Advertisement

Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 1. Impact on peak and extreme rainfall values

  • Dongkyun KimEmail author
  • Francisco Olivera
  • Huidae Cho
Original Paper

Abstract

A noble approach of stochastic rainfall generation that can account for inter-annual variability of the observed rainfall is proposed. Firstly, we show that the monthly rainfall statistics that is typically used as the basis of the calibration of the parameters of the Poisson cluster rainfall generators has significant inter-annual variability and that lumping them into a single value could be an oversimplification. Then, we propose a noble approach that incorporates the inter-annual variability to the traditional approach of Poisson cluster rainfall modeling by adding the process of simulating rainfall statistics of individual months. Among 132 gage-months used for the model verification, the proportion that the suggested approach successfully reproduces the observed design rainfall values within 20 % error varied between 0.67 and 0.83 while the same value corresponding to the traditional approach varied between 0.21 and 0.60. This result suggests that the performance of the rainfall generation models can be largely improved not only by refining the model structure but also by incorporating more information about the observed rainfall, especially the inter-annual variability of the rainfall statistics.

Keywords

Extreme Rainfall Rainfall Statistic Rainfall Depth Rainfall Time Series Precipitation Depth 
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.

Notes

Acknowledgments

This work was supported by the Hongik University new faculty research support fund.

References

  1. Asquith WH (1998) Depth-duration frequency of precipitation for Texas. US Geological Survey, Water-Resources Investigations Report 98-4044 (http://pubs.usgs.gov/wri/wri98-4044)
  2. Bo Z, Islam S, Eltahir EAB (1994) Aggregation-disaggregation properties of a stochastic rainfall model. Water Resour Res 30(12):3423–3435CrossRefGoogle Scholar
  3. Botter G, Settin T, Marani M, Rinaldo A (2006) A stochastic model of nitrate transport and cycling at basin scale. Water Resour Res 42(4):1–5CrossRefGoogle Scholar
  4. Burton A, Kilsby CG, Fowler HJ, Cowpertwait PSP, O’Connell PE (2008) RainSim: a spatial-temporal stochastic rainfall modeling system. Environ Model Softw 23:1356–1369CrossRefGoogle Scholar
  5. Cho H, Kim D, Olivera F, Guikema SD (2011) Enhanced speciation in particle swarm optimization for multi-modal problems. Eur J Oper Res 213(1):15–23CrossRefGoogle Scholar
  6. Cowpertwait PSP (1998) A Poisson-cluster model of rainfall: high-order moments and extreme values. Proc R Soc Lond Ser A 454:885–898. doi: 10.1098/rspa.19980191 CrossRefGoogle Scholar
  7. Cowpertwait PSP, O’Connell PE, Metclafe AV, Mawdsley JA (1996) Stochastic point process modelling of rainfall. I Single-site fitting and validation. J Hydrol 175(1–4):17–46CrossRefGoogle Scholar
  8. Evin G, Favre AC (2012) Further developments of transient Poisson-cluster model for rainfall. Stoch Environ Res Risk Assess 2012:8. doi: 10.1007/s00477-012-0612-y Google Scholar
  9. Glasbey CA, Cooper G, McGehan MB (1995) Disaggregation of daily rainfall by conditional simulation from a point-process model. J Hydrol 165:1–9CrossRefGoogle Scholar
  10. Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B52:105–124 JSTOR 2345653Google Scholar
  11. Isham S, Entekhabi D, Bras RL (1990) Parameter estimation and sensitivity analysis for the modified Bartlett-Lewis rectangular pulses model of rainfall. J Geophys Res 95(D3):2093–2100CrossRefGoogle Scholar
  12. Kavvas ML and Delleur JW (1975) The stochastic and chronologic structure of rainfall sequences—application to Indiana, Technical Report 57. Water Resources Research Center, Purdue University, West LafayetteGoogle Scholar
  13. Khaliq M, Cunnane C (1996) Modelling point rainfall occurrences with the modified Bartlett-Lewis rectangular pulses model. J Hydrol 180:109–138CrossRefGoogle Scholar
  14. Kim D, Olivera F (2012) On the relative importance of the different rainfall statistics in the calibration of stochastic rainfall generation models. J Hydrol Eng 17:368CrossRefGoogle Scholar
  15. Laio F, Tamea S, Ridolfi L, D’Odorico P, Rodriguez-Iturbe I (2009) Ecohydrology of groundwater-dependent ecosystems: 1. Stochastic water table dynamics. Water Resour Res 45:W05419. doi: 10.1029/2008WR007292 CrossRefGoogle Scholar
  16. Lall U, Sharma A (1996) A nearest neighbor bootstrap for resampling hydrological time series. Water Resour Res 32:679–693CrossRefGoogle Scholar
  17. Lovejoy S, Schertzer D (1990) Multifractals, universality classes, and satellite and radar measurements of cloud and rain fields. J Geophys Res 95:2021–2031CrossRefGoogle Scholar
  18. NCDC (2011) Precipitation Data, National Climatic Data Center (NCDC)—National Oceanic and Atmospheric Administration (NOAA). Available at http://gis.ncdc.noaa.gov/map/precip/as August 19, 2011
  19. Olsson J, Burlando P (2002) Reproduction of temporal scaling by a rectangular pulses rainfall model. Hydrol Process 16:611–630CrossRefGoogle Scholar
  20. Onof C, Wheater HS (1994) Improvements to the modeling of British rainfall using a modified random parameter Bartlett-Lewis rectangular pulse model. J Hydrol 157(1–4):177–195CrossRefGoogle Scholar
  21. Onof C, Northrop P, Wheater HS, Isham V (1996) Spatiotemporal storm structure and scaling property analysis for modeling. J Geophys Res Atmospheres 101:26415–26425CrossRefGoogle Scholar
  22. Onof C, Chandler RE, Kakou A, Northrop P, Wheater HS, Isham V (2000) Rainfall modelling using Poisson-cluster processes: a review of developments. Stoch EnvironRes Risk Assess 14(6):384–411CrossRefGoogle Scholar
  23. Ozturk A (1981) On the study of a probability–distribution for precipitation totals. J Appl Meteorol 20(12):1499–1505CrossRefGoogle Scholar
  24. Rodriguez-Iturbe I, Cox DR, Isham V (1987) Some models for rainfall based on stochastic point processes. Proc R Soc Lond Ser A 410(1839):269–288CrossRefGoogle Scholar
  25. Rodriguez-Iturbe I, Cox DR, Isham V (1988) A point process model for rainfall: further developments. Proc R Soc Lond Ser A 417(1853):283–298CrossRefGoogle Scholar
  26. Tarboton DG, Sharma A, Lall A (1998) Disaggregation procedures for stochastic hydrology based on nonparametric density estimation. Water Resour Res 34(1):107–119CrossRefGoogle Scholar
  27. Verhoest N, Troch PA, De Troch FP (1997) On the applicability of Bartlett-Lewis rectangular pulses models in the modeling of design storms at a point. J Hydrol 202(1–4):108–120CrossRefGoogle Scholar
  28. Westra SP, Mehrotra R, Sharma A, Srikanthan R (2012) Continuous rainfall simulation: 1. A regionalized subdaily disaggregation approach. Water Resour Res 48:W01535-1-W01535-16Google Scholar
  29. Wheater HS et al (2005) Spatial-temporal rainfall modeling for flood risk estimation. Stoch Environ Res Risk Assess 19(6):403–416CrossRefGoogle Scholar
  30. Yoo C, Kim D, Kim TW, Hwang KN (2008) Quantification of drought using a rectangular pulses Poisson process model. J Hydrol 355(1–4):34–48CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Urban and Civil EngineeringHongik UniversitySeoulRepublic of Korea
  2. 2.Zachry Department of Civil EngineeringTexas A&M UniversityCollege StationUSA
  3. 3.Water Resources EngineerDewberryFairfaxUSA

Personalised recommendations