The need of understanding and modelling the space-time variability of natural processes in geosciences produced a large body of literature over the last thirty years. Scaling approaches provide parsimonious models which can be applied to a wide scale range of geoprocesses and are based on the empirical detection of some patterns in observational data, i.e., a scale invariant mechanism repeating scale after scale. Models following this approach are based upon the assumption that the relationship of raw moments vs. time scale is a power law. In this context, the multifractal framework has been extensively studied and it has become clear that multiplicative cascades are the generic multifractal process. In this work we investigate random multiplicative cascades in terms of their capability of downscaling rainfall in time. By appropriate assumptions we form “crash test” conditions (e.g. theoretically infinite raw moments) and we investigate whether the cascades are able to capture and respect these conditions.
Lombardo, F., Volpi, E., Papalexiou, S.m., Koutsoyiannis, D. (2012). Multifractal downscaling models: A crash test. In 3nd STAHY International Workshop on Advances in Statistical Methods for Hydrology and Water Resources Management.