A nonlinear regression model for weekly stream temperatures

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Abstract
To estimate weekly stream temperatures needed for fish habitat evaluation throughout an annual cycle, a four‐parameter, nonlinear function of weekly air temperatures was used. The regression function was developed separately for the warming season and the cooling season to take heat storage effects (hysteresis) into account. Regression functions were developed for stream temperatures recorded over a 3‐year period (1978–1980) at 584 U.S. Geological Survey (USGS) gaging stations in the contiguous United States. Representative air temperatures were obtained from the closest of 197 weather stations. The distance between a stream gaging station and the corresponding weather station was from 1.4 to 244 km. These distances did not have a significant effect on the goodness of fit. The regression model fitted the weekly stream temperatures at 573 stream gaging stations (98% of all records used) with a coefficient of determination larger than 0.7. For 491 records (84% of all gaging stations) the coefficient was >0.9. At 56 gaging stations (10% of all records used), estimated maximum stream temperatures were smaller than at least four weekly stream temperatures recorded for the period of study. Consequently, the model is deemed successfully applicable (with 99% confidence) to more than 89% of the stream gaging stations. The average coefficient of determination of the stream temperature projection for these stations is 0.93 ± 0.01.