Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multifractal approach
- 1École des Ponts Paristech (ENPC), Laboratory of Hydrology Meteorology & Complexity
- 2SOPREMA
- 1École des Ponts Paristech (ENPC), Laboratory of Hydrology Meteorology & Complexity
- 2SOPREMA
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)
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RC1: 'Comment on hess-2021-580', Anonymous Referee #1, 03 Jan 2022
The manuscript presents a stochastic approach to generate an ensemble of reference rainfall scenarios (giving a desired rainfall amount P, rainfall duration D and return period T). This approach is based on multi-fractal theory, which is parsimonious and easy to apply. While this research topic is generally relevant for the readership of HESS, there is still a bit of issue which needs to be addressed. Please find the attached comments. Those comments should be addressed before considering publishing this article.
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AC1: 'Reply on RC1', Arun Ramanathan, 10 Jan 2022
We thank the referee for meticulously reviewing our manuscript and providing several constructive suggestions. We are especially grateful for the referee’s positive feedback. In the supplementary document attached here, we provide our detailed response to the referee’s supplementary comments and also mention how we plan to address these issues in a future version of this manuscript.
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AC1: 'Reply on RC1', Arun Ramanathan, 10 Jan 2022
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RC2: 'Comment on hess-2021-580', Anonymous Referee #2, 21 Feb 2022
Overall review comment:
This paper presents the use of universal multifractal to generate ensembles of rainfall time series that recreates the Intensity (I), Duration (D), and Frequency (F) of rainfall time series, commonly used in the design of storm-water infrastructure. This paper may become an essential contribution to the literature body of stochastic simulations of rainfall time series. However, I found two pitfalls in the paper: (1) There is no clear definition of the research gap (including connections to previous works), and (2) Even though the paper assesses their methodology, the discussion about the results is almost non-existent. I hope my comments provide a road map to improve the important contribution done by the authors. See the attached file for a detailed description of my concerns.
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AC2: 'Reply on RC2', Arun Ramanathan, 21 Mar 2022
We thank the referee for reviewing our manuscript and providing several constructive suggestions. We are especially grateful for the positive feedback. In the attached Supplement document, we provide our detailed response to the detailed description of the reviewer’s comments and also mention how we plan to address these issues (especially regarding research gap definition and result discussion) in a future version of this manuscript.
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AC2: 'Reply on RC2', Arun Ramanathan, 21 Mar 2022
Arun Ramanathan et al.
Arun Ramanathan et al.
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