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Application of copula-based and ARCH-based models in storm prediction

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Abstract

In this study, Vector Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (VAR-GARCH), copula, and copula-GARCH models were used for joint frequency analysis of storms in the Aras river basin in northwestern Iran in period of 1998–2018. The heteroskedasticity in the series was considered using the vector autoregressive model. Two-dimensional copulas were also used for bivariate analysis. After confirming the correlation between the pair variables of storm with one event lag (S1) and storm with no lag (S0), bivariate frequency analysis was performed. In the simulation step, the residual series of the VAR model was extracted and fitted to the GARCH model. Then, the residual series of the GARCH model was modeled using the copula model. Finally, storm with no lag (S0) affected by storm with one event lag (S1) was simulated by VAR-GARCH, copula, and copula-GARCH models. According to the coefficient of determination (R2) and Nash–Sutcliffe Efficiency coefficient (NSE) and root mean square error (RMSE), the VAR-GARCH model had higher accuracy than copula and copula-GARCH models. The RMSE in the simulation of storm height using the VAR-GARCH model was estimated to be 18% and 11% less than copula and copula-GARCH models, respectively. The VAR-GARCH model provided higher accuracy in the simulations due to the consideration of different lags in the simulations and modeling the variance of the residual series. According to the Taylor diagram, the certainty of all three models in simulating storm height are acceptable. Finally, by two-dimensional analysis of pair variables of storm height and storm duration, typical curve was produced that can estimate the storm duration with different probabilities. In fact, having the storm information that has happened in the present can accurately predict the next storm information. It can be very useful in flood management and the generated curves can be used as a flood warning system in the basin.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

It is available from the first author upon reasonable request.

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Acknowledgements

The authors would like to thank Iran’s Meteorological Organization (IRIMO) for providing the data.

Funding

The authors would like to acknowledge the financial support of University of Birjand for this research under contract number 1399/D/15691.

Author information

Authors and Affiliations

  1. Department of Water Engineering, University of Birjand, Birjand, Iran

    Yousef Ramezani & Mohammad Nazeri Tahroudi

  2. Department of Civil and Environmental Engineering, Politecnico Di Milano, Milan, Italy

    Carlo De Michele

  3. Department of Water Engineering, Shahrekord University, Shahrekord, Iran

    Rasoul Mirabbasi

Authors
  1. Yousef Ramezani
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  2. Mohammad Nazeri Tahroudi
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  3. Carlo De Michele
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  4. Rasoul Mirabbasi
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Contributions

All authors contributed to the study conception and design. Data collection, analysis, and general literature review were performed by M. Nazeri Tahroudi. The first draft of the manuscript was written by M. Nazeri Tahroudi. Y. Ramezani has supervised the research work. Y. Ramezani, C. De Michele, and R. Mirabbasi have reviewed and commented on the first draft of the manuscript. All authors read and approved the final version of the manuscript.

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Correspondence to Yousef Ramezani.

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Highlights

1. With a simulation approach based on hybrid models and copula functions, the values obtained from the bivariate frequency curve will be more reliable. Due to the heteroskedasticity in various meteorological and hydrological data, the use of nonlinear ARCH models may increase the accuracy of the simulations.

2. The aim of the present study was to investigate the performance of the VAR-GARCH model, copula model, and copula-GARCH model in simulating pair variables of storm with no lag (S0) affected by storm with one event lag (S1) in the Aras river basin, Iran.

3. By two-dimensional analysis of pair variables of storm height and storm duration, typical curve was produced that can estimate the storm duration with different probabilities.

4. Having the storm information that has happened in the present can accurately predict the next storm information.

5. It can be very useful in flood management and the generated curves can be used as a flood warning system in the basin.

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Ramezani, Y., Nazeri Tahroudi, M., De Michele, C. et al. Application of copula-based and ARCH-based models in storm prediction. Theor Appl Climatol 151, 1239–1255 (2023). https://doi.org/10.1007/s00704-022-04333-9

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  • DOI: https://doi.org/10.1007/s00704-022-04333-9

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