Snowmelt Runoff

Both conceptual and physical approaches have been employed in snowmelt-runoff modeling. Conceptual models propose a mathematical relationship between snowmelt and measured quantities; thus melt can be calculated without treating in detail all the physical processes and parameters that affect snowmelt. Conceptual models have the benefit of requiring less informational input, but suffer from the uncertainty that parameters estimated under one set of model conditions are applicable to other conditions. Though non-linear relations may improve the prediction of seasonal snowmelt volume versus that from linear models, their use is limited by the failure of transformed data to satisfy the condition of nonlinearity [ Dey et al., 1992]. Conceptual models based on temperature index methods have been used to illustrate the sensitivity of snow-covered basins to climate change [ van Katwijk et al., 1993], and such efforts will improve with the development of models that more directly incorporate radiative exchange into the calculation [ Kustas et al., 1994].

One of the main obstacles to physically based modeling is the accumulation of the necessary meteorological and snow-cover data to run, calibrate, and validate such models. For example, basin discharge has frequently been used as the sole physical criterion of model calibration and performance assessment for conceptual snowmelt models. But as it is an integrated response to melt and runoff, basin discharge is not sufficient to discriminate between the effects of the multiplicity of data inputs driving physical models and that distributed snowcover data are required to assess model performance [ Bloschl et al., 1991 a; Bloschl, 1991 b]. A comparison of a detailed research-oriented point-snowmelt model and a simpler operational model revealed that in the absence of detailed measurements of snowpack variables, a detailed physical model of the snowpack is needed to reduce the need for parameter calibration [ Bloschl and Kirnbauer, 1991]. Several simplifying assumptions are necessarily made in order to solve physically based point models, thus limiting their validity in many field situations [ Illangasekare et al., 1990]. Nevertheless, physically based models are being tested and applied in alpine catchments [ Ranzi and Rosso, 1991].

Estimation of distributed snow-water equivalence (SWE) is challenging because of the many factors that affect its distribution, and the small correlation length of the SWE spatial distribution. Further, difficulties associated with accurately determining the time of maximum accumulation present a problem for snowmelt-runoff forecasters. The simplicity of regression models makes them an attractive means of estimating SWE because of the large amount of work required to directly measure SWE on the catchment scale. Using only meteorological variables, SWE estimates with variations in the 60-81% range were obtained for sites in New England [ Samelson and Wilks, 1993], but such methods can be confounded by the highly variable topography found in mountainous areas. Photogrammetry shows promise as a technique to measure snow depth in alpine catchments by differencing snow-free digital elevation surfaces from snow-covered digital elevation surfaces [ Cline, 1993]. Regression-tree [ Davis et al., 1992] and maximum-likelihood [ Elder et al., 1991 b] methods of classification have also been applied to SWE distributions in alpine basins. A combination of regression of elevation, vegetation, and insolation with geostatistical interpolation of residuals has been used to map SWE distributions; elevation exerted the greatest influence on SWE distribution [ Hosang and Dettwiler, 1991]. Sommerfeld et al. [1990] reported differences of 20-30% between five different methods of estimating SWE in a small alpine catchment in Wyoming. For one year, the degree-day method agreed with an intensive field snow survey to within 6% [ Sommerfeld et al., 1991 b]. In all cases, careful planning of snow surveys is required to obtain a statistically representative data set [ Yang et al., 1991].

Redistribution of snow by wind was found to affect snowmelt runoff in an Arctic watershed in Northern Alaska [ Kane et al., 1991], with snow damming an important consideration in the timing of snowmelt runoff [ Hinzman and Kane, 1991]. Cline [1992] used a geographical information system based analysis of slope and terrain variability to model the redistribution of snow by wind in alpine terrain.

Snowmelt models that work well at the catchment scale may still be inadequate for some applications, such as integrated chemical modeling [ Bales et al., 1992] or erosion [ Tarboton et al., 1991]. For erosion, one needs to capture the spatial distribution of snowmelt delivery at each point on a hillside or small basin, and use time steps on the order of one to a few hours. Similarly, integrated chemical models require detailed spatial distributions of snowmelt to properly route meltwater through soil parcels.

An approach to modeling spatially distributed snowmelt in steep, alpine basins was proposed using net potential radiation, distributed across the basin using a digital elevation model, as the main factor determining relative snowmelt [ Elder et al., 1991 a]. Such an approach enables using a detailed, physically based snowmelt model for each physically different subregion of the basin at the scale of interest. Testing this approach on the 1.2 Emerald Lake basin in California's Sierra Nevada suggests that little information is lost in going from a 5-m to 25-m grid, but that use of a 100-m grid may result in significant inaccuracies [ Bales et al., 1992].

The diurnal pattern in snowmelt results in a phase shifted and modulated pattern in streamflow with respect to snowmelt. Snowpack depth and snow-covered area decrease as the melt season progress, decreasing the time lag between peaks in meltwater generation and streamflow. This decrease in time lag was used to obtain a measure of catchment wide snowpack hydraulic conductivity in the 40-80 cm hr range [ Caine, 1992]. Daily snowmelt runoff from a catchment in southwestern Idaho was shown to have a large number of degrees of freedom, characteristic of a random rather than chaotic process, and suggesting that observed patterns result from the interactions of many factors, rather than from low-dimensional chaotic dynamics [ Wilcox et al., 1991].

Several researchers have reported on efforts to incorporate remote-sensing data into snowmelt-runoff modeling. Rango [1993] reviewed the progress that has been made incorporating remote-sensing data into regional hydrologic models of snowmelt runoff. The National Oceanic and Atmospheric Administration's Advanced Very High Resolution Radiometer (AVHRR) sensor provides daily views over large areas (1000 km swath) and snow-cover maps are produced operationally. Estimates of snow-covered area based on remote sensing data can significantly improve the performance of even simple snowmelt models in alpine terrain [ Kite, 1991; Armstrong and Hardman, 1991]. For operational purposes, empirical approaches using combining remote sensing data to estimate snow-covered area, and snow-depth networks to estimate SWE are continuing to improve [ Martinec and Rango, 1991; Martinec et al., 1991]. Mcmanamon et al. [1993] have combined airborne and ground based measurements to produce gridded SWE estimates for the upper Colorado River region.

Operational hydrology still depends largely on ground-based methods to develop estimates of SWE. Since remote sites are often not telemetered, it is desirable to develop correlations between remote, high-elevation sensors and those at lower elevations. Limited success toward this end was reported in a California study involving ten pairs of high and low elevation sensors [ McGurk et al., 1993]. In a 4000-m elevation basin in China's Tien Shan, comparison between an intensive snow survey and SWE estimates based on a stake network suggest that while the stake network adequately estimated mass balance, the spatial details of the SWE distribution were not well reproduced [ Elder et al., 1992]. Runoff from the surrounding basin underwent delays of 5-15 days before reaching the stream, confounding problems with snowmelt modeling based primarily on energy balance [ Kattelmann and Yang, 1992].

The prospect of climatic change is particularly critical to regions with seasonal snowcover, because increased frequency of rain-on-snow events, changes in precipitation volumes, changes in timing of accumulation and ablation seasons, and changes in location of the snow line all affect snowmelt runoff occurrence and the ecosystemic availability of water [ Lettenmaier and Gan, 1990]. It cannot be overemphasized that the results of such modeling efforts depend on what the altered climate is assumed to be, and such assumptions are themselves highly uncertain. Calculations to determine the countervailing effects of increased evapotranspiration and increased precipitation are confounded by uncertainty in such factors as the effect of increased atmospheric CO on transpiration and precipitation volume [ van Katwijk et al., 1993]. Karl et al. [1993] found that 78% of the variance of regional snowcover can be explained by anomalies in monthly mean maximum daily temperature. Cooler, seasonally snow-covered areas have a longer memory of the past season's precipitation than do warm low-elevation basins. Since synoptic-scale weather patterns drive the catchment scale accumulation of snow, large-scale averages of temperature and precipitation perform nearly as well as local measures when assessing the annual variability of individual streams or watersheds [ Cayan et al., 1993]. In an analysis of station records for 1951-85, snow accumulation anomalies in the Rocky Mountain states fell into three types: i) years where snow accumulation deviates throughout the whole region, ii) years with a distinct north-south gradient, and iii) average years [ Changnon et al., 1993]. Increased winter and early spring streamflow for two streams in the Sierra Nevada of California during the period 1965-1990 versus 1939-1964 were attributed to small increases in temperature, which increased the rain-to-snow ratio at lower altitudes and caused the snowpack to melt earlier in the season at higher altitudes [ Pupacko, 1993]. Reductions in forest density and area as well as climate warming would be expected to increase the severity of peak spring floods [ Kattelmann, 1991]. Rango and van Katwijk [1990] reported that increasing temperatures could markedly advance the onset of snowmelt runoff, increasing spring runoff and decreasing runoff later in the year. Using satellite-derived snow cover maps for sites in Alaska, Canada, Scandinavia, and Siberia, it was determined that there has been a tendency towards earlier snowmelt during the 1980's [ Foster et al., 1991].