Skip to main content
SpringerLink
Log in

A joint probability approach for coincidental flood frequency analysis at ungauged basin confluences

  • Original Paper
  • Published:
Natural Hazards Aims and scope Submit manuscript

Abstract

A reliable and accurate flood frequency analysis at the confluence of streams is of importance. Given that long-term peak flow observations are often unavailable at tributary confluences, at a practical level, this paper presents a joint probability approach (JPA) to address the coincidental flood frequency analysis at the ungauged confluence of two streams based on the flow rate data from the upstream tributaries. One case study is performed for comparison against several traditional approaches, including the position-plotting formula, the univariate flood frequency analysis, and the National Flood Frequency Program developed by US Geological Survey. It shows that the results generated by the JPA approach agree well with the floods estimated by the plotting position and univariate flood frequency analysis based on the observation data.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Ang AH-S, Tang HW (1975) Probability concepts in engineering planning and design. In: Basic principles, vol 1. Wiley, New York, 424 pp

  • Ashkar F, El Jabi N, Issa M (1998) A bivariate analysis of the volume and duration of low-flow events. Stoch Hydrol Hydraul 12:97–116

    Article  Google Scholar 

  • Beersma JJ, Buishand TA (2004) Joint probability of precipitation and discharge deficits in the Netherlands. Water Resour Res. doi:10.1029/2004WR003265

    Google Scholar 

  • Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. Wiley, New York, 424 PP

    Google Scholar 

  • Cunnane C (1988) Methods and merits of regional flood frequency analysis. J Hydrol 100:269–290

    Article  Google Scholar 

  • Durrans SR, Eiffe MA, Thomas WO Jr, Goranflo HM (2003) Joint seasonal/annual flood frequency analysis. J Hydrol Eng 8:181–189

    Article  Google Scholar 

  • Favre AC, El Adlouni S, Perreault L et al (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res. doi:10.1029/2003wr002456

    Google Scholar 

  • Flynn KM, Kirby WH, Hummel PR (2006) User’s manual for program PeakFQ, annual flood-frequency analysis using Bulletin 17B guidelines. U.S. Geological Survey, Techniques and methods book 4, chap B4. U.S. Geological Survey, Reston, VA, 42 pp

  • Genest C, Favre AC, Beliveau J, Jacques C (2007) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour Res. doi:10.1029/2006wr005275

    Google Scholar 

  • Griffis VW, Stedinger JR (2007a) Log-Pearson type 3 distribution and its application in flood frequency analysis. II: parameter estimation methods. J Hydrol Eng 12:492–500

    Article  Google Scholar 

  • Griffis VW, Stedinger JR (2007b) The log-Pearson type 3 distribution and its application in flood frequency analysis, 3. Sample skew and weighted skew estimators. J Hydrol Eng 14:121–130. doi:10.1061/_ASCE_1084-0699_2009_14:2_121

    Article  Google Scholar 

  • Griffis VW, Stedinger JR (2007c) Log-Pearson Type 3 distribution and its application in flood frequency analysis. I: distribution characteristics. J Hydrol Eng 12:482–491

    Article  Google Scholar 

  • Grimaldi S, Serinaldi F (2006) Design hyetograph analysis with 3-copula function. Hydrol Sci J 51:223–238

    Article  Google Scholar 

  • Johnson ME (1987) Multivariate statistical simulation. Wiley, New York

    Book  Google Scholar 

  • Karmakar S, Simonovic SP (2009) Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions. J Flood Risk Manag 2:32–44

    Article  Google Scholar 

  • Kite GW (1977) Frequency and risk analyses in hydrology. Water Resources Publications, Fort Collins, Colorado

  • Kotz S, Balakrishnan N, Johnson N (2000) Continuous multivariate distributions, vol 1: models and applications of series in probability and statistics

  • Kundzewicz ZW (2007) Prediction in ungauged basins—a systemic perspective. In: Hubert P (ed) Predictions in ungauged basins: PUB Kick-off. IAHS Publ. 309

  • Nelsen RB (2006) An introduction to copulas, ser. Lect. Notes Stat. Springer, New York

    Google Scholar 

  • Rao AR, Hamed HK (2000) Flood frequency analysis. CRC Press, New York

    Google Scholar 

  • Salarpour M, Yusop Z, Yusof F (2013a) Comparison of distribution models for peakflow, flood volume and flood duration. Res J Appl Sci Eng Technol 6:733–738

    Google Scholar 

  • Salarpour M, Yusop Z, Yusof F et al (2013b) Flood frequency analysis based on t-copula for Johor River, Malaysia. J Appl Sci 13:1021–1028

    Article  Google Scholar 

  • Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res. doi:10.1029/2004wr003133

    Google Scholar 

  • Shiau J-T, Feng S, Nadaraiah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol Process 21:2157–2163. doi:10.1002/hyp.6400

    Article  Google Scholar 

  • Singh VP, Jain SK, Tyagi A (2007) Risk and reliability analysis: a handbook for civil and environmental engineers. ASCE Press, Reston

    Book  Google Scholar 

  • Smith OE, Adelfang SI, Tubbs JD (1982) A bivariate gamma probability distribution with application to gust modeling. NASA Tech Memo 82483

  • Todini E, Partner S (1991) Hydraulic and hydrologic flood routing schemes. In: Bowles DS, O’Connell PE (eds) Recent advances in the modeling of hydrologic systems. NATO ASI Series C, vol 345. pp 389–406

  • U.S. Army Corps of Engineers (1994) Engineering and design—hydrologic engineering analysis concepts for cost-shared flood damage reduction studies

  • U.S. Geological Survey (2002) The national flood frequency program, version 3: a computer program for estimating magnitude and frequency of floods for ungaged sites

  • U.S. Geological Survey (2009) No Title. http://nm.water.usgs.gov/projects/floodanalysis/. Accessed 10 Feb 2010

  • Geological Survey US (2001) Techniques for estimating flood-frequency discharges for streams in Iowa. Iowa City, Iowa

    Google Scholar 

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

    Article  Google Scholar 

  • Wang QJ (2001) A Bayesian joint probability approach for flood record augmentation. Water Resour Res 37:1707–1712

    Article  Google Scholar 

  • Wang C (2007) A joint probability approach for the confluence flood frequency analysis. Iowa State University

  • Wang C, Chang N-B, Yeh G-T (2009) Copula-based flood frequency (COFF) analysis at the confluences of river systems. Hydrol Process 23:1471–1486

    Article  Google Scholar 

  • Yue S (2001) A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Process 15:1033–1045

    Article  Google Scholar 

  • Yue S, Rasmussen P (2002) Bivariate frequency analysis: discussion of some useful concepts in hydrological application. Hydrol Process 16:2881–2898

    Article  Google Scholar 

  • Yue S, Wang CY (2004) A comparison of two bivariate extreme value distributions. Stoch Environ Res Risk Assess 18:61–66

    Article  Google Scholar 

  • Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11:150–164. doi:10.1061/(asce)1084-0699(2006)11:2(150)

    Article  Google Scholar 

  • Zhang L, Singh VP (2007) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332:93–109. doi:10.1016/j.jhydrol.2006.06.033

    Article  Google Scholar 

Download references

Acknowledgments

Argonne National Laboratory’s work was supported under US Department of Energy contract DE-AC02-06CH11357.

Author information

Author notes

  1. Cheng Wang

    Present address: Environmental Science Division, Argonne National Laboratory, Lemont, IL, 60521, USA

Authors and Affiliations

  1. Department of Agricultural and Biosystems Engineering, Iowa State University, Ames, IA, 50010, USA

    Cheng Wang

Authors
  1. Cheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng Wang.

Additional information

The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a US Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The US Government retains for itself, and others acting on its behalf, a paid-up non-exclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C. A joint probability approach for coincidental flood frequency analysis at ungauged basin confluences. Nat Hazards 82, 1727–1741 (2016). https://doi.org/10.1007/s11069-016-2265-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-016-2265-5

Keywords

Search

Navigation