Developing numerical equality to regional intensity–duration–frequency curves using evolutionary algorithms and multi-gene genetic programming

This study aims to carry out regional intensity − duration − frequency (IDF) equality using the relationship with IDF obtained from point frequency analysis. Eleven empirical equations used in the literature for seven climate regions of Turkey were calibrated using particle swarm optimization (PSO)...

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Published in:	Acta geophysica Vol. 71; no. 1; pp. 469 - 488
Main Authors:	Citakoglu, Hatice, Demir, Vahdettin
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.02.2023 Springer Nature B.V
Subjects:	Algorithms Calibration Climate change Correlation analysis Earth and Environmental Science Earth Sciences Empirical equations Equality Evolutionary algorithms Frequency analysis Genetic algorithms Geophysics/Geodesy Geotechnical Engineering & Applied Earth Sciences Keywords Particle swarm optimization Precipitation Rain Regional development Regions Research Article - Hydrology Root-mean-square errors Software Stormwater management Structural Geology Canada United States > US Turkey Multi-gene genetic programming Regional intensity–duration–frequency analysis Turkey Genetic algorithm Particle swarm optimization
ISSN:	1895-7455, 1895-6572, 1895-7455
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Abstract	This study aims to carry out regional intensity − duration − frequency (IDF) equality using the relationship with IDF obtained from point frequency analysis. Eleven empirical equations used in the literature for seven climate regions of Turkey were calibrated using particle swarm optimization (PSO) and genetic algorithm (GA) optimization techniques and the obtained results were compared. In addition, in this study, new regional IDF equations were obtained for each region utilizing Multi-Gene Genetic Programming (MGGP) method. Finally, Kruskal–Wallis (KW) test was applied to the IDF values obtained from the methods and the observed values. As a result of the study, it was observed that the coefficients of 11 empirical equations calibrated with PSO, and GA techniques were different from each other. The mean absolute error (MAE), root mean square error (RMSE), mean absolute relative error (MARE), coefficient of determination ( R 2 ), and Taylor diagram were used to evaluate the performances of PSO, GA, and MGGP techniques. According to the performance criteria, it has been determined that the IDF equations obtained by the MGGP method for the Eastern Anatolia, Aegean, Southeastern Anatolia, and Central Anatolia regions are more successful than the empirical equations calibrated with the PSO and GA method. The empirical IDF equations produced with PSO and the IDF equations acquired with MGGP have similar findings in the Mediterranean, Black Sea, and Marmara. In addition, the KW test results showed that the data of all models were from the same population.
AbstractList	This study aims to carry out regional intensity − duration − frequency (IDF) equality using the relationship with IDF obtained from point frequency analysis. Eleven empirical equations used in the literature for seven climate regions of Turkey were calibrated using particle swarm optimization (PSO) and genetic algorithm (GA) optimization techniques and the obtained results were compared. In addition, in this study, new regional IDF equations were obtained for each region utilizing Multi-Gene Genetic Programming (MGGP) method. Finally, Kruskal–Wallis (KW) test was applied to the IDF values obtained from the methods and the observed values. As a result of the study, it was observed that the coefficients of 11 empirical equations calibrated with PSO, and GA techniques were different from each other. The mean absolute error (MAE), root mean square error (RMSE), mean absolute relative error (MARE), coefficient of determination ( R 2 ), and Taylor diagram were used to evaluate the performances of PSO, GA, and MGGP techniques. According to the performance criteria, it has been determined that the IDF equations obtained by the MGGP method for the Eastern Anatolia, Aegean, Southeastern Anatolia, and Central Anatolia regions are more successful than the empirical equations calibrated with the PSO and GA method. The empirical IDF equations produced with PSO and the IDF equations acquired with MGGP have similar findings in the Mediterranean, Black Sea, and Marmara. In addition, the KW test results showed that the data of all models were from the same population. This study aims to carry out regional intensity − duration − frequency (IDF) equality using the relationship with IDF obtained from point frequency analysis. Eleven empirical equations used in the literature for seven climate regions of Turkey were calibrated using particle swarm optimization (PSO) and genetic algorithm (GA) optimization techniques and the obtained results were compared. In addition, in this study, new regional IDF equations were obtained for each region utilizing Multi-Gene Genetic Programming (MGGP) method. Finally, Kruskal–Wallis (KW) test was applied to the IDF values obtained from the methods and the observed values. As a result of the study, it was observed that the coefficients of 11 empirical equations calibrated with PSO, and GA techniques were different from each other. The mean absolute error (MAE), root mean square error (RMSE), mean absolute relative error (MARE), coefficient of determination (R2), and Taylor diagram were used to evaluate the performances of PSO, GA, and MGGP techniques. According to the performance criteria, it has been determined that the IDF equations obtained by the MGGP method for the Eastern Anatolia, Aegean, Southeastern Anatolia, and Central Anatolia regions are more successful than the empirical equations calibrated with the PSO and GA method. The empirical IDF equations produced with PSO and the IDF equations acquired with MGGP have similar findings in the Mediterranean, Black Sea, and Marmara. In addition, the KW test results showed that the data of all models were from the same population.
Author	Demir, Vahdettin Citakoglu, Hatice
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Copyright_xml	– notice: The Author(s) under exclusive licence to Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s) under exclusive licence to Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2022.
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Keywords	Multi-gene genetic programming Regional intensity–duration–frequency analysis Turkey Genetic algorithm Particle swarm optimization
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SubjectTerms	Algorithms Calibration Climate change Correlation analysis Earth and Environmental Science Earth Sciences Empirical equations Equality Evolutionary algorithms Frequency analysis Genetic algorithms Geophysics/Geodesy Geotechnical Engineering & Applied Earth Sciences Keywords Particle swarm optimization Precipitation Rain Regional development Regions Research Article - Hydrology Root-mean-square errors Software Stormwater management Structural Geology
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Title	Developing numerical equality to regional intensity–duration–frequency curves using evolutionary algorithms and multi-gene genetic programming
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