Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec, Canada)

Abstract

AbstractSuccessful applications of stochastic models for simulating and predicting daily stream temperature have been reported in the literature. These stochastic models have been generally tested on small rivers and have used only air temperature as an exogenous variable. This study investigates the stochastic modelling of daily mean stream water temperatures on the Moisie River, a relatively large unregulated river located in Québec, Canada. The objective of the study is to compare different stochastic approaches previously used on small streams to relate mean daily water temperatures to air temperatures and streamflow indices. Various stochastic approaches are used to model the water temperature residuals, representing short‐term variations, which were obtained by subtracting the seasonal components from water temperature time‐series. The first three models, a multiple regression, a second‐order autoregressive model, and a Box and Jenkins model, used only lagged air temperature residuals as exogenous variables. The root‐mean‐square error (RMSE) for these models varied between 0·53 and 1·70 °C and the second‐order autoregressive model provided the best results.A statistical methodology using best subsets regression is proposed to model the combined effect of discharge and air temperature on stream temperatures. Various streamflow indices were considered as additional independent variables, and models with different number of variables were tested. The results indicated that the best model included relative change in flow as the most important streamflow index. The RMSE for this model was of the order of 0·51 °C, which shows a small improvement over the first three models that did not include streamflow indices. The ridge regression was applied to this model to alleviate the potential statistical inadequacies associated with multicollinearity. The amplitude and sign of the ridge regression coefficients seem to be more in agreement with prior expectations (e.g. positive correlation between water temperature residuals of different lags) and make more physical sense. Copyright © 2006 John Wiley & Sons, Ltd.