Spatial-temporal rainfall modelling for flood risk estimation

  • H. S. Wheater
  • R. E. Chandler
  • C. J. Onof
  • V. S. Isham
  • E. Bellone
  • C. Yang
  • D. Lekkas
  • G. Lourmas
  • M.-L. Segond
Original Paper

Abstract

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.

Keywords

Rainfall simulation Poisson cluster processes Generalized linear models Spatial-temporal disaggregation 

Notes

Acknowledgements

Much of the recent research reported here has been supported by the UK Department for Environment, Food and Rural Affairs under contract FD2105. Georgios Lourmas acknowledges the financial support provided through the European Community’s Human Potential Programme under contract HPRN-CT-2000-00100, DYNSTOCH.

References

  1. Beven KJ, Binley AM (1992) The future of distributed models: model calibration and predictive uncertainty. Hydrol Process 6:279–298CrossRefGoogle Scholar
  2. Bowman A, Azzalini A (1997) Applied smoothing techniques for data analysis—the kernel approach with S-plus illustrations. Oxford University Press, OxfordGoogle Scholar
  3. Chandler RE (1997) A spectral method for estimating parameters in rainfall models. Bernoulli 3:301–322CrossRefGoogle Scholar
  4. Chandler RE, Wheater HS (2002). Climate change detection using generalized linear models for rainfall—a case study from the West of Ireland. Water Resour Res 38(10). DOI 10.1029/2001WR000906Google Scholar
  5. Coe R, Stern R (1982) Fitting models to daily rainfall. J Appl Meteorol 21:1024–1031CrossRefGoogle Scholar
  6. Cowpertwait PSP (1991) Further developments of the Neyman-Scott clustered point process for modelling rainfall. Water Resour Res 27(7):1431–1438CrossRefGoogle Scholar
  7. Cowpertwait PSP (1994) A generalized point process model for rainfall. Proc Roy Soc Lond A447:23–37Google Scholar
  8. Cowpertwait PSP (1998) A Poisson-cluster model of rainfall: some high-order moments and extreme values. Proc Roy Soc Lond A454:885–898CrossRefGoogle Scholar
  9. Cowpertwait PSP, Metcalfe AV, O’Connell PE, Maudsley JA, Threlfall JL (1991) Stochastic generation of rainfall time series, Foundation for Water Research Report, No. FR 0217Google Scholar
  10. Eagleson PS (1978) Climate, soil and vegetation, 2. The distribution of annual precipitation derived from observed storm sequences. Water Resour Res 14(5):713–721CrossRefGoogle Scholar
  11. Entekhabi D, Rodriguez-Iturbe I, Eagleson PS (1989) Probabilistic representationof the temporal rainfall process by a modified Neyman-Scott rectangular pulses model: parameter estimation and validation. Water Resour Res 25(2):295–302Google Scholar
  12. Foufoula-Georgiou E, Lettenmaier D (1986) Compatibility of continuous rainfall occurrence models with discrete rainfall observations. Water Resour Res 22(8):1316–1322Google Scholar
  13. Fowler HJ, Kilsby C, O’Connell PE (2000) A stochastic rainfall model for the assessment of regional water resource systems under changed climatic conditions. Hydrol Earth Syst Sci 4(2):263–282CrossRefGoogle Scholar
  14. Freer J, Beven K, Abroise B (1996) Bayesian uncertainty in runoff prediction and the value of data: an application of the GLUE approach. Water Resour Res 32:2163–2173CrossRefGoogle Scholar
  15. Gershenfeld NA (1999) The nature of mathematical modelling. Cambridge University Press, CambridgeGoogle Scholar
  16. Godambe VP, Kale BK (1991) Estimating functions: an overview. In: Godambe VP (ed) Estimating functions. Oxford University Press, Oxford, pp 3–20Google Scholar
  17. Hurrell JW (1995) Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation. Science 269:676–679CrossRefGoogle Scholar
  18. Institute of Hydrology (1999) Flood estimation handbook. Wallingford, UKGoogle Scholar
  19. Koutsoyiannis D, Onof C (2000) HYETOS—a computer program for stochastic disaggregation of fine-scale rainfall(http://www.itia.ntua.gr/e/softinfo/3/)
  20. Koutsoyiannis D, Onof C (2001) Rainfall disaggregation using adjusting procedures on a Poisson cluster model. J Hydrol 246:109–122CrossRefGoogle Scholar
  21. Lamb R, Kay AL (2004) Confidence intervals for a spatially generalized, continuous simulation flood frequency model for Great Britain. Water Resour Res 40(7). DOI 10.1029/2003WR002428Google Scholar
  22. Lovejoy S, Schertzer D (1995) Multifractals and rain, in uncertainty concepts. In: Kundzewicz AW (ed) Hydrology and hydrological modelling. Cambridge University Press, Cambridge, pp 62–103Google Scholar
  23. Northrop PJ (1998) A clustered spatial-temporal model of rainfall. Proc R Soc Lond A454:1875–1888Google Scholar
  24. Northrop PJ (2005) Estimating the parameters of rainfall models using maximum marginal likelihood. Student 5(3): (in press)Google Scholar
  25. Onof C, Townend J (2004) Modelling 5 minute rainfall extremes, In: Webb B, Arnell N, Onof C, MacIntyre N, Gurney R, Kirby C (eds) Hydrology: science and practice for the 21st Century, vol I. British Hydrological Society, pp 203–209Google Scholar
  26. Onof C, Wheater HS (1994) Improvements to the modelling of British rainfall using a modified random parameter Bartlett-Lewis rectangular pulse model. J Hydrol 157:177–195CrossRefGoogle Scholar
  27. Onof C, Chandler RE, Kakou A, Northrop P, Wheater HS, Isham VS (2000) Rainfall modelling using Poisson-cluster processes: a review of developments. Stochastic Environ Res And Risk Assessm 14:384–411CrossRefGoogle Scholar
  28. OPW (1998) An investigation of the flooding problems in the Gort-Ardrahan area of South Galway, by Southern Water Global and Jennings O’Donovan and partners. Office of Public Works, DublinGoogle Scholar
  29. Ormsbee LE (1989) Rainfall disaggregation model for continuous hydrologic modelling. J Hydraulic Eng ASCE 115:507–525CrossRefGoogle Scholar
  30. Qian B, Corte-Real J, Xu H (2002) Multisite stochastic weather models for impact studies. Int J Climatol 22:1377–1397CrossRefGoogle Scholar
  31. R Development Core Team (2004) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (http://www.R-project.org)
  32. Rodriguez-Iturbe I, Cox DR, Isham VS (1987) Some models for rainfall based on stochastic point processes. Proc R Soc Lond A410:269–288Google Scholar
  33. Rodriguez-Iturbe I, Cox DR, Isham VS (1988) A point process model: further developments. Proc R Soc Lond A 417:283–298Google Scholar
  34. Samuel C (1999) Stochastic rainfall modelling of convective storms in Walnut Gulch, Arizona. PhD Thesis, Imperial College LondonGoogle Scholar
  35. Smithers J, Schulze R, Pegram G (1999) Predicting short duration design storms in South Africa using inadequate data, hydrological extremes: understanding, predicting, mitigating, proceedings of the IUGG 99, symposium HS1, BirminghamGoogle Scholar
  36. Wagener T, Wheater HS, Gupta HV (2004) Rainfall-runoff modeling in gauged and ungauged catchments. Imperial College Press, LondonGoogle Scholar
  37. Wheater HS (2002) Progress in and prospects for fluvial flood modelling. Phil Trans R Soc Lond A 360:1409–1431CrossRefGoogle Scholar
  38. Wheater HS, Isham VS, Onof C, Chandler RE, Northrop PJ, Guiblin P, Bate SM, Cox DR, Koutsoyiannis D (2000) Generation of spatially consistent rainfall data Report to the Ministry of Agriculture, Fisheries and Food (2 volumes). Also available as Research Report No. 204, Department of Statistical Science, University College London, Gower Street, London WC1E 6BT (http://www.ucl.ac.uk/research/Resrprts/abstracts.html)
  39. Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210:178–191CrossRefGoogle Scholar
  40. Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr 23(3):329–357CrossRefGoogle Scholar
  41. Wood SJ, Jones DA, Moore RJ (2000) Static and dynamic calibration of radar data for hydrological use. HESS 4(4):545–554Google Scholar
  42. Yang C, Chandler RE, Isham VS, Wheater HS (2004) Spatial-temporal rainfall simulation using generalized linear models. Research Report, No 247, Department of Statistical Science, University College London. Available from http://www.ucl.ac.uk/Stats/research/Resrprts/abstracts.html

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • H. S. Wheater
    • 1
  • R. E. Chandler
    • 2
  • C. J. Onof
    • 1
  • V. S. Isham
    • 2
  • E. Bellone
    • 1
    • 2
  • C. Yang
    • 2
  • D. Lekkas
    • 1
  • G. Lourmas
    • 2
  • M.-L. Segond
    • 1
  1. 1.Department of Civil and Environmental EngineeringImperial College LondonLondonUK
  2. 2.Department of Statistical ScienceUniversity College LondonLondonUK

Personalised recommendations