An Experimental Forecast of Maximum Daily Snowmelt Discharge for the Year 2002
The relation between initial snowpack and maximum daily discharge is near-linear. Thus, an empirical regression equation based on historical records of initial snowpack (independent variable) and maximum daily discharge (dependent variable) can be used to predict maximum daily discharge in the upcoming spring snowmelt season, weeks in advance, based solely on routine observations of initial snowpack. This paper gives such a maximum daily snowmelt discharge forecast for the late spring/early summer 2002 using the regression equations as per the 2000 forecast (Peterson et al., 2000). This study is limited to the same number of watersheds (eleven) in western U.S. as in the 2001 and 2000 spring forecasts. Their locations and descriptions are in the above citation.
The forecast values are in Table 1 and Snow Stations are in Table 2.
TABLE 1. Maximum Daily Discharge Forecasts for late spring-early summer 2002.
RIVER OBSERVATION April 1 Snow, in inches REGRESSION EQUATION\1 PREDICTION Spring-Summer 2002, in cubic meters per second (percent of normal) MEAN Qmax (cms) MEAN DAY OF Qmax CARSON\2 49.9 Qd = 0.24(d) - 2.9 17 (106%) 16 130 GUNNISON\3 77.0 Qs = 1.83(s) - 21.67 85 (84%) 101 155 KERN\2 98.6 Qd = 1.25(d) - 55 68 (86%) 79 148 KINGS 82.0 Qd = 0.90(d) - 25.7 48 (94%) 51 139 MERCED 98.0 Qd = 0.55(d) + 9.3 63 (94%) 67 148 SAN JOAQUIN 84.5 Qd = 0.88(d) + 13.1 88 (90%) 98 149 WALKER 61 Qd = 0.62(d) + 5.1 43 (100%) 43 152 WEBER 16.5 Qs = 2.44(s) + 6.0 46 (98%) 47 154 CLARKS FORK YELLOWSTONE 32.4 Qs = 3.75(s) + 85 207 (95%) 218 161
\1 Qd is based on snow depth; Qs is based on snow water equivalent.
\2 Based on a proxy snowpack measurement from a nearby watershed.
\3 Snow water equivalent in inches times 10.
TABLE 2. Snow Stations \1
RIVER BASIN SNOW STATION START OF RECORD CARSON\2 #331 lower Carson Pass (American River) 1939 GUNNISON Snowtel, Porphry Creek ID 06L03S 1979 KERN\2 #205 Mammoth Pass, DWR (Owens River) 1929 KINGS #227 Woodchuck Meadow 1930 MERCED #176 Snow Flat 1930 SAN JOAQUIN #190 Kaiser Pass 1930 WALKER #152 Sonora Pass 1947 WEBER Snowtel, Chalk Creek #2 ID 11J02S 1970 YELLOWSTONE Snowtel, Fisher Creek 9933 ID 09D065 1970
\1 Snowtel sites measured as snow water equivalent; all others as snow depth.
\2 Based on a proxy snowpack from a nearby watershed.
This last section gives a few relevant definitions and highlights some of the characteristics of snowmelt discharge.
The index of initial snowpack is the sum of daily discharge from calendar day 105 to 195. These days were selected to minimize major rain contamination.
The initial snowpack is the snow depth or snow water equivalent measured on or near April 1.
The maximum daily snowmelt discharge is the peak daily value observed during the snowmelt season, from calendar days 105 to 195.
The potential forecast skill is estimated as the strength in the correlation between maximum daily discharge and the predictor variables.
The relation between maximum daily discharge and initial snowpack is linear or near-linear largely because the climatology of air temperature is near-linear over the snowmelt season (see Fig. 4 in Peterson et al., 2000). A larger initial snowpack takes more energy to melt than a small one and therefore more time (Cayan et al., 2000), but energy is not "delivered" uniformly in time. Therefore, in years of the same initial snowpack size, the same watershed snowpack distribution, and the same initial snowpack temperature, their daily maximum discharge does not fall on the same day because their air temperature histories were different. Although snowmelt discharge depends in complex ways on the initial snowpack size and on air temperature history, it can be shown that both the initial snowpack size and air temperature history influence the amplitude and phase of snowmelt discharge over the snowmelt season. The difference is that initial snowpack size has a stronger influence on amplitude and air temperature history has a stronger influence on phase. Note, for the 9 watersheds the average correlation between maximum daily discharge and the calendar day of maximum daily discharge is weak, R=0.44+0.15.
Future work will extend the forecasts to 110 snowmelt watersheds in western US (see Fig. 2c in Cayan et al., 2001) with the goal of making annual forecasts on a routine basis. The index of initial snowpack more fully represents the watershed. Therefore, it more strongly correlates with maximum daily discharge than the more local observation of initial snowpack. For example, for the nine watersheds considered, the average correlation coefficient for the index of initial snowpack is R=0.92+0.06 and the average correlation coefficient for observed initial snowpack is R=0.79+0.15. The extent of this difference in correlation may provide a simple measure of how well the snowpack station represents the entire watershed.
Cayan, D.R., Kammerdiener, S., Dettinger, M.D., Caprio, J.M. and Peterson, D.H., Changes in the onset of spring in the western United States: Bulletin, American Meteorological Society, vol. 82, No. 3, 399-415.
Cayan, D.R., Peterson, D.H., Riddle, L., Dettinger, M.D., and Smith, 2000, The spring runoff pulse from the Sierra Nevada. Preprints, American meteorological Society's 14th Conference of Hydrology, Dallas January 1999, 77-79.
Peterson, D.H., Cayan, D.R., Smith, R.E. Dettinger, M.D. and Riddle, L.G., 2000, Retrospective Appraisal of the 2000 Maximum Flow Forecasts (http://meteora.ucsd.edu/cap/max_discharge_fcst.html)