×

Spatial-temporal rainfall modelling for flood risk estimation. (English) Zbl 1120.62344

Summary: 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.

MSC:

62P12 Applications of statistics to environmental and related topics
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics

Software:

R; sm
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beven KJ, Binley AM (1992) The future of distributed models: model calibration and predictive uncertainty. Hydrol Process 6:279-298 · doi:10.1002/hyp.3360060305
[2] Bowman A, Azzalini A (1997) Applied smoothing techniques for data analysis—the kernel approach with S-plus illustrations. Oxford University Press, Oxford · Zbl 0889.62027
[3] Chandler RE (1997) A spectral method for estimating parameters in rainfall models. Bernoulli 3:301-322 · Zbl 0890.62070 · doi:10.2307/3318594
[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 10.1029/2001WR000906
[5] Coe R, Stern R (1982) Fitting models to daily rainfall. J Appl Meteorol 21:1024-1031 · doi:10.1175/1520-0450(1982)021<1024:FMTDRD>2.0.CO;2
[6] Cowpertwait PSP (1991) Further developments of the Neyman-Scott clustered point process for modelling rainfall. Water Resour Res 27(7):1431-1438 · doi:10.1029/91WR00479
[7] Cowpertwait PSP (1994) A generalized point process model for rainfall. Proc Roy Soc Lond A447:23-37 · Zbl 0811.60035
[8] Cowpertwait PSP (1998) A Poisson-cluster model of rainfall: some high-order moments and extreme values. Proc Roy Soc Lond A454:885-898 · Zbl 0915.62098 · doi:10.1098/rspa.1998.0191
[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 0217
[10] Eagleson PS (1978) Climate, soil and vegetation, 2. The distribution of annual precipitation derived from observed storm sequences. Water Resour Res 14(5):713-721 · doi:10.1029/WR014i005p00713
[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):295-302
[12] Foufoula-Georgiou E, Lettenmaier D (1986) Compatibility of continuous rainfall occurrence models with discrete rainfall observations. Water Resour Res 22(8):1316-1322
[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):263-282 · doi:10.5194/hess-4-263-2000
[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 32:2163-2173 · doi:10.1029/96WR03723
[15] Gershenfeld NA (1999) The nature of mathematical modelling. Cambridge University Press, Cambridge · Zbl 0905.00015
[16] Godambe, VP; Kale, BK; Godambe, VP (ed.), Estimating functions: an overview, 3-20 (1991), Oxford · Zbl 0755.62027
[17] Hurrell JW (1995) Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation. Science 269:676-679 · doi:10.1126/science.269.5224.676
[18] Institute of Hydrology (1999) Flood estimation handbook. Wallingford, UK
[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 246:109-122 · doi:10.1016/S0022-1694(01)00363-8
[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 10.1029/2003WR002428
[22] Lovejoy, S.; Schertzer, D.; Kundzewicz, AW (ed.), Multifractals and rain, in uncertainty concepts, 62-103 (1995), Cambridge
[23] Northrop PJ (1998) A clustered spatial-temporal model of rainfall. Proc R Soc Lond A454:1875-1888 · Zbl 0915.76071
[24] Northrop PJ (2005) Estimating the parameters of rainfall models using maximum marginal likelihood. Student 5(3): (in press)
[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 203-209
[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 157:177-195 · doi:10.1016/0022-1694(94)90104-X
[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 14:384-411 · Zbl 1054.62613 · doi:10.1007/s004770000043
[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, Dublin
[29] Ormsbee LE (1989) Rainfall disaggregation model for continuous hydrologic modelling. J Hydraulic Eng ASCE 115:507-525 · doi:10.1061/(ASCE)0733-9429(1989)115:4(507)
[30] Qian B, Corte-Real J, Xu H (2002) Multisite stochastic weather models for impact studies. Int J Climatol 22:1377-1397 · doi:10.1002/joc.808
[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 A410:269-288 · Zbl 0626.60044
[33] Rodriguez-Iturbe I, Cox DR, Isham VS (1988) A point process model: further developments. Proc R Soc Lond A 417:283-298 · Zbl 0644.60041
[34] Samuel C (1999) Stochastic rainfall modelling of convective storms in Walnut Gulch, Arizona. PhD Thesis, Imperial College London
[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, Birmingham
[36] Wagener T, Wheater HS, Gupta HV (2004) Rainfall-runoff modeling in gauged and ungauged catchments. Imperial College Press, London
[37] Wheater HS (2002) Progress in and prospects for fluvial flood modelling. Phil Trans R Soc Lond A 360:1409-1431 · doi:10.1098/rsta.2002.1007
[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 210:178-191 · doi:10.1016/S0022-1694(98)00186-3
[40] Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr 23(3):329-357 · doi:10.1191/030913399666525256
[41] Wood SJ, Jones DA, Moore RJ (2000) Static and dynamic calibration of radar data for hydrological use. HESS 4(4):545-554
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.