Techniques of Multifractal Nowcasting With Rada Data
Résumé
In deterministic weather forecast models, the rain and many other physical processes are highly parameterized by rather ad-hoc sub-grid modelling. A consequence is the poor rain forecast; and further disadvantage is the long spin-up and computational time of these models prevents them to deliver nowcasting, which are indispensable in emergency situations. We have developed techniques of nowcasting based on the multifractal approach, applying cascade models which include continuous scales, scaling space-time anisotropy and causality. These models have the advantage of requiring a very limited number of theoretical or empirical parameters. Due to these properties, the multifractal models have been more and more used for analysing and simulating rainfall. To produce multifractal forecasts, we exploit the fact that at the core of a multifractal process there is a Levy white-noise -its "sub-generator"- whose future is therefore independent of its past. A first step corresponds to a backward simulation in order to estimate the past sub-generator from past observations (e.g. rain radar data). This raises several technical issues due to the fact it involve inversions. The second step corresponds to a forward simulations based on the sub-generator extended to a future period. This extension can be done along several modes and we discuss those corresponding respectively to deterministic and stochastic sub- grid modelling, as well as the question of stochastic forecast versus ensemble forecast. We focus on a case study of the extreme rainfall that occurs on the 8th and 9th of September 2002 in the Gard basin, France.