Abstract

Hydrological applications such as storm-water management or flood design usually deal with and are driven by region-specific reference rainfall regulations or guidelines based on Intensity-Duration-Frequency (IDF) curves. IDF curves are usually obtained via frequency analysis of rainfall data using which the exceedance probability of rain intensity for different durations are determined. It is also rather common for reference rainfall to be expressed in terms of precipitation P, accumulated in a duration D (related to rainfall intensity ), with a return period T (inverse of exceedance probability). Meteorological modules of hydro-meteorological models used for the aforementioned applications therefore need to be capable of simulating such reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes (non-homogeneity or intermittency, scale invariance and extremal statistics) seems to suit this purpose. Here we propose a discrete-in-scale universal multifractal (UM) cascade based approach. Daily, Hourly and six-minute rainfall time series datasets (with lengths ranging from 100 to 15 years) over three regions (Paris, Nantes, and Aix-en-Provence) in France that are characterized by different climates are analyzed to identify scaling regimes and estimate corresponding UM parameters (α, C1) required by the UM cascade model. Suitable renormalization constants that correspond to the P, D, T values of reference rainfall are used to simulate an ensemble of reference rainfall scenarios, and the simulations are finally compared with datasets. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.

Highlights

  • Reference rainfall events characterized by amount of precipitation P, duration D and return period T are required for sizing 20 storm-water management infrastructures such as conduits, retention basin, and even green roofs if considered as a storm-water management tool

  • As shown in 50 Fig. 1 most of the aforementioned models (10 out of 12) seem to be more focussed on computational and conceptual simplicity than on physics. Alternatives such as Universal Multifractal (UM) cascades that aren’t computationally that complicated seem to be attractive choices especially since they are capable of representing fields with high spatio-temporal variability (Schertzer and Lovejoy, 1989; Ladoy et al, 1993; Tessier et al, 1996; Lovejoy and Schertzer, 55 2006, 2007; Schertzer et al, 2010; Schertzer and Lovejoy, 2011; Hoang et al, 2012; Lovejoy and Schertzer, 2013; Gires et al, 2013; Hoang et al, 2014)

  • Lower values of Multifractal Comparison Metric (MCM) imply that the simulation has multifractal properties close to that of observed data

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Summary

Introduction

Reference rainfall events characterized by amount of precipitation P , duration D and return period T are required for sizing 20 storm-water management infrastructures such as conduits, retention basin, and even green roofs if considered as a storm-water management tool. As shown in 50 Fig. 1 most of the aforementioned models (10 out of 12) seem to be more focussed on computational and conceptual simplicity than on physics Alternatives such as Universal Multifractal (UM) cascades that aren’t computationally that complicated (compared to high-resolution Numerical Weather Prediction models that explicitly represent given atmospheric processes on a limited range of scale) seem to be attractive choices especially since they are capable of representing fields with high spatio-temporal variability (Schertzer and Lovejoy, 1989; Ladoy et al, 1993; Tessier et al, 1996; Lovejoy and Schertzer, 55 2006, 2007; Schertzer et al, 2010; Schertzer and Lovejoy, 2011; Hoang et al, 2012; Lovejoy and Schertzer, 2013; Gires et al, 2013; Hoang et al, 2014).

Regions considered and observational datasets used
Trace Moment (TM) Analysis
Double Trace Moment (DTM) Analysis
Discrete-in-scale Universal Multifractal cascades
Simulating reference rainfall scenarios
Comparing simulations with observational datasets
Rainfall Comparison Metric (RCM)
Conclusions
315 References
Full Text
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