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 (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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of data and material
The data were provided by the General Directorate of State Meteorology Affairs (MGM).
Code availability
The codes were written by Hatice Citakoglu and the analyses were done by Vahdettin Demir. Accessible MATLAB codes have been adapted to study. Code availability is not accessible.
References
Acar R, Çelik S, Senocak S (2008) Rainfall intensity-duration-frequency (IDF) model using an artificial neural network approach. J Sci Ind Res (india) 67:198–202
Adarsh S, Janga Reddy M (2018) Developing hourly intensity duration frequency curves for urban areas in India using multivariate empirical mode decomposition and scaling theory. Stoch Environ Res Risk Assess 32:1889–1902. https://doi.org/10.1007/s00477-018-1545-x
Al-Amri NS, Subyani AM (2017) Generation of rainfall intensity duration frequency (IDF) curves for ungauged sites in arid region. Earth Syst Environ 1:8. https://doi.org/10.1007/s41748-017-0008-8
Al-Khalaf HA (1997) Predicting short duration, high-intensity rainfall in Saudi Arabia. Faculty of the college of graduate studies
Al-Shaikh AA (1985) Rainfall Frequency Studies for Saudi Arabia. M.S. Thesis, Dept. C.E., King Saud University, Riyadh, p 156
Al-Wagdany AS (2021) Construction of IDF curves based on NRCS synthetic rainfall hyetographs and daily rainfall records in arid regions. Arab J Geosci 14:527. https://doi.org/10.1007/s12517-021-06922-w
Alramlawi K, Fıstıkoğlu O (2022) Estimation of intensity-duration-frequency (IDF) curves from large scale atmospheric dataset by statistical downscaling. Tek Dergi 33:11591–11615. https://doi.org/10.18400/tekderg.874035
Aly A, Pathak C, Teegavarapu RSV et al (2009) Evaluation of Improvised spatial interpolation methods for infilling missing precipitation records. World environmental and water resources congress 2009. American Society of Civil Engineers, Reston, VA, pp 1–10
Tuğçe A, Ömer Y, Fatih S, Emrah O (2022) Rainfall intensity-duration-frequency analysis in Turkey, with the emphasis of eastern black sea basin. Teknik Dergi. https://doi.org/10.18400/tekderg.727085
Asikoglu OL, Benzeden E (2014) Simple generalization approach for intensity-duration-frequency relationships. Hydrol Process 28:1114–1123. https://doi.org/10.1002/hyp.9634
Awadallah AG, Magdy M, Helmy E, Rashed E (2017) Assessment of rainfall intensity equations enlisted in the Egyptian code for designing potable water and sewage networks. Adv Meteorol 2017:1–10. https://doi.org/10.1155/2017/9496787
Barbero R, Fowler HJ, Blenkinsop S et al (2019) A synthesis of hourly and daily precipitation extremes in different climatic regions. Weather Clim Extrem 26:100219. https://doi.org/10.1016/j.wace.2019.100219
Başakın EE, Ekmekcioğlu Ö, Özger M, Citakoglu H (2021) Determination of intensity-duration-frequency relation by particle swarm optimization and genetic programming. In: In II. International Applied Statistics Conference (UYIK-2021). Tokat, Turkey, pp 1–8
Bell FC (1969) Generalized rainfall-duration-frequency relationships. J Hydraul Div ASCE 95:311–327
Bernard MM (1932) Formulas for rainfall intensities of long duration. Trans Am Soc Civ Eng 96:592–606. https://doi.org/10.1061/taceat.0004323
Borga M, Vezzani C, Fontana GD (2005) Regional rainfall depth–duration–frequency equations for an alpine region. Nat Hazards 36:221–235. https://doi.org/10.1007/s11069-004-4550-y
Buba LF, Kura NU, Dakagan JB (2017) Spatiotemporal trend analysis of changing rainfall characteristics in Guinea Savanna of Nigeria. Model Earth Syst Environ 3:1081–1090. https://doi.org/10.1007/s40808-017-0356-2
Bulti DT, Abebe BG, Biru Z (2021) Climate change–induced variations in future extreme precipitation intensity–duration–frequency in flood-prone city of Adama, central Ethiopia. Environ Monit Assess 193:784. https://doi.org/10.1007/s10661-021-09574-1
Chang KB, Lai SH, Faridah O (2013) RainIDF: automated derivation of rainfall intensity–duration–frequency relationship from annual maxima and partial duration series. J Hydroinformatics 15:1224–1233. https://doi.org/10.2166/hydro.2013.192
Chen C (1983) Rainfall intensity-duration-frequency formulas. J Hydraul Eng 109:1603–1621. https://doi.org/10.1061/(asce)0733-9429(1983)109:12(1603)
Citakoglu H (2021) Comparison of multiple learning artificial intelligence models for estimation of long-term monthly temperatures in Turkey. Arab J Geosci 14:2131. https://doi.org/10.1007/s12517-021-08484-3
Citakoglu H, Babayigit B, Haktanir NA (2020) Solar radiation prediction using multi-gene genetic programming approach. Theor Appl Climatol. https://doi.org/10.1007/s00704-020-03356-4
Cook LM, McGinnis S, Samaras C (2020) The effect of modeling choices on updating intensity-duration-frequency curves and stormwater infrastructure designs for climate change. Clim Change 159:289–308. https://doi.org/10.1007/s10584-019-02649-6
Dastagir MR (2015) Modeling recent climate change induced extreme events in Bangladesh: a review. Weather Clim Extrem 7:49–60. https://doi.org/10.1016/j.wace.2014.10.003
Deb P, Babel MS, Denis AF (2018) Multi-GCMs approach for assessing climate change impact on water resources in Thailand. Model Earth Syst Environ 4:825–839. https://doi.org/10.1007/s40808-018-0428-y
Demir V (2022) Enhancing monthly lake levels forecasting using heuristic regression techniques with periodicity data component: application of Lake Michigan. Theor Appl Climatol 148:915–929. https://doi.org/10.1007/s00704-022-03982-0
Egodawatta P, Thomas E, Goonetilleke A (2007) Mathematical interpretation of pollutant wash-off from urban road surfaces using simulated rainfall. Water Res 41:3025–3031. https://doi.org/10.1016/j.watres.2007.03.037
Elbaz K, Shen SL, Zhou A et al (2019) Optimization of EPB shield performance with adaptive neuro-fuzzy inference system and genetic algorithm. Appl Sci. https://doi.org/10.3390/app9040780
Elbaz K, Shen SL, Sun WJ et al (2020) Prediction model of shield performance during tunneling via incorporating improved particle swarm optimization into ANFIS. IEEE Access 8:39659–39671. https://doi.org/10.1109/ACCESS.2020.2974058
Elsebaie IH (2012) Developing rainfall intensity–duration–frequency relationship for two regions in Saudi Arabia. J King Saud Univ - Eng Sci 24:131–140. https://doi.org/10.1016/j.jksues.2011.06.001
Elsebaie IH, El Alfy M, Kawara AQ (2021) Spatiotemporal variability of intensity–duration–frequency (idf) curves in arid areas: wadi al-lith, Saudi Arabia as a case study. Hydrology 9:6. https://doi.org/10.3390/hydrology9010006
Eman Ahmed Hassan El-Sayed (2011) Generation of rainfall intensity duration frequency curves for ungauged sites. Nile Basin Water Sci Eng J 4:112–124
Eray O, Mert C, Kisi O (2018) Comparison of multi-gene genetic programming and dynamic evolving neural-fuzzy inference system in modeling pan evaporation. Hydrol Res 49:1221–1233. https://doi.org/10.2166/nh.2017.076
Ewea HA, Elfeki AM, Al-Amri NS (2017) Development of intensity–duration–frequency curves for the Kingdom of Saudi Arabia. Geomat Nat Hazards Risk 8:570–584. https://doi.org/10.1080/19475705.2016.1250113
Fadhel S, Rico-Ramirez MA, Han D (2017) Uncertainty of intensity–duration–frequency (IDF) curves due to varied climate baseline periods. J Hydrol 547:600–612. https://doi.org/10.1016/j.jhydrol.2017.02.013
Froehlich DC (1995) Long-duration–rainfall intensity equations. J Irrig Drain Eng 121:248–252. https://doi.org/10.1061/(asce)0733-9437(1995)121:3(248)
Galiatsatou P, Iliadis C (2022) Intensity-duration-frequency curves at ungauged sites in a changing climate for sustainable stormwater networks. Sustainability 14:1229. https://doi.org/10.3390/su14031229
Gandomi AH, Alavi AH (2012) A new multi-gene genetic programming approach to non-linear system modeling. Part II: geotechnical and earthquake engineering problems. Neural Comput Appl 21:189–201. https://doi.org/10.1007/s00521-011-0735-y
García-Bartual R, Schneider M (2001) Estimating maximum expected short-duration rainfall intensities from extreme convective storms. Phys Chem Earth, Part B Hydrol Ocean Atmos 26:675–681. https://doi.org/10.1016/S1464-1909(01)00068-5
Gebru TA (2020) Rainfall intensity-duration-frequency relations under changing climate for selected stations in the tigray region. Ethiopia J Hydrol Eng 25:05020041. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001999
Gen M, Cheng R (1997) Genetic algorithms and engineering design. John Wiley, Hoboken
Gen M, Cheng R, Lin L (2008) Network models and optimization: multiobjective genetic algorithm approach, 1st edn. Springer Publishing Company, Incorporated
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning, 1st edn. Addison-Wesley Longman Publishing Co., Inc, USA
Goldberg DE, Deb K (1991) A Comparative analysis of selection schemes used in genetic algorithms. In Found Genet Algorithms 1:69–93
Görkemli B, Citakoglu H, Haktanir T, Karaboga D (2022) A new method based on artificial bee colony programming for the regional standardized intensity–duration-frequency relationship. Arab J Geosci. https://doi.org/10.1007/s12517-021-09377-1
Haktanir T, Citakoglu H, Seckin N (2016) Regional frequency analyses of successive-duration annual maximum rainfalls by L-moments method. Hydrol Sci J 61:647–668. https://doi.org/10.1080/02626667.2014.966722
Hamaamin YAH (2016) Developing of rainfall intensity-duration-frequency model for Sulaimani city. J Zankoy Sulaimani - Part A 19:93–102. https://doi.org/10.17656/jzs.10634
Hasan I, Saeed Y (2020) Analysis of rainfall data for a number of stations in northern Iraq. Al-Rafidain Eng J (AREJ) 25(2):105–117. https://doi.org/10.33899/rengj.2020.127531.1044
Hay JE, Easterling D, Ebi KL et al (2016) Conclusion to the special issue: observed and projected changes in weather and climate extremes. Weather Clim Extrem 11:103–105. https://doi.org/10.1016/j.wace.2015.11.002
Hayder AM, Al-Mukhtar M (2021) Modelling the IDF curves using the temporal stochastic disaggregation BLRP model for precipitation data in Najaf City. Arab J Geosci 14:1957. https://doi.org/10.1007/s12517-021-08314-6
Hershfield DM (1963) Estimating the probable maximum precipitation. Trans Am Soc Civ Eng 128:534–551. https://doi.org/10.1061/taceat.0008684
Karahan H, Ayvaz MT, Gürarslan G (2008) Determination of intensity-duration-frequency relationship by genetic algorithm: case study of GAP. Tek Dergi/technical J Turkish Chamb Civ Eng 19:4393–4407
Karahan H, Ceylan H, Tamer Ayvaz M (2007) Predicting rainfall intensity using a genetic algorithm approach. Hydrol Process 21:470–475. https://doi.org/10.1002/hyp.6245
Kareem DA, Rahman A, Amen M et al (2022) Comparative analysis of developed rainfall intensity-duration-frequency curves for Erbil with other Iraqi Urban Areas. Water 14:1–17. https://doi.org/10.3390/w14030419
Kennedy J, Eberhart R (2010) Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks. IEEE, pp 1942–1948
Jaleel LA, Farawn MA (2013) Developing rainfall intensity-duration frequency relationship for Basrah city. Kufa J Eng 5:105–112
Legouhy A (2021) Al_goodplot - boxblot & violin plot. In: MATLAB Cent. Mathworks. https://www.mathworks.com/matlabcentral/fileexchange/91790-al_goodplot-boxblot-violin-plot
Lestari S, King A, Vincent C et al (2019) Seasonal dependence of rainfall extremes in and around Jakarta. Indones Weather Clim Extrem 24:100202. https://doi.org/10.1016/j.wace.2019.100202
Liew S, Raghavan SV, Liong S-Y (2014) Development of intensity-duration-frequency curves at ungauged sites: risk management under changing climate. Geosci Lett 1:8. https://doi.org/10.1186/2196-4092-1-8
Lopcu Y (2007) Modeling the intensity−duration−frequency relationships of annual maximum storms. Dokuz Eylul University
Mahdi ES, Mohamedmeki MZ (2020) Analysis of rainfall intensity-duration-frequency (IDF) curves of Baghdad city. IOP Conf Ser Mater Sci Eng 888:012066. https://doi.org/10.1088/1757-899X/888/1/012066
Matlab (2022a) Particleswarm. In: Introd. R2014b. https://www.mathworks.com/help/gads/particleswarm.html
Matlab (2022b) Genetic Algorithm. https://www.mathworks.com/help/gads/genetic-algorithm.html
Matlab (2022c) Matlab. In: MATLAB Cent. Mathworks. https://www.mathworks.com/help/stats/kruskalwallis.html
MGM (2022) Annual areal precipitation in Turkey. In: Turkish state Meteorol. Serv. https://mgm.gov.tr/veridegerlendirme/yillik-toplam-yagis-verileri.aspx
Mirhosseini G, Srivastava P, Stefanova L (2013) The impact of climate change on rainfall intensity–duration–frequency (IDF) curves in Alabama. Reg Environ Chang 13:25–33. https://doi.org/10.1007/s10113-012-0375-5
Moujahid M, Stour L, Agoumi A, Saidi A (2018) Regional approach for the analysis of annual maximum daily precipitation in northern Morocco. Weather Clim Extrem 21:43–51. https://doi.org/10.1016/j.wace.2018.05.005
Ouali D, Cannon AJ (2018) Estimation of rainfall intensity–duration–frequency curves at ungauged locations using quantile regression methods. Stoch Environ Res Risk Assess 32:2821–2836. https://doi.org/10.1007/s00477-018-1564-7
Shaban WM, Elbaz K, Yang J, Shen SL (2021) A multi-objective optimization algorithm for forecasting the compressive strength of RAC with pozzolanic materials. J Clean Prod 327:129355. https://doi.org/10.1016/j.jclepro.2021.129355
Searson DP, Leahy DE, Willis MJ (2010) GPTIPS: an open source genetic programming toolbox for multigene symbolic regression. In: In Proceedings of the International multiconference of engineers and computer scientists Citeseer. pp 77–80
Searson DP (2009) GPTIPS: Genetic programming and symbolic regression for MATLAB
Şen O, Kahya E (2021) Impacts of climate change on intensity–duration–frequency curves in the rainiest city (Rize) of Turkey. Theor Appl Climatol 144:1017–1030. https://doi.org/10.1007/s00704-021-03592-2
Şen Z (2019) Annual daily maximum rainfall-based IDF Curve derivation methodology. Earth Syst Environ 3:463–469. https://doi.org/10.1007/s41748-019-00124-x
Shahid S, Wang X-J, Bin HS et al (2016) Climate variability and changes in the major cities of Bangladesh: observations, possible impacts and adaptation. Reg Environ Chang 16:459–471. https://doi.org/10.1007/s10113-015-0757-6
Sillmann J, Thorarinsdottir T, Keenlyside N et al (2017) Understanding, modeling and predicting weather and climate extremes: challenges and opportunities. Weather Clim Extrem 18:65–74. https://doi.org/10.1016/j.wace.2017.10.003
Stephenson AG, Lehmann EA, Phatak A (2016) A max-stable process model for rainfall extremes at different accumulation durations. Weather Clim Extrem 13:44–53. https://doi.org/10.1016/j.wace.2016.07.002
Subyani AM, Al-Amri NS (2015) IDF curves and daily rainfall generation for Al-Madinah city, western Saudi Arabia. Arab J Geosci 8:11107–11119. https://doi.org/10.1007/s12517-015-1999-9
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192. https://doi.org/10.1029/2000JD900719
Tyralis H, Langousis A (2019) Estimation of intensity–duration–frequency curves using max-stable processes. Stoch Environ Res Risk Assess 33:239–252. https://doi.org/10.1007/s00477-018-1577-2
Uncuoğlu E, Latifoğlu L, Özer AT (2021) Modelling of lateral effective stress using the particle swarm optimization with machine learning models. Arab J Geosci 14:2441. https://doi.org/10.1007/s12517-021-08686-9
VOSviewer welcome to VOSviewer. In: 2022 Cent Sci Technol Stud Leiden Univ Netherlands. https://www.vosviewer.com/
Voyant C, Notton G, Kalogirou S et al (2017) Machine learning methods for solar radiation forecasting: a review. Renew Energy 105:569–582. https://doi.org/10.1016/j.renene.2016.12.095
Yavuz K (2018) Determination of the appropriate probability distribution function and formula of the relationship between the period of intensity-rainfall duration-return period for standard rainfall in Turkey. Erciyes University
Yilmaz AG, Hossain I, Perera BJC (2014) Effect of climate change and variability on extreme rainfall intensity–frequency–duration relationships: a case study of Melbourne. Hydrol Earth Syst Sci 18:4065–4076. https://doi.org/10.5194/hess-18-4065-2014
Yu PS, Yang TC, Lin CS (2004) Regional rainfall intensity formulas based on scaling property of rainfall. J Hydrol 295:108–123. https://doi.org/10.1016/j.jhydrol.2004.03.003
Zahiri E-P, Bamba I, Famien AM et al (2016) Mesoscale extreme rainfall events in West Africa: the cases of Niamey (Niger) and the Upper Ouémé Valley (Benin). Weather Clim Extrem 13:15–34. https://doi.org/10.1016/j.wace.2016.05.001
Zeder J, Fischer EM (2020) Observed extreme precipitation trends and scaling in Central Europe. Weather Clim Extrem 29:100266. https://doi.org/10.1016/j.wace.2020.100266
Acknowledgements
The data used in this study were obtained from the master’s thesis titled “Determination of the Appropriate Probability Distribution Function and Formula of the Relationship Between the Period of Intensity-Rainfall Duration-Return Period for Standard Rainfall in Turkey” written by Kemal Yavuz. The authors thank Kemal Yavuz for providing data.
Funding
No funding or support was received for research from any funding institutions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare no conflicts of interest.
Ethical approval
In the study, the scientists paid close attention to ethical guidelines. There was no ethical infraction.
Consent for publication
This manuscript can be published in the Acta Geophysica.
Additional information
Edited by Dr. Ankit Garg (ASSOCIATE EDITOR) / Dr. Michael Nones (CO-EDITOR-IN-CHIEF).
Rights and permissions
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.
About this article
Cite this article
Citakoglu, H., Demir, V. Developing numerical equality to regional intensity–duration–frequency curves using evolutionary algorithms and multi-gene genetic programming. Acta Geophys. 71, 469–488 (2023). https://doi.org/10.1007/s11600-022-00883-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11600-022-00883-8