مدلسازی مشخصات رویدادهای بارش با استفاده از مفصل دی-واین

محورهای موضوعی : مدیریت آب در مزرعه با هدف بهبود شاخص های مدیریتی آبیاری

مریم شفائی ¹ (دانشگاه تبریز)
احمد فاخری فرد ² (دانشگاه تبریز، دانشکده مهندسی آب)
یعقوب دین پژوه ³ (دانشگاه تبریز، دانشکده مهندسی آب)
رسول میرعباسی ⁴ (گروه مهندسی آب، دانشگاه شهرکرد)

تاریخ دریافت : 1395/01/11 تاریخ پذیرش : 1395/04/13 تاریخ انتشار : 1395/11/01

کلید واژه: شبیه‌سازی, توزیع احتمالی, جفت-مفصل, ماکزیمم بارش, مفصل ارشمیدسی, عمق بارش,

چکیده مقاله :

بررسی ویژگی‌های بارش در شناخت و پیش‌بینی پدیده‌های حاصل از بارش مانند رواناب و سیلاب ضروری است، لذا در این مطالعه وابستگی میان ویژگی های مهم رویدادهای بارش (عمق بارش(R) ، ماکزیمم بارش (M)، مدت خشک (D) و مرطوب(L) ) با استفاده از ساختار دی-واین مدلسازی شد. ابتدا توزیع های احتمالی چند متغیره با توجه به جایگشت های مختلف متغیرهای شرطی ساخته شد و سپس خانواده های مفصل های ارشمیدسی و بیضوی جهت برازش بر جفت-مفصل های ساختارهای دی-واین مورد آزمون قرار گرفتند و مناسب ترین خانواده مفصل جهت برازش بر هر جفت-مفصل با توجه به معیارهای مختلف انتخاب گردیدند. در مرحله بعد با توجه به معیارهای اطلاعات آکائیکه (AIC) و بیزین(BIC) ساختار M-R-D-L (یعنی D با L، R با D و L، M با R، D و L شرطی شده‌اند) بعنوان بهترین ساختار شناخته شد. در نهایت با استفاده از ساختار منتخب دی- واین ویژگی های مهم رویداد بارش شبیه‌سازی شد و به منظور ارزیابی دقت شبیه‌سازی مدل پیشنهادی، آماره های مهم هر یک از متغیرهای شبیه‌سازی شده‌ی رویداد بارش با آماره های متغیرهای مشاهداتی مقایسه گردیدند. نتایج نشان دادند که اکثر آماره های شبیه‌سازی شده توسط مدل چهار بعدی دی-واین دارای تطابق خوبی با آماره های متغیرهای مشاهداتی می باشند.

چکیده انگلیسی:

Investigation of precipitation characteristics is necessitate in understanding and predicting phenomena of precipitation such as runoff and flood. Therefore in this study, dependence among the main characteristics of a rainfall event (i.e., rainfall depth R, maximum rainfall depth M, wet period L, and dry period D) were modeled using D-vine structure. Firstly, different multivariate probability distributions were built, making all the permutations of the conditioning variables and then Archimedean and Elliptic copulas were used for fitting each pair-copula. The best copula family was selected for fitting on each pair-copula according to different criteria. In the next stage, M-R-D-L structure, i.e., with D conditioned by L, R by D and L, and M by R, D, and L, was known as the most suitable structure considering to AIC and BIC criteria. Finally, rainfall event characteristics were simulated using the selected structure. In order to evaluation of simulation accuracy of proposed model, the main statistics of simulated variables were compared with those of observed variables. The results showed that the majority of simulated statistics have good accordance with observed statistics. 

منابع و مأخذ:

Aas, K., Czado, C., Frigessi., A. and Bakken, H. 2009. Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44 (2): 182–198.

Bedford, T. and Cooke, R. 2001. Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32 (1): 245–268.

Bedford, T. and Cooke, R. 2002. Vines – A new graphical model for dependent random variables, Annals of Statistics. 30 (4), 1031–1068.

Brechmann, E. C., Czado, C. and Aas, K. 2012. Truncated regular vines in high dimensions with applications to financial data. Canadian Journal of Statistics, 40 (1): 68-85.

De Michele, C., Salvadori, G., Canossi, M., Petaccia, A. and Rosso, R. 2005. Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydrologic Engineering, 10 (1): 50–57.

De Michele, C., Salvadori, G., Passoni, G., and Vezzoli, R. 2007. A multivariate model of sea storms using copulas. Coastal Engineering, 54 (10): 734–751.

Genest, C., Favre, A., Beliveau, J., and Jacques, C. 2007. Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resources Research.43 (9), W09401,doi:10.1029/2006WR00527.

Genest, C. and Rivest, L.-P. 1993. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88 (423): 1034–1043.

Gräler, B., van den Berg, M. J., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., and Verhoest, N. E. C. 2013. Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrology and Earth System Science, 17 (4): 1281–1296

Gyasi-Agyei, Y. and Melching, C. 2012. Modelling the dependence and internal structure of storm evens for continuous rainfall simulation. Journal of Hydrology, 464-465: 249–261.

Joe, H. 1996. Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In L. Rueschendorf, B. Schweizer, and M. D. Taylor (Eds.), Distributions with fixed marginal and related topics. Vol. 28, pp. 120-141. Hayward: Institute of Mathematical Statistics.

Kao S, and Govindaraju, R. 2008. Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resources Research 44, (2) W02415, doi:10.1029/2007WR006261.

Kao, SC. and Govindaraju, RS. 2010. A copula-based joint deficit index for droughts. Journal of Hydrology, 380(1–2):121–134.

Karmakar, S., and Simonovic, SP. 2009. Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions. Journal of Flood and Risk Management, 2(1):32–44.

Mirabbasi, R., Fakheri-Fard, A., and Dinpashoh, Y. 2012. Bivariate drought frequency analysis using the copula method. Theoretical and  Applied Climatology, 108 (1): 191–206.

Mirabbasi, R., Anagnostou, E.N., Fakheri-Fard, A., Dinpashoh, Y. and Eslamian, S. 2013. Analysis of meteorological drought in northwest Iran using the Joint Deficit Index. Journal of  Hydrology, 492: 35–48.

Nikololoupoulos, A., Joe, H. and Li, H. 2012. Vine copulas with asymmetric tail dependence and applications to financial return data. Computational Statistics and Data Analysis, 56 (11): 3659–3673.

Pham, M. T., Vernieuwe, H., De Baets, B., Willems, P. and. Verhoest, N.E.C.  2015. Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas. Stochastic Environmental and Reseaarch Risk Assessment, 1-18. DOI 10.1007/s00477-015-1181-7

Reddy, MJ. and Ganguli, P. 2012a. Application of copulas for derivation of drought severity–duration– frequency curves. Hydrological Processes, 26 (11): 1672–1685

Reddy, MJ., Ganguli, P. 2012b. Bivariate flood frequency analysis of upper Godavari River flows using Archimedean copulas. Water Resources Management, 26 (14): 3995–4018.

Salvadori, G. and De Michele, C. 2006. Statistical characterization of temporal structure of storms. Advances in Water Resources, 29 (6): 827–842.

Salvadori, G., De Michele, C., Kottegoda, N.T. and Rosso, R. 2007. Extremes in nature: an approach using copulas, Springer, Dordrecht.

Salvadori, G. and De Michele, C. 2015. Multivariate real-time assessment of droughts via copula-based multi-site Hazard Trajectories and Fans. Journal of Hydrology, 526: 101-115.

Serinaldi, F. and Grimaldi, S. 2007. Fully nested 3-copula: procedure and application on hydrological data. Journal of Hydrologic Engineering, 12 (4): 420–430.

Sklar, A. 1959. Fonction de repartition a n dimensions et leurs marges, vol. 8. Publications de L’Institute de Statistique, Universite’ de Paris: Paris, pp 229–231.

Singh, V. P. and Zhang, L. 2007. IDF curves using the Frank Archimedean copula. J Hydrol Eng, 12 (6): 651–662.

Song, S. and Singh, V. 2010. Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stochastic Environmental and Research Risk A, 24 (3): 425–444.

Sraj, M., Bezak, N. and Brilly, M. 2015. Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River. Hydrologic Processes, 29 (2): 225–238.

Vernieuwe, H., Vandenberghe, S., De Baets, B. and Verhoest NEC. 2015. A continuous rainfall model based on vine copulas. Hydrology and Earth System Science, 19(6):2685–2699

Xiong, L., Yu, K. and Gottschalk, L. 2014. Estimation of the distribution of annual runoff from climatic variables using copulas. Water Resources Research, 50 (9): 7134–7152.

Zhang, L., Singh, V. P. 2006. Bivariate flood frequency analysis using copula method. Journal of Hydrologic Engineering, 11 (2): 150–164.

Zhang, D. 2014. Vine copulas and applications to the European Union sovereign debt analysis, International Review of Financial Analysis, 36: 46–56.