Evidence of chaos in the rainfall-runoff process

Abstract

The transformation of rainfall into runoff is one of the most important processes in hydrology. In the past few decades, a wide variety of automated or computer-based approaches have been applied to model this process. However, many such approaches have an important limitation in that they treat the rainfall-runoff process as a realization of only a few parameters of linear relationships rather than the process as a whole. What is required, therefore, is an approach that can capture not only the overall appearance but also the intricate details of the nonlinear behaviour of the process. The purpose of this study is to investigate the possibility of understanding the dynamics of the rainfall-runoff process from a new perspective, as a chaotic process. The possible existence of chaotic behaviour in the rainfall-runoff process is studied by investigating the rainfall and runoff time series: (a) separately; and (b) jointly (using the runoff coefficient). Monthly rainfall and runoff observed over a period of 131 years (January 1807-December 1937) at the Gôta River basin in the south of Sweden are analysed. The correlation dimension method is employed to identify the presence of chaos. The correlation dimensions obtained for the rainfall and runoff time series are 6.4 and 5.5, respectively. The finite dimensions obtained for the rainfall and runoff time series indicate the possible existence of chaos in these processes, implying that the joint rainfall-runoff process might also exhibit chaotic behaviour. The correlation dimension of about 7.8 obtained for the runoff coefficient also indicates the possible presence of chaos and supports the above results.Key words rainfall-runoff models; runoff coefficient; chaotic dynamics; Gôta River. Sweden; nonlinear analysis; time series analysis; correlation dimension Preuve de l'existence de chaos dans le processus pluie-débit Résumé La transformation de la pluie en débit est l'un des plus importants processus hydrologiques. Au cours des dernières décennies un grand nombre d'approches automatisées ou informatisées ont été mises en oeuvre pour modéliser ce processus. Ces approches demeurent toutefois limitées, car elles traitent le processus pluie-débit comme dépendant de quelques paramètres attachés à des relations linéaires au lieu de considérer ce processus comme un tout. Une approche permettant de saisir non seulement les grands traits du processus mais aussi la complexité des détails résultant de son comportement non linéaire est nécessaire. Le but de la présente étude est de chercher à comprendre la dynamique du processus pluie-débit dans une nouvelle perspective, celle des processus chaotiques. On a cherché à mettre en évidence l'existence éventuelle d'un comportement chaotique en étudiant des séries chronologiques de pluies et de débits: (a) séparément; et (b) conjointement (en utilisant le coefficient de ruissellement). Nous avons étudié les pluies et les débits mensuels observés pendant une période de 131 ans (Janvier 1807-Décembre 1937) sur le bassin de la rivi...

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