Skip to main content

Streamflow Drought Frequency Analysis

  • Chapter
Drought and Drought Mitigation in Europe

Part of the book series: Advances in Natural and Technological Hazards Research ((NTHR,volume 14))

Abstract

An overview of methods for streamflow drought frequency analysis for a single site is presented. A streamflow drought is defined as a period when the discharge is below a given threshold level. A distinction is made between the minimum low flow discharge of a drought event, and the corresponding deficit volume and duration of the event. Different ways of defining low flow and drought events and different approaches to estimate drought characteristics and extreme events from time series of flow are discussed. The paper focuses on frequency analysis: in this case sample properties of the selected events are used as a basis for estimating design events. Finally, some alternatives to traditional at-site frequency analysis are outlined.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Al-Mashidani, G., Lal, B.B., and Quadri, I. (1980) Drought Flow Analysis of River Tigris in Baghdad, Hydrological Science Journal 25 (4): 453–459.

    Article  Google Scholar 

  • Ashkar, F., Jabi, N.EI., and Issa, M. (1998) A Bivariate Analysis of the Volume and Duration of Low-Flow Events, Stochastic Hydrol. Hydraul. 12: 97–116.

    Article  Google Scholar 

  • Ashkar, F. and Ouarda, Taha B.M.J. (1996) On some Methods of Fitting the Generalized Pareto Distribution, Journal Hydrol. 177: 117–141.

    Article  Google Scholar 

  • Askew, A.J., Yeh, W.W-G., and Hall, W.A. (1971) A Comparative Study of Critical Drought simulation, Water Resources Research 7 (1): 52–62.

    Article  Google Scholar 

  • Bernier, J. (1964) La prévision statistique des bas débits, in Symposium on Surface Waters (General Assembly of Berkley), IAHS Pub1. 63, 340–351.

    Google Scholar 

  • Bonacci, O. (1993) Hydrological Identification of Drought, Hydrol. Proc. 7: 249–262.

    Article  Google Scholar 

  • Bulu, A. (1997) Statistical Analysis of Low Flow with Zero Discharges, in FRIEND: Flow Regimes from international experimental and network data, Third report, Cemagref, 167–170.

    Google Scholar 

  • Chang, T.J. and Stenson, J.R. (1990) Is it realistic to define a 100-year drought for water management? Water Resources Bulletin 26 (5): 823–829.

    Article  Google Scholar 

  • Clausen, B. and Pearson, C.P. (1995) Regional Frequency Analysis of Annual Maximum Streamflow Drought, Journal of Hydrology, 173: 111–130.

    Article  Google Scholar 

  • Coles, S. (1999) Extreme Value Theory and Applications, Course notes, http://www.maths.lancs.ac.uk/coless

  • Cramér, H. and Leadbetter, M.R. (1967) Stationary and Related Stochastic Processes, New York, John Wiley and Sons.

    Google Scholar 

  • Cunnane, C. (1979) A Note on the Poisson Assumption in Partial Duration Series Models, Water Resources Research 15 (2): 489–494.

    Article  Google Scholar 

  • Cunnane, C. (1985) Factors Affecting Choice of Distribution for Flood Series, Hydrological Science Journal 30 (1): 25–36.

    Article  Google Scholar 

  • Dracup, J.A., Lee, K.S., and Paulson, E.G. (1980) On the Definition of Droughts, Water Resources Research 16 (2): 297–302.

    Article  Google Scholar 

  • Drayton, R.S., Kidd, C.H.R., Mandeville, A.N., and Miller, J.B. (1980) A Regional Analysis of River Floods and Low Flows in Malawi, Report No 72, Institute of Hydrology, Wallingford, UK.

    Google Scholar 

  • Embrechts, P., Kliippelberg, C., and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance,Springer.

    Google Scholar 

  • Ewart, Ch.J. and Brutsaert, W. (1972) Some Generalized Characteristics of the Floods and Droughts of the Lower Mekong, Hydrological Science Journal 17 (3): 323–338.

    Article  Google Scholar 

  • Filliben, J.J. (1975) The Probability Plot correlation Test for Normality, Technometrics 17(1): 111–117. Fisher, R.A. and Tippett, L.H.C. (1928) Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample, Proc. Cambridge Philosophical Society 24 (2): 180–190.

    Google Scholar 

  • Gordon, N.D., McMahon, T.A. and Finlayson, B.L. (1992) Stream Hydrology (An Introduction for Ecologists),J. Wiley and Sons.

    Google Scholar 

  • Gottschalk, L., Tallaksen, L.M., and Perzyna, G. (1997) Derivation of Low Flow Distribution Functions Using Recession Curves, Journal Hydrol. 194: 239–262.

    Article  Google Scholar 

  • Gumbel, E.J. (1958) Statistics of Extremes, Columbia Univ. Press. New York.

    Google Scholar 

  • Gustard, A., Roald, L.A., Demuth, S., Lumadjeng, H.S., and Gross, R. (1989) Flow Regimes from Experimental and Network Data (FRIEND), vol. 1 Hydrological Studies, Institute of Hydrology, Wallingford, UK.

    Google Scholar 

  • Güven, O. (1983) A Simplified Semi-empirical Approach to Probabilities of Extreme Hydrologic Drought, Water Resources Research 19 (2): 441–453.

    Article  Google Scholar 

  • Haan, Ch.T. (1977) Statistical Methods in Hydrology, The Iowa State University Press, Ames.

    Google Scholar 

  • Hosking, J.R.M. (1990) L-moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics, Journal Royal Statistical Society 52 (1): 105–124.

    Google Scholar 

  • Institute of Hydrology (1980) Low Flow Studies Report, Wallingford, UK.

    Google Scholar 

  • Institute of Hydrology (1988) Water Balance Study, Phase 3 Report: Investigation of Dry Season Flows (Lower Mekong Basin) Wallingford, UK.

    Google Scholar 

  • Jenkingson, A.F. (1955) The Frequency Distribution of the Annual Maximum (or Minimum) Values of Meteorological Elements, Quat. Journal Royal Met. Soc. 87 (158).

    Google Scholar 

  • Joseph, E.S. (1970) Probability Distribution of Annual Droughts, Journal Irrig. Drain. Div., ASCE 96 (IR4), 461–474.

    Google Scholar 

  • Kite, G.W. (1977) Frequency and Risk Analyses in Hydrology, Water Res. Publ., Fort Collins, Colorado.

    Google Scholar 

  • Kjeldsen, T.R. and Lundorf, A. (1997) Drought Management and Modelling — Zimbabwe Case, MSc Thesis, DTU, Technical University of Denmark.

    Google Scholar 

  • Klemes, V. (1993) Probability of Extreme Hydrometeorological Events - a Different Approach, in Extreme Hydrological Events: Precipitation, Floods and Droughts (Proc. Yokohama Symp., July, 1993), IAHS Publ. 213.

    Google Scholar 

  • Kundzewicz, Z.W., Rosbjerg, D., Simonovic, S.P., and Takeuchi, K. (1993) Extreme Hydrological Events in Perspective, in Extreme Hydrological Events: Precipitation, Floods and Droughts (Proc. Yokohama Symp., July, 1993), IAHS Publ. 213.

    Google Scholar 

  • Madsen, H. and Rosbjerg, D. (1995) A Regional Bayesian Method for Estimation of Extreme Streamflow Droughts, Paper presented at the Conference on Statistical and Bayesian Methods in Hydrology, Paris, UNESCO, September 11–13, 1995.

    Google Scholar 

  • Matalas, N.C. (1963) Probability Distribution of Low Flows, U.S.G.S. Prof. Pap. 434-A, Washington, D.C.

    Google Scholar 

  • Matalas, N.C. (1991) Drought Description, Stochastic Hydrol. Hydraul. 5: 255–260.

    Article  Google Scholar 

  • Mathier, L., Perreault, L., and Bobeé B. (1992) The Use of Geometric and Gamma Related Distributions for Frequency Analysis of Water Deficit, Stochastic Hydrol. Hydraul. 6: 239–254.

    Article  Google Scholar 

  • McKay, G.A., Godwin, R.B., and Maybank, J. (1989) Drought and Hydrological Drought Research in Canada, An Evaluation of the State of the Art, Canadian Water Res. Journal 14 (3): 71–84.

    Article  Google Scholar 

  • Milian, J. and Yevjevich, V., (1971) Probabilities of Observed Droughts, Colorado State University, Hydrology Paper 50, Fort Collins, Colorado, USA.

    Google Scholar 

  • Mises, R. von (1936) La distribution de la plus grande de n valeurs, in Ph. Frank, S. Goldstein, M. Kac, W. Prager, G. Szegö, and G Birkhoff (eds.), Selected papers of Richard von Mises, vol II: Probability and Statistics, General, Amer. Math. Soc., Providence, R.I. (1964), 271–294.

    Google Scholar 

  • Moyé, L.A. and Kapadia, A.S. (1995) Predictions of Drought Length Extreme Order Statistics Using Run Theory, Journal Hydrol. 169: 95–110.

    Article  Google Scholar 

  • Nathan, R.J. and McMahon, T.A. (1990) Practical Aspect of Low-Flow Frequency Analysis, Water Resources Research 26 (9): 2135–2141.

    Google Scholar 

  • Nordin, C.F. (1968) The Statistical Properties of Dune Profiles, U.S.Geol. Survey Open File Report.

    Google Scholar 

  • Nordin, C.F. and Rosbjerg (1970) Application of Crossing Theory in Hydrology, Bull. Int. Ass. Sci. Hydrol., XV 1 (3): 27–43.

    Article  Google Scholar 

  • Phien, H.N. (1982) Moments of the Run-sum for Independent Sequences, Journal Hydrol. 54: 389–400.

    Google Scholar 

  • Pickands, J. III (1975) Statistical Inference Using Extreme Order Statistics, Ann. Statist. 3: 119–131.

    Google Scholar 

  • Pilon, P.J. (1990) The Weibull Distribution Applied to Regional Low Flow Frequency Analysis, in Regionalization in Hydrology (Proc. Ljubljana Symp., April 1990 ), IAHS Publ. 191: 227–237.

    Google Scholar 

  • Polarski, M. (1989) Fitting Distributions to Annual Minimum Flows of Different Duration, in FRIENDS in Hydrology, IAHS Publ. 187: 97–104.

    Google Scholar 

  • Rice, S.O. (1945) Mathematical Analysis of Random Noise, Bell System Tech. Journal 24: 46–156.

    Google Scholar 

  • Rodriguez-Iturbe, I. (1968) A Modern Statistical Study of Monthly Levels of the Orinoco River, Bull. Int. Assoc. Scientific Hydrology 13 (4): 25–40.

    Article  Google Scholar 

  • Rosbjerg, D., (1977) Crossing and Extremes in Dependent Annual Series, Nordic Hydrol. 8: 257–266.

    Google Scholar 

  • Rossi, F., Fiorentino, M. and Versace, P. (1984) Two-component Extreme Value Distribution for Flood Frequency Analysis, Water Resources Research, 20 (7): 847–856.

    Article  Google Scholar 

  • Rossi, G., Benedini, M., Tsakiris, G., and Giakoumakis, S. (1992) On Regional Drought Estimation and Analysis, Wat. Res. Man. 6: 249–277.

    Google Scholar 

  • Saldarriaga, J. and Yevjevich, V. (1970) Application of Run-lengths to Hydrologic Series, Colorado State University, Hydrology Paper 40, Fort Collins, Colorado, USA.

    Google Scholar 

  • Santos, M.A. (1983) Regional Droughts: a Stochastic Characterisation, Journal Hydrol. 66: 183–211.

    Article  Google Scholar 

  • Sen, Z. (1976) Wet and Dry Periods of Annual Flow Series, Journal Hydraul. Div., ASCE 102 (HY10): 1503–1514.

    Google Scholar 

  • Sen, Z. (1977) Run-sums of Annual Flow Series, Journal Hydrol. 35: 311–324.

    Article  Google Scholar 

  • Sen, Z. (1980a) Statistical Analysis of Hydrological Critical Droughts, Journal Hydraul. Div., ASCE 106 (HY1): 99–114.

    Google Scholar 

  • Sen, Z. (1980b) Regional Drought and Flood Frequency Analysis: Theoretical Consideration, Journal Hydrol. 46: 265–279.

    Article  Google Scholar 

  • Stahl, K. and Demuth, S. (1999) Investigating the Influence of Atmospheric Circulation Patterns on Regional Streamflow Drought in Southern Germany, Proceedings of XXII General Assembly of the International Union of Geodesy and Geophysics, Birmingham, UK, 18–30 July 1999, IAHS Publ. 255: 19–27.

    Google Scholar 

  • Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E. (1993) Frequency Analysis of Extreme Events, in D.R. Maidment (ed.), Handbook of Hydrology, McGraw-Hill.

    Google Scholar 

  • Tallaksen, L.M., Madsen, H., and Clausen, B. (1997) On the Definition and Modelling of Streamflow Drought Duration and Deficit Volume, Hydrological Science Journal 42 (1).

    Google Scholar 

  • Tallaksen, L.M. and Hisdal, H. (1997) Regional Analysis of Extreme Streamflow Drought Duration and Deficit Volume, Proceedings of the 3’ d International conference on FRIEND, 1–4 Oct. 1997, Postojna, Slovenia, IAHS Publ. 246: 141–150.

    Google Scholar 

  • Tase, N. (1976) Area-deficit-intensity Characteristics of Droughts, Hydrology Paper 87, Colorado State University, Fort Collins, Co., USA.

    Google Scholar 

  • Todorovic, P., (1970) On Some Problems Involving Random Number of Random variables, Ann. Math. Statist. 41 (3): 1059–1063.

    Article  Google Scholar 

  • Troutman, B. M. (1978) Reservoir Storage with Dependent, Periodic Net Inputs, Water Resources Research 14 (3): 395–401.

    Article  Google Scholar 

  • Vogel, R.M. and Fennessey, N.M. (1993) L-moment Diagrams Should Replace Product Moment Diagrams, Water Resour. Res. 29 (6): 1745–1752.

    Article  Google Scholar 

  • Weibull, W. (1961) Fatigue Testing and Analysis of Results, Pergamon Press.

    Google Scholar 

  • Woo, M-K. and Tarhule, A. (1994) Streamflow Droughts of Northern Nigerian Rivers, Hydrological Science Journal 39 (1): 19–34.

    Article  Google Scholar 

  • Yevjevich, V. (1967) An Objective Approach to Definition and Investigations of Continental Hydrologic Droughts, Hydrology paper 23, Colorado State University, Fort Collins, Co., USA.

    Google Scholar 

  • Zelenhasic, E. and Salvai, A. (1987) A method of Streamflow Drought Analysis, Water Resources Research 23(1): 156168.

    Google Scholar 

  • Zucchini, W. and Adamson, P.T. (1984) Assessing Risk of Deficiencies in Streamflow, Water Res. Comm. Rep. 91(2), Univ. of Stellenbosch, Stellenbosch, S.A.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Tallaksen, L.M. (2000). Streamflow Drought Frequency Analysis. In: Vogt, J.V., Somma, F. (eds) Drought and Drought Mitigation in Europe. Advances in Natural and Technological Hazards Research, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9472-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9472-1_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5568-2

  • Online ISBN: 978-94-015-9472-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics