Author(s): David Labat; Rachid Ababou; Alain Mangin
Linked Author(s):
Keywords: Karstic systems; Rainfall-runoff; Floods; Convolution; Nonlinear Volterraexpansions; Continuous wavelet transform; Orthogonal multiresolution analysis
Abstract: Karstic aquifers are distributed all around the world (USA, China, Europe, .. .). They provide large underground reserves of water of high quality but are quite difficult to exploit since their behaviour is not well-understood (floods and low-flow). A temporal and/or spatial model would have applications not only in water management (pollution and pumping) but also in flood prevention. A karstic watershed is a three-dimensional basin which involves both surface and subsurface flows including infiltration, surface runoff and subsurface processes through fissures, underground streams and reservoirs. Due to the complexity of the physical structure of these systems, we focus on the relations between two temporal signals: an input constituted by the basin-averaged rainfall rate and an output constituted by runoff at the supposed main outlet of the basin. We will study more carefully two karstic basins located in the Pyrenees mountains in France (Aliou and Baget) for which we have long records of daily and semi-hourly rainfall-runoff data. The proposed input-output causal relations are based on kernels of increasing orders, which relate input to output via nonlinear Volterra convolution expansions. Truncated to the first order, this yields the classical linear convolution model. Higher order terms correspond to nonlinear input/input products. However, we restrict our approach to order two. In the present work, we analyse the limitations of linear models and the performance of the nonlinear ones using a stochastic interpretation of the signals. The latter are able to take into account in a satisfying statistical way the complexity of the temporal behaviour of karstic basins. Finally, we show that we can also take in account nonstationarity thanks to other methods: the continuous wavelet transform and the orthogonal multiresolution wavelet analysis. The mathematical aspects of those techniques are briefly exposed, and they are both applied to springflow pumping and intermittent springflow data from two other karstic springs (Larzac plateau, Aveyron, France) in order to filter and to identify specific sub-processes.
Year: 1999