Modelling of maximum daily water temperatures in a small stream using air temperatures

Abstract

Maximum daily stream water temperature information is very important when assessing fish habitat in terms of distribution and fish growth rate. For instance, coldwater fishes such as the Atlantic salmon can be adversely affected by these maximum summer temperatures or by those exacerbated by land use practices such as deforestation. The present study deals with the modelling of maximum daily stream water temperatures using regression and stochastic models to relate air and water temperatures in Catamaran Brook, a small stream in New Brunswick where long-term multidisciplinary habitat research is being carried out. The regression model was a logistic type function while the stochastic model was based on the autocorrelation structure of the water temperature time series. The first step in the stochastic modelling was to establish the long-term annual component in stream water temperatures. This was possible by fitting a combination of a Fourier and Sine function to stream water temperatures. The short-term residual temperatures (departure from the long-term annual component) were modelled using a second order Markov process. Results showed that the regression type model was only possible on a weekly basis with a root-mean-square error (RMSE) of 1.93°C. Alternatively, the stochastic model showed that it was possible to predict maximum daily water temperatures for small streams using air temperatures only. The RMSE varied between 1.48 and 1.62°C on an annual basis from 1992 to 1997, which were lower than the regression model. Calibrations were carried out on a seasonal basis as well as during the summer of each year. However, the improvements in the modelling were less than 0.1°C. It was also noted that the empirical coefficient linking air to water temperatures residuals varied on a seasonal and summer basis, and this coefficient was related to summer discharge. Although variable, this empirical coefficient did not improve the modelling significantly on a seasonal or summer basis.