Multisite stochastic simulation of daily precipitation from copula modeling with a gamma marginal distribution

Original Paper


Multisite stochastic simulations of daily precipitation have been widely employed in hydrologic analyses for climate change assessment and agricultural model inputs. Recently, a copula model with a gamma marginal distribution has become one of the common approaches for simulating precipitation at multiple sites. Here, we tested the correlation structure of the copula modeling. The results indicate that there is a significant underestimation of the correlation in the simulated data compared to the observed data. Therefore, we proposed an indirect method for estimating the cross-correlations when simulating precipitation at multiple stations. We used the full relationship between the correlation of the observed data and the normally transformed data. Although this indirect method offers certain improvements in preserving the cross-correlations between sites in the original domain, the method was not reliable in application. Therefore, we further improved a simulation-based method (SBM) that was developed to model the multisite precipitation occurrence. The SBM preserved well the cross-correlations of the original domain. The SBM method provides around 0.2 better cross-correlation than the direct method and around 0.1 degree better than the indirect method. The three models were applied to the stations in the Nakdong River basin, and the SBM was the best alternative for reproducing the historical cross-correlation. The direct method significantly underestimates the correlations among the observed data, and the indirect method appeared to be unreliable.


  1. Burton A, Fowler HJ, Kilsby CG, O'Connell PE (2010) A stochastic model for the spatial-temporal simulation of nonhomogeneous rainfall occurrence and amounts. Water Resour Res 46Google Scholar
  2. Cannon AJ (2008) Probabilistic multisite precipitation downscaling by an expanded Bernoulli-gamma density network. J Hydrometeorol 9:1284–1300CrossRefGoogle Scholar
  3. Charles SP, Bates BC, Hughes JP (1999) A spatiotemporal model for downscaling precipitation occurrence and amounts. J Geophy Res D: Atmos 104:31657–31669CrossRefGoogle Scholar
  4. Favre AC, El Adlouni S, Perreault L, Thiemonge N, Bobee B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40Google Scholar
  5. Frost AJ, Charles SP, Timbal B, Chiew FHS, Mehrotra R, Nguyen KC, Chandler RE, McGregor JL, Fu G, Kirono DGC, Fernandez E, Kent DM (2011) A comparison of multi-site daily rainfall downscaling techniques under Australian conditions. J Hydrol 408:1–18CrossRefGoogle Scholar
  6. Gabriel KR, Neumann J (1962) A Markov chain model for daily rainfall occurrence at Tel Aviv. Q J R Meteorol Soc 88:90–95CrossRefGoogle Scholar
  7. Jeong DI, St-Hilaire A, Ouarda TBMJ, Gachon P (2013) A multi-site statistical downscaling model for daily precipitation using global scale GCM precipitation outputs. Int J Climatol 33:2431–2447CrossRefGoogle Scholar
  8. Johnson, R.A., Wichern, D.W. (2001). Applied multivariate statistical analysis, Prentice Hall.Google Scholar
  9. Lee T (2012) Serial dependence properties in multivariate streamflow simulation with independent decomposition analysis. Hydrol Process 26:961–972CrossRefGoogle Scholar
  10. Lee T, Modarres R, Ouarda TBMJ (2013) Data-based analysis of bivariate copula tail dependence for drought duration and severity. Hydrol Process 27:1454–1463CrossRefGoogle Scholar
  11. Lee T, Salas JD (2011) Copula-based stochastic simulation of hydrological data applied to Nile River flows. Hydrol Res 42:318–330CrossRefGoogle Scholar
  12. Lee T, Salas JD, Prairie J (2010) An enhanced nonparametric streamflow disaggregation model with genetic algorithm. Water Resour Res 46:W08545Google Scholar
  13. Lu Y, Qin XS (2014) Multisite rainfall downscaling and disaggregation in a tropical urban area. J Hydrol 509:55–65CrossRefGoogle Scholar
  14. Mehrotra R, Evans JP, Sharma A, Sivakumar B (2014) Evaluation of downscaled daily rainfall hindcasts over Sydney, Australia using statistical and dynamical downscaling approaches. Hydrol Res 45:226–249CrossRefGoogle Scholar
  15. Mehrotra R, Sharma A, Kumar DN, Reshmidevi TV (2013) Assessing future rainfall projections using multiple GCMS and a multi-site stochastic downscaling model. J Hydrol 488:84–100CrossRefGoogle Scholar
  16. Nelsen RB (1999) An introduction to copulas. Springer-Verlag, New YorkCrossRefGoogle Scholar
  17. Prairie J, Nowak K, Rajagopalan B, Lall U, Fulp T (2008) A stochastic nonparametric approach for streamflow generation combining observational and paleoreconstructed data Water Resources Research:44Google Scholar
  18. Robertson AW, Kirshner S, Smyth P (2004) Downscaling of daily rainfall occurrence over Northeast Brazil using a hidden Markov model. J Clim 17:4407–4424CrossRefGoogle Scholar
  19. Roldan J, Woolhiser DA (1982) Stochastic daily precipitation models: 1. A comparison of occurrence processes. Water Resour Res 18:1451–1459CrossRefGoogle Scholar
  20. Sklar, M. (1959). Fonctions de r’epartition `a n dimensions et leurs marges. 8, 229–231.Google Scholar
  21. Srikanthan R, McMahon TA (2001) Stochastic generation of annual, monthly and daily climate data: a review. Hydrol Earth Syst Sci 5:653–670CrossRefGoogle Scholar
  22. Vandenberghe, S., Verhoest, N.E.C., De Baets, B. (2010). Fitting bivariate copulas to the dependence structure between storm characteristics: a detailed analysis based on 105 year 10 min rainfall. Water resources Research, 46, −.Google Scholar
  23. Westra S, Brown C, Lall U, Sharma A (2007) Modeling multivariable hydrological series: principal component analysis or independent component analysis? Water Resour Res 43Google Scholar
  24. Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210:178–191CrossRefGoogle Scholar
  25. Wilks DS (2006) Statistical methods in the Athmospheric sciences. Academic Press, BurlingtonGoogle Scholar
  26. Wilks DS (2009) A gridded multisite weather generator and synchronization to observed weather data. Water Resour Res 45:W10419CrossRefGoogle Scholar
  27. Williams IN, Riley WJ, Torn MS, Biraud SC, Fischer ML (2014) Biases in regional carbon budgets from covariation of surface fluxes and weather in transport model inversions. Atmos Chem Phys 14:1571–1585CrossRefGoogle Scholar
  28. Wilson LL, Lettenmaier DP, Skyllingstad E (1992) A hierarchical stochastic model of large-scale atmospheric circulation patterns and multiple station daily precipitation. J Geophys Res 97:2791–2809CrossRefGoogle Scholar
  29. Yang C, Chandler RE, Isham VS, Wheater HS (2005) Spatial-temporal rainfall simulation using generalized linear models. Water Resour Res 41:1–13Google Scholar
  30. Zheng X, Katz RW (2008) Simulation of spatial dependence in daily rainfall using multisite generators. Water Resour Res 44Google Scholar
  31. Zheng X, Thompson CS (2011) Simulation of spatial dependence in daily precipitation using a mixture of generalized chain-dependent processes at multisites. J Hydrometeorol 12:286–293CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.Department of Civil Engineering, ERIGyeongsang National UniversityJinjuSouth Korea

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