Generating a missing half of multifractal fields with a blunt extension of discrete cascades

ABSTRACT

Despite strong limitations, discrete random multiplicative cascades are often used to address scale issues that are ubiquitous in geosciences. A blunt extension based on the parsimonious framework of universal multifractals has recently been suggested. It preserves its simplicity and intuitiveness while overcoming its non-stationarity features. It relies on smoothing through a geometrical moving average the increments at each cascade step. Here, a space-time extension is suggested. Theoretically expected multifractal behaviour is retrieved on numerical simulations for typical rainfall parameters. A new algorithm to generate the missing half of multifractal fields in one, two or three dimensions is developed and tested on rainfall fields and numerical simulations. It consists in stochastically generating half of the increments and deterministically iteratively reconstructing the others to retrieve the available data and ensure a smooth transition with the unknown portion while preserving the multifractal behaviour. Potential applications to nowcasting of hydro-meteorological extremes are discussed.

KEYWORDS:

• discrete random multiplicative cascades
• multifractals
• nowcasting
• rainfall

Editor A. Castellarin Associate Editor H. Tyralis

Editor A. Castellarin Associate Editor H. Tyralis

Additional information

Funding

The authors gratefully acknowledge partial financial support from the Chair “Hydrology for Resilient Cities” (endowed by Veolia) of Ecole des Ponts ParisTech, the Île-de-France region RadX@IdF Project, and the ANR JCJC RW-Turb project (ANR-19-CE05-0022-01).