Characterizing and simulating with blunt extension of discrete cascades rainfall anisotropy in a Universal Multifractals framework

Rainfall fields exhibit extreme variability over wide range of space-time scales which make them complex to characterize, model and even measure. Furthermore, rainfall, as most geophysical fields, is strongly anisotropic. Fortunately, scaling anisotropy has been developed for a few decades to generalise scaling in an anisotropic framework, e.g., in the simplest case iso-surfaces become self-affines ellipsoids instead of self-similar spheres. This is particularly straightforward for continuous in scale cascades. For them, as well as for discrete in scale cascades, Universal Multifractals (UM) have been widely used to analyse and simulate such geophysical fields with the help of a very limited number of physically meaningful parameters. Recently blunt cascades have been introduced. They enable to remain in the simple framework of discrete cascades while partly overcoming their well known strong limitations such as non-stationnarity. It basically consists in geometrically interpolating over moving windows the multiplicative increments at each cascade steps.

Here we suggest to incorporate observed features in blunt 2D and 3D (space-time) blunt discrete cascade simulations. The data analysis corresponds to a 1D analysis along various directions ,considering each lof them as a different “sample” of the process. Analysing how the UM parameters change with the angle of the chosen direction enables to unveil underlying rainfall anisotropy features. Impacts, and notably potential biases, of these features on standard spatial analysis in 2D are also explored and discussed. For this purpose high resolution space-time rainfall data collected with help of a dual polarisation X-band radar operated by HM&Co-ENPC is used .

To simulate anisotropy features with the help of blunt extension of discrete UM cascades, we tentatively suggest to use moving window shaped as ellipses instead of squares. Tuning the eccentricity and orientation of the ellipses enables to introduce various levels of anisotropy within the simulated fields. First, multifractal expected behaviour is theoretically established and then it is numerically confirmed with the help of ensembles of stochastic simulations and the previously developed analysis approach.

Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for partial financial support.