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What a Difference a Day Makes: Spring Snowmelt in the Sierras
D. Peterson, M. Dettinger, D. Cayan, R. Smith, L. Riddle and N. Knowles
From the Interagency Ecological Studies Program for the Sacramento San Joaquin Estuary News Letter, Summer 97, p.16-19.

Daily fluctuations in air temperature can explain much of the variability in snowmelt-driven discharge in the High Sierra Nevada river basins during spring (Dettinger, this issue; Cayan, this issue). Statistical-dynamical methods appear useful in exploring this linkage between air temperature and discharge in the Merced River basin above Happy Isles, Yosemite National Park, California. As a first step, input (air temperature) is filtered to estimate output (discharge) using constant parameter difference equations (constant over the snowmelt cycle but varying from year-to-year). The discharge response to present and past temperatures determines the filter characteristics. In general, as might be expected, the response is larger in springs following wet than dry winters. In a more realistic model, the parameters are time-varying such as in daily estimates using a Kalman filter. Ultimately, as snowpack wains, air temperature is less and less "in control" and the time-varying response coefficients decline. Does this phenomenon mark the beginning of summer (i.e., a hydroclimate "summer transition")? Difference equation models appear to be useful in curve fitting and at the very least show the strong connection between air temperature and discharge (which could be exploited for filling gaps in time series, exploring data quality, etc). But to the extent air temperature can be predicted, can we also forecast discharge (i.e., can useful discharge forecasts extend out as far as temperature forecasts?). With each new day both forecast and model errors accumulate. In a preliminary example, alternating between a Kalman filter to estimate model coefficients and a difference filter to estimate discharge, this method seems useful. Although we are only in the initial stages of developing a reliable prediction scheme, the strong correspondence apparent in daily temperature and streamflow emphasizes "what a difference a day makes".

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