Evidence of chaos in the rainfall-runoff process

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.