Advertisement

Rainfall Generators for Application in Flood Studies

  • Uwe Haberlandt
  • Yeshewatesfa Hundecha
  • Markus Pahlow
  • Andreas H. Schumann
Chapter

Abstract

This chapter discusses various approaches for stochastic rainfall synthesis focusing on methods for generation of short time step precipitation as required for flood studies. A brief introduction motivates the utilisation of rainfall generators for flood modelling. Then special characteristics of rainfall as stochastic process are discussed. The rainfall models presented in the following are classified in alternating renewal models, time series models, point process models, disaggregation and resampling approaches. They are usually applied for continuous unconditional simulation of rainfall series in time and/or in space. Two case studies at the end of the chapter illustrate the application of daily and hourly space-time precipitation models for flood studies.

Keywords

Daily Precipitation Time Series Model Generalize Extreme Value ARMA Model Generalise Pareto Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Acreman MC (1990) Simple stochastic model of hourly rainfall for Farnborough, England. Hydrol Sci J 35(2):119–148CrossRefGoogle Scholar
  2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automatic Control AC-19:716–723CrossRefGoogle Scholar
  3. Aronica GT, Candela A (2007) Derivation of flood frequency curves in poorly gauged Mediterranean catchments using a simple stochastic hydrological rainfall-runoff model. J Hydrol 347(1–2):132–142CrossRefGoogle Scholar
  4. Bárdossy A (1998) Generating precipitation time series using simulated annealing. Water Resour Res 34(7):1737–1744CrossRefGoogle Scholar
  5. Bárdossy A, Plate EJ (1992) Space-time model for daily rainfall using atmospheric circulation patterns. Water Resour Res 28(5):1247–1259CrossRefGoogle Scholar
  6. Beven K, Freer J (2001) Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology. J Hydrol 249(1–4):11–29CrossRefGoogle Scholar
  7. Blazkova S, Beven K (2004) Flood frequency estimation by continuous simulation of subcatchment rainfalls and discharges with the aim of improving dam safety assessment in a large basin in the Czech Republic. J Hydrol 292(1–4):153–172CrossRefGoogle Scholar
  8. Brandsma T, Buishand TA (1998) Simulation of extreme precipitation in the Rhine basin by nearest neighbour resampling. Hydrol Earth Syst Sci 2:195–209CrossRefGoogle Scholar
  9. Bras RL, Rodriguez-Iturbe I (1994) Random functions and hydrology. Dover, New York, NY, 559 ppGoogle Scholar
  10. 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
  11. Cameron DS, Beven KJ, Tawn J, Blazkova S, Naden P (1999) Flood frequency estimation by continuous simulation for a gauged upland catchment (with uncertainty). J Hydrol 219(3–4):169–187CrossRefGoogle Scholar
  12. Chang TJ, Kavvas ML, Delleur JW (1984a) Daily precipitation modelling by discrete autoregressive moving average processes. Water Resour Res 20:565–580CrossRefGoogle Scholar
  13. Chang TJ, Kavvas ML, Delleur JW (1984b) Modelling of sequences of wet and dry days by binary discrete autoregressive moving average processes. J Climate Appl Meteorol 23:1367–1378CrossRefGoogle Scholar
  14. Coles S (2001) An introduction to statistical modeling of extreme values. Springer, London, 208 ppGoogle Scholar
  15. Cowpertwait PSP (2006) A spatial-temporal point process model of rainfall for the Thames catchment, UK. J Hydrol 330(3–4):586–595CrossRefGoogle Scholar
  16. Delleur JW, Kavvas ML (1978) Stochastic models for monthly rainfall forecasting and synthetic generation. J Appl Meteorol 17:1528–1536CrossRefGoogle Scholar
  17. De Michele C, Salvadori G (2003) A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas. J Geophys Res 108 (D2):4067. doi:10.1029/2002JD002534Google Scholar
  18. Efron B, Tibshirani RJ (1998) An introduction to the bootstrap. Chapman and Hall, New York, NY, 436 ppGoogle Scholar
  19. Foufoula-Georgiou E, Georgakakos KP (1991) Hydrologic advances in space-time precipitation modeling and forcasting. In: Bowles DS, Connel O (eds) Recent advances in the modeling of hydrologic systems. Kluwer, Dordrecht, 47–65 ppGoogle Scholar
  20. Frigessi A, Haug O, Rue H (2003) A dynamic mixture model for unsupervised tail estimation without threshold selection. Extremes 5:219–235CrossRefGoogle Scholar
  21. Gaume E, Mouhous N, Andrieu H (2007) Rainfall stochastic disaggregation models: calibration and validation of a multiplicative cascade model. Adv Water Resour 30(5):1301–1319CrossRefGoogle Scholar
  22. Gilks W, Richardson S, Spiegelhalter D (1996) Markov chain Monte Carlo methods in practice. CRC Press, Boca Raton, FL, 486 ppGoogle Scholar
  23. Grace RA, Eagleson PS (1966) The synthesis of short-time-increment rainfall sequences. Hydrodynamics Laboratory, Massachusetts Institute of Technology, Cambridge, MAGoogle Scholar
  24. Güntner A, Olsson J, Calver A, Gannon B (2001) Cascade-based disaggregation of continuous rainfall time series: the influence of climate. Hydrol Earth Syst Sci 5:145–164CrossRefGoogle Scholar
  25. Haan CT, Allen DM, Street JO (1976) A Markov Chain model of daily rainfall. Water Resour Res 12(3):443–449CrossRefGoogle Scholar
  26. Haberlandt U (1998) Stochastic rainfall synthesis using regionalized model parameters. J Hydrol Eng 3(3):160–168CrossRefGoogle Scholar
  27. Haberlandt U, Ebner von Eschenbach A-D, Buchwald I (2008) A space-time hybrid hourly rainfall model for derived flood frequency analysis. Hydrol Earth Syst Sci 12:1353–1367CrossRefGoogle Scholar
  28. Hastings W (1970) Monte Carlo sampling methods using Markov Chains and their applications. Biometrika 57:97–109CrossRefGoogle Scholar
  29. Hipel KW, McLeod AI (1994) Time series modelling of water resources and environmental systems. Elsevier, Amsterdam, 1013 pp.Google Scholar
  30. Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, New York, NY, 240 pp.Google Scholar
  31. Hundecha Y, Pahlow M, Schumann A (2009) Modeling of daily precipitation at multiple locations using a mixture of distributions to characterize the extremes. Water Resour Res 45:W12412. doi:10.1029/2008WR007453CrossRefGoogle Scholar
  32. Hutchinson MF (1995) Stochastic space-time weather models from ground-based data. Agric Forest Meteorol 73:237–264CrossRefGoogle Scholar
  33. Jacobs PA, Lewis PAW (1978a) A discrete time series generated by mixture I: correlation and run properties. J R Stat Soc B 40(1):94–105Google Scholar
  34. Jacobs PA, Lewis PAW (1978b) A discrete time series generated by mixture II: asymptotic properties. J R Stat Soc B 40(2):222–228Google Scholar
  35. Katz RW (1977) Precipitation as a chain-dependent process. J Appl Meteorol 16:671–676CrossRefGoogle Scholar
  36. Kavvas ML, Delleur JW (1975) Removal of periodicities by differencing and month subtraction. J Hydrol 26:335–353CrossRefGoogle Scholar
  37. Koutsoyiannis D, Onof C, Wheater HS (2003) Multivariate rainfall disaggregation at a fine timescale. Water Resour Res 39(7): 1173. doi:10.1029/2002WR001600CrossRefGoogle Scholar
  38. Lall U, Sharma A (1996) A nearest neighbor bootstrap for resampling hydrological time series. Water Resour Res 32:679–693CrossRefGoogle Scholar
  39. Lovejoy S, Schertzer D (2006) Multifractals, cloud radiances and rain. J Hydrol 322(1–4):59–88CrossRefGoogle Scholar
  40. Lu M, Yamamoto T (2008) Application of a random cascade model to estimation of design flood from rainfall data. J Hydrol Eng 13(5):385–391CrossRefGoogle Scholar
  41. Mielke PW, Jr (1973) Another family of distributions for describing and analyzing precipitation data. J Appl Meteorol 10(2):275–280CrossRefGoogle Scholar
  42. Moretti G, Montanari A (2008) Inferring the flood frequency distribution for an ungauged basin using a spatially distributed rainfall-runoff model. Hydrol Earth Syst Sci 12:1141–1152CrossRefGoogle Scholar
  43. Nelsen RB (2006) An introduction to Copulas. Springer, New York, NY, 270 ppGoogle Scholar
  44. Olsson J (1998) Evaluation of a scaling cascade model for temporal rainfall disaggregation. Hydrol Earth Syst Sci 2:19–30CrossRefGoogle Scholar
  45. Onof C, Chandler RE, Kakou A, Northrop P, Wheater HS, Isham V (2000) Rainfall modelling using Poisson-cluster processes: a review of developments. Stoch Environ Res Risk Assess 14:384–411CrossRefGoogle Scholar
  46. Pegram GGS, Clothier AN (2001) High resolution space–time modelling of rainfall: the "string of beads" model. J Hydrol 241(1–2):26–41CrossRefGoogle Scholar
  47. Rajagopalan B, Lall U (1999) A k-nearest-neighbor simulator for daily precipitation and other weather variables. Water Resour Res 35:3089–3101CrossRefGoogle Scholar
  48. Richardson CW (1982) Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 17:182–190CrossRefGoogle Scholar
  49. Rodríguez-Iturbe I, Cox DR, Isham V (1987a) Some models for rainfall based on stochastic point processes. Proc R Soc, London A 410:269–288CrossRefGoogle Scholar
  50. Rodríguez-Iturbe I, Febres de Power B, Valdés JB (1987b) Rectangular pulses point process models for rainfall: analysis of empirical data. J Geophys Res 92(D8):9645–9656CrossRefGoogle Scholar
  51. Roldan J, Woolhiser DA (1982) Stochastic daily precipitation models 1. A comparison of occurrence processes. Water Resour Res 18(5):1451–1459CrossRefGoogle Scholar
  52. Scharffenberg WA, Fleming MJ (2005) Hydrologic modelling system, HEC-HMS. User's Manual, 248 ppGoogle Scholar
  53. Stedinger JR, Vogel RM, Foufoula-Georgiou E (1993) Frequency analysis of extreme events. In: Maidment DR (ed) Handbook of hydrology. MacGraw-Hill, New York, NY, pp 18.1–18.66Google Scholar
  54. Stehlík J, Bárdossy A (2002) Multivariate stochastic downscaling model for generating daily precipitation series based on atmospheric circulation. J Hydrol 256(1–2):120–141CrossRefGoogle Scholar
  55. Stern RD, Coe R (1984) A model fitting analysis of daily rainfall data (with discussion). J R Stat Soc A 147:1–34CrossRefGoogle Scholar
  56. Vrac M, Naveau P (2007) Stochastic downscaling of precipitation: from dry events to heavy rainfalls. Water Resour Res 43:W07402. doi:10.1029/2006WR005308CrossRefGoogle Scholar
  57. Wendling U, Schellin H-G, Thomä M (1991) Bereitstellung von täglichen Informationen zum Wasserhaushalt des Bodens für die Zwecke der agrarmeteorologischen Beratung. Meteorologische Zeitschrift 41:468–474Google Scholar
  58. Wheater H, Chandler R, Onof C, Isham V, Bellone E, Yang C, Lekkas D, Lourmas G, Segond ML (2005) Spatial-temporal rainfall modelling for flood risk estimation. Stoch Environ Res Risk Assess (SERRA) 19(6):403–416CrossRefGoogle Scholar
  59. Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210(1–4):178–191CrossRefGoogle Scholar
  60. Woolhiser DA, Roldan J (1982) Stochastic daily precipitation models. 2. A comparison of distribution amounts. Water Resour Res 18:1461–1468CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Uwe Haberlandt
    • 1
  • Yeshewatesfa Hundecha
    • 2
  • Markus Pahlow
    • 3
  • Andreas H. Schumann
    • 4
  1. 1.Institute for Water Resources Management, Hydrology and Agricultural Hydraulic EngineeringLeibniz Universität HannoverHannoverGermany
  2. 2.GFZ German Research Centre for GeosciencesPotsdamGermany
  3. 3.Institute of Hydrology, Water Resources Management and Environmental EngineeringRuhr-University BochumBochumGermany
  4. 4.Ruhr-University Bochum, Chair of Hydrology and Water ManagementBochumGermany

Personalised recommendations