Skip to main content
SpringerLink
Log in

Nondimensional UH-Based Smoothing of S-Curve-Derived UH Oscillations

  • Conference paper
  • First Online:
Hydrologic Modeling

Part of the book series: Water Science and Technology Library ((WSTL,volume 81))

  • 1874 Accesses

Abstract

This paper proposes nondimensional unit hydrograph (UH)-based procedure for eliminating the oscillations frequently observed in the recession part of altered duration UHs derived from conventional S-curve approach. Such occurrence of oscillations and/or even negative ordinates cannot be ignored or left unadjusted, and therefore, their elimination by often suggested manual/visual adjustments is attempted, which is quite cumbersome and time-consuming. Proposed procedure employs the peak (Q p ) and time to peak (t p ) of altered duration (τ-h) UH for its derivation, which is derived by using analytical S-shaped model-efficient enough to exactly reproduce the oscillation-free S-curve. The suggested approach is found to be superior to the conventional S-curve approach. On the whole, the complexity associated with the lagging of S-curve, interpolation—if altered UH duration is not a multiple of parent UH duration (D-h), manual/visual adjustments to eliminate oscillations in derived S-curve or altered duration UHs and also for reasons of maintaining unit volume of UH has been fully resolved.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aron G, White EL (1982) Fitting a gamma distribution over a synthetic unit hydrograph. Water Resour Bull 18(1):95–98

    Article  Google Scholar 

  • Bhunya PK, Mishra SK, Berndtsson R (2003) Simplified two-parameter gamma distribution for derivation of synthetic unit hydrograph. J Hydrol Eng, ASCE 8(4):226–230

    Article  Google Scholar 

  • Blank D, Delleur JW, Giorgini A (1971) Oscillatory kernel functions in linear hydrologic models. Water Resour Res 7(5):1102–1117

    Article  Google Scholar 

  • Boufadel MC (1998) Unit hydrographs derived from the Nash model. J Am Water Resour Assoc 34(1):167–177

    Article  Google Scholar 

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

    Google Scholar 

  • CWC (1984) Flood estimation report for upper Indo-Ganga plains subzone-1(e)-a method based on unit hydrograph principle. Hydrology Directorate, CWC, New Delhi, India

    Google Scholar 

  • Dooge JCI (1973) Linear theory of hydrologic systems. USDA-ARS Tech. Bull. No. 1968. U.S. Govt. Printing Office, Washington

    Google Scholar 

  • Edson CG (1951) Parameters for relating unit hydrograph to watershed characteristics. Trans—Am Geophys Union 32(4):591–596

    Article  Google Scholar 

  • Hall MJ (1977) On the smoothing of oscillations in finite-period unit hydrographs derived by the harmonic method. Hydrol Sci Bull 22(2):313–324

    Article  Google Scholar 

  • Hunt B (1985) The meaning of oscillations in unit hydrograph S-curves. Hydrol Sci J 30(3):331–342

    Article  Google Scholar 

  • Lasdon LS, Waren AD, Jain A, Ratner M (1978) Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Trans Math Softw 4(1):34–50

    Article  MATH  Google Scholar 

  • Linsley RK, Kohler MA, Paulhus JLH (1975) Hydrology for engineers, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Meyer PS (1994) Bi-logistic growth. Technol Forecast Soc Chang 47:89–102

    Article  Google Scholar 

  • Mockus V (1957) Use of storm and watershed characteristics in synthetic hydrograph analysis and application. Am Geophys Union, Pacific Southwest Region, Sacramento, CA

    Google Scholar 

  • Nadarajah S (2007) Probability models for unit hydrograph derivation. J Hydrol 344:185–189

    Article  Google Scholar 

  • Naki Cenovic N (1988) U.S. transport Infrastructures in cities and their vital systems. National Academy Press, Washington, D.C

    Google Scholar 

  • Nash JE (1957) The form of the instantaneous unit hydrograph. Int Assoc Sci Hydrol Publ 45(3):114–121

    Google Scholar 

  • Nash JE (1958) Determining runoff from rainfall. Inst Civ Eng Proc 10:163–184

    Google Scholar 

  • Nash JE (1960) A unit hydrograph study with particular reference to British catchments. Inst Civ Eng Proc 17:249–282

    Google Scholar 

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I-A discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  • Ohba M (1984) Software reliability analysis models. IBM J Res Dev 28(4):428–443

    Article  Google Scholar 

  • Ojha CSP, Bhunya P, Berndtsson R (2008) Engineering hydrology. Oxford University Press, New Delhi, India

    Google Scholar 

  • Patil PR, Mishra SK, Sharma N (2016) Oscillation free altered duration UH derivation using nondimensional approach. Perspect Sci. doi:10.1016/j.pisc.2016.06.059

    Google Scholar 

  • Rai RK, Sarkar S, Singh VP (2009) Evaluation of the adequacy of statistical distribution functions for deriving unit hydrograph. Water Resour Manage 23(5):899–929

    Article  Google Scholar 

  • Raghunath HM (1995) Hydrology: principles, analysis, design. New Age International Publishers, New Delhi, India

    Google Scholar 

  • Sangal BP (1986) Recursion formula for unit hydrographs. Can J Civ Eng 13(3):386–388

    Article  Google Scholar 

  • Singh VP (1988) Hydrologic systems: rainfall-runoff modeling, vol 1. Prentice-Hall, Englewood Cliffs, N.J.

    Google Scholar 

  • Singh VP (1992) Elementary hydrology. Prentice Hall, New York

    Google Scholar 

  • Singh SK (2000) Transmuting synthetic unit hydrographs into gamma distribution. J Hydrol Eng 5(4):380–385

    Article  Google Scholar 

  • Singh SK (2004) Simplified use of gamma-distribution/nash model for runoff modeling. J Hydrol Eng 9(3):240–243

    Article  Google Scholar 

  • Singh SK (2005) Clark’s and Espey’s unit hydrographs vs the gamma unit hydrograph. J Hydrol Sci 50(6):1053–1067

    Article  Google Scholar 

  • Singh SK (2006) Optimal instantaneous unit hydrograph from multistorm data. J Irrig Drainage Eng 132(3):298–302

    Article  Google Scholar 

  • Singh SK (2007) Use of gamma distribution/nash model further simplified for runoff modeling. J Hydrol Eng 12(2):222–224

    Article  MathSciNet  Google Scholar 

  • Stone R (1980) Sigmoids. Bull Appl Stats 7(1):59–119

    Article  Google Scholar 

  • Subramanya K (2013) Engineering hydrology, 4th edn. McGraw Hill Education, India

    Google Scholar 

  • Tauxe GW (1978) S-Hydrographs and change of unit hydrograph duration. J Hydraulics Div, ASCE 104(3):439–444

    Google Scholar 

  • Verhulst PF (1838) Notice sur la loi que la population poursuit dans son accroissement. Corresp Math Phys 10:113–121

    Google Scholar 

  • Verhulst PF (1845) Recherches mathĂ©matiques sur la loi d’accroissement de la population [Mathematical researches into the law of population growth increase]. Nouv. M´em Acad R Sci B-Lett Brux 18:1–45

    Google Scholar 

  • Verhulst PF (1847) “Deuxième mĂ©moire sur la loi d’accroissement de la population. M´em Acad R Sci Lett B-Arts Belg 20:142–173

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Water Resources Development & Management, Indian Institute of Technology Roorkee, Roorkee, 247667, Uttarakhand, India

    P. R. Patil, S. K. Mishra & Nayan Sharma

  2. Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, 77843-2117, USA

    Vijay P. Singh

Authors
  1. P. R. Patil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. K. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nayan Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vijay P. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. R. Patil .

Editor information

Editors and Affiliations

  1. Department of Biological and Agricultural Engineering, and Zachry Department of Civil Engineering, Texas A&M University, College Station, Texas, USA

    Vijay P Singh

  2. Department of Civil Engineering, AISECT University, Bhopal, Madhya Pradesh, India

    Shalini Yadav

  3. AISECT University, Hazaribagh, Jharkhand, India

    Ram Narayan Yadava

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Patil, P.R., Mishra, S.K., Sharma, N., Singh, V.P. (2018). Nondimensional UH-Based Smoothing of S-Curve-Derived UH Oscillations. In: Singh, V., Yadav, S., Yadava, R. (eds) Hydrologic Modeling. Water Science and Technology Library, vol 81. Springer, Singapore. https://doi.org/10.1007/978-981-10-5801-1_42

Download citation

Publish with us

Policies and ethics

Search

Navigation