Statistics of low flow: Theoretical derivation of the distribution of minimum streamflow series

Journal of Hydrology

Volumn 481, Issue , 2013, Pages 204-219

  Gottschalk, Lars ^a   Yu, Kun xia ^a   Leblois, Etienne ^b   Xiong, Lihua ^a  

^a WUHAN UNIVERSITY   (China)

^b CEMAGREF   (France)

Author keywords

Block method; Derived distribution; Low flow; Pit Under Threshold; Power law distribution; Weibull distribution

Indexed keywords

BLOCK METHODS; DERIVED DISTRIBUTION; LOW FLOW; PIT UNDER THRESHOLD; POWER LAW DISTRIBUTION;

STATISTICAL METHODS; STREAM FLOW; UNCERTAINTY ANALYSIS; WEIBULL DISTRIBUTION;

PARAMETER ESTIMATION;

DATA PROCESSING; DRAINAGE BASIN; OPTIMIZATION; PARAMETERIZATION; REGIONAL PATTERN; STATISTICAL ANALYSIS; STREAMFLOW; THEORETICAL STUDY; WEIBULL THEORY;

FRANCE; LORRAINE; MOSELLE;

EID: 84873258812     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2012.12.047     Document Type: Article

References (41)

1. Bernier, J., 1964. La prévision statistique des bas débits. In: Symp. on Surface Waters, General Assembly of Berkley, IAHS Publication No. 63, pp. 340-351.
2. Bernier J. Inventaire des modelés de processus stochastiques applicables à la description des débits journaliers des rivières. Revue de l'Institute International de Statistique 1970, 38(1):49-61.
3. Brutsaert W., Nieber J.L. Regionalized drought flow hydrographs from mature glaciated plateau. Water Resour. Res. 1977, 13(3):637-643.
4. Chaves, A., Krasovskaia, I., Gottschalk, L., 2006. Environmental demands for sustainable regulation schemes in humid tropics. In: Climate Variability and Change-Hydrological Impacts. Proceedings of the Fifth FRIEND World Conference held at Havana, Cuba, November 2006. IAHS Publ. 308. IAHS Press, Wallingford, UK, pp. 569-572.
5. Chen Y.D., Huang G., Shao Q., Xu C. Regional analysis of low flow using L-moments for Dongjiang basin, South China. Hydrol. Sci. J. 2006, 51(6):1051-1064.
6. Cramér H. Mathematical Methods of Statistics. Twelfth Printing 1971, Princeton University Press, Princeton.
7. Dooge, J.C.I., 1973. Linear Theory of Hydrologic Systems. Technical Bulletin No. 1468. US Department of Agriculture, Washington.
8. Dunbar, M.J., Gustard, A., Acreman, M.C., Elliott, C.R.N., 1998. Overseas Approaches to Setting River Flow Objectives. Institute of Hydrology, R&D Technical Report W6-161.
9. Eagleson P.S. Dynamics of flood frequency. Water Resour. Res. 1972, 8(4):878-898.
10. Embrechts P., Klüppelberg C., Mikosch T. Modelling Extremal Events for Insurance and Finance. Second Printing 1999, Springer, Berlin.
11. Fenessey N.M., Vogel R.M. Regional flow-duration curves for ungauged sites in Massachussets. J. Water Resour. Plann. Manage. 1990, 116(4):530-549.
12. Fisher R.A., Tippet L.H.C. Limiting forms of the frequency distributions of the largest or smallest member of a sample. Proc. Camb. Philos. Soc. 1928, 24:180-190.
13. Gottschalk L., Perzyna G. A physically based distribution function of low flows. J. Hydrol. Sci. 1989, 34(5):559-573.
14. Gottschalk L., Tallaksen L., Perzyna G. Determination low flow distribution functions with the help of recession curves. J. Hydrol. 1997, 194:239-262.
15. Gottschalk L., Leblois E., Skøien J.O. Correlation and covariance of runoff revisited. J. Hydrol. 2011, 398:76-90.
16. Gottschalk L., Krasovskaia I., Yu K.-X., Leblois E., Xiong L. Joint mapping of streamflow descriptors. J. Hydrol. 2013, 478:15-28.
17. Gumbel E.J. Statistics of Extremes 1958, Columbia University Press, New York.
18. Gustard A., Roald L.A., Demuth S., Lumadjeng H.S., Gross R. Flow Regimes from Experimental and Network Data (FREND). Hydrological Studies 1989, vol. 1. Institute of Hydrology, Wallingford.
19. Hisdal, H., Tallaksen, L.M., Clausen, B., Peters, E., Gustard, A., 2004. Hydrological drought characteristics. In: Tallaksen, L., van Lanen, H.A.J. (Eds.), Hydrological Drought. Elsevier, pp. 139-198 (Chapter 5).
20. Jowett I.C. Instream flow methods: a comparison of approaches. Regul. Rivers: Res. Manage. 1997, 13:115-127.
21. Kroll, C., 2005. Modeling recession curves and low streamflow. In: Anderson, M.G., McDonnell, J.J. (Eds.), Encyclopaedia of Hydrological Sciences, vol. 3. John Wiley & Sons, pp. 1955-1966 (Chapter 126).
22. Krasovskaia, I., Gottschalk, L., Leblois, E., Pacheco, A., 2006. Regionalization of flow duration curves. IAHS Publ. 308. IAHS Press, Wallingford, UK. pp. 105-110.
23. Langbein W.B. Annual floods and the partial-duration flood series. Trans. Am. Geophys. Union 1949, 30(6):879-881.
24. Lee K.S., Kim S.U. Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method. Hydrol. Process. 2008, 22:1949-1964.
25. Mamun A.A., Hashim A., Daoud J.I. Regionalisation of low flow frequency curves for the Peninsular Malaysia. J. Hydrol. 2010, 381(1-2):174-180.
26. Önöz B., Bayazit M. Through under threshold modeling of minimum flows in perennial streams. J. Hydrol. 2002, 258:187-197.
27. Pacheco, A., Gottschalk, L., Krasovskaia, I., 2006. Regionalization of low flow in Costa Rica. In: Climate Variability and Change-Hydrological Impacts. Proceedings of the Fifth FRIEND World Conference Havana, Cuba, November 2006. IAHS Publ. 308. IAHS Press, Wallingford, UK, pp. 111-116.
28. Perzyna G. Spatial and temporal characteristics of maximum dry spells in southern Norway. Int. J. Climatol. 1994, 14:895-909.
29. Pickands J. Statistical inference using extreme order statistics. Ann. Stat. 1975, 3(1):119-131.
30. Reiss R.-D., Thomas M. Statistical Analysis of Extreme Values 2001, Birkhäuser, Basel, p. 23. second ed.
31. Ryu J.H., Lee J.H., Jeong S., Park S.K., Han K. The impacts of climate change on local hydrology and low flow frequency in the Geum River Basin, Korea. Hydrol. Process. 2011, 25(22):3437-3447.
32. Smakhtin V.U. Low flow hydrology: a review. J. Hydrol. 2001, 240:147-186.
33. Tallaksen, L., van Lanen, H.A.J. (Eds.), 2004. Hydrological Drought. Elsevier.
34. Tennant D.L. Instream Flow regimes for fish, wildlife, recreation and related environmental resources. Fisheries 1976, 1(4):6-10.
35. Weibull, W.A., 1939. A Statistical Theory of the Strength of Materials. Ingeniörsvetenskaps-akademien, Handlingar 151, Stockholm.
36. Weiss G. Shot noise models for the generation of synthetic streamflow data. Water Resour. Res. 1977, 13(1):101-108.
37. Vidal J.-P., Martin E., Franchistéguy L., Baillon M., Soubeyroux J.-M. A 50-year high-resolution atmospheric reanalysis over France with the Safran system. Int. J. Climatol. 2010, 30(11):1627-1644.
38. Vogel R.M., Fennessey N.M. L-moment diagrams should replace product moment diagrams. Water Resour. Res. 1993, 29(6):1745-1752.
39. Wilson E.M. Engineering Hydrology 1969, Macmillan, London.
40. Xu Z.X., Schultz G.A., Schumann A. A conceptually based stochastic point process model for daily stream-flow generation. Hydrol. Process. 2002, 16:3003-3017.
41. Yue S., Hashino M., Bobee B., Rasmussen P.F., Ouarda T.B.M.J. Derivation of streamflow statistics based on a filtered point process. Stoch. Environ. Res. Risk Assess. 1999, 13:317-326.