Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Stochastic simulation of daily precipitation: A copula approach

  • Choi, Changhui (Korea Insurance Research Institute) ;
  • Ko, Bangwon (Department of Statistics and Actuarial Science, Soongsil University)
  • Received : 2013.12.02
  • Accepted : 2014.04.12
  • Published : 2014.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

The traditional methods of simulating daily precipitation have paid little attention to the inherent dependence structure between the total precipitation amount and the precipitation frequency for a fixed period of time. To address this issue, we propose a new simulation algorithm using copula in order to incorporate the dependence into the traditional methods. The algorithm consists of two parts: First, while reflecting the observed dependence, we generate the total precipitation amount (S) and the frequency (N) during the period of interest; then we simulate the daily precipitation whose aggregation matches the pair of (N; S) generated in the first part. Our result shows that the proposed method substantially improves the traditional methods.

Keywords

References

  1. Cherubini, U., Luciano, E. and Vecchiato, W. (2004). Copula methods in finance, John Wiley & Sons, New Jersey.
  2. Chin, E. H. (1977). Modeling daily precipitation occurrence process with Markov chain. Water Resources Research, 13, 949-956. https://doi.org/10.1029/WR013i006p00949
  3. Choi. C, Lee, H. and Joo, H. (2013), Analyzing rainfall patterns and pricing rainfall insurance using copula. Journal of the Korean Data & Information Science Society, 24, 1598-9402. https://doi.org/10.7465/jkdi.2013.24.3.603
  4. Duan, J., Selker, J. and Gordon, E. G. (1998). Evaluation of probability density function in precipitation models for the Pacic Northwest. Journal of the American Water Resources Association, 24, 617-627.
  5. Favre, A.-C., El Adouni, S., Perreault, L., Thiemonge, N. and Bobee, B. (2004). Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40 .
  6. Genest, C. and Favre, A.-C. (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12, 347-368. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347)
  7. Hayhoe, H. N. (2000). Improvements of stochastic weather data generators for diverse climates. Climate Research, 14, 75-87. https://doi.org/10.3354/cr014075
  8. Hogg, R. V. and Craig, A. T. (1978). Introduction to mathematical statistics, 4th Edition, Macmillan, New York.
  9. Joe, H. (1997) Multivariate models and dependence concepts, Chapman and Hall, New York.
  10. Katz, R. W. and Parlange, M. B. (1998) Over dispersion phenomenon in stochastic modeling of precipitation. Journal of Climate, 11, 591-601. https://doi.org/10.1175/1520-0442(1998)011<0591:OPISMO>2.0.CO;2
  11. Kim, E. and Lee, T. (2011). A numerical study on portfolio VaR forecasting based on conditional copula, Journal of the Korean Data & Information Science Society, 22, 1065-1074.
  12. Kittel, T. G. F., Rosenbloom, N. A., Painter, T. H., Schimel, D. S. and VEMAP Modeling Participants. (1995). The VEMAP integrated database for modeling United States ecosystem/vegetation sensitivity to climate change. Journal of Biogeography, 22, 857-862. https://doi.org/10.2307/2845986
  13. Leobacher, G. and Ngare, P. (2011). On modeling and pricing rainfall derivatives with seasonality. Applied Mathematical Finance, 18, 71-91. https://doi.org/10.1080/13504861003795167
  14. Malevergne, Y. and Sornette, D. (2006). Extreme financial risks: From dependence to risk management, Springer, New York.
  15. Nelsen, R. B. (2006). An introduction to copulas, Springer, New York.
  16. Nicks, A. D. and Gander, G. A. (1994). CLIGEN: A weather generator for climate inputs to water resource and other models. In Proceedings Fifth International Conference on Computers in Agriculture, American Society of Agricultural Engineers, Orlando, FL, 903-909.
  17. Pickering, N. B., Stedinger, J. R. and Haith, D. A. (1988). Weather input for nonpoint-source pollution models. Journal of Irrigation and Drainage Engineering, 114, 674-690. https://doi.org/10.1061/(ASCE)0733-9437(1988)114:4(674)
  18. Richardson C. W. (1981). Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research, 17, 182-190. https://doi.org/10.1029/WR017i001p00182
  19. Richardson, C. W. and Wright, D. A. (1984). WGEN: A model for generating daily weather variables. Agricultural Research Service, ARS-8, 83, Washington DC, USA.
  20. Ross, S. M. (2007). Introduction to probability models, 9th Edition, Academic Press, New York.
  21. Sharpley, A. N. and Williams, J. R. (1990a). Erosion/productivity impact calculator 1. Model documentation , Technical Bulletin 1768, U. S. Department of Agriculture, Washington DC, USA.
  22. Sharpley, A. N. and Williams, J. R. (1990b). Erosion/productivity impact calculator 2. User manual, Technical Bulletin 1768, U.S. Department of Agriculture, Washington DC, USA.
  23. Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Paris Institute of Statistics, 8, 229-231.
  24. Stern, R. D. (1980). The calculation of probability distributions for models of daily precipitation. Archiv fur Meteorologie, Geophysik und Bioklimatologie B, 28, 137-137. https://doi.org/10.1007/BF02243841
  25. Stern, R. D. and Coe, R. (1984). A model fitting analysis of daily rainfall data. Journals of the Royal Statistical Society A, 147, 1-34. https://doi.org/10.2307/2981736
  26. Wan, H., Zhang, X. and Barrow, E. M. (2005). Stochastic modeling of daily precipitation for Canada. Atmosphere-Ocean, 43, 23-32. https://doi.org/10.3137/ao.430102
  27. Wilks, D. S. (1998). Multisite generalization of a daily stochastic precipitation generation model. Journal of Hydrology, 210, 178-191. https://doi.org/10.1016/S0022-1694(98)00186-3
  28. Zhang, L. and Singh, V. P. (2007). Bivariate rainfall frequency distributions using Archimedean copulas. Journal of Hydrology, 332, 93-109. https://doi.org/10.1016/j.jhydrol.2006.06.033

Cited by

  1. Performance comparison of random number generators based on Adaptive Rejection Sampling vol.26, pp.3, 2015, https://doi.org/10.7465/jkdi.2015.26.3.593
  2. Improving a stochastic multi-site generation model of daily rainfall using discrete wavelet de-noising: a case study to a semi-arid region vol.12, pp.2, 2019, https://doi.org/10.1007/s12517-018-4168-0