Identification of chaos in rainfall temporal disaggregation: Application of the correlation dimension method to 5-minute point rainfall series measured with a tipping bucket and an optical raingage

Are point rainfall time series resulting from stochastic or low-dimensional deterministic chaotic processes? This issue is still controversial, but important for the choice of the best suited rainfall simulation approach to generate realistic synthetic series. It is firstly shown, through a simple theoretical example (the logistic model), that the efficiency of the nonlinear analysis tools dedicated to the identification of chaotic behavior, especially the correlation dimension method (CDM), is drastically reduced if the data are contaminated by noise. The results of a CDM based analysis of a eight year point rainfall record with a time resolution of five minutes are then presented. More precisely, the series of rainfall disaggregation weights between the 10-minute and 5-minute time steps is studied. The discrete nature of tipping bucket data appears as a limiting factor at this time resolution for the analysis. To overcome this problem, optical raingage data are also studied. The results obtained in both - tipping bucket and optical raingage - cases show actually no clear evidence of a low-dimensional chaotic behavior. Furthermore, the results obtained suggest that the CDM is an effective tool for exploring data also in other contexts in addition to chaos analysis. The CDM analysis reveals in the present case study that the time series are neither chaotic nor composed of independent and identically distributed random variables. This is also verified on the basis of standard statistical tests.