22 Nov 2021
22 Nov 2021
Status: this preprint is currently under review for the journal HESS.

Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multifractal approach

Arun Ramanathan1, Pierre-Antoine Versini1, Daniel Schertzer1, Remi Perrin2, Lionel Sindt2, and Ioulia Tchiguirinskaia1 Arun Ramanathan et al.
  • 1École des Ponts Paristech (ENPC), Laboratory of Hydrology Meteorology & Complexity

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.

Arun Ramanathan et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-580', Anonymous Referee #1, 03 Jan 2022
    • AC1: 'Reply on RC1', Arun Ramanathan, 10 Jan 2022
  • RC2: 'Comment on hess-2021-580', Anonymous Referee #2, 21 Feb 2022
    • AC2: 'Reply on RC2', Arun Ramanathan, 21 Mar 2022

Arun Ramanathan et al.

Arun Ramanathan et al.


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Short summary
A new method is suggested for simulating rainfall scenarios of specified Intensity, Duration, and Frequency that are indispensable for hydrological applications such as storm-water management. Novel metrics are proposed to quantify the effectiveness of the suggested simulation procedure. The efficiency of the proposed framework illustrates its suitability for framing reference rainfall regulations or Intensity, Duration, and Frequency values that guide hydrological applications.