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Derivation of rainfall IDF relations by third-order polynomial normal transform

  • Lingwan You
  • Yeou-Koung Tung
Original Paper
  • 69 Downloads

Abstract

Establishing the rainfall intensity–duration–frequency (IDF) relations by the conventional method, the use of parametric distribution models has the advantage of automatic compliance of monotonicity condition of rainfall intensity and frequency. However, fitting rainfall data to a distribution separately by individual duration may possibly produce undulation and crossover of IDF curves which does not comply physical reality. This frequently occurs when rainfall record length is relatively short which often is the case. To tackle this problem this study presents a methodological framework that integrates the third-order polynomial normal transform (TPNT) with the least squares (LS) method to establish rainfall IDF relations by simultaneously considering multi-duration rainfall data. The constraints to preserve the monotonicity and non-crossover in the IDF relations can be incorporated easily in the LS-based TPNT framework. Hourly rainfall data at Zhongli rain gauge station in Taiwan with 27-year record are used to establish rainfall IDF relations and to illustrate the proposed methodology. Numerical investigation indicates that the undulation and crossover behavior of IDF curves can be effectively circumvented by the proposed approach to establish reasonable IDF relations.

Keywords

Rainfall intensity–duration–frequency relations Rainfall frequency analysis Third-order polynomial normal transform Least-square method 

Notes

Acknowledgements

This study is supported by the Joint Research under the National Research Foundation (Korea)-Ministry of Science & Technology (Taiwan) Cooperative Program (MOST 105–2923-E-009-004-MY2). All data used in this paper is properly cited and referred to in the reference list.

References

  1. Akan AO, Houghtalen RJ (2003) Urban hydrology, hydraulics, and stormwater quality. Wiley, HobokenGoogle Scholar
  2. Asadieh B, Krakauer N (2015) Global trends in extreme precipitation: climate models versus observations. Hydrol Earth Syst Sci 19:877–891CrossRefGoogle Scholar
  3. Asikoglu OL, Benzeden E (2014) Simple generalization approach for intensity–duration–frequency relationships. Hydrol Process 28(3):1114–1123CrossRefGoogle Scholar
  4. Bernard M (1932) Formulas for rainfall intensities of long duration. Trans ASCE 96(1):592–606Google Scholar
  5. Blom G (1958) Statistical estimates and transformed beta-variates. Wiley, New YorkGoogle Scholar
  6. Boggs PT, Tolle JW (1995) Sequential quadratic programming. Acta Numer 4:1–51CrossRefGoogle Scholar
  7. Cai D, Shi D, Chen J (2013) Probabilistic load flow computation with polynomial normal transformation and Latin hypercube sampling. IET Gener Transm Distrib 7(5):474–482CrossRefGoogle Scholar
  8. Chen XY, Tung YK (2003) Investigation of polynomial normal transform. Struct Saf 25(4):423–445CrossRefGoogle Scholar
  9. Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill Book Company, New YorkGoogle Scholar
  10. Ciapessoni E, Cirio D, Massucco S, Morini A, Pitto A, Silvestro F (2017) Risk-based dynamic security assessment for power system operation and operational planning. Energies 10(4):475–490CrossRefGoogle Scholar
  11. Cleveland, T.G., Herrmann, G.R., Tay, C.C., Neale, C.M., Schwarz, M.R., and Asquith, W.H. (2015). New rainfall coefficients—including tools for estimation of intensity and hyetographs in Texas, final report. Texas Department of Transportation. Research Project Number 0-6824Google Scholar
  12. Cunnane C (1978) Unbiased plotting positions—a review. J Hydrol 37:205–222CrossRefGoogle Scholar
  13. Demirtas H, Hedeker D, Mermelstein RJ (2012) Simulation of massive public health data by power polynomials. Stat Med 31(27):3337–3346CrossRefGoogle Scholar
  14. Doong DJ, Lo WC, Vojinovic Z, Lee WL, Lee SP (2016) Development of new generation of flood inundation maps—a case study of the coastal city of Tainan, Taiwan. Water 8:521–540.  https://doi.org/10.3390/w8110521 CrossRefGoogle Scholar
  15. Fleishman AL (1978) A method for simulating non-normal distributions. Psychometrika 43(4):521–532CrossRefGoogle Scholar
  16. Haktanir T (2003) Divergence criteria in extreme rainfall series frequency analyses. Hydrol Sci J 48(6):917–937CrossRefGoogle Scholar
  17. Headrick TC (2010) Statistical simulation: power method polynomials and other transformations. Chapman & Hall, Boca RatonGoogle Scholar
  18. Hong HP (1998) Application of polynomial transformation to normality in structural reliability analysis. Can J Civ Eng 25(2):241–249CrossRefGoogle Scholar
  19. Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme value distribution by the method of probability-weighted moments. Technometrics 27(3):251–261CrossRefGoogle Scholar
  20. Kite GW (1988) Frequency and risk analyses in hydrology. Water Resources Publications, Littleton COGoogle Scholar
  21. Koutsoyiannis D, Kozonis D, Manetas A (1998) A mathematical framework for studying rainfall intensity–duration–frequency relationships. J Hydrol 206:118–135CrossRefGoogle Scholar
  22. Lopez-Lambrantilde A, Fuentes C, González-Sosa E, López-Ramos A, Pliego-Díaz M, Gómez-Meléndez D, Altamirano-Corro A (2013) Effect of interception by canopy in the IDF relation in a semiarid zone. Afr J Agric Res 8(43):5285–5295Google Scholar
  23. Makkonen L, Pajari M, Tikanmaki M (2013) Discussion on “Plotting positions for fitting distributions and extreme value analysis”. Can J Civ Eng 40:130–139CrossRefGoogle Scholar
  24. Montgomery DC, Peck EA, Vining GG (2012) Introduction to linear regression analysis, 5th edn. Wiley, New YorkGoogle Scholar
  25. Nhat LM, Tachikawa Y, Sayama T, Takara K (2006) Derivation of rainfall intensity–duration–frequency relationships for short-duration rainfall from daily data. In: Proceedings, international symposium on managing water supply for growing demand, technical document in hydrology, vol 6, pp 89–96Google Scholar
  26. Porras PJ Sr, Porras PJ Jr (2001) New perspective on rainfall frequency curves. J Hydrol Eng 6(1):82–85CrossRefGoogle Scholar
  27. Rao AR, Hamed KH (2000) Flood frequency analysis. CRC Publications, New YorkGoogle Scholar
  28. Sahoo SN, Sreeja P (2015) Development of flood inundation maps and quantification of flood risk in an urban catchment of Brahmaputra river. J Risk Uncertain Eng Syst Part A Civ Eng.  https://doi.org/10.1061/ajrua6.0000822 CrossRefGoogle Scholar
  29. Sarhadi A, Soulis ED (2017) Time-varying extreme rainfall intensity–duration–frequency curves in a changing climate. Geophys Res Lett.  https://doi.org/10.1002/2016gl072201 CrossRefGoogle Scholar
  30. Sherman CW (1931) Frequency and intensity of excessive rainfalls at Boston, Massachusetts. Trans ASCE 95:951–960Google Scholar
  31. Singh VP, Strupczewski WG (2002) On the status of flood frequency analysis. Hydrol Process 16:3737–3740CrossRefGoogle Scholar
  32. Stedinger JR (2017) Ch.76—flood frequency analysis. In: Singh VP (ed) Handbook of applied hydrology, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  33. Stedinger JR, Vogel RM, Foufoula-Georgiou E (1993) Ch.18—frequency analysis of extreme events. In: Maidment D (ed) Handbook of hydrology. McGraw-Hill Inc, New YorkGoogle Scholar
  34. Sun SA, Djordjević S, Khu ST (2010) Decision making in flood risk based storm sewer network design. Water Sci Technol 64(1):247–254CrossRefGoogle Scholar
  35. Vogel RM, Fennessey NM (1993) L-moment diagrams should replace product moment diagram. Water Resour Res 296:1745–1752CrossRefGoogle Scholar
  36. Weibull W (1939) A statistical theory of the strength of materials. R Swed Inst Eng Res Proc 151:1–45Google Scholar
  37. Wilson RB (1963) A simplicial method for convex programming, PhD thesis, Harvard University, Boston, MAGoogle Scholar
  38. Xu Y, Tung YK (2009) Constrained scaling approach for design rainfall estimation. Stoch Env Res Risk Assess 23(6):697–705CrossRefGoogle Scholar
  39. Yan L, Xiong L, Guo S, Xu CY, Xia J, Duc T (2017) Comparison of four nonstationary hydrologic design methods for changing environment. J Hydrol 551:132–150CrossRefGoogle Scholar
  40. Yang, H., and Zou, B. (2012). The point estimate method using third-order polynomial normal transformation technique to solve probabilistic power flow with correlated wind source and load. In: Proceedings, Asia–Pacific power and energy engineering conference, Shanghai, pp 1–4Google Scholar
  41. Zhao YG, Lu ZH (2007) Fourth moment standardization for structural reliability assessment. J Struct Eng ASCE 133(7):916–924CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Disaster Prevention and Water Environmental Research CenterNational Chiao-Tung UniversityHsinchuTaiwan

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