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Net rainfall estimation by discharge deconvolution through inversed geomorphology-based transfer function

Congress: 2008
Author(s): Houda Boudhraâ , Christophe Cudennec, Mohamed Slimani, Hervé Andrieu
Houda Boudhraâ (1,2), Christophe Cudennec(3), Mohamed Slimani(1), Hervé Andrieu(4) 1 INAT, Lab. STE, 43 Av Charles Nicolle, 1082 Tunis Mahrajène, Tunisie boudhraa_hda@yahoo.fr 2 IRD, UMR G-EAU, Tunis, Tunisie 3 INRA, Agrocampus Rennes, UMR SAS, R

Keyword(s): Net rainfall, deconvolution, inversion, geomorphology-based transfer function, semi-arid basin
AbstractThe geomorphological structure of hydrological paths can be observed for any basin, from information –of various kinds and qualities– about relief and watercourses. Moreover it can be translated into basin-level transfer functions, through more or less complex conceptualisations, according to the available data and knowledge. In data-scarce contexts, the use of geomorphology-based transfer functions is a strong perspective. The water path from any point in a basin down to the outlet is considered as the composition of a set of hillslope paths, due to the different flow processes, and of a single channelized path. The probability density function of the hydraulic length L of this channelized path is a structural geomorphometric function used as the basis of a non-calibrated rainfall-runoff transfer function. Assuming that most of the whole basin nonlinearity of the rainfall-runoff relationship comes from nonlinearity of hillslope processes allows to translate the geomorphometric function into a travel time distribution function through the use of a simple average channelized flow velocity. Furthermore, an initial assumption of spatially homogeneous rainfall input is made at this stage. With such a framework, the obtained transfer function is equivalent to a unit hydrograph, but limited to channelized flows. This is considered to be the first step of a downward approach, robust enough to be used in data-scarce contexts, but also promising in the sense of accounting for various additional structured causes of complexity. Net rainfall is thus considered as the coupling variable between the production function which embraces hillslope hydrology and the transfer function which describes fluvial transfers. It corresponds to a flow through the whole hillslope/river network interface in the basin and cannot be observed in situ. Net rainfall is thus assessed by discharge deconvolution through the inversion of the geomorphology-based transfer function. Inverse problems theory is used to account for various availability and quality of information, as well as modelling-induced errors. Such an assessment of the net rainfall coupling variable, in coherence with the hydro-geomorphological conceptual framework, is of major interest for isolating hillslope hydrology from downstream; and thus for deglobalising basin non-stationarities and nonlinearities as well as for improving geomorphology-based rainfall-runoff modelling itself. A full application is proposed for a set of Tunisian semiarid basins (192, 180, 18.1 and 3.16 km²). Relevance and relative roles of error sources are discussed for the most spatially homogeneous rainfall events, in relation to scale. Practical application perspectives are explored. The main cause of additional complexity is confirmed to be the space-time variability of rainfall, whose accounting for appears to be the next step of the downward approach.
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