Blunt extension of discrete universal multifractal cascades: development and application to downscaling
Résumé
Scale issues are ubiquitous in the geosciences. Because of their simplicity and intuitiveness, and despite strong limitations, notably its nonstationarity features, discrete random multiplicative cascade processes are very often used to address these scale issues. A novel approach based on the parsimonious framework of universal multifractals (UM) is introduced to tackle this issue while preserving the simple structure of discrete cascades. It basically consists in smoothing at each cascade step the random multiplicative increments with the help of a geometric interpolation over a moving window. The window size enables us to introduce non-conservativeness in the simulated fields. It is established theoretically, and numerically confirmed, that the simulated fields also exhibit a multifractal behaviour with expected features. It is shown that such an approach remains valid over a limited range of UM parameters. Finally, we test downscaling of rainfall fields with the help of this blunt discrete cascade process and discuss challenges for future developments.
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