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Multivariate analysis of rainfall–runoff characteristics using copulas

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Abstract

Most hydrological phenomena have stochastic behaviour; therefore, the theory of statistics and probability usually uses to describe and analyse them. Rainfall and runoff are two hydrological phenomena, described with different characteristics, e.g., volume, peak flow, and time base (runoff), and intensity, duration and depth (rainfall). In the current study, we used the copula functions for multivariate modelling of rainfall and runoff characteristics. To do this, the performance of 10 different copulas was examined in a multivariate analysis of rainfall and runoff characteristics measured in Kasilian basin located in northeastern Iran during a 37-yr period (1984–2020). The rainfall characteristics, including intensity, duration, and depth for 562 recorded rainfall events for the Kasilian basin at intervals of 15–30 min were extracted for rainfall–runoff analysis. Then, the rainfall histograms and flood hydrographs were drawn, and rainfall characteristics (i.e., depth, duration, and intensity) and runoff characteristics (i.e., peak discharge, peak discharge time, time base, flood volume, the width flood hydrograph at 50 and 75% of peak discharge (W50 and W75)) were extracted. In the next step, the univariate distributions with best fitness on every studied rainfall and runoff characteristics were determined. The results demonstrated that the GEV has the best fitness on all studied rainfall and runoff characteristics. Also, the Joe copula had the best fitness for joining the duration and depth of rainfall, as well as the intensity and depth of rainfall, and the Gumbel–Barnett and Farlie–Gumbel–Morgenstern were in the following ranks. Then the multivariate probability and return period were computed in two states of ‘AND’ and ‘OR’. It was demonstrated that in the ‘AND’ mode, the joint return period for a rainfall depth of 60 mm and rainfall intensity of 60 mm/h is less than 20 years, while for the same rainfall depth and intensity values, in the ‘OR’ mode, the joint return period is obtained about 6 years.

Research Highlights

  • Multivariate probabilistic rainfall–runoff model created using copula functions.

  • The GEV distribution had the best fitness on all studied rainfall and runoff characteristics.

  • The Joe copula had the best fitness for joining the duration and depth of rainfall, as well as the intensity and depth of rainfall.

  • The difference between standard return periods and Kendall return periods increases with increasing the probability level.

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Authors and Affiliations

  1. Department of Water Engineering, Faculty of Engineering, Islamic Azad University, Kerman Branch, Kerman, Iran

    Samira Moradzadeh Rahmatabadi & Mohsen Irandoust

  2. Water Engineering Department, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran

    Rasoul Mirabbasi

Authors
  1. Samira Moradzadeh Rahmatabadi
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  2. Mohsen Irandoust
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  3. Rasoul Mirabbasi
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Contributions

The participation of S Moradzadeh Rahmatabadi and M Irandoust was collecting the required data, model running and preparing the draft, and the participation of R Mirabbasi included writing the codes, analysis of results, and reviewing and editing the manuscript.

Corresponding author

Correspondence to Mohsen Irandoust.

Additional information

Communicated by P A Francis

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Moradzadeh Rahmatabadi, S., Irandoust, M. & Mirabbasi, R. Multivariate analysis of rainfall–runoff characteristics using copulas. J Earth Syst Sci 132, 93 (2023). https://doi.org/10.1007/s12040-023-02105-1

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  • DOI: https://doi.org/10.1007/s12040-023-02105-1

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