Application and Evaluation of the Ability of Copulas in Estimating Daily Precipitation in the East of Lake Urmia Basin

فصلنامه آب و توسعه پایدار

Article 5, Volume 9, Issue 4 - Serial Number 26, March 2023, Pages 37-46   

Document Type: Applied Article

DOI: 10.22067/jwsd.v9i4.2206.1156

Authors

Mohammad Khaledi-Alamdari¹; Abolfazl Majnooni-Heris^{* 2}; ahmad Fakheri-Fard³

¹Ph.D. Student in Irrigation and Drainage, Department of Water Science and Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

²Associate Professor, Department of Water Science and Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

³Professor, Department of Water Science and Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

Abstract

The use of accurate and continuous data series is a necessary condition for most statistical and hydrological studies. Due to the importance of precipitation as one of the most important climatic and hydrological variables, in the present study, in order to predict the daily precipitation of Tabriz, Copula functions were used and the results were compared with intelligent methods and classical statistics. To predict precipitation in Tabriz station, precipitation data of Sarab, Sahand, and Maragheh stations were also used as auxiliary stations. Based on the obtained results, among all the methods studied, the M5 method with RMSE values of 3.14 mm, and the MAD method with 2.13 mm and the RF method with RMSE values of 5.18 mm and MAD 3.04 mm have the highest and lowest accuracy in estimating precipitation events, respectively. Among Archimedean copulas, the RMSE and MAD values for the Gambel function are 3.89 and 2.51 mm, respectively. Despite the range of estimation data is still very close to other methods, considering the capabilities of Copula functions, including the ability to apply multiple conditions and its probabilistic nature, which considers the behavior of the phenomenon, it can be acknowledged that in similar circumstances, the ability of Copula functions to estimate the missing data of phenomena such as rainfall is acceptable.

Keywords

Probabilistic Analysis; Missing Data; Forecasting; Archimedean Copulas

References

منهاج، م‌.ب. 1384. مبانی شبکه‌های عصبی (هوش محاسباتی) جلد اول. مرکز نشر دانشگاه صنعتی امیرکبیر. چاپ سوم. تهران، ایران.
Abebe A.J., Solomatine D.P. and Venneker R.G. 2000. Application of adaptive fuzzy rule-based models for reconstruction of missing precipitation events. Hydrological Sciences Journal, 45(3): 425-36.
Armanuos A.M., Al-Ansari N. and Yaseen Z.M. 2020. Cross assessment of twenty-one different methods for missing precipitation data estimation. Atmosphere, 11(4): 389.
Bessa R.J., Miranda V., Botterud A., Zhou Z. and Wang J. 2012. Time-adaptive quantile-copula for wind power probabilistic forecasting. Renewable Energy, 1;40(1): 29-39.
Boser B.E., Guyon I.M. and Vapnik V.N. 1992. A training algorithm for optimal margin classifiers. InProceedings of the fifth annual workshop on Computational learning theory. Pennsylvania, Pittsburgh, USA.
Breiman L. 2001. Random forests. Machine learning, 45(1): 5-32.
Genest C. and Rivest L.P. 1993. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American statistical Association, 88(423): 1034-43.
Hassani B.K. 2016. Dependencies and relationships between variables. Scenario Analysis in Risk Management. Springer International  Publishing Switzerland.
Huang J.J., Lee K.J., Liang H. and Lin W.F. 2009. Estimating value at risk of portfolio by conditional copula-GARCH method. Insurance: Mathematics and economics, 45(3): 315-24.
Jarvis C., Darbyshire R., Eckard R., Goodwin I. and Barlow E. 2018. Influence of El Niño-Southern oscillation and the Indian Ocean Dipole on winegrape maturity in Australia. Agricultural and Forest Meteorology, 248: 502-10.
Kao S.C. and Govindaraju R.S. 2010. A copula-based joint deficit index for droughts. Journal of Hydrology, 380(1-2): 121-34.
Kotsiantis S. and Pintelas P. 2004. Combining bagging and boosting. International Journal of Computational Intelligence, 1(4): 324-33.
Kuan C.M. and White H. 1994. Artificial neural networks: An econometric perspective. Econometric reviews, 13(1): 1-91.
Kuss M. 2006. Gaussian process models for robust regression, classification, and reinforcement learning. Ph. D. dissertation, Technische Universität Darmstadt, Darmstadt, Germany.
Liu Z., Zhou P., Chen X. and Guan Y. 2015. A multivariate conditional model for streamflow prediction and spatial precipitation refinement. Journal of Geophysical Research: Atmospheres, 120(19): 10-16.
Lu X.F., Lai K.K. and Liang L. 2014. Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model. Annals of operations research, 219(1): 333-57.
Manning C., Widmann M., Bevacqua E., Van Loon A.F., Maraun D. and Vrac M. 2018. Soil moisture drought in Europe: a compound event of precipitation and potential evapotranspiration on multiple time scales. Journal of Hydrometeorology, 19(8): 1255-71.
Nguyen-Huy T., Deo R.C., An-Vo D.A., Mushtaq S. and Khan S. 2017. Copula-statistical precipitation forecasting model in Australia’s agro-ecological zones. Agricultural water management, 191: 153-72.
Nguyen-Huy T., Deo R.C., Mushtaq S., An-Vo D.A. and Khan S. 2018. Modeling the joint influence of multiple synoptic-scale, climate mode indices on Australian wheat yield using a vine copula-based approach. European journal of agronomy, 98: 65-81.
Paulhus J.L. and Kohler M.A. 1952 Interpolation of missing precipitation records. Monthly Weather Review, 80(8): 129-33.
Srinivas S., Menon D. and Meher Prasad A. 2006. Multivariate simulation and multimodal dependence modeling of vehicle axle weights with copulas. Journal of transportation engineering, 132(12): 945-55.
Talebizadeh M., Morid S., Ayyoubzadeh S.A. and Ghasemzadeh M. 2010. Uncertainty analysis in sediment load modeling using ANN and SWAT model. Water Resources Management, 24(9): 1747-61.
Teegavarapu R.S. and Chandramouli V. 2005. Improved weighting methods, deterministic and stochastic data-driven models for estimation of missing precipitation records. Journal of hydrology, 312(1-4): 191-206.
Vapnik V.N. 1998. Statistical learning theory. Wiley, New York.
Vapnik V. 1995. The nature of statistical learning theory. Springer, New York.
Young K.C. 1992. A three-way model for interpolating for monthly precipitation values. Monthly Weather Review, 120(11): 2561-9.
Yuan C. and Yamagata T. 2015. Impacts of IOD, ENSO and ENSO Modoki on the Australian winter wheat yields in recent decades. Scientific reports, 5(1): 1-8.
Zhang L. and Singh V.P. 2014. Trivariate flood frequency analysis using discharge time series with possible different lengths: Cuyahoga river case study. Journal of Hydrologic Engineering, 19(10): 05014012.
Zscheischler J. and Seneviratne S.I. 2017. Dependence of drivers affects risks associated with compound events. Science advances, 3(6): e1700263.