Modeling of magnitude and frequency of floods on the Narmada River: India

Abstract

The concept of magnitude–frequency was introduced by Fuller, and since then, it has been widely used, especially in Europe and Asia. Over the past, 9–11 decades, several probability distribution models have been developed and applied. The principal objective of the present study is to identify the best-fit magnitude–frequency model at various sites on the Narmada River amongst the Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). Therefore, Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) tests of goodness-of-fit were applied to find out best-fit model at each site on the river under review. The result shows that LP-III model is the best fit for Dindori, Manot, Barman, Sandia, Hoshangabad, Handia, and Mandleshwar, and GEVI model is the best fit for the Garudeshwar site. Accordingly, flood magnitudes for 2, 5, 10, 25, 50, 100, and 200 year return period were predicted. The analysis shows that the return period of largest peak flood on record (69400 m3/s) on the Narmada River at Garudeshwar is 96 years. These models demonstrate satisfactory results for predicting discharges and return periods. In addition to this, magnitude–frequency curves reveal that fitted lines are fairly close to the most of stream flow data points. Therefore, GEVI and LP-III are the best-fit distributions for modeling of magnitude and frequency of floods on the Narmada River.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Availability of data and material

Hydrological data: Water Year Book (2015–16), Central Water Commission, New Delhi, India. Meteorological data: India Meteorological Department, Pune, India.

References

  1. Barve M (2019) Meteorological aspects of the Severe Floods on the Narmada River: Central India. Unpublished Master’s Dissertation, Savitribai Phule Pune University, Pune

  2. Beard LR (1975) Generalized evaluation of flash-flood potential. Technical Report: University of Texas, Austin. Central Research Water Resource CRWR- 124:1-27

  3. Bedient PB, Huber WC (1989) Hydrology and floodplain analysis. Addison Wesley Publication Company, New York

    Google Scholar 

  4. Benson MA (1968) Uniform flood frequency estimating methods for federal agencies. Water Resour Res 4(5):891–908

    Article  Google Scholar 

  5. Bhat MS, Alam A, Ahmad B, Kotlia BS, Farooq H, Taloor AK, Ahmad S (2019) Flood frequency analysis of river Jhelum in Kashmir basin. Quatern Int 507:288–294

    Article  Google Scholar 

  6. Blackburn J, Hicks F (2002) Combined flood routing and flood level forecasting. Can J Civ Eng 29:64–75

    Article  Google Scholar 

  7. Bobee B (1975) The log Pearson type 3 distribution and its applications in hydrology. Water Resour Res 11(3):365–369

    Google Scholar 

  8. Castillo E (1988) Extreme value theory in engineering. Academic Press, New York

    Google Scholar 

  9. Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw Hill, New York

    Google Scholar 

  10. Cunnane C (1978) Unbiased plotting positions, a review. J Hydrol 39:205–222

    Article  Google Scholar 

  11. Cunnane C (1989) Statistical distributions for flood frequency analysis. Operational Hydrology Report no.33, WMO no. 718, World Meteorological Organization, Geneva, Switzerland

  12. Dandekar MM, Sharma KN (2013) Water power engineering, 2nd edn. Vikas Publishing House Pvt. Ltd, New Delhi

  13. Devia GK, Ganasri B, Dwarakish G (2015) A review on hydrological models. Aquatic Proc 4:1001–1007

    Article  Google Scholar 

  14. Elleder L (2010) Reconstruction of the 1784 flood hydrograph for the Vltava River in Prague, Czech Republic. Glob Planet Change 70:117–124

    Article  Google Scholar 

  15. Elleder L, Herget J, Roggenkamp T, Nießen A (2013) Historic floods in the city of Prague-a reconstruction of peak discharges for 1481–1825 based on documentary sources. Hydrol Res 44(2):202–214

    Article  Google Scholar 

  16. Foster HA (1924) Theoretical frequency curves and their application to engineering problems. Trans Am Soc Civ Eng 87(1):142–173

    Google Scholar 

  17. Fuller WE (1914) Flood flows. Trans Am Soc Civ Eng 77(1293):564–617

    Google Scholar 

  18. Gaal L, Szolgay J, Kohnova S, Hlavcova K, Viglione A (2010) Inclusion of historical information in flood frequency analysis using a Bayesian MCMC technique: a case study for the power dam Orlik, Czech Republic. Contrib Geophys Geodesy 40(2):121–147

    Google Scholar 

  19. Garde RJ (1998) Floods and flood control: engineering approach. In: Kale VS (ed) Flood studies in India, vol 41. Memoir of Geological Society of India, Bangalore, pp 173–193

    Google Scholar 

  20. Griffis VW, Stedinger JR (2007) The log-Pearson type III distribution and its application in flood frequency analysis. 1: Distribution characteristics. J Hydrol Eng 12(5):482–491

    Article  Google Scholar 

  21. Griffis VW, Stedinger JR (2009) Log-Pearson type 3 distribution and its application in flood frequency analysis, III—sample skew and weighted skew estimators. J Hydrol 14(2):121–130

    Google Scholar 

  22. Gringorten II (1963) A plotting rule for extreme probability paper. J Geophys Res 68(3):813–814

    Article  Google Scholar 

  23. Gumbel EJ (1941) The return period of flood flows. Ann Math Stat 12:163–190

    Article  Google Scholar 

  24. Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York

    Google Scholar 

  25. Haan CT (1977) Statistical methods in hydrology. Iowa State University Press, Ames, p 378

    Google Scholar 

  26. Haddad K, Rahman A (2011) Selection of the best fit flood frequency distribution and parameter estimation procedure: A case study for Tasmania in Australia. Stoch Environ Res Risk Assess 25:415–428

    Article  Google Scholar 

  27. Helsel DR, Hirsch RM (2010) Statistical methods in water resources. U.S. Geological Survey, Investigations Book 4, Chapter A3. U.S. Geological Survey

  28. Hire PS, Patil AD (2018) Flood frequency analysis of the Par River: Western India. Int J Sci Res Sci Technol 5(1):164–168

    Google Scholar 

  29. Hire PS (2000) Geomorphic and hydrologic studies of floods in the Tapi Basin. Unpublished Ph.D. Thesis, University of Pune, Pune, India

  30. Holmes RR (2014) Floods: Recurrence intervals and 100-year floods (USGS). http://www.water.usgs.gov/edu/. Website Retrieved February 2, 2014. Accessed 23 Nov 2019

  31. Hosking JRM, Wallis JR (1997) Regional frequency analysis—an approach based on l-Moments. Cambridge University Press, Cambridge, p 224

    Google Scholar 

  32. IPCC (2012) Managing the risks of extreme events and disasters to advance climate change adaptation. A special report of working groups i and ii of the intergovernmental panel on climate change. Cambridge University Press, Cambridge

    Google Scholar 

  33. Jha VC, Bairagya H (2011) Environmental impact of flood and their sustainable management in deltaic region of West Bengal, India. Caminhos de Geografia 12(39):283–296

    Google Scholar 

  34. Kale VS, Ely LL, Enzel Y, Baker VR (1994) Geomorphic and hydrologic aspects of monsoon floods on the Narmada and Tapi Rivers in central India. Geomorphology 10:157–168

    Article  Google Scholar 

  35. Kale VS, Gupta A (2010) Introduction to Geomorphology. Universities Press Pvt. Ltd., Hyderabad

    Google Scholar 

  36. Kamal V, Mukherjee S, Singh P, Sen R, Vishwakarma CA, Sajadi P, Asthana H, Rena V (2016) Flood frequency analysis of Ganga River at Haridwar and Garhmukteshwar. Appl Water Sci 7:1–8

    Article  Google Scholar 

  37. Kottegoda NT, Rosso R (1997) Statistics, probability, and reliability for civil and environmental engineers. McGraw Hill, New York

    Google Scholar 

  38. Koutrouvelis IA, Canavos GC (2000) A comparison of moment-based methods of estimation for the log Pearson type 3 distributions. J Hydrol 234(1):71–81

    Article  Google Scholar 

  39. Kumar R, Chatterjee C, Kumar S, Lohani AK, Singh RD (2003) Development of regional flood frequency relationships using l moments for middle Ganga plains subzone 1(f) of India. Water Resour Managt 17:243–257

    Article  Google Scholar 

  40. Laio F, Di Baldassarre G, Montanari A (2009) Model selection techniques for the frequency analysis of hydrological extremes. Water Resour Res 45:1–11

    Google Scholar 

  41. Law GS, Tasker, GD (2003) Flood frequency prediction methods for unregulated streams of Tennessee, 2000. Water Resources Investigations Report 03-4176, Nashville, Tennessee

  42. Matalas NC, Wallis JR (1973) Eureka! It fits a Pearson type 3 distribution. Water Resour Res 9(2):281–289

    Article  Google Scholar 

  43. Merz R, Blöschl G (2008) Flood frequency hydrology: 1. Temporal, spatial and the causal expansion of information. Water Resour Res 44(8):1–17

    Google Scholar 

  44. Millington N, Das S, Simonovic SP (2011) The comparison of GEV, Log-Pearson Type 3 and Gumbel distributions in the Upper Thames River watershed under global climate models. Water Resources Research Report Department of Civil and Environmental Engineering, University of Western Ontario

  45. Patil AD (2017) Bedrock channel of the Par River: its forms and processes. Unpublished Ph.D. Thesis, Tilak Maharashtra Vidyapeeth, Pune

  46. Pawar UV, Hire PS (2019) Flood frequency analysis of the Mahi Basin by using Log Pearson type III probability distribution. Hydrosp Anal 2(2):102–112

    Google Scholar 

  47. Pearson K (1916) Mathematical contributions to the theory of evolution, IXI: second supplement to a memoir on skew variation. Philos Trans R Soc Lond Ser A 216:429–457

    Article  Google Scholar 

  48. Phien HN, Jivajirajah T (1984) Applications of the log Pearson type-3 distribution in hydrology. J Hydrol 73:359–372

    Article  Google Scholar 

  49. Pilgrim DH (ed) (1987) Australia rainfall and runoff. The Institution of Engineers Australia, Barton

    Google Scholar 

  50. Popescu I, Jonoski A, Van Andel S, Onyari E, Moya Quiroga V (2010) Integrated modelling for flood risk mitigation in Romania: case study of the Timis-Bega river basin. Int J River Basin Manag 8:269–280

    Article  Google Scholar 

  51. Raghunath HM (2006) Hydrology: principles, analysis and design, 2nd edn. New Age International (P) Limited, 4835/24, Ansari Road, Daryaganj, New Delhi

  52. Sakthivadivel R, Raghupathy A (1978) Frequency analysis of floods in some Indian rivers. Hydrol Rev 4:57–67

    Google Scholar 

  53. Shaw EM (1983) Hydrology in Practice. Van Nostrand Reinhold, Berkshire

    Google Scholar 

  54. Shaw EM (1988) Hydrology in practice. Van Nostrand Reibhold Int. Co., Ltd., London

    Google Scholar 

  55. Shaw EM (1994) Hydrology in practice. Taylor & Francis e-Library, Milton Park (2005)

    Google Scholar 

  56. Srikanthan R, McMahon TA (1981) Log Pearson III distribution—an empirically derived plotting position. J Hydrol 52:161–163

    Article  Google Scholar 

  57. Stedinger JR, Vogel RM, Georgiou EF (1993) Frequency analysis of extreme events. In: Maidment DR (ed) Chapter 18 handbook of hydrology. McGraw-Hill, New York

    Google Scholar 

  58. Todorovic P (1978) Stochastic models of floods. Water Resour Res 14(2):345–356

    Article  Google Scholar 

  59. U.S. Water Resources Council (1967) A uniform technique for determining flood flow frequencies, Bulletin No. 15. Washington D.C

  60. U.S. Water Resources Council (1976) Guidelines for determining flood flow frequency, Bulletin 17.Washington D.C

  61. U.S. Water Resources Council (1981) Guidelines for determining flood flow frequency, Bulletin 17B. Washington D.C

  62. United States Geological Survey (1982) Guidelines for determining flood flow frequency, Bulletin. 17B. USGS Interagency Advisory Committee on Water Data 194, Reston, Virginia

  63. Vogel RM (1986) The probability plot correlation coefficient test for the normal, lognormal and Gumbel distributional hypotheses. Water Resour Res 22(4):587–590

    Article  Google Scholar 

  64. Vogel RM, Thomas WO, McMahon TA (1993) Flood-flow frequency model selection in the southwestern United States. J Water Resour Plan Manag ASCE 119(3):353–366

    Article  Google Scholar 

  65. Wallis JR (1988) Catastrophes, computing and containment: living in our restless habitat. Specul Sci Technol 11(4):295–315

    Google Scholar 

  66. Wallis JR, Wood EF (1985) Relative accuracy of log Pearson III procedure. J Hydr Eng 111(7):1043–1056

    Article  Google Scholar 

  67. Ward R (1978) Floods: a geographical perspective. The MacMillan Press Ltd., London

    Google Scholar 

  68. Watt WE, Lathem KW, Neill CR, Richard TL, Rousselle J (1989) Hydrology of floods in Canada: a guide to planning and design. National Research Council of Canada, Ottawa

    Google Scholar 

Download references

Acknowledgements

The authors are grateful to Central Water Commission, New Delhi for providing hydrological data and India Meteorological Department, Pune, for supplying rainfall data. The authors are indebted to Snehal Rahane for spelling and grammatical corrections and for her valuable comments to improve the draft of this paper. Thanks are due to Gitanjali Bramhankar, Vinod Vishwakarma, and Madhura Barve for their support during this work. We also thank the Editor, Modeling Earth Systems and Environment (MESE), and anonymous reviewers for their constructive comments that considerably improved the clarity of an earlier version of this paper.

Funding

No funding for this work.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Pramodkumar S. Hire.

Ethics declarations

Conflicts of interest

No potential conflict of interest was reported by the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pawar, U.V., Hire, P.S., Gunjal, R.P. et al. Modeling of magnitude and frequency of floods on the Narmada River: India. Model. Earth Syst. Environ. (2020). https://doi.org/10.1007/s40808-020-00839-1

Download citation

Keywords

  • Narmada River
  • Best fit
  • Magnitude–frequency
  • Return period
  • Gumbel Extreme Value type I (GEVI) model
  • Log Pearson type III (LP-III) model