A four parameter, logistic stream temperature model using weekly air temperature
as the predictor of weekly stream temperature was fitted by least squares regression to
records varying in length from 12 to 32 years. The records were from four streams in
Minnesota and three streams in Oklahoma. The purpose of the study was to test if stream
temperature models formulated from 3-year samples were representative of stream
temperature models developed from the seven, full-length records. This test was done
because the model had previously been applied to 3-year records from 585 streams and
associated weather stations in the US (Mohseni et aI., 1997). Each full-length record was
divided into 3-year samples containing up to 156 weekly air temperature and stream
temperature data. The logistic stream temperature model was then fitted to the 3~year
samples, as well as the full~length records. The models formulated from the full~length
records were assumed to represent the "true" weekly air temperature/stream temperature
relationships or "population" relationships. F-tests were used to determine whether
statistical similarity between the 3~year sample and the full~length models existed. The
results showed that approximately 33% of the 3-year sample relationships were not
statistically similar to their respective population models. Further analysis of the 3-year
sample and population regression parameters revealed notable discrepancies, especially
for the parameter representing upper bound stream temperature. Twenty-six of thirty-one
3-year samples produced estimates of this parameter less than their respective popUlation
model. In addition, the 3-year sample estimates of upper bound stream temperature
demonstrated a large variance. Nonlinear, least squares parameter estimates were found
to be inherently biased. The bias of nonlinear regression parameters is reduced with
increasing sample length. Three-year weekly air temperature and stream temperature
records can not exhibit the natural variance found in longer records. Records of more
than 3-year duration are therefore necessary for the consistent representation of long-term
weekly air temperature/stream temperature relationships.
Grazing Land Research Laboratory, US Department of Agriculture; Mid-Continent Ecology Division, US Environmental Protection Agency
Erickson, Troy R.; Mohseni, Omid; Stefan, Heinz G..
The Effect of Record L.ength on a Nonlinear Regression Model for Weekly Stream Temperatures.
St. Anthony Falls Laboratory.
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