Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multi-fractal approach

Abstract

Hydrological applications such as storm-water management usually deal with region-specific reference rainfall regulations based on intensity–duration–frequency (IDF) curves. Such curves are usually obtained via frequency analysis of rainfall and exceedance probability estimation of rain intensity for different durations. It is also common for reference rainfall to be expressed in terms of precipitation P, accumulated in a duration D, with a return period T. Meteorological modules of hydro-meteorological models used for the aforementioned applications therefore need to be capable of simulating such reference rainfall scenarios. This paper aims to address three research gaps: (i) the discrepancy between standard methods for defining reference precipitation and the strong multi-scale intermittency of precipitation, (ii) a lack of procedures to adapt multi-fractal precipitation modelling to specified partial statistical references, and (iii) scarcity of proper multi-scale tools to quantitatively estimate the effectiveness of such simulation procedures. Therefore, it proposes (i) a procedure based on extreme non-Gaussian statistics in two scaling regimes due to earth's finite size to tackle multi-scale intermittency head on, (ii) a renormalization technique to make simulations comply with the aforementioned partial statistical references, and (iii) multi-scale metrics to compare simulated rainfall time series with those observed. While the first two proposals are utilized to simulate reference rainfall scenarios for three regions (Paris, Nantes, and Aix-en-Provence) in France that are characterized by different climates, the last one is used to validate them. The scope of this paper is that the baseline precipitation scenarios simulated here can be used as realistic inputs into hydrological models for applications such as the optimal design of storm-water management infrastructure, especially green roofs. Although only purely temporal simulations are considered, this approach could possibly be generalized to space–time as well.