1. Introduction
In the western United States, over half of the water supply comes from mountain snowpacks, and over the past 50 yr, warmer winters and springs have led to earlier snowmelt (Stewart et al. 2005). The fraction of annual streamflow that runs off during late spring and early summer has declined by 10% to 25% (Roos 1991; Wahl 1992; Dettinger and Cayan 1995). Snowmelt runoff timing has advanced by approximately one to three weeks in the large majority of mountainous catchments across western North America (Stewart et al. 2005; Regonda et al. 2005). In response to increasing greenhouse gas concentrations in the atmosphere, these trends are likely to continue (Dettinger et al. 2004). Using linear regression models, Stewart et al. (2004) projected that, at many gauges, flow timing could shift 30 to 40 days earlier by the end of the twenty-first century. These latter results are in good agreement with other, more detailed simulations, such as those by Wood et al. (2004) using the Variable Infiltration Capacity model (VIC; Cherkauer et al. 2003) and by Dettinger et al. (2004) and Jeton et al. (1996) using the Precipitation-Runoff Modeling System (PRMS; Leavesley et al. 1983).
March 2004 provided an example of an early spring of the sort likely to become more common as the regional climate warms. Record-high temperatures occurred across the western United States, causing a simultaneous record-breaking early onset of snowmelt across the region (Pagano et al. 2004). Fed by the early melt in 2004, snowfed streams across the western United States began flowing about a month earlier than usual (Pagano et al. 2004). In the Sierra Nevada of California, a rapid warming of over 12°C during the first week of March 2004 was enough to raise and sustain temperatures above freezing at elevations up to at least 3000 m. Thus, snowmelt was expected to commence simultaneously at all elevations at or below 3000 m, as had occurred previously in late March 2002 (Lundquist et al. 2004).
Streamflow began rising at most locations at the same time in early March 2004. However, in 2004, stream stage recorders in a set of nested subbasins in the high country of Yosemite National Park, on the western slopes of the Sierra Nevada, California, told a more complicated story. Temperatures during early March 2004 were as high as temperatures in late March 2002, when streams gauged at elevations from 1200 to 3000 m began flowing simultaneously. Despite the warm air temperatures, in 2004 several streams draining high-elevation basins did not start flowing until later in the spring.
This paper analyzes how and why these two years differed and what the implications are for snowmelt timing if the regional climate continues to warm. Section 2 describes the data and methods. Section 3 demonstrates how the energy balance in the Sierra Nevada differed between 2002 and 2004, why topographic shading resulted in more spatial variability of streamflow timing in 2004, and why a current operational snowmelt model (Snow-17; Anderson 1976) would fail to capture these differences. Section 4 examines 67 yr of historic discharge data from two basins with opposite aspects in the Gunnison River drainage in Colorado, to demonstrate how shading, radiation, and the timing of spring streamflow have interacted in the past. Section 5 presents a simplified version of the Utah Energy Balance (UEB) model (Tarboton and Luce 1996) that incorporates shading effects and projects how, as temperatures warm, the timing of spring streamflow is likely to advance differently in basins with differing topographies and in basins at different latitudes. Section 6 offers conclusions and considerations for the future.
2. Data
a. CA DWR snow pillows
The California Department of Water Resources (CA DWR) manages a network of automated snow-monitoring stations throughout the Sierra Nevada. Snow pillows at these stations measure the weight of the snow accumulation and thereby record the snow water equivalent (SWE) of the snow column. In this study, 112 stations spanning elevations from 1500 to 3500 m were examined (Fig. 1). As outlined in Lundquist et al. (2004), the onset of spring melt at each snow pillow was identified by the day of maximum SWE because more melt than accumulation occurred thereafter. In years having multiple days of maximum SWE, the onset of spring was taken to be the last day of maximum SWE for that year.
b. Yosemite streamflow sensors
In summer 2001, 20 stream pressure sensors (Solinst Leveloggers1) were installed to record hourly water level and temperature in the upper reaches of the Merced and Tuolumne Rivers (Fig. 2). These streams drain a range of snowmelt-contributing elevations from 1200 to 3700 m in the high country of Yosemite National Park. Sensor locations were selected to monitor snowmelt from a variety of topographic characteristics. The monitored streams include drainages that are primarily north-facing slopes, and some that are primarily south-facing slopes. Subbasin areas along the Tuolumne River range from 6 to 775 km2; gauge elevations range from 1200 m at Hetch Hetchy to 2900 m at Gaylor Creek. Table 1 details basin characteristics for a subset of these basins. The listed potential radiation and hours of daylight are basin averages, calculated as detailed below.
c. Distributed potential radiation
Potential incoming solar radiation was calculated for each pixel of a 30-m digital elevation model (DEM) of the Yosemite subbasins for each day from 1 March to 1 April, and for each pixel of 30-m DEMs of the East River and Lakefork subbasins of the Gunnison River in Colorado (Fig. 3) for 1 April and 1 May. For each of the subbasins investigated, we calculated potential direct and diffuse solar radiation for each tenth hour (6 min) of the day as a function of solar angle, elevation, aspect, and shading from the surrounding topography, following the methods outlined in Flint and Childs (1987). For each pixel of the DEM within a subbasin, we summed the calculated radiation over the day to obtain daily radiation exposure. We then averaged the daily radiation for all pixels within the subbasin. Variations in clouds and land cover were not considered in these calculations.
d. Yosemite temperature sensors
During summers 2001 to 2003, 32 temperature sensors (Onset Computer Corporation Stowaway Tidbits and Hobos) were installed in small radiation shields in trees throughout Yosemite National Park (Fig. 2). The sensors were located at a range of elevations adjacent to the Tioga Road (Highway 120) and were collocated near the streamflow sensors described above. These sensors record every half hour and are accurate to within ±0.2°C. Further details are available in Lundquist et al. (2003).
e. Yosemite radiation sensors
Downwelling solar radiation was measured with LI-COR silicon pyranometers at the Tuolumne Meadows and Dana Meadows snow pillow sites (Fig. 2). These instruments may not be optimal for quantitative energy balance studies, but yield useful qualitative information about spatial and temporal variations in downwelling solar radiation.
f. Mammoth Mountain energy balance station
Net radiative and turbulent fluxes for 2002 and 2004 were calculated from data collected at the University of California, Santa Barbara, energy balance station (http://neige.bren.ucsb.edu/mmsa/) at the Mammoth Mountain Ski Resort, located on a flat site southeast of Yosemite National Park (Fig. 1). Net solar radiation was calculated as the difference between upward-looking and downward-looking pyranometers. Wind speed, temperature, and relative humidity were measured on a mast adjusted daily to stay at a height of 3.17 m above the snowpack. Downwelling longwave radiation was measured by a pyrgeometer. Upwelling longwave radiation was calculated by the Stefan–Boltzman equation, using the estimated snow surface temperature, which was assumed to match air temperature or remain at 0°C, whichever was lower. Equations and parameters used to calculate the energy fluxes are detailed in appendix A.
g. Gunnison drainage USGS gauges
Daily discharges for the primarily south-facing East River basin, U.S. Geological Survey (USGS) gauge 9112500, and the primarily north-facing Lakefork basin of the Gunnison River, USGS gauge 9124500 (Fig. 3), were obtained from the USGS data distribution system (http://co.water.usgs.gov/Data/) for the period from 1938 to 2004. The onset date of the start of spring runoff each year was calculated using the combined inflection point and cumulative departure technique detailed in Lundquist et al. (2004). The date when 50% of the annual discharge passed the gauge was calculated by summing the accumulated daily discharge for each day since 1 January and dividing by the total annual discharge. Table 2 details basin characteristics.
3. Comparing 2002 and 2004 spring melt onsets in Yosemite National Park
a. Temperatures and snowmelt timing
Average temperatures in March 2004 were among the warmest 5% on record throughout most of the western United States (Pagano et al. 2004; NCDC 2004), with values 5° to 10°C above climatic means. In Yosemite National Park, the mean daily temperature increase of 14°C from 28 February to 8 March 2004 was similar in magnitude to the increase of 15°C from 15 to 29 March 2002 (Fig. 4). At all monitored sites within the Yosemite study area, mean daily temperatures were above freezing by 29 March 2002 (Fig. 4a) and by 8 March 2004 (Fig. 4b), the dates when snowmelt began and flow in most streams began to increase. Many instruments were added between 2002 and 2004, resulting in a larger range of temperatures being reported in the later year (Figs. 4a and 4b).
Based solely on temperature, snowmelt would be expected to begin by 8 March 2004 at all study sites. The coldest mean temperature reported on 8 March 2004 was 0.5°C at the Tioga Pass entrance station (3031 m). Two higher-elevation sites also reported mean temperatures above freezing: Gaylor Peak (3206 m, 1.0°C on 8 March) and Vogelsang (3109 m, 3.9°C). At one of the colder sites that was operational both years, Budd Creek (2600 m), the temperatures on days immediately before and after 29 March 2002 and 8 March 2004 were virtually identical (Fig. 4c).
In both years, melting began at most (83% in 2002 and 86% in 2004) of the CA DWR snow stations within ±5 days of the dates when the flow in most streams began to increase (Fig. 5). However, in 2002, 10 stations recorded melt onset more than 5 days earlier than 29 March and only 5 stations recorded onsets more than 5 days later. In contrast, in 2004, no stations recorded melt more than 5 days before 8 March, and snow at 16 stations began melting over 5 days later. Figure 1 identifies the locations of snow pillows with melt onset more than 5 days later than the date most rivers’ stage rose in the two years. All 5 sites with a delayed onset in 2002 also experienced a delayed onset in 2004, and 11 more sites had delayed onsets in 2004 but not in 2002. All of the snow pillow stations with delayed melt in 2004 (Fig. 1) are near the headwaters of their respective basins, located north of steep mountains and shaded by the surrounding topography (F. Gehrke 2004, personal communication, based on site maps from the California Snow Survey archives).
The streamflow response (Fig. 6) was also very different between the two years, with stages at all monitored streams rising simultaneously in 2002 but with a staggered onset of spring streamflow in some basins in 2004. Budd Creek, which drains the shadiest monitored basin (Table 1), had an increase in streamflow 1 day after the 29 March 2002 onset date but 8 days after the 8 March 2004 onset date. In 2004, the increase in streamflow in Dana Fork of the Tuolumne River was also delayed 8 days after the onset date, and the increase in streamflow in Ireland Creek was delayed 28 days. Unfortunately, neither of these locations was monitored in 2002, so a direct comparison cannot be made. Stream stages at all of the other monitored subbasins (Fig. 2) in the Tuolumne watershed rose within ±3 days of the marked onset dates in both years. These subbasins had intermediate levels of shading and experienced slightly warmer temperatures than the three shadiest basins, which experienced melt delays. Likely causes for the timing differences between these years, particularly the extra one-week delay observed at Budd Creek in 2004, are discussed below.
b. Land cover/vegetation
Land cover was determined for the Yosemite subbasins by examining 30-m-resolution GIS maps of vegetation. The widest ranges in land cover occur in the Merced River subbasins, from 25% forest cover in the Lyell Fork of the Merced, to 75% forest cover for the Merced basin as a whole (Fig. 2). Streams draining these subbasins all had an increase in streamflow at the same time in springs 2002 and 2004. For comparison, forest cover is about 67% in Budd Creek, 75% in Conness Creek, and 57% in Gaylor Creek. Gauges in the latter two basins both recorded earlier melt onsets than at Budd Creek. Thus, percent forest cover is not a primary cause of the differences observed in the Tuolumne River subbasins.
c. Energy balances
During spring melt in the Sierra Nevada, net radiation dominates the energy balance (Marks and Dozier 1992). Days are sunny, and vapor pressures are low. Latent and sensible heat fluxes are of opposite sign and generally cancel. Thus, variations in net radiation between the years may be more important than variations in temperature alone. Net solar radiation and sensible heat fluxes measured at the Mammoth Energy Balance Station during melt onset in 2002 and 2004 are compared in Figs. 7a and 7b. Longwave radiation and latent heat fluxes cannot be compared because of instrument malfunctions. While sensible heat transfers were similar in the two years, due to similar air temperatures and wind speeds, the daily net solar radiation totals were about 30 W m−2 less during melt onset in 2004 than in 2002. Simply, in 2004, melt onset was earlier in the year, so that daylight was shorter, and the sun was lower in the sky than during the 2002 melt onset. Less incoming solar radiation during the 2004 melt onset resulted in slower melt rates everywhere. Using water’s latent heat of fusion, Lf = 3.34 × 108 J m−3; a difference of 30 W m−2 corresponds to a potential melt difference of about 8 mm day−1. This is similar to the different rates of snowmelt observed at the Tuolumne Meadows snow pillow between the two years (Fig. 7c). However, while this explains a slower rise in stream stage in 2004 than 2002, it alone cannot explain the spatial variation in dates of snowmelt onset.
d. Antecedent temperatures and snowpack ripening
Differences in the timing of snowmelt onset are controlled not only by the local energy balance but also by the energy required to bring the snowpack to an isothermal 0°C and to increase the liquid water within the pack to holding capacity. These related snow properties are termed the heat deficit and the liquid water deficiency (Anderson 1976). Different temperature patterns in the weeks preceding the snowmelt onset (Figs. 4a and 4b) suggest that the internal snow temperatures and liquid water contents differed between the two years.
The model was initialized on 1 October 2001 or 2003 with no snow and was run for two simulations each at two point locations for both years. The model was forced by measured precipitation (increased SWE) at the Tuolumne Meadows and Slide Canyon snow pillow sites (Fig. 2) and 6-hourly temperature averages from Budd Creek in Tuolumne Meadows (Fig. 4). Tuolumne Meadows was chosen because of its proximity to most stream sensors. Slide Canyon was chosen because it was the closest snow pillow that measured a delay in melt onset in 2004 but not 2002 (Fig. 1). Also, Slide Canyon accumulates roughly twice as much snow as Tuolumne Meadows each year. Measured temperatures at the two snow pillow sites were very similar to each other and to the Budd Creek record. Because of numerous data gaps in the snow pillow temperature records and to maintain consistency, the Budd Creek temperature record was used to represent temperatures at both sites. On occasions when the temperature records did differ, Budd Creek reported the coolest temperatures of the three. Thus, using Budd Creek instead of local temperatures might cause snowmelt to begin slightly later than would be predicted by local temperatures. Because the model errs on the side of early snowmelt, this is not considered a problem.
At these high elevations, all precipitation is assumed to fall as snow. Comparisons of snow depth and rain gauge measurements suggest that this assumption is valid for the time periods considered here. Using measured temperature and precipitation as input, the model calculates a residual heat deficit for the snowpack at each time step. This heat deficit represents the energy required to make the pack isothermal before actual snowmelt begins. The modeled snowpack also has a liquid water deficit (determined as a percentage of the total SWE), which must be satisfied before snowmelt flows out of the pack. Deeper snowpacks have a greater mass and therefore greater heat and liquid water storage, and thus require more energy before snowmelt is discharged. Principal equations and parameters used in the Snow-17 model are detailed in appendix B.
Snow pillows measure the weight of the snowpack, which includes both frozen water and retained liquid water. Snow-17 models these variables separately. Thus, modeled frozen SWE plus liquid water content (dashed lines in Figs. 8a and 8b) should best match the snow pillow observations. Modeled frozen SWE alone is also plotted to illustrate the conversion of snow water from solid to liquid form.
The simulated snow densities and liquid water contents were markedly higher prior to snowmelt onset in 2002 than in 2004 due to warm spells in both February and early March 2002 (Fig. 4a). In the present simulations, liquid-water-holding capacity is defined as 15% of total SWE (appendix B). From 10 to 28 February 2002, the modeled liquid water content rose from 7% to 74% of saturation capacity at Tuolumne Meadows and from 4% to 45% saturation at Slide Canyon (Fig. 8c). When warm temperatures returned from 19 to 23 March 2002, liquid water content at Tuolumne rose from 71% to 91% of saturation capacity, and at Slide Canyon rose from 40% to 54% saturation (Fig. 8c). In contrast, modeled liquid water on 7 March 2004 was only 11% of saturation at Tuolumne and 14% at Slide Canyon. Thus, the model indicates that the liquid water content of the snowpack prior to the 2002 snowmelt onset was near saturation capacity, whereas the liquid water content of the snowpack prior to 2004 snowmelt onset was minimal. Because the rate of surface snowmelt was slower in 2004 than 2002 (Fig. 7b), the time required for snowmelt to fill the liquid water deficit contributed to a greater delay in the onset of spring streamflow.
Both the mass of the snowpack and the rate of melt forcing (i.e., the air temperature and the melt factor in the Snow-17 model) control the duration of the delay in the onset of spring streamflow. The effect of snowpack mass on snowmelt timing was tested by running the Snow-17 model with precipitation measured at both Tuolumne Meadows, which received about 400 mm SWE in both years, and Slide Canyon, which received about 900 mm SWE in both years. The effect of melt forcing was tested by modeling melt at both sites for two simulations, one with observed temperatures and one with temperatures lowered 3°C (Table 3). In simulations using observed temperatures, the liquid water saturation reached capacity at Tuolumne on 27 March 2002, and at Slide Canyon on 1 April 2002, both within ±3 days of the 29 March onset date. In simulations with temperatures 3°C lower, the liquid water saturation did not begin to increase until 29 March (Fig. 8c), and snowmelt discharge began 8 days later at Tuolumne (on 4 April) and 22 days later at Slide Canyon (on 23 April). These results illustrate that a combination of deep snow and weak melt forcing, that is, cold temperatures, produce the longest delay in the onset of spring melt. In 2002, the Snow-17 model closely reproduced SWE measured at the two sites using observed temperatures and standard parameters (Fig. 8a).
In 2004, liquid water content began increasing on 7 March for all four simulations (Fig. 8b). In the simulation with observed temperatures, modeled snowmelt discharge began at Tuolumne on 13 March and at Slide Canyon on 17 March (Fig. 8d). These results were close to observations at Tuolumne, where observed snowmelt began slowly on 8 March and then accelerated on 13 March (Fig. 8b). However, observed snowmelt at Slide Canyon began 3 April, much later than the simulation. When a 3°C temperature decrease was imposed, simulated snowmelt began 5 April at Slide Canyon, more closely matching observations. The problem to be explained is why the 2004 Tuolumne observations were well simulated but the Slide Canyon observations were simulated as melting too soon unless temperatures were artificially reduced. Even when differences in SWE and overall lower radiative forcing (through the melt factor) are accounted for, some other difference in melt forcing between sites in 2004 is needed to reproduce the observed results.
e. Spatial and temporal variations in melt forcing
The above analysis provides a partial explanation for why the Tuolumne River subbasins responded differently than other Sierra watersheds in 2004 but not in 2002. In summary, the water content of the snowpack was low prior to the 2004 onset, and therefore, more melt was needed before the snowpacks would release water. Also, because of shorter day lengths, there was less energy available to melt the snowpack. However, results from the Snow-17 model suggest that these factors alone cannot fully explain the observed differences. With observed temperatures, the model simulation with a deep snowpack, that is, Slide Canyon, released meltwater about 4 days later than a shallower snowpack, that is, Tuolumne Meadows, in both years. However, the comparison of simulations and observations above suggests that in 2004, snowmelt at Slide Canyon responded as if the energy available for melt at that site was lower than the energy available at the Tuolumne site and also lower than the local temperatures might suggest. One explanation is that Slide Canyon is in a very shaded location compared to the open-meadow Tuolumne site (Fig. 2). Similarly, the river basins with a delayed snowmelt onset in 2004 are the shadiest subbasins of the Tuolumne River Watershed (Fig. 2).
Both measurements and calculations of incoming radiation demonstrate that radiation differences between sites are greater earlier in the calendar year. Pyranometers at the CA DWR snow pillow sites at Tuolumne Meadows and Dana Meadows (Fig. 2) illustrate that incoming solar radiation not only varies with location, but the relationship between sites may change at different times of year (Fig. 9). In March 2004, Tuolumne received about 20 W m−2 more incoming solar radiation than Dana because the latter was partially shaded by Mt. Gibbs and its adjacent ridge. However, by May, the sun angle above the horizon was greater, and because Dana is at a higher elevation, Dana received about 30 W m−2 more incoming solar radiation than Tuolumne (Fig. 9).
Radiation differences that vary with both location and time of year are typical in mountainous regions (Dozier and Frew 1990). The change in calculated average daily potential incoming solar radiation between 1 March and 1 April varies from −46 to 278 W m−2 across a 30-m DEM of the Yosemite study area (Fig. 10). While solar radiation increases almost everywhere from 1 March to 1 April, the amount of increase is commonly twice as much on north-facing slopes, which may not see the sun at all until later in the spring. In contrast, steep, south-facing slopes can actually receive less solar radiation as the sun moves higher in the sky.
Table 1 details the calculated basin-averaged potential solar radiation and hours of daylight for each basin on both 1 March and 1 April. All of the streams with delayed snowmelt in 2004 drained basins that primarily face north and receive a larger than average increase in solar radiation over the month of March (Fig. 10). On 1 March, the sunniest basin, Gaylor Creek, has 1.1 more hours of daylight than the shadiest basin, Budd Creek, and has 4.2 MJ day−1 more potential radiation (equivalent to 49 W m−2 or 12.6 mm meltwater day−1). By 1 April, these differences have diminished. On 1 April, Gaylor Creek has only 0.6 more hours of daylight and 3.2 MJ day−1 (37 W m−2 or 9.6 mm water day−1) more radiation, 25% less than a month earlier. Thus, based solely on the geometry of the sun angle and the surrounding topography, we would expect differences in snowmelt timing to be greater between these basins in a year with an early snowmelt onset, like 2004, than an average date of snowmelt onset, like 2002.
4. Case study: Gunnison River drainage, Colorado
The north-facing Tuolumne River subbasins with delayed snowmelt in 2004 are too small to have a significant impact on water management practices downstream. Overall, the Merced and Tuolumne Rivers of California drain primarily to the west, so they contain similar portions of north- and south-facing subbasins, such that the effects of aspect and shading are diminished in operational gauge records. However, large portions of the Upper Colorado and Gunnison River basins of Colorado are north-facing and are in dry regions where solar radiation dominates the energy balance. The south-facing East River basin (748 km2) and north-facing Lakefork basin (865 km2) of the Gunnison River drainage (Fig. 3) have long (67 yr) discharge records and are used as a test case of how larger basins with different shading characteristics respond in years with earlier versus later snowmelt onsets. Both rivers drain similar elevations (Table 2) and latitudes so that average temperature differences are negligible.
In both basins, snowmelt typically begins in mid-to-late April and peaks in early June. The south-facing East River basin has more early-season streamflow than the north-facing Lakefork basin (Fig. 11a). The date on which half the annual streamflow passes the gauge at East River is 9 June, with 49% of the season’s streamflow occurring before this date. On 9 June, only 41% of Lakefork’s annual average streamflow has passed, 8% less than at the East River. For Lakefork basin, half the annual streamflow passes the gauge on 17 June, 8 days later. Comparison of streamflow records from the two basins indicates that during the 20 yr of record with earliest snowmelt onset dates, both basins lose a greater percentage of their annual streamflow before 9 June. However, the early-season hydrograph rises more for the East River than the Lakefork River during years with early snowmelt onset (Fig. 11b; Table 4). Thus, 63% of the East River streamflow occurs prior to 9 June, but only 53% of Lakefork River streamflow occurs before this date, a 10% difference. At the other extreme, the 20 yr with the latest snowmelt onset dates on record reveal more similar hydrographs between the two basins than on average (Fig. 14c). In late-onset years, 40% of the East River streamflow occurs prior to 9 June, and 34% of the Lakefork River streamflow occurs before this date, only a 6% difference. These differences between East and Lakefork streamflow for the two groups (early versus late onset) are statistically significant at a 99% confidence interval. For basins of this size, a 2% shift in streamflow is the equivalent of 3–4 × 106 m3 (about 2800 acre ft) of water.
On average, the East River basin receives more precipitation, so that area-normalized annual streamflow is 287 mm yr−1 for the East River basin and only 173 mm yr−1 for Lakefork basin. Thus, deeper snowpacks require longer ripening periods and yield longer runoff delays in the East River basin. However, the date when 50% of the annual streamflow has passed the gauge is a week or more later, on average, in the Lakefork River compared to the East River (Table 2). The observed later streamflow in the Lakefork River is due to the different aspects and orientations of the basins, which result in less incoming solar radiation in Lakefork basin throughout the year.
As with the Yosemite basins, the increased difference in streamflow timing during years with early snowmelt onset can be at least partially explained by an increased difference in solar radiation. On 1 May, a near-average snowmelt onset date, East River basin receives a basin-average of 28.6 MJ day−1 calculated potential solar radiation, while Lakefork basin receives 28.0 MJ day−1 (Table 2), a difference of 2%, or 1.8 mm meltwater day−1. On 1 April, an early snowmelt onset date, both basins receive less potential solar radiation (24.0 and 24.7 MJ day−1), and the difference between them increases to 3%, or 2.1 mm day−1 potential snowmelt. To compare this with the streamflow differences presented above, a 0.3 mm day−1 difference in potential snowmelt would add up to 9 mm more area-normalized streamflow over the course of a month, which is 3% of the East River’s annual streamflow, or about 6 × 106 m3 of water. Also, the spatial variation in potential radiation within each basin increases earlier in the spring (Table 2). For example, on 1 April the sun never rises on some steep north-facing slopes in the Lakefork basin. These very shaded areas thus are unlikely to contribute any meltwater until later in the season.
National Centers for Environmental Prediction (NCEP) reanalysis maps (Kalnay et al. 1996) of 700-hPa temperatures and precipitation were examined to determine whether meteorological conditions other than incoming solar radiation might exist between the basins during early and late snowmelt onset years. As expected, early-onset years (1969, 1981, 1982, 1988, 1998, 2002, 2004) had anomalously warm temperatures in April (about 1°C greater than average) and May (about 0.75°C greater than average), but temperatures did not (on average) differ between the basins. Early-onset years also had about 0.2 mm day−1 less precipitation in January–March than late onset years, but precipitation was not systematically different between the basins from early to late years. Thus, differences in solar radiation seem to be important in determining snowmelt timing differences.
5. Simple shading model
a. Model setup
Both the Yosemite, California, study for 2002 and 2004 and the Gunnison, Colorado, study for 1938 to 2004 illustrate that, during years with early spring snowmelt, differences in snowmelt timing increase between basins with different solar exposures. To use this knowledge to predict how snowmelt timing might change if the regional climate were to warm, a simple model is developed to isolate the effects of shading on the snowmelt energy balance and on streamflow timing. Model parameters are set to be representative of points in the Yosemite study area, at a latitude of 37.5°N.
The maximum available, or potential, values of incoming solar radiation, QSWi, depend on the solar radiation reaching the top of the atmosphere, the pathlength through the atmosphere, and atmospheric absorption. Equations to estimate QSWi are detailed in appendix C. Topographic shading modifies this maximum available incoming solar radiation. For simplicity, consider a flat snowmelt site located on the north side of a ridge that stretches infinitely from east to west (Fig. 12). The angle from the site on the ground to the top of a blocking ridge is defined as α. When the angle of the sun above the horizon, αs, is less than α, we assume the ridge blocks all incoming solar radiation, thus shortening the length of day. Diffuse radiation is neglected here for two reasons: first, it is small compared to direct radiation (e.g., it is calculated to be only about 20% of the total solar radiation in early March in the Yosemite basins), and second, most of the diffuse radiation is caused by the strong forward scatter component of nearby aerosols (92% at sunrise, 85% at a zenith of 50°, and 50% near solar noon), and thus, when the solar disk is blocked by ridges, a significant portion of the diffuse radiation is blocked as well (Flint and Childs 1987; McArthur and Hay 1981). Thus, during hours of the day when the sun does not rise above the ridge, the solar radiation in this simplified model is assumed to be 0. If the angle between the site and the ridge line is larger, the length of day and potential solar radiation decrease, so that in the extreme case of α ≥ 45°, the site receives no direct sunlight during the winter months (Fig. 13).
b. Model results
Net radiation is, by design, less at the shady site, α = 45°, than at the sunniest site, which has no ridge. Hence, snowmelt always begins earlier at the site with no ridge (Fig. 14a). Warmer temperatures of +3°, +6°, and +9°C were imposed in the model to simulate global warming. However, while longwave radiation increases uniformly with warming at both sites, the net radiation at the shaded site is limited until the day of year when the sun rises above the ridge and solar radiation first reaches the site. Therefore, the advance of snowmelt is delayed in response to the imposed warming. Thus, the date of spring snowmelt advances at different rates under various imposed warming scenarios, depending on shading.
Figure 14b shows calculated changes in the timing of snowmelt as a function of shading and temperature increases. To simplify comparisons, the model’s climatological dates of melt onset (6 March, 9 March, 27 March, and 18 April, for α of 0°, 15°, 30°, and 45°, respectively) are set to 0 for all levels of shading. The simple model presented here neglects air temperature influences other than downwelling longwave radiation, such as turbulent energy transfer. As a result, it has a much slower snowmelt-timing response to warming than has been modeled and observed elsewhere (e.g., a 30-day shift in snowmelt timing resulting from 2° to 3°C warming; Stewart et al. 2005). In the radiation-only model, for temperature increases less than 2°C, snowmelt advances less than 1 week, and the snowmelt onset at the shadiest site shifts only about 2 days less than that at the sunnier sites. When warming is greater than 2°C, the differences between times of melt onset become larger, such that for an extreme temperature increase of 10°C, the snowpack at the sunniest site begins melting about 2 months earlier than under historical temperatures, whereas the snowpack at the shadiest site begins melting only about 1 month earlier. In this extreme case, the snowpack at the sunniest site starts melting 5 January, while the snowpack at the shadiest site remains frozen until 14 March. Thus, the historical average difference of one-month between snowmelt onset dates at the shady and sunny sites becomes more than a two-month difference with warmer temperatures.
Sites with intermediate levels of shading (α = 15° and α = 30°) differ from the unshaded case in their responses only once warming greater than 5°C is imposed, and only differ by more than a couple days after ΔT > 7°C. This large temperature increase is required to shift the snowmelt onset to a date when the sun is low enough in the sky so that the hours of daylight are decreased at these sites. In a real-world illustration of this, monthly average Sierra Nevada temperatures for March 2004 were about 5°C warmer than the historic average, and resulting differences in melt onset timing were detected only in the shadiest basins (equivalent of α = 45°).
c. Latitude
The calculations thus far were for sites at the latitude of Yosemite, 37.5°N, which has a large change in the relative radiation between shady and sunny sites during the month of March. At higher latitudes, the season with largest month-to-month changes in relative radiation will come later in the year. Shading influences (for α = 0° and α = 45°) were recalculated for latitudes ranging from 35° to 50°N (Fig. 15a). Higher latitudes have a much larger range of potential radiation during the year (Fig. 15a). This results in larger differences in solar radiation between shaded and sunny sites during summer months. Conversely, smaller differences result during the winter (Fig. 15b), when even the sites with no shading receive little sun. At all latitudes, the largest differences between the sunny and shady modeled radiation occur on the day when the sun first rises above the ridge (Fig. 15b). This date occurs progressively later in the year at higher latitudes. Thus, for the southern United States, including as far north as the Yosemite and Gunnison River study areas, the difference in radiation between sites changes most dramatically during the month of March, whereas at higher latitudes, radiation differences change most rapidly in April (Fig. 15b).
The latitude analysis reveals that the combined effects of warming temperatures and topographic shading will vary strongly with location, and may not always act to increase the snowmelt timing differences between basins. For example, long-term average temperatures at Yellowstone National Park (44′58″N, 110′42″W) were compared with calculated solar radiation at 45°N. With these parameters, increasing temperatures would move snowmelt onset to a time of year with smaller shading-induced differences in shortwave radiation. This could result in smaller between-site differences in snowmelt timing as temperatures warm. Thus, the effects of solar radiation and shading should be considered carefully when predicting how individual basins will respond to warming temperatures.
6. Conclusions
A range of observations and models demonstrate that differences between the timing of snowmelt and streamflow in basins with different aspects are larger during years when temperatures warmed earlier in the year. The larger differences are caused primarily by the increased effects of shading earlier in the year. In 2004, snow in the majority of the Sierra Nevada began melting unusually early (early March). However, snow in the most shaded basins of the Tuolumne River drainage and at the most shaded CA DWR snow pillows began melting one to four weeks later than snow in most of the Sierra Nevada. A corresponding delay was not observed in late March 2002, which was characterized by simultaneous snowmelts (Lundquist et al. 2004). Records from 1938 to 2004 in the East and Lakefork basins of the Gunnison River also show a greater basin-to-basin difference in melt timing in early-onset years.
A very simple model (section 5) demonstrates how topographic differences can cause the onset of snowmelt to advance, in response to warming trends, at different rates depending on solar exposure, which is a function of topography, latitude, and time of year. The model assumes that air temperatures do not vary between different topographic sites, and that only the incoming solar radiation changes. Not included in the model is the fact that shaded locations are likely to have cooler air temperatures and more winter ice formation, which will further increase the spatial differences. These findings suggest that far from responding linearly and simply to warming trends, western snowmelt and streamflow timing changes in response to future warming will be 1) geographically complex (depending on complex seasonally varying shading patterns), 2) latitudinally dependent (the shading differences will influence snowmelt timing differently with latitudes), and 3) a complex interplay of latitude versus the season when onset occurs (i.e., in some places, warmer temperatures will move the snowmelt onset toward times of peak radiation differences between topographic locations, as in the Sierra Nevada, and in other places, warmer temperatures will shift the snowmelt onset to times with smaller radiation differences). Thus, distributed snowmelt modeling incorporating topography and radiation may become more important as the regional climate continues to warm.
Snow hydrologists have been modeling topographic variations in solar radiation for years (Dozier and Frew 1990; Kumar et al. 1997). However, these variations are typically not included in operational streamflow forecasts or in climate projections of future runoff timing. For example, the Snow-17 model is used operationally by the Sacramento River Forecast Office of the National Weather Service to forecast streamflow in rivers across California, but without modification, it could not represent the significant added delay in snowmelt observed at Slide Canyon in 2004. Shamir and Georgakakos (2005) modified a distributed version of the Snow-17 model by increasing the melt factor by 20% for south-facing slopes and decreasing it by 20% for north-facing slopes. This procedure captures spatial variations well for an average-onset year, but it would actually decrease the difference in melt forcing between shaded and sunny locations earlier in the spring compared to later in the spring because multiplying by 20% results in a smaller offset when the original melt factor is smaller. A better approach might be to define melt factors that change at different rates seasonally based on location. For example, the melt factor should vary according to curves of potential solar radiation (such as those in Fig. 13), rather than always as a perfect sinusoid. Climate projections using regressions against temperature, such as that used by Stewart et al. (2004), would fail to predict differences in the rate of advance of streamflow timing between sunny and shaded basins.
The importance of topography and shading on snowmelt timing will vary regionally. In California, many river basins drain to the west, so they contain equal portions of north- and south-facing subbasins. However, on the east side of the Sierra Nevada, the Walker and Carson Rivers are more north-facing. Large portions of the Upper Colorado and Gunnison basins are north-facing and are in dry regions where solar radiation is the primary factor driving snowmelt. The Pacific Northwest has large north-facing basins, including the area north of Mt. Ranier and the Canadian Rockies in British Columbia, but the maritime climate and frequent cloud cover in this region may partially reduce the effects of solar radiation. For example, while net radiation dominates the energy balance in drier regions, turbulent fluxes have been found to dominate the energy balance in maritime alpine sites (Prowse and Owens 1982; Moore and Owens 1984; both working in New Zealand).
Overall, the increased effects of shading earlier in the year may help protect some water resources in the western United States. In many regions, such as in California and Colorado, snowpacks in shaded, north-facing basins will be the least sensitive to regionally warming temperatures, and will shift streamflow toward earlier in the year at a slower pace than sunnier neighboring basins. Thus, shaded basins may provide refuges for plants against climate change and could be targeted by resource managers for protection. These shaded basins are also likely to provide the most reliable source of late-season streamflow. As water managers increasingly consider interbasin water transfers in their plans to meet growing water needs, an understanding of how local topography and shading will affect snowmelt and streamflow in different basins will prove useful.
Acknowledgments
Thank you to Randy Dole, Andrey Shcherbina, Mike Dettinger, Eylon Shamir, Jim Borchers, and Satish Kumar Regonda for editorial comments and suggestions. Thank you to Brian Huggett, Heidi Roop, and Jim Roche for field work, to Frank Gehrke for CA DWR data, to Eylon Shamir for help with the Snow-17 model, to Dan Cayan, Larry Riddle, Jim Wells, Mike Dettinger, and Julia Dettinger for help with temperature sensor installations, and to Kelly Redmond and the Western Regional Climate Center for historic climate data. Mammoth Mountain data were provided by Michael Colee and the NASA investigation “Hydrology, Hydrochemical Modeling, and Remote Sensing in Seasonally Snow-Covered Alpine Drainage Basins,” the Donald Bren School of Environmental Science and Management at the University of California, Santa Barbara, the U.S. Army Corps of Engineers Cold Regions Research and Engineering Laboratory (CRREL), and the Mammoth Mountain Ski Area. Funding was provided by a Canon National Parks Science Scholarship, by a CIRES postdoctoral fellowship, by the Edna Baily Sussman Foundation, by Cal-IT2, and by a cooperative agreement between the U.S. Geological Survey and Scripps Institution of Oceanography.
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APPENDIX A
Mammoth Mountain Sensible Heat Flux
APPENDIX B
Calculations and Parameters Used in the Snow-17 Model
APPENDIX C
Radiation Balance Calculations and Parameters
Map of CA DWR snow pillow sites, Yosemite study area, Mammoth Mountain Energy Balance Site, Donner Memorial State Park, and Bishop Airport. Lines surrounding the study area delineate the Merced (lower outlined) and Tuolumne River (upper outlined) basins. Snow pillows with spring melt onset that occurred later than most are marked.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Map of sensor locations in Yosemite National Park, overlaid on map of 1 March potential radiation. Average daily temperatures on 9 Mar 2004 are represented by different-sized circles and identify locations of temperature sensors. Snow pillows and river subbasins discussed later in the paper are labeled, with the Tuolumne Meadows snow pillow label connected by a line. Heavy-black outlined basins show the Merced and Tuolumne River basins, and correspond to the purple study basins in Fig. 1.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Map of East River basin and Lakefork basin in the Gunnison drainage in Colorado.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Average daily temperatures measured throughout Yosemite National Park for (a) 2002 and (b) 2004. Shift in date labels occurs because 2004 was a leap year. Thick black line identifies the temperature record at Budd Creek, and vertical dashed line indicates the date most Yosemite streams began rising (29 March and 8 March). (c) Budd Creek temperatures for both years, centered around the date of melt onset.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Date of melt onset at CA DWR snow pillows for 2002 and 2004. Vertical dashed lines represent melt onset dates for most streams for each year.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Spring onset as measured by standard deviations from the mean stage at a subset of Tuolumne River subbasins for (a) 2002 and (b) 2004. In 2002, spring onset was synchronous at all gauged locations. In 2004, most streams began rising on or before 8 March. Budd Creek and the Dana Fork above Gaylor Creek began rising 16 March, and Ireland Creek began flowing 5 April. Depths more than two std devs above the mean immediately following the spring onset are associated with ice dams and do not represent actual discharge amounts.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Daily means of (a) net solar radiation (QSW) and (b) sensible heat fluxes (Qh) at the Mammoth Mountain energy balance station, and of (c) snowmelt rates at the Tuolumne Meadows snow pillow site for 2002 (solid lines) and 2004 (dashed lines). The x axis is shifted by 20 days to aid in comparison. Dates to the left (right) of the slash correspond to 2002 (2004).
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Results of Snow-17 model for (a) 2001–02 and (b) 2003–04 water years for Tuolumne Meadows (TUM) and Slide Canyon (SLI) snow pillow sites. The solid black lines in (a) and (b) are observed SWE at the two sites (Slide Canyon, the upper solid black line, has about twice as much snow at Tuolumne). Solid gray lines are modeled frozen snow water content and dashed lines are modeled snow water content plus modeled liquid water retained in the pack. Snow pillows report this sum. The model is forced with the observed precipitation at TUM and SLI and with the observed temperatures at Budd Creek in the first simulation, and with temperatures decreased 3°C in the second simulation, at each site. (c), (d) The modeled liquid water content of the snowpack as a fraction of liquid water saturation for each of the four scenarios.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Seasonal-spatial changes in solar radiation measured by pyranometers at the Tuolumne Meadows and Dana Meadows snow pillows in 2004.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Change in modeled daily potential solar radiation between 1 March and 1 April for Yosemite Study area.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Composite discharge as a fraction of total annual discharge for (a) all 67 yr (climatology), (b) 20 earliest-onset years, and (c) 20 latest-onset years for East River and Lakefork River in the Gunnison Basin, Colorado. Vertical dashed line is date when 50% of the streamflow has passed for climatology for East River.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Diagram of conceptual shading model, where α represents the angle from the site to the top of the ridge, which in this diagram, is the same as αs, the angle of the sun above the horizon.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Average daily potential solar radiation at 37.5°N, for different angles between a point and the top of a ridge.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
(a) Average daily potential net radiation for different temperature increases for no ridge (black, higher set of patterned lines) and a ridge crest at an angle of 45° (gray, lower set of patterned lines). (b) Shift of date on which potential net radiation becomes positive, compared to historical average date, as a function of increased temperature and angle from a shading ridge.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
(a) Potential incoming radiation as a function of latitude for sunny locations with no ridge (solid lines) and shady, α = 45°, locations (dashed lines). Latitude varies from 35° (darkest gray) to 50°N (lightest gray). (b) Difference in potential radiation between sunny and shady locations at four different latitudes as a function of time of year.
Citation: Journal of Hydrometeorology 7, 6; 10.1175/JHM539.1
Yosemite subbasin characteristics.
East River and Lakefork basin characteristics and climatology.
Simulated vs observed melt onset days at Tuolumne Meadows and Slide Canyon snow pillow sites.
East vs Lakefork flow distributions for years with early vs late melt onsets.
Use of trade names are for reference only and do not constitute endorsement by the U.S. government.
