The adequacy of stochastically generated climate time series for water resources systems risk and performance assessment

  • Abdullah AlodahEmail author
  • Ousmane Seidou
Original Paper


Stochastic weather generators are designed to produce synthetic sequences that are commonly used for risk discovery, as they would contain rare events that can lead to potentially catastrophic impacts on the environment, or even human lives. These time series are sometimes used as inputs to rainfall-runoff models to simulate the hydrological impacts of these rare events. This paper puts forward a method that evaluates the usefulness of weather generators by assessing how the statistical properties of simulated precipitation, temperatures, and streamflow deviate from those of observations. This is achieved by plotting a large ensemble of (1) synthetic precipitation and temperature time series in a Climate Statistics Space, and (2) hydrological indices using simulated streamflow data in a Risk and Performance Indicators Space. Assessment of weather generator’s performance is based on visual inspection and the Mahalanobis distance between statistics derived from observations and simulations. A case study was carried out on the South Nations watershed in Ontario, Canada, using five different weather generators: two versions of a single-site Weather Generator, two versions of a multi-site Weather Generator (MulGETS) and the K-Nearest Neighbour weather generator (k-nn). Results show that the MulGETS model often outperformed the other weather generators for that particular study area because: (a) the observations were well centered within a point cloud of the synthetically-generated time series in both spaces, and (b) the points generated using MulGETS had a smaller Mahalanobis distance to the observations than those generated with the other weather generators. The \(k\)-nn weather generator performed particularly well in simulating temperature variables, but was poor at modelling precipitation and streamflow statistics.


Weather generator assessment Stochastic hydrological modelling Risk and performance indicators 


  1. Abbaspour KC, Vejdani M, Haghighat S, Yang J (2007) SWAT-CUP calibration and uncertainty programs for SWAT. In: MODSIM 2007 international congress on modelling and simulation, modelling and simulation society of Australia and New Zealand, pp 1596–1602Google Scholar
  2. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables, vol 9. Chicago, DoverGoogle Scholar
  3. Ailliot P, Allard D, Monbet V, Naveau P (2015) Stochastic weather generators: an overview of weather type models. Journal de la Société Française de Statistique 156(1):101–113Google Scholar
  4. Arnold JG, Srinivasan R, Muttiah RS, Williams JR (1998) Large area hydrologic modeling and assessment part I: model development 1. J Am Water Resour Assoc 34(1):73–89CrossRefGoogle Scholar
  5. Arnold JG, Kiniry JR, Sirinivasan R, Williams JR, Haney EB, Neitsh SL (2012) SWAT input–output documentation, version 2012. Texas Water Resource Institute. TR-439Google Scholar
  6. Arnold JG, Moriasi DN, Gassman PW, Abbaspour KC, White MJ, Srinivasan R, Santhi C, Harmel R, Van Griensven A, Van Liew MW et al (2012b) SWAT: model use, calibration, and validation. Trans ASABE 55:1491–1508CrossRefGoogle Scholar
  7. Baigorria GA, Jones JW (2010) GiST: a stochastic model for generating spatially and temporally correlated daily rainfall data. J Clim 23(22):5990–6008CrossRefGoogle Scholar
  8. Bastola S, Murphy C, Fealy R (2012) Generating probabilistic estimates of hydrological response for Irish catchments using a weather generator and probabilistic climate change scenarios. Hydrol Process 26(15):2307–2321CrossRefGoogle Scholar
  9. Benestad RE, Nychka D, Mearns LO (2012) Specification of wet-day daily rainfall quantiles from the mean value. Tellus A: Dyn Meteorol Oceanogr 64(1):14981CrossRefGoogle Scholar
  10. Brissette FP, Khalili M, Leconte R (2007) Efficient stochastic generation of multi-site synthetic precipitation data. J Hydrol 345(3–4):121–133CrossRefGoogle Scholar
  11. Brocca L, Liersch S, Melone F, Moramarco T, Volk M (2013) Application of a model-based rainfall-runoff database as efficient tool for flood risk management. Hydrol Earth Syst Sci 17(8):3159CrossRefGoogle Scholar
  12. Brown C, Ghile Y, Laverty M, Li K (2012) Decision scaling: linking bottom up vulnerability analysis with climate projections in the water sector. Water Resour Res 48(9):9537CrossRefGoogle Scholar
  13. Camera C, Bruggeman A, Hadjinicolaou P, Michaelides S, Lange MA (2016) Evaluation of a spatial rainfall generator for generating high resolution precipitation projections over orographically complex terrain. Stoch Environ Res Risk Assess 31:757CrossRefGoogle Scholar
  14. Chen J, Brissette F (2014) Comparison of five stochastic weather generators in simulating daily precipitation and temperature for the Loess Plateau of China. Int J Climatol 34(10):3089–3105CrossRefGoogle Scholar
  15. Chen J, Brissette FP, Leconte R, Caron A (2012) A versatile weather generator for daily precipitation and temperature. Trans ASABE 55(3):895–906CrossRefGoogle Scholar
  16. Chen JF, Brissette X, Zhang J (2014) A multi-site stochastic weather generator for daily precipitation and temperature. Trans ASABE 2014:1375–1391. Google Scholar
  17. Cunnane C (1989) Statistical distributions for flood frequency analysis. Operational hydrology report (WMO)Google Scholar
  18. Environment Canada (2012) National climate data and information archive: climate normals from 1971–2000 environment CanadaGoogle Scholar
  19. Forsythe N, Fowler HJ, Blenkinsop S, Burton A, Kilsby CG, Archer DR, Harpham C, Hashmi MZ (2014) Application of a stochastic weather generator to assess climate change impacts in a semi-arid climate: the Upper Indus Basin. J Hydrol 517:1019–1034CrossRefGoogle Scholar
  20. Fowler HJ, Blenkinsop S, Tebaldi C (2007) Linking climate change modelling to impacts studies: recent advances in downscaling techniques for hydrological modelling. Int J Climatol 27:1547–1578CrossRefGoogle Scholar
  21. Frich P, Alexander LV, Della-Marta PM, Gleason B, Haylock M, Tank AK, Peterson T (2002) Observed coherent changes in climatic extremes during the second half of the twentieth century. Clim Res 19(3):193–212CrossRefGoogle Scholar
  22. Fritsch V, Varoquaux G, Thyreau B, Poline J, Thirion B (2012) DETECTING outliers in high-dimensional neuroimaging datasets with robust covariance estimators. Med Image Anal 16:1359–1370CrossRefGoogle Scholar
  23. Govindaraju RS, Kavvas ML (1991) Stochastic overland flows. Stoch Hydrol Hydraul 5(2):105–124CrossRefGoogle Scholar
  24. Goyal MK, Burn DH, Ojha CSP (2013) Precipitation simulation based on k-nearest neighbor approach using gamma kernel. J Hydrol Eng 18:481–487CrossRefGoogle Scholar
  25. Guo T, Mehan S, Gitau MW, Wang Q, Kuczek T, Flanagan DC (2017) Impact of number of realizations on the suitability of simulated weather data for hydrologic and environmental applications. Stoch Environ Res Risk Assess. Google Scholar
  26. Gupta H, Sorooshian S, Yapo P (1999) Status of automatic calibration for hydrologic models: comparison with multilevel expert calibration. J Hydrol Eng 4(2):135–143CrossRefGoogle Scholar
  27. Hansen JW, Ines AV (2005) Stochastic disaggregation of monthly rainfall data for crop simulation studies. Agric For Meteorol 131:233–246CrossRefGoogle Scholar
  28. Hardin J, Rocke DM (2005) The distribution of robust distances. J Comput Graph Stat 14:928–946CrossRefGoogle Scholar
  29. 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 25:475–484CrossRefGoogle Scholar
  30. Helsel DR, Hirsch RM (1992) Statistical methods in water resources, studies in environmental science, vol 49. Elsevier, AmsterdamGoogle Scholar
  31. Huber PJ, Ronchetti EM (2009) Robust tests, in robust statistics, 2nd edn. Wiley, Hoboken, NJ. CrossRefGoogle Scholar
  32. Iman RL, Conover WJ (1982) A distribution-free approach to inducing rank correlation among input variables. Commun Stat Simul Comput 11(3):311–334CrossRefGoogle Scholar
  33. Kavvas ML, Herd KR (1985) A radar-based stochastic model for short-time-increment rainfall. Water Resour Res 21(9):1437–1455CrossRefGoogle Scholar
  34. Kim BS, Kim HS, Seoh BH, Kim NW (2007) Impact of climate change on water resources in Yongdam Dam Basin, Korea. Stoch Environ Res Risk Assess 21:355CrossRefGoogle Scholar
  35. Kim D, Olivera F, Cho H (2013) Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 1. Impact on peak and extreme rainfall values. Stoch Env Res Risk Assess 27(7):1601–1610CrossRefGoogle Scholar
  36. Kim D, Cho H, Onof C, Choi M (2017) Let-It-Rain: a web application for stochastic point rainfall generation at ungaged basins and its applicability in runoff and flood modeling. Stoch Env Res Risk Assess 31(4):1023–1043CrossRefGoogle Scholar
  37. Klein Tank AMG, Zwiers FW, Zhang X (2009) Guidelines on Analysis of extremes in a changing climate in support of informed decisions for adaptation. World Meteorological Organization. 72 and WMO Tech. Doc. 1500Google Scholar
  38. Kovalchuk SV, Krikunov AV, Knyazkov KV, Boukhanovsky AV (2017) Classification issues within ensemble-based simulation: application to surge floods forecasting. Stoch Env Res Risk Assess 31(5):1183–1197CrossRefGoogle Scholar
  39. Lennartsson J, Baxevani A, Chen D (2008) Modelling precipitation in Sweden using multiple step Markov chains and a composite model. J Hydrol 363(1):42–59CrossRefGoogle Scholar
  40. Liew MW, Veith TL, Bosch DD, Arnold JG (2007) Suitability of SWAT for the conservation effects assessment project: a comparison on USDA-ARS experimental watersheds. J Hydrol Eng 12(2):173–189CrossRefGoogle Scholar
  41. Loucks D, Stedinger J, Haith D (1981) Water resource systems planning and analysis. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  42. Mahalanobis PC (1936) On the generalised distance in statistics. Proc Natl Inst Sci India 12(1936):49–55Google Scholar
  43. Markov AA (1906) Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga. Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete 15(135–156):18Google Scholar
  44. Mehrotra R, Srikanthan R, Sharma A (2006) A comparison of three stochastic multi-site precipitation occurrence generators. J Hydrol 331(1–2):280–292CrossRefGoogle Scholar
  45. Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900CrossRefGoogle Scholar
  46. Nash JE, Sutcliffe WH (1970) River flow forecasting through conceptual models: part 1. A discussion of principles. J Hydrol 10(3):282–290CrossRefGoogle Scholar
  47. Neitsch SL, Arnold JG, Kiniry JR, Williams JR (2011) Soil and water assessment tool theoretical documentation version 2009. Texas Water Resources InstituteGoogle Scholar
  48. Palutikof JP, Goodess CM, Watkins SJ, Holt T (2002) Generating rainfall and temperature scenarios at multiple sites: examples from the Mediterranean. J Clim 15(24):3529–3548CrossRefGoogle Scholar
  49. Pilon PJ (1990) The Weibull distribution applied to regional low flow frequency analysis. Water resources branch, inland waters directorate, environment, CanadaGoogle Scholar
  50. Polade SD, Pierce DW, Cayan DR, Gershunov A, Dettinger MD (2014) The key role of dry days in changing regional climate and precipitation regimes. Sci Rep 4:4364CrossRefGoogle Scholar
  51. Rajagopalan B, Lall U, Tarboton DG, Bowles DS (1997) Multivariate nonparametric resampling scheme for generation of daily weather variables. Stoch Hydrol Hydraul 11(1):65–93CrossRefGoogle Scholar
  52. Ramesh NI, Garthwaite AP, Onof C (2018) A doubly stochastic rainfall model with exponentially decaying pulses. Stoch Environ Res Risk Assess 32:1645CrossRefGoogle Scholar
  53. Richardson CW (1981) Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 17(1):182–190CrossRefGoogle Scholar
  54. Richardson CW, Wright DA (1984) WGEN: a model for generating daily weather variables. US Department of Agriculture, Agricultural Research Service, ARS-8Google Scholar
  55. Salas JD, Lee TS (2010) Nonparametric simulation of single-site seasonal streamflows. J Hydrol Eng 15(4):284–296CrossRefGoogle Scholar
  56. Santhi C, Arnold J, Williams J, Dugas W, Srinivasan R, Hauck L (2001) Validation of the SWAT model on a large river basin with point and nonpoint sources 1. J Am Water Resour Assoc 37(5):1169–1188CrossRefGoogle Scholar
  57. Semenov MA, Barrow EM (2002) LARS-WG, a stochastic weather generator for use in climate impact studies, user manual.
  58. Shao Q, Zhang L, Wang QJ (2016) A hybrid stochastic-weather-generation method for temporal disaggregation of precipitation with consideration of seasonality and within-month variations. Stoch Environ Res Risk Assess 30(6):1705–1724CrossRefGoogle Scholar
  59. Sharif M, Burn DH (2007) Improved K-nearest neighbor weather generating model. J Hydrol Eng 12(1):42–51CrossRefGoogle Scholar
  60. Singh J, Knapp HV, Arnold JG, Demissie M (2005) Hydrological modeling of the Iroquois River watershed using HSPF and SWAT. JAWRA J Am Water Resour Assoc 41(2):343–360CrossRefGoogle Scholar
  61. Srinivasan R, Arnold JG (1994) Integration of a basin-scale water quality model with GIS. Water Resour Bull 30(3):453–462CrossRefGoogle Scholar
  62. Sun Y, Solomon S, Dai A, Portmann RW (2006) How often does it rain? J Clim 19(6):916–934CrossRefGoogle Scholar
  63. Sveinsson OGB, Salas JD, Lane WL, Frevert DK (2007) Stochastic Analysis, Modeling, and Simulation (SAMS) version 2007 user’s manual. Technical report no. 11. Computing Hydrology Laboratory, Department of Civil and Environmental Engineering. Colorado State University, Fort Collins, COGoogle Scholar
  64. Tuppad P, Douglas-Mankin KR, Lee T, Srinivasan R, Arnold JG (2011) Soil and Water Assessment Tool (SWAT) hydrologic/water quality model: extended capability and wider adoption. Trans ASABE 54(5):1677–1684CrossRefGoogle Scholar
  65. Wang MY, Zwilling CE (2015) Multivariate computing and robust estimating for outlier and novelty in data and imaging sciences. In: Advances in bioengineering. InTechGoogle Scholar
  66. Warner T (2010) Climate modeling and downscaling. In: Warner T (ed) Numerical weather and climate prediction. Cambridge University Press, Cambridge, pp 407–455. CrossRefGoogle Scholar
  67. White KL, Chaubey I (2005) Sensitivity analysis, calibration, and validations for a multisite and multivariable SWAT model. J Am Water Resour Assoc 41(5):1077–1089CrossRefGoogle Scholar
  68. Wilby RL, Fowler HJ (2011) Regional climate downscaling: modelling the impact of climate change on water resources. In: Fai Fung C, Lopez A, New M (eds) Modelling the impact of climate change on water resources. Wiley, Hoboken. ISBN 978-1-405-19671-0Google Scholar
  69. Wilby RW, Tomlinson OJ, Dawson CW (2003) Multisite simulation of precipitation by conditional resampling. Clim Res 23(3):183–194CrossRefGoogle Scholar
  70. Wilks DS (1998) Multi-site generalization of a daily stochastic precipitation model. J Hydrol 210:178–191CrossRefGoogle Scholar
  71. 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(7):1199CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringQassim UniversityBuraidahSaudi Arabia
  2. 2.Department of Civil EngineeringUniversity of OttawaOttawaCanada

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