Coupled stochastic weather generation using spatial and generalized linear models

  • Andrew Verdin
  • Balaji Rajagopalan
  • William Kleiber
  • Richard W. Katz
Original Paper


We introduce a stochastic weather generator for the variables of minimum temperature, maximum temperature and precipitation occurrence. Temperature variables are modeled in vector autoregressive framework, conditional on precipitation occurrence. Precipitation occurrence arises via a probit model, and both temperature and occurrence are spatially correlated using spatial Gaussian processes. Additionally, local climate is included by spatially varying model coefficients, allowing spatially evolving relationships between variables. The method is illustrated on a network of stations in the Pampas region of Argentina where nonstationary relationships and historical spatial correlation challenge existing approaches.


Spatial correlation Pampas Precipitation Temperature Weather simulation 



Research partially supported by NSF EaSM grant 1049109. Thanks to Guillermo Podesta for providing daily weather data for Argentine Pampas.


  1. Apipattanavis S, Podestá G, Rajagopalan B, Katz RW (2007) A semiparametric multivariate and multisite weather generator. Water Resour Res 43:1–19. doi: 10.1029/2006WR005714
  2. Baigorria GA, Jones JW (2010) GiST: a stochastic model for generating spatially and temporally correlated daily rainfall data. J Clim 23(22):5990–6008Google Scholar
  3. Beersma JJ, Buishand TA (2003) Multi-site simulation of daily precipitation and temperature conditional on the atmospheric circulation. Clim Res 25(2):121–133CrossRefGoogle Scholar
  4. Brissette FP, Khalili M, Leconte R (2007) Efficient stochastic generation of multi-site synthetic precipitation data. J Hydrol 345:121–133CrossRefGoogle Scholar
  5. Buishand T (1978) Some remarks on the use of daily rainfall models. J Hydrol 36(3):295–308CrossRefGoogle Scholar
  6. Buishand TA, Brandsma T (2001) Multisite simulation of daily precipitation and temperature in the Rhine basin by nearest-neighbor resampling. Water Resour Res 37(11):2761–2776CrossRefGoogle Scholar
  7. Calanca P, Semenov MA (2013) Local-scale climate scenarios for impact studies and risk assessments: integration of early 21st century ENSEMBLES projections into the ELPIS database. Theor Appl Climatol 113:445–455CrossRefGoogle Scholar
  8. Caraway NM, McCreight JL, Rajagopalan B (2014) Multisite stochastic weather generation using cluster analysis and k-nearest neighbor time series resampling. J Hydrol 508:197–213CrossRefGoogle Scholar
  9. Chandler RE (2005) On the use of generalized linear models for interpreting climate variability. Environmetrics 16:699–715CrossRefGoogle Scholar
  10. Chilès JP, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New YorkCrossRefGoogle Scholar
  11. Fassò A, Finazzi F (2011) Maximum likelihood estimation of the dynamic coregionalization model with heterotopic data. Environmetrics 22(6):735–748CrossRefGoogle Scholar
  12. Foufoula-Georgiou E, Georgakakos KP (1991) Hydrologic advances in space-time precipitation modeling and forecasting. In: Bowles DS, O’Connell (eds) Recent advances in the modeling of hydrologic systems. Springer, Netherlands, pp 47–65Google Scholar
  13. Friend AD, Stevens AK, Knox RG, Cannell MGR (1997) A process-based terrestrial biosphere model of ecosystem dynamics. Ecol Model 95:249–287CrossRefGoogle Scholar
  14. Furrer EM, Katz RW (2007) Generalized linear modeling approach to stochastic weather generators. Clim Res 34:129–144CrossRefGoogle Scholar
  15. Furrer EM, Katz RW (2008) Improving the simulation of extreme precipitation events by stochastic weather generators. Water Resour Res 44:1–13. doi: 10.1029/2008WR007316
  16. Harrold TI, Sharma A, Sheather SJ (2003) A nonparametric model for stochastic generation of daily rainfall amounts. Water Resour Res 39(12):1–11Google Scholar
  17. Hashmi MZ, Shamseldin AY, Melville BW (2011) Comparison of SDSM and LARS-WG for simulation and downscaling of extreme precipitation events in a watershed. Stoch Environ Res Risk Assess 25(4):475–484CrossRefGoogle Scholar
  18. Hauser T, Demirov E (2013) Development of a stochastic weather generator for the sub-polar North Atlantic. Stoch Environ Res Risk Assess 27(7):1533–1551CrossRefGoogle Scholar
  19. Katz RW (1977) Precipitation as a chain-dependent process. J Appl Meteorol 16:671–676CrossRefGoogle Scholar
  20. Khalili M, Brissette F, Leconte R (2009) Stochastic multi-site generation of daily weather data. Stoch Environ Res Risk Assess 23(6):837–849CrossRefGoogle Scholar
  21. Kim T-W, Ahn H, Chung G, Yoo C (2008) Stochastic multi-site generation of daily rainfall occurrence in south Florida. Stoch Environ Res Risk Assess 22(6):705–717CrossRefGoogle Scholar
  22. Kleiber W, Katz RW, Rajagopalan B (2012) Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes. Water Resour Res 48:1–17. doi: 10.1029/2011WR011105
  23. Kleiber W, Katz RW, Rajagopalan B (2013) Daily minimum and maximum temperature simulation over complex terrain. Ann Appl Stat 7:588–612CrossRefGoogle Scholar
  24. Lall U, Sharma A (1996) A nearest neighbor bootstrap for resampling hydrological time series. Water Resour Res 32:679–693CrossRefGoogle Scholar
  25. Lennartsson J, Baxevani A, Chen D (2008) Modelling precipitation in Sweden using multiple step Markov chains and a composite model. J Hydrol 363(1–4):42–59. URL
  26. Lima CHR, Lall U (2009) Hierarchical Bayesian modeling of multisite daily rainfall occurrence: rainy season onset, peak and end. Water Resour Res 45:1–14. doi: 10.1029/2008WR007485
  27. McCullagh P, Nelder JA (1989) Generalized linear models. Chapman and Hall, LondonCrossRefGoogle Scholar
  28. Mehrotra R, Sharma A (2007) A semi-parametric model for stochastic generation of multi-site daily rainfall exhibiting low-frequency variability. J Hydrol 335:180–193CrossRefGoogle Scholar
  29. Mehrotra R, Srikanthan R, Sharma A (2006) A comparison of three stochastic multi-site precipitation occurrence generators. J Hydrol 331:280–292CrossRefGoogle Scholar
  30. Qian B, Corte-Real J, Xu H (2002) Multisite stochastic weather models for impact studies. Int J Climatol 2002:1377–1397CrossRefGoogle Scholar
  31. Racsko P, Szeidl L, Semenov M (1991) A serial approach to local stochastic weather models. Ecol Model 57:27–41CrossRefGoogle Scholar
  32. Rajagopalan B, Lall U (1999) A k-nearest neighbor simulator for daily precipitation and other weather variables. Water Res Res 35(10):3089–3101CrossRefGoogle Scholar
  33. Rajagopalan B, Lall U, Tarboton DG (1997a) Evaluation of kernel density estimation methods for daily precipitation resampling. Stoch Hydrol Hydraul 11(6):523–547CrossRefGoogle Scholar
  34. Rajagopalan B, Lall U, Tarboton DG, Bowles DS (1997b) Multivariate nonparametric resampling scheme for generation of daily weather variables. Stoch Hydrol Hydraul 11:523–547CrossRefGoogle Scholar
  35. Richardson CW (1981) Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 17(1):182–190CrossRefGoogle Scholar
  36. Richardson CW, Wright DA (1984) WGEN: a model for generating daily weather variables. ARS (USA) 1–83Google Scholar
  37. Semenov MA (2008) Simulation of extreme weather events by a stochastic weather generator. Clim Res 35:203–212CrossRefGoogle Scholar
  38. Semenov MA, Barrow EM (1997) Use of a stochastic weather generator in the development of climate change scenarios. Clim Change 35:397–414CrossRefGoogle Scholar
  39. Semenov P-BS, Pilkington-Bennett S, Calanca P (2013) Validation of ELPIS 1980–2010 baseline scenarios using the European Climate Assessment observed dataset. Clim Res 51:1–9CrossRefGoogle Scholar
  40. Sharif M, Burn DH (2007) Improved k-nearest neighbor weather generating model. J Hydrol Eng 12(1):42–51CrossRefGoogle Scholar
  41. Srikanthan R, Pegram GGS (2009) A nested multisite daily rainfall stochastic generation model. J Hydrol 371:142–153CrossRefGoogle Scholar
  42. Stern RD, Coe R (1984) A model fitting analysis of daily rainfall data. J R Stat Soc Ser A Gen 147:1–34CrossRefGoogle Scholar
  43. Wallis TW, Griffiths JF (1997) Simulated meteorological input for agricultural models. Agric Forest Meteorol 88:241–258CrossRefGoogle Scholar
  44. Wheater H, Chandler R, Onof C, Isham V, Bellone E, Yang C, Lekkas D, Lourmas G, Segond M-L (2005) Spatial-temporal rainfall modelling for flood risk estimation. Stoch Environ Res Risk Assess 19(6):403–416CrossRefGoogle Scholar
  45. Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210:178–191CrossRefGoogle Scholar
  46. Wilks DS (1999) Simultaneous stochastic simulation of daily precipitation, temperature and solar radiation at multiple sites in complex terrain. Agric Forest Meteorol 96:85–101CrossRefGoogle Scholar
  47. Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr 23:329–357CrossRefGoogle Scholar
  48. Woolhiser DA (1992) Modeling daily precipitation: progress and problems. Stat Environ Earth Sci 5:71–89Google Scholar
  49. Yang C, Chandler RE, Isham VS, Wheater HS (2005) Spatial-temporal rainfall simulation using generalized linear models. Water Resour Res 41:1–13. doi: 10.1029/2004WR003739
  50. Yates D, Gangopadhyay S, Rajagopalan B, Strzepek K (2003) A technique for generating regional climate scenarios using a nearest-neighbor algorithm. Water Resour Res 39:1199CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrew Verdin
    • 1
  • Balaji Rajagopalan
    • 1
  • William Kleiber
    • 2
  • Richard W. Katz
    • 3
  1. 1.Department of Civil, Environmental and Architectural EngineeringUniversity of ColoradoBoulderUSA
  2. 2.Department of Applied MathematicsUniversity of ColoradoBoulderUSA
  3. 3.Institute for Mathematics Applied to GeosciencesNational Center for Atmospheric ResearchBoulderUSA

Personalised recommendations