Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Impact of number of realizations on the suitability of simulated weather data for hydrologic and environmental applications


Stochastic weather generators are widely used in hydrological, environmental, and agricultural applications to simulate weather time series. However, such stochastic models produce random outputs hence the question on how representative the generated data are if obtained from only one simulation run (realization) as is common practice. In this study, the impact of different numbers of realizations (1, 25, 50, and 100) on the suitability of generated weather data was investigated. Specifically, 50 years of daily precipitation, and maximum and minimum temperatures were generated for three weather stations in the Western Lake Erie Basin (WLEB), using three widely used weather generators, CLIGEN, LARSWG and WeaGETS. Generated results were compared with 50 years of observed data. For all three generators, the analyses showed that one realization of data for 50 years of daily precipitation, and maximum and minimum temperatures may not be representative enough to capture essential statistical characteristics of the climate. Results from the three generators captured the essential statistical characteristics of the climate when the number of realizations was increased from 1 to 25, 50 or 100. Performance did not improve substantially when realizations were increased above 25. Results suggest the need for more than a single realization when generating weather data and subsequently utilizing in other models, to obtain suitable representations of climate.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. Bai A, Zhai P, Liu X (2007) Climatology and trends of wet spells in China. Theoret Appl Climatol 88:139–148

  2. Banerjee A, Dolado JJ, Galbraith JW, Hendry D (1993) Co-integration, error correction, and the econometric analysis of non-stationary data. Advanced texts in econometrics. Oxford University Press, Oxford

  3. Bradley JV (1980) Nonrobustness in Z, t, and F tests at large sample sizes. Bull Psychon Soc 16:333–336

  4. Bright J, Smith C, Taylor P, Crook R (2015) Stochastic generation of synthetic minutely irradiance time series derived from mean hourly weather observation data. Sol Energy 115:229–242

  5. Caron A, Leconte R, Brissette F (2008) An improved stochastic weather generator for hydrological impact studies. Can Water Resour J 33:233–256

  6. Chaubey I, Chiang L, Gitau MW, Mohamed S (2010) Effectiveness of best management practices in improving water quality in a pasture-dominated watershed. J Soil Water Conserv 65:424–437

  7. Chen J, Brissette FP (2014a) Comparison of five stochastic weather generators in simulating daily precipitation and temperature for the Loess Plateau of China. Int J Climatol 34:3089–3105

  8. Chen J, Brissette FP (2014b) Stochastic generation of daily precipitation amounts: review and evaluation of different models. Clim Res 59:189–206

  9. Chen J, Brissette FP, Leconte R (2010) A daily stochastic weather generator for preserving low-frequency of climate variability. J Hydrol 388:480–490

  10. Chen J, Brissette F, Leconte R (2011) Assessment and improvement of stochastic weather generators in simulating maximum and minimum temperatures. Trans ASABE 54:1627–1637

  11. Chen J, Brissette F, Leconte R, Caron A (2012a) A versatile weather generator for daily precipitation and temperature. Trans ASABE 55:895–906

  12. Chen J, Brissette FP, Leconte R (2012b) Downscaling of weather generator parameters to quantify hydrological impacts of climate change. Clim Res 51:185–200

  13. Chen J, Brissette FP, Zhang XJ (2014) A multi-site stochastic weather generator for daily precipitation and temperature. Trans ASABE 57:1375–1391

  14. Cheung Y-W, Lai KS (1995) Lag order and critical values of the augmented Dickey–Fuller test. J Bus Econ Stat 13:277–280

  15. Cohen J (1977) Statistical power analysis for the behavioural sciences, Rev edn. Academic. New York, NY, New York

  16. Cohen J (1992) Statistical power analysis. Curr Dir Psychol Sci 1:98–101

  17. Daly C, Gibson WP, Taylor GH, Doggett MK, Smith JI (2007) Observer bias in daily precipitation measurements at United States cooperative network stations. Bull Am Meteorol Soc 88:899–912

  18. Denis DJ (2003) Alternatives to null hypothesis significance testing. Theory Sci 4:21

  19. Dieterichs H (1956) Frequency of dry and wet spells in san salvador. Geofisica Pura e Applicata 33:267–272

  20. Douguedroit A (1987) The variations of dry spells in Marseilles from 1865 to 1984. J Climatol 7:541–551

  21. Eames M, Kershaw T, Coley D (2012) A comparison of future weather created from morphed observed weather and created by a weather generator. Build Environ 56:252–264

  22. Elliot W, Arnold C (2001) Validation of the weather generator CLIGEN with precipitation data from Uganda. Trans ASAE 44:53–58

  23. Figueiredo Filho DB, Paranhos R, Rocha ECd, Batista M, Silva Jr JAd, Santos MLWD, Marino JG (2013) When is statistical significance not significant? Braz Polit Sci Rev 7:31–55

  24. Fuller WA (2009) Introduction to statistical time series, vol 428. Wiley, Hoboken

  25. Furrer EM, Katz RW (2008) Improving the simulation of extreme precipitation events by stochastic weather generators. Water Resour Res 44:W12439.

  26. Gitau M (2016) Long-term seasonality of rainfall in the southwest Florida Gulf coastal zone. Clim Res 69:93–105

  27. Gitau MW, Mehan S, Guo T (2017) Weather generator utilization in climate impact studies: implications for water resources modeling. Eur Water. Accepted 05 Sept 2017

  28. Guo T, Engel BA, Shao G, Arnold JG, Srinivasan R, Kiniry JR (2015) Functional approach to simulating short-rotation woody crops in process-based models. Bio Energy Res 8:1598–1613

  29. Hansen JW, Ines AV (2005) Stochastic disaggregation of monthly rainfall data for crop simulation studies. Agric For Meteorol 131:233–246

  30. Hansen J, Jones J (2000) Scaling-up crop models for climate variability applications. Agric Syst 65:43–72

  31. Harmel R, Richardson C, King K (2000) Hydrologic response of a small watershed model to generated precipitation. Trans ASAE 43:1483

  32. Jolliffe IT, Stephenson DB (eds) (2012) Forecast verification: a practitioner’s guide in atmospheric science, 2nd edn. John Wiley & Sons Ltd, Chichester

  33. Kalnay E, Hunt B, Ott E, Szunyogh I (2006) Ensemble forecasting and data assimilation: two problems with the same solution. In: Palmer T, Hagedorn R (eds) Predictability of weather and climate. Cambridge University Press, Cambridge, pp 157–180.

  34. Kou X, Ge J, Wang Y, Zhang C (2007) Validation of the weather generator CLIGEN with daily precipitation data from the Loess Plateau, China. J Hydrol 347:347–357

  35. Koutsoyiannis D, Manetas A (1996) Simple disaggregation by accurate adjusting procedures. Water Resour Res 32:2105–2117

  36. Li C, Singh VP, Mishra AK (2012) Simulation of the entire range of daily precipitation using a hybrid probability distribution. Water Resour Res 48:W03521.

  37. Liew VK-S (2004) Which lag length selection criteria should we employ? Econ Bull 3:1–9

  38. Mehan S, Guo T, Gitau M, Flanagan DC (2017) Comparative study of different stochastic weather generators for long-term climate data simulation. Climate 5:26.

  39. Mithen S, Black E (2011) Water, life and civilisation: climate, environment and society in the Jordan Valley, vol Cambridge. University Press, Cambridge

  40. Moon SE, Ryoo SB, Kwon JG (1994) A Markov chain model for daily precipitation occurrence in South Korea. Int J Climatol 14:1009–1016

  41. NCDC (2017) NCDC.

  42. Neild RE, Newman JE (1987) Growing season characteristics and requirements in the Corn Belt. Iowa State University, Cooperative Extension Service, Ames

  43. Ng S, Perron P (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69:1519–1554

  44. Nicks AD, Gander GA (1994) CLIGEN: a weather generator for climate inputs to water resource and other models. In: Proceedings of the fifth international conference on computers in agriculture, pp 903–909

  45. Nicks AD, Lane LJ, Gander GA (1995) Chapter 2. Weather Generator. In USDA-Water Erosion Prediction Project: Hillslope Profile and Watershed Model Documentation; NSERL Report #10; USDA-ARS National Soil Erosion Research Laboratory: West Lafayette, IN, USA, 1995.

  46. Qian B, Hayhoe H, Gameda S (2005) Evaluation of the stochastic weather generators LARS-WG and AAFC-WG for climate change impact studies. Clim Res 29:3–21

  47. Racsko P, Szeidl L, Semenov M (1991) A serial approach to local stochastic weather models. Ecol Model 57:27–41

  48. Rajagopalan B, Lall U (1999) A k-nearest-neighbor simulator for daily precipitation and other weather variables. Water Resour Res 35:3089–3101

  49. Richardson CW (1981) Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 17:182–190

  50. Richardson CW, Wright DA (1984) WGEN: a model for generating daily weather variables. In. US Department of Agriculture, Agricultural Research Service Washington, DC

  51. Roldán J, Woolhiser DA (1982) Stochastic daily precipitation models: 1. A comparison of occurrence processes. Water Resour Res 18:1451–1459

  52. Royall RM (1986) The effect of sample size on the meaning of significance tests. Am Stat 40:313–315

  53. Said SE, Dickey DA (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71:599–607

  54. Schneider T (2001) Analysis of incomplete climate data: estimation of mean values and covariance matrices and imputation of missing values. J Clim 14:853–871

  55. Semenov MA (2008) Simulation of extreme weather events by a stochastic weather generator. Clim Res 35:203–212

  56. Semenov MA, Barrow EM (1997) Use of a stochastic weather generator in the development of climate change scenarios. Clim Change 35:397–414

  57. Semenov MA, Brooks RJ, Barrow EM, Richardson CW (1998) Comparison of the WGEN and LARS-WG stochastic weather generators for diverse climates. Clim Res 10:95–107

  58. Sharif M, Burn DH (2006) Simulating climate change scenarios using an improved K-nearest neighbor model. J Hydrol 325:179–196

  59. Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt K, Tignor M, Miller H (2007) Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, 2007. Cambridge University Press, Cambridge

  60. Soltani A, Hoogenboom G (2003) A statistical comparison of the stochastic weather generators WGEN and SIMMETEO. Clim Res 24:215–230

  61. Srikanthan R, McMahon T (2001) Stochastic generation of annual, monthly and daily climate data: a review. Hydrol Earth Syst Sci Dis 5:653–670

  62. 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 Env Res Risk Assess 19:403–416

  63. Wilks DS (1999) Interannual variability and extreme-value characteristics of several stochastic daily precipitation models. Agric For Meteorol 93:153–169

  64. Wilks D (2002) Realizations of daily weather in forecast seasonal climate. J Hydrometeorol 3:195–207

  65. Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr 23:329–357

  66. Zhang XC (2013) Verifying a temporal disaggregation method for generating daily precipitation of potentially non-stationary climate change for site-specific impact assessment. Int J Climatol 33:326–342

  67. Zhang X, Garbrecht JD (2003) Evaluation of CLIGEN precipitation parameters and their implication on WEPP runoff and erosion prediction. Trans ASAE 46:311

Download references


This study was made possible in part by funding from the Purdue Climate Change Research Center, Purdue University, West Lafayette, Indiana and funding provided by USDA National Institute of Food and Agriculture (Project No. IND010639R).

Author information

Correspondence to Margaret W. Gitau.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Figure S1: Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots; Figure S2: Number of wet spells obtained from the generated precipitation; Figure S3: Number of dry spells obtained from the generated precipitation; Figure S4: Number of days with no rainfall; Figure S5: 99th percentile of daily precipitation; Figure S6: Number of days with maximum temperature greater than 32 °C precipitation; Figure S7: Number of days with minimum temperature less than 0 °C; Figure S8: Cumulative probability plots for percent error between the statistical characteristics; Table S1: The probability of percent error between the statistical characteristics of the simulated and observed data between − 5 and 5% (DOCX 10718 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Guo, T., Mehan, S., Gitau, M.W. et al. Impact of number of realizations on the suitability of simulated weather data for hydrologic and environmental applications. Stoch Environ Res Risk Assess 32, 2405–2421 (2018).

Download citation


  • Stochastic weather generators
  • Simulation approaches
  • Climate realizations
  • Statistical properties
  • Statistical analysis