translation through snow. However, a closer look revealed that delay times caused by snow translation, subsurface flow, and river translation processes at a seasonal scale varied by as much as 0.5–3.2, 0.9–6.4, and 0.1–0.9 h, respectively. The wide range in delay time caused by each individual process raises the possibility of different processes dominating in different years. Further analyses revealed that the snow translation process was dominant in delaying DPTs in wetter years while subsurface flow was dominant in drier years. For example, average delay times caused by snow translation, subsurface flow, and stream channel translation time were 2.8, 1.9, and 0.3 h, respectively, in the wettest five WYs during the simulation period, while the corresponding delay times in the driest five WYs were 1.2, 5.8, and 0.4 h, respectively. The delay in DPTs from snow translation process was more prominent in early melting period. The average delay times due to snow translation, subsurface flow, and stream channel translation in the five wettest years during the first third of the melt season were 4.1, 2.4, and 0.4 h, respectively. The delay from subsurface flow in dry years tended to be prominent throughout the melt period. For example, average delays due to subsurface flow processes in the five driest years were 6.5 and 4.6 h during the first and last third of the melt period, while the delays due to snow translation for the corresponding periods were only 2.0 and 0.9 h. Overall, the average translation time through snow showed a high correlation with snowfall amount (r = 0.80). This was not surprising, as years with greater snowfall amounts tended to generate snowpacks with greater depths, leading to longer melt translation times. In addition, more snowfall resulted in a higher groundwater table near the end of melt season, which in turn reduced the delay attributable to subsurface flow processes. As a result, variation of average delay time caused by subsurface flow processes had a negative correlation with annual snowfall (r = −0.46). This weak correlation revealed that other confounding factors such as the multimodal behavior of melt flux and change in net storage and losses [as discussed in section 4a(2)(iii)] may also contribute to variations in delay time between years. Since increased snowfall can lead to a larger DPT delay from the snow translation process but a smaller DPT delay from subsurface flow, these two translation processes may compensate each other. This results in seasonally moderate average DPT delays in wetter years. The correlation between seasonally averaged DPT and snowfall amount is only 0.19, indicating that the average DPT delay may not show a clear relationship to snow depth and melt recharge volume. However, the shift in DPT during each melt season (i.e., the difference in DPT between beginning and end of the melt season) was still larger in years with high snowfall amounts because of both larger decreases in snow translation and subsurface flow time between the beginning and end of each melt season. Average DPT shift for each year, calculated as the difference in the last third and first third of the melt season, had a correlation of 0.42 with the snowfall amount. Our analysis indicates that wet years tended to have larger DPT shift within the melt season. While the process of translation of meltwater through snow was a more dominant control on DPTs in wetter years than in drier years, the influence was more important in the beginning of the melt period. In contrast, subsurface flow processes were a more important control in drier years and maintained this influence on DPTs throughout the melt season in these years.

5. Summary and conclusions

This study explored the day-to-day intra- and interseasonal variation in the timing of peak daily streamflow (DPT) in a snow-dominated watershed. We quantitatively evaluated the role of hydrologic process controls on DPT and its variations. Results indicate that the physics-based integrated model, which consisted of a snowmelt model coupled to a hydrologic model, was able to reasonably capture both DPT and its seasonal variations, with the exception of the first few days in the melt season in drier years. For days when the model could capture the melt-affected signal shown in observed data, 80% of variation in observed DPT could be captured by the model. A process-unmixing approach was then used to evaluate the relative influence of process controls in determining DPT and its variation during the melt season. Results show that subsurface flow was the most dominant influence on DPT delays in this catchment. The influence of meltwater translation through the snowpack was a close second. Translation time in the river channel had negligible contributions to both peak hour and its variations because of the small spatial area assessed in this study. Though subsurface flow was assumed to have minimal effect on DPT in previous studies (e.g., Lundquist et al. 2005), the results presented here indicate that for basins with groundwater flow as the dominant control in the streamflow diurnal signal (such as RME), the effect of subsurface could not be neglected.

The relative influence of process controls on DPT varies during the melt season. Intraseasonally, delay in peak time from translation of meltwater through snow was generally larger early in the melt period while subsurface flow played a much more prominent role later in the melt period when most of the snow had ablated. The average shift in DPT to earlier in the day in the later part of the melt season was mostly contributed by the process of meltwater translation through the snowpack, with contributions from subsurface flow being secondary. Interseasonally, translation of meltwater through snow is the most dominant process in delaying DPT in wet years while subsurface flow plays a more dominant role in drier years. Overall, the contribution of meltwater translation through snow and the subsurface on DPT delay show a high positive correlation and a moderate negative correlation with seasonal snow amount, respectively. Average DPT delay due to translation through snow is larger in wet years because of larger snow depth. At the same time, the contribution of translation through subsurface on DPT delay is smaller in wet years because of increased effective subsurface conductivity. While of only marginal influence in this watershed, translation time through stream channels can be expected to be more important in larger watersheds with longer river reaches. Our results identify the dominant process controls on DPTs at both intra- and interseasonal scales and could be used to prioritize measurement strategies for determination and monitoring the timing of peak daily streamflow. The results suggest that one should be cautious while analyzing DPT delays, as they are the product of interactions between several processes controlled by the complex physiography and variable weather conditions typically encountered in mountain regions.

The physically based coupled modeling system presented here is ideally suited for process-unmixing experiments to isolate the role of individual processes on daily peak time. The methodology can be used in other watersheds and in conjunction with other process-explicit models. The presented analyses also highlight that diurnal streamflow data may carry important information regarding the hydrologic partitioning in the watershed and can further aid in model diagnosis and validation. For example, overall increase in observed daily streamflow magnitude (before the seasonal peak) even as the daily melt peak varied contrapositively (see section 3a) indicates that groundwater contribution to streamflow during the melt season was significant in the RME watershed. Similarly, the inability of the model to capture early diurnal signals in dry, cool years [see section 2c(2)(ii)(A)] while it overestimated the groundwater recharge indicates errors in simulated runoff during early melt season and highlight the need to incorporate the effects of changes in hydraulic conductivity vis-à-vis soil temperature.

It is important to be aware that the magnitude of DPT delays and the relative contribution of each process presented in this paper are specific to this watershed and may vary elsewhere. The relative controls on meltwater translation through snowpack, the subsurface, and in the stream may vary between watersheds and can be influenced by a range of factors, including hydrologic partitioning of melt between surface and subsurface flow, changes in streambed hydraulic conductivity triggered by temperature variations, dynamics of watershed hydrologic connectivity and preferential pathways in the snowpack, and anthropogenic activities (Gribovszki et al 2006; Lundquist and Cayan 2002; Marks et al 1998; McNamara et al 2005; Morgenschweis 1995). The modeling experiment conducted here does not account for uncertainty. Further studies focused on providing detailed maps of subsurface properties, evolution of preferential pathways in snowpack, and relative contributions of surface and subsurface discharge that could be used to refine our results and provide an estimate of, and ultimately help reduce, the uncertainty.

Acknowledgments

Datasets used in the paper are publicly available from the Northwest Watershed Research Center, USDA anonymous ftp site (ftp://ftp.nwrc.ars.usda.gov/public/RME_25yr_database). The data and analysis presented in this paper were funded in part by NSF CAREER award (EAR 1454983) and USDA-ARS CRIS Snow and Hydrologic Processes in the Intermountain West (5362-13610-008-00D). We thank Jeff Dozier and Jessica Lundquist for providing constructive comments that greatly improved this manuscript.

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1

A water year runs from 1 Oct of the previous year through 30 Sep of the given WY and is used in regions dominated by winter precipitation, like the western United States. In this paper, any reference to years is to water years, with the year referring to the calendar year of that spring’s snowmelt runoff.

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