Water temperature prediction using neural networks and multiple linear regression
Water temperature is a parameter of great importance for water resources. For instance, modifications of the thermal regime of a river can have a significant impact on fish habitat. Therefore, understanding and predicting water temperatures is essential in order to help prevent or forecast high temperature problems. In order to predict water temperatures, data series are necessary. Many data series exist for air temperatures, but water temperature series are relatively scarce and those available are often short or have missing values. This study presents the modelling of water temperature using neural networks and multiple linear regression to relate water temperature to air temperature and discharge in Catamaran Brook, New Brunswick, Canada. Catamaran Brook is a small stream (51 km2) where long-term multidisciplinary habitat research is being carried out. Many variables can impact water temperatures in a river, such as air temperature, solar radiation, wind speed, discharge, groundwater flow, etc. For this study, only air temperature and discharge were used. These were judged to be the most often available parameters for modelling temperatures in rivers, and to have the greatest impact on water temperature. More precisely, input variables included current air temperature (°C), air temperature of the previous day (°C), air temperature two days earlier (°C), discharge (m3 /s) and a trigonometric function of time (days). Data used for the analysis were from 1991 to 2000. Data from 1991 to 1995 were used to calibrate the model while data from 1996 to 2000 were used for validation purposes. Observed and predicted water temperatures for each model were presented for the calibration data and the validation data. The coefficient of determination, R2, was used to compare the efficiency of both models as well as the residual standard deviation and the bias. This is equivalent to basing the comparison on the standard deviation (or variance) of the residuals. Coefficients of determination for calibration were 94.2% for the neural networks and 92.6% for the multiple linear regression, which correspond to a residual standard deviation of 1.01°C for the neural networks and of 1.05°C for the multiple linear regression. For validation, coefficients of determination were 92.2% for the neural networks and 91.6% for the multiple linear regression, which correspond to a residual standard deviation of 1.10°C for the neural networks, and of 1.25°C for the multiple regression. The overall bias during the study period (1991-2000) was calculated at +0.11°C for the neural network model and at -0.26°C for the regression model. Results indicated that it was possible to predict water temperature for a small stream using air temperature, flow and time, as input variables, with neural networks and multiple linear regression. The residual series obtained by both models were very similar. Of the two models, neural networks gave slightly better results in terms of fit, but the small difference in results lets us believe that both approaches are equally good in predicting stream water temperatures.