A Non-Linear Regression Model for Weekly Stream Temperatures at 585 Gaging Stations in the U.S.

Abstract

To estimate weekly stream temperatures throughout an annual cycle, a 4- parameter, non-linear function of weekly air temperatures was used. Two parameters of the regression function represented the estimated minimum and maximum stream temperatures and the remaining two parameters described gradients and inflection points of the air temperature/stream temperature relationship. The model also included a seasonal heat storage effect (hysteresis). The regression function was applied to 585 gaging stations in the contiguous U.S. To represent air temperatures at any stream gaging station, the closest of 197 first order weather stations was used. The distance between a stream gaging station and the corresponding weather station ranged from 1.4 km to 244 km, and did not have a significant effect on the goodness of fit. The model simulated weekly stream temperatures at 573 (98%) gaging stations, with a coefficient of determination (Nash-Sutcliffe Coefficient) larger than 0.7 and at 491 gaging stations (84%) with a coefficient larger than 0.9. At 11 gaging stations the coefficient of determination ranged from 0.45 to 0.7. There were also 57 gaging stations with estimated maximum stream temperatures smaller than at least four weekly recorded data for the period of study. Consequently, the model is deemed successfully applicable (with 99% confidence) to more than 89% of the stream gaging stations, and the average coefficient of determination of the stream temperature projection is 0.93±0.01. The root mean squared error between· actual measurements and proj ections by the· regression equations is 1.64±0.46 DC. To study the probability of absence or presence of warmwater fish in cold region streams (Scheller et al., 1997), the model is applicable to 98% of streams. No significant correlation was evident between the mean annual air temperatures and the non-linear function parameters. There was a weak correlation between the latitude of the gaging stations and two parameters of the non-linear function. Further studies are required to find correlations between the regression model parameters and the geographical, hydrological or meteorological conditions by dividing the gaging stations in the database into free flowing rivers and regulated rivers.