Multifractal downscaling of a GCM rainfield

In order to get a more efficient production management of reservoirs, it would be helpful to apply long-term meteorological forecasts to hydrological models. Unfortunately, the explicit scales of present GCM's are quite larger (e.g. 243kmx243kmx32 days) than those of hydrological models (e.g. 1 kmx1kmx1day). Therefore it is indispensable to proceed to a downscaling of the output of the former in order to obtain an input for the latter. In this paper, we present a multifractal downscaling procedure. The site of the study is the area of Doubs river, with the help of a dense local hydrological network, but in order to get a larger spatial scale ratio we extend our multifractal analysis to France, with the help of Météo-France PRECIP data base. We first argue that it is indispensable to consider a multifractal downscaling procedure in order to respect the scaling properties of the hydro-meteorological fields. We performed time, scale and time-space multifractal analysis of the available data and evaluate the corresponding universal exponents, as well as the anisotropy/dynamical exponent of the time-space generalized scale. We show that these exponents are quite robust. We compare our analysis to similar works, but restricted to the use of Log-Poison cascade and space-time isotropy. We show both theoretically and empirically that these restrictions are untenable, in particular with respect to the extremes. We also show simulations should be done with the help of continuous (in scale) and causal cascade models, not with ad-hoc time-space cascades, and present the corresponding numerical simulations. of space-time downscaling of (meso-scale) GCM data down to (micro-scale) hydrological scales. We greatly acknowledge the financial support from Electricité de France, as well as Météo-France for providing access to its PRECIP data base.