The bayesian-regularized neural network approach to model daily water temperature in a small stream

Understanding and predicting water temperatures is essential in order to help prevent or forecast high temperature problems. To attain this objective, we define in this work a model that predicts temperature variations in a small stream according to climatic variables, such as air temperature, water flow and quantity of rainfall in the river catchment. Static neural networks were used as a technique for evaluation of the relations among the various variables, with a mean error of 0.7 degree C. In addition, we developed a forecasting model able to estimate the short-term and mid-term variations of water temperature . Two methods were used: the first one is iterative and uses the estimated value of day j to estimate the value of the water temperature for day j+1. The second method is much simpler, involving an estimate of the temperature of all days at once. The Levenberg-Marquardt algorithm implemented in the Matlab neural network toolbox allowed a marked improvement in the performance of the model. Very satisfactory results were then obtained by testing the validity by cross validation technique with a mean error of 1.5 degree C for long term prediction of 7 days.Original Abstract: Dans ce travail, nous avons elabore un modele de prediction des variations de la temperature d'un cours d'eau en fonction de variables climatiques, telles que la temperature de l'air ambiant, le debit d'eau et la quantite de precipitation recue par le cours d'eau. Les reseaux de neurones statiques ont ete utilises pour approximer la relation entre ces differentes variables avec une erreur moyenne de 0,7 degree C. Deux methodes ont ete appliquees : la premiere, de type iterative, utilise la valeur estimee du jour j pour predire la valeur de la temperature de l'eau au jour j + 1; la seconde methode, beaucoup plus simple a mettre en oeuvre, consiste a estimer la temperature de tous les jours consideres en une seule fois. L'optimisation de la fonction de cout par l'algorithme de Levenberg-Marquardt, disponible dans l'outil < reseaux de neurones > de MATLAB a permis d'ameliorer nettement la performance des modeles. Des resultats tres satisfaisants sont alors obtenus en testant la validite du modele par la validation croisee avec des erreurs moyennes de prediction a sept jours de 1,5 degree C.