Stochastic modelling of water temperatures in a small stream using air to water relations

Abstract

Stream water temperature is a very important parameter when assessing aquatic ecosystem dynamics. For instance, cold-water fishes such as salmon can be adversely affected by maximum summer temperatures or by those exaggerated by land-use activities such as deforestation. The present study deals with the modelling of stream water temperatures using a stochastic approach 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 first step in the modelling approach was to establish the long-term annual component (pattern) in stream water temperatures. This was possible by fitting a Fourier series to stream water temperatures. The short-term residual temperatures (departure from the long-term annual component) were modelled using different air to water relations, namely a multiple regression analysis, a second-order Markov process, and a Box-Jenkins time-series model. The results indicated that it was possible to predict daily water temperatures for small streams using air temperatures and that the three models produced similar results in predicting stream temperatures. The root mean square error (RSME) varied between 0.59°C and 1.68°C on an annual basis from 1990 to 1995, with the warmest year (1994) showing the highest RMSE. Although 1992 was an exceptionally cold summer (coldest in 30 years), good predictions of stream water temperature were obtained, with an RMSE of approximately 1.24°C. Of the three models, the second-order Markov process was preferred based on its performance and its simplicity in development.Key words: small stream, water temperature, model, stochastic, root mean square error, Markov process.