Estimation of an Upper Bound for Weekly Stream Temperatures

A four parameter, logistic stream temperature model has been previously developed to describe the S-shaped, weekly stream temperature/air temperature relationship (Mohseni et al., 1998). The four model parameters, evaluated by nonlinear, least squares regression, have specific physical interpretations. However, the least squares estimate of the model parameter representing upper bound stream temperature has been found to have several deficiencies. The deficiencies associated with the nonlinear, least squares fitting method with respect to the estimate of upper bound stream temperature are frequent underestimation, highly variable estimation with respect to record length and an insensitivity to the actual trends occurring at the extreme upper end of the stream temperature/air tern perature relationship. Two alternate statistical methods were therefore considered for the estimation of upper bound stream temperature that focused exclusively on the uppennost stTeam temperatures: the standard deviate method and the frequency distribution method.