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
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.
Grazing Land Research Laboratory, US Department of Agriculture; Mid-continent Ecology Division, US Environmental Protection Agency
Mohseni, Omid; Erickson, Troy R.; Stefan, Heinz G..
A Non-Linear Regression Model for Weekly Stream Temperatures at 585 Gaging Stations in the U.S..
St. Anthony Falls Laboratory.
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