Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Kim, Tae-Woong

Kim, Ungtae

Kwon, Hyun-Han

Yoo, Ji-Young

English

Hydraulic Engineering Repository

Conference Paper, Published VersionYoo, Ji-Young; Kim, Tae-Woong; Kwon, Hyun-Han; Kim, UngtaeApplication of Copula-Based Markov Model to GenerateMonthly PrecipitationZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/109801Vorgeschlagene Zitierweise/Suggested citation:Yoo, Ji-Young; Kim, Tae-Woong; Kwon, Hyun-Han; Kim, Ungtae (2012): Application ofCopula-Based Markov Model to Generate Monthly Precipitation. In: Hagen, S.; Chopra, M.;Madani, K.; Medeiros, S.; Wang, D. (Hg.): ICHE 2012. Proceedings of the 10th InternationalConference on Hydroscience & Engineering, November 4-8, 2012, Orlando, USA.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.The 10th Int.  Conf. on Hydroscience and Engineering (ICHE-2012), Nov. 4 – Nov. 7, Orlando, USA 176      APPLICATION OF COPULA-BASED MARKOV MODEL TO GENERATE MONTHLY PRECIPITATION  Ji-Young Yoo1, Tae-Woong Kim2, Hyun-Han Kwon3, and Ungtae Kim4   In this study, a framework for stochastic simulation of monthly precipitation is presented. The framework incorporates the concept of Markov process and the copula function to preserve the first order persistence considering the dependent relationship of two successive monthly precipitations. Copula functions have the advantage of easily connecting individual marginal probability distribution functions. Typically, copula functions are more appropriate to generate random variate simultaneously due to their simplicity of determining the dependency structure between two or more variables. In this study, the proposed Copula-based Markov model is applied to several rainfall gauging stations in South Korea and their performance is evaluated using various performance measures. As a result, generated monthly rainfalls can represent more efficiently variability of precipitation.  Figure 1 compares the probability density functions of generated monthly precipitation with those of observed monthly precipitation. Table 1 also provides the brief summary of statistical properties of generated precipitations as well as observed precipitations.  Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec Figure 1 Comparison of the PDFs observed and generated precipitation.                                                   1 Doctoral Research Assistant, Department of Civil and Environmental Engineering, Hanyang University, Seoul, 133-791, Korea (email: 7924pooh@hanyang.ac.kr) 2 Corresponding Author, Associate Professor, Department of Civil and Environmental Engineering, Hanyang University, Ansan, 426-791, Korea (email: twkim72@hanyang.ac.kr) 3 Assistant Professor, Department of Civil Engineering, Chonbuk National University, Jeonju, 561-756, Korea (email: hkwon@jbnu.ac.kr) 4 Research Assistant Professor, Department of Civil and Environmental Engineering, The University of Tennessee, Knoxville, TN, 37996, USA (email: ukim2@utk.edu) The 10th Int.  Conf. on Hydroscience and Engineering (ICHE-2012), Nov. 4 – Nov. 7, Orlando, USA 177  Table 1 Basic statistics of observed and generated precipitation.   Month Mean Std Skew Max 25%tile 50%tile 75%tile Serial CC Observed precipitation 1 20.8 16.3 1.21 62.6 10.4 16.5 28.0 0.12 2 25. 22.3 1.33 108.1 6.4 20.5 36.2 -0.03 3 45.2 28.3 0.74 123.5 25.3 41.5 60.6 -0.14 4 84.3 67.8 1.60 338.8 41.8 62.4 103.0 0.26 5 100.7 60.5 1.02 291.3 59.6 85.5 126.6 0.01 6 133.5 99.4 1.72 497.2 68.1 111.4 165.0 0.19 7 383.4 187.0 1.21 1014.0 242.2 348.9 487.8 -0.26 8 336.1 227.8 1.75 1237.8 193.3 271.7 418.8 0.13 9 167.3 143.3 1.53 671.5 61.1 127.6 236.4 -0.02 10 49.9 41.8 2.06 214.5 25.6 39.7 66.9 0.17 11 49.5 34.9 1.43 164.8 26.4 41.1 66.6 0.22 12 21.4 14.7 1.21 71.4 11.1 16.7 27.8 -0.26 Generated precipitation 1 20.9 15.2 0.51 88.1 8.4 19.8 31.4 0.02 2 39.7 95.6 11.11 1775.1 5.7 25.0 43.2 -0.03 3 50.6 47.7 3.15 513.9 23.5 43.9 68.1 -0.20 4 87.5 61.8 0.44 282.6 39.4 83.2 129.0 0.21 5 101.2 67.7 0.63 416.5 53.0 98.5 145.6 -0.01 6 150.6 128.4 2.22 1443.9 61.1 135.0 215.5 0.22 7 393.4 187.1 0.11 1081.8 256.2 391.1 528.7 -0.25 8 341.4 211.0 0.24 1046.3 184.3 338.9 485.8 0.14 9 170.0 127.7 0.51 605.7 69.6 156.7 255.8 0.00 10 58.3 49.6 1.28 388.9 17.7 51.4 88.8 0.19 11 51.3 32.7 0.25 155.1 26.9 50.9 74.9 0.09 12 26.2 31.1 7.86 585.9 10.4 22.0 33.8 -0.27  

Application of Copula-Based Markov Model to Generate Monthly Precipitation

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Application of Copula-Based Markov Model to Generate Monthly Precipitation

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