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 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.

Automated summary

Despite limitations, a new extension method based on the parsimonious framework of universal multifractals is suggested to address scale issues in geosciences. The method smooths the increments at each cascade step through a geometrical moving average, preserving simplicity and intuitiveness while overcoming non-stationarity features. The numerical simulations show that the expected multifractal behavior is retrieved for typical rainfall parameters. A new algorithm is developed to generate the missing half of multifractal fields in various dimensions, tested on rainfall fields and simulations, and discussed for potential applications in hydro-meteorological extremes nowcasting.