Water temperature modelling: comparison between the generalized additive model, logistic, residuals regression and linear regression models

Water temperature has a significant influence on aquatic organisms, including stenotherm fish such as salmonids. It is thus of prime importance to build reliable tools to forecast water temperature. This study evaluated a statistical scheme to model average water temperature based on daily average air temperature and average discharge at the Sainte-Marguerite River, Northern Canada. The aim was to test a non-parametric water temperature generalized additive model (GAM) and to compare its performance to three previously developed approaches: the logistic, residuals regression and linear regression models. Due to its flexibility, the GAM was able to capture some of the nonlinear response between water temperature and the two explanatory variables (air temperature and flow). The shape of these effects was determined by the trends shown in the collected data. The four models were evaluated annually using a cross-validation technique. Three comparison criteria were calculated: the root mean square error (RMSE), the bias error and the Nash-Sutcliffe coefficient of efficiency (NSC). The goodness of fit of the four models was also compared graphically. The GAM was the best among the four models (RMSE=1.44 degrees C, bias= -0.04 and NSC=0.94).