Rainfall–runoff relations for karstic springs: multifractal analyses

Karstic watersheds appear as highly as non-linear and non-stationary systems. The behaviour of karstic springs has been previously studied using non-linear simulation methods (Volterra expansion) and non-stationary analyses methods based on wavelet transforms. The main issue of karstic spring behaviour consists of the presence and the identification of characteristic time-scales. In order to highlight more precisely the scale-properties of the rainfall–runoff relations for karstic springs, the multifractal analysis is introduced. These methods are applied daily and half-hourly rainfall rates and runoffs measured on a three French karstic springs located in the Pyrénées Mountains (Ariège, France): Aliou, Baget and Fontestorbes. They are characterised by a variable development of the drainage systems. We have at our disposal long and uninterrupted series of data over period of several years, which constitute a high quality bank data. Multifractal analyses of both daily and half-hourly rainfall rates and runoffs give evident a scale-dependant behaviour. Effectively, it highlights the presence of different multifractal processes at each sampling rate. Using a universal class of multifractal models based on cascade multiplicative processes, the identified multifractal sub-processes are characterised by the classical parameters α and C1. All these results should lead to several improvements in karstic springflow simulation models.