Accounting for anisotropy in the simulation of rainfall fields with blunt extension of discrete Universal Multifractal cascades
Résumé
Universal Multifractals have been widely used to characterize and simulate geophysical fields extremely variable over a wide range of scales such as rainfall. Despite strong limitations, notably its non-stationnarity, discrete cascades are often used to simulate such fields. Recently, blunt cascades have been introduced in 1D, 2D, and space-time to cope with this issue while remaining in the simple framework of discrete cascades. It basically consists in geometrically interpolating over moving windows the multiplicative increments at each cascade steps. While being a well-known feature of rainfall fields, anisotropy is not yet addressed with blunt extensions of discrete Universal Multifractal cascades. In this paper, we suggest to extend this framework to account for anisotropy. It basically consists in using different sizes according to the direction for the moving window over which the interpolation is carried out. In a first step Multifractal expected behaviour is theoretically established. Then it is numerically confirmed with the help of ensembles of stochastic simulations. Finally, the features of simulated fields are compared with actual rainfall data ones. Data collected with help of a dual polarisation X-band radar operated by HM&Co-ENPC is used (radx.enpc.fr/).