Generating a missing half of multifractal fields with a blunt extension of discrete cascades
Résumé
Generating a missing half of multifractal fields with a blunt extension of discrete cascades Despite strong limitations, discrete random multiplicative cascades are often used to address scale issues which 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 1D, 2D or 3D is developed and tested on rainfall fields and numerical simulations. It basically 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.