Experimental Forecast of Maximum Daily Snowmelt Discharge

Retrospective Appraisal of the 2000 Maximum Flow Forecasts
 

As of September 2000, the maximum flows during Spring-Summer 2000 have been measured and compared to the April 1 forecasts of same. Forecast errors were distributed as follows:

These errors are generally within the range of errors that were expected, given the error bars reported in Table 1. For example, the largest forecast errors were about plus and minus 1.25 standard deviations. In a strictly normal distribution, such errors would be expected 20% of the time, or 1.6 times in the sample size used here; in fact, such errors occurred 2 times among the sample of rivers forecasted here. The figure below  compares the expected and realized distributions of forecast errors in more detail.

For the most part, the expected and realized errors are plot close to the one-to-one line (are nearly equal). Deviations from a perfect fit mostly reflect a more-than-random tendency for this year's forecast errors to be near zero, giving the plot a flattening around errors of about 0 standard deviations. Thus, on the whole, the forecast performed somewhat better than would be expected from a simple analysis of the regression statistics that underlay it.

April 2000 Forecast
 

Background, Data and Methods

An experimental forecast of maximum daily snowmelt discharge is given for upper elevation watersheds mostly along the central/southern Sierra and in several other river basins of the western United States (Fig. 1). Although the number of basins addressed by this study is limited, other high elevation watersheds with small spring- rain totals would probably yield similar results. Minimal spring rains are important because the statistical method used herein does not account for rainfall contributions to snowmelt discharge. The forecast window in this study is limited to calendar days 105 (April 14, 2000) to 195 (July 13, 2000) to avoid most rain-on-snow events.

Figure 1.  Study Location

Forecast Results

Figure 2. Maximum daily snowmelt discharge versus initial snowpack water equivalent, Kings River.

Outlook

 This forecast effort is work in progress, to be expanded to other alpine snowmelt watersheds in the near future. The forecasts can be degraded by rain on snow, and may suffer from using only one snowpack site each to represent watershed-average snowpack conditions.  For an example of the first, note the extreme outlier at the top of Figure 2. This represents the maximum daily discharge during spring 1996 (Fig. 3). A major rain on snow event (2.5 inches in three days in mid-May) yielded this unusually sharp peak in snowmelt/discharge variation and could not have been predicted from initial snowpack conditions alone.

Figure 3. Daily discharge Kings River, 1996.

 Further studies are needed to determine why some watersheds are more predictable than others. Perhaps more fundamental is why the relation is even remotely linear. One factor may be the near-linear rise in temperature over the snowmelt season (chosen here as days 105-195). More importantly, the snowmelt season is over before the seasonal temperature starts to decline (c.f. Fig. 4). In essence, the system has an excess capacity to melt snow. If, however, the peak snowmelt discharge more closely matched the peak air temperature timing (or solar insolation) a snow carryover could be expected in some years. Then the snowpack-peak flow relation would be expected to be nonlinear, at best. This nonlinear effect due to the close energy-balance linkages between air temperature and snowmelt could be tested using physically based models (Jeton, Dettinger and Smith 1996) as well as by selecting snowpack observations from basins at higher altitudes (and lower air temperatures).

Figure 4. Seasonal climatology of air temperature and discharge, Merced River, Happy Isles. Low-pass mean daily observations using a 15-day boxcar filter (applied forward and backward)

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