Required Record Length for a Nonlinear Weekly Air-Stream Temperature Regression Model

Abstract

A four-parameter, logistic stream temperature model was fitted to nine records ranging in length from approximately 12 to 29 years, Samples ranging in length from 3 to 15 years were extracted from each of the nine records and also fitted with the model. Statistical comparisons of the model parameters derived from the long-term records were made with those obtained from the samples by means of an F-test. No significant change in the percentage of sample models determined to be statistically nonsimilar occurred until IS-year sample models were introduced. Of the sample models derived with 15 years of data, 19% were not statistically similar to corresponding population models, assuming that the full record represented the population. Stream temperature/air temperature relationships obtained from short record lengths, e.g. three years, are characterized by fluctuations due to extraordinary meteorological and/or anthropogenic influences. Population stream temperature/air temperature relationships are, in essence, composed of an aggregate of characteristic stream temperature/air temperature relationships. Because fluctuations in weather parameters have many different time scales, i.e. diurnal, seasonal, multiyear (EI Nino) and longer (cooling and warming cycles), the most consistent representation of long-term stream temperatures will therefore result from stream temperature/air temperature relationships developed from records of more than 15 years length.