Prediction of Flow Duration Curves for Ungauged Basins with Quasi-Newton Method


Prediction of flow-duration-curves (FDC) is an important task for water resources planning, management and hydraulic energy production. Classification of the basins as carstic and non-carstic may be used to estimate parameters of the FDC with predictive tools for catchments with/without observed stream flow. There is a need for obtaining FDC for ungauged stations for efficient water resource planning. Thus, study proposes a quite new approach, called the EREFDC model, for estimating the parameters of the FDC for which the parameters of the FDC are obtained with quasi-Newton method. Estimation are made for using the bv gauged stations at first than the FDC parameters are estimated for ungauged stations based on drainage area, annual mean precipitation, mean permeability, mean slope, latitude, longitude, and elevation from the mean sea level are used. The EREFDC model consists of various type of linear- and nonlinear mathematical equations, is able to predict a wide range of the FDC parameters for gauged and ungauged basins. The method is applied to 72 unimpaired catchments studied are about for 50 years average daily measured stream flow. Results showed that the EREFDC model may be used for estimating. FDC parameters for ungauged hydrological basins in order to find FDC for ungauged stations. Results also showed that the EREFDC model performs better in carstic regions than non-carstic regions. In addition, parameters of FDC for tributaries at the basins with insufficient flow data or without flow data may be determined by using basin characteristics.

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M. Yaşar and N. Baykan, "Prediction of Flow Duration Curves for Ungauged Basins with Quasi-Newton Method," Journal of Water Resource and Protection, Vol. 5 No. 1, 2013, pp. 97-110. doi: 10.4236/jwarp.2013.51012.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. M. Vogel and N. M. Fennessey, “Flow Duration Curves II: A Review of Applications in Water Resources Planning,” Journal of the American Water Resources Association, Vol. 31, No. 6, 1995, pp. 1029-1039. doi:10.1111/j.1752-1688.1995.tb03419.x
[2] C. C. Warnick, “Hydropower Engineering,” Englewood Cliffs, New Jersey, 1984.
[3] D. R. Maidment, “Handbook of Hydrology,” McGraw-Hill, Colombus, 1992.
[4] N. Fennessey and R. M. Vogel, “Regional Flow Duration Curves for Ungauged Sites in Massachusetts,” Journal of Water Resources Planning and Management, Vol. 116, No. 4, 1990, pp. 530-549. doi:10.1061/(ASCE)0733-9496(1990)116:4(530)
[5] M. Mimikou and S. Kaemaki, “Regionalization of Flow Duration Characteristics,” Journal of Hydrology, Vol. 82, No. 1-2, 1985, pp. 77-91. doi:10.1016/0022-1694(85)90048-4
[6] A. Alkan, “Karst Pinar Katkili Akarsularda, Serbest Yüzeyli Akisli Cevirme Santrallar1 iCin Ak1m Sürek Egrilerinin Modellenmesi,” III. Ulusal Hidroloji Kongresi, IzmIr, 2001, pp. 247-255.
[7] R. D. SIngh, S. K. MIshra and H. Chowdhary, “RegIonal Flow-DuratIon Models for Large Number of Ungauged HImalayan Catchments for PlannIng MIcrohydro Projects, Journal of HydrologIc EngIneerIng, Vol. 6, No. 4, 2001, pp. 310-316. doI:10.1061/(ASCE)1084-0699(2001)6:4(310)
[8] P. S. Yu and T. C. Yang, “UncertaInty AnalysIs of RegIonal Flow DuratIon Curves,” Journal of Water Resources PlannIng and Management, Vol. 128, No. 6, 2002, pp. 424-430. doI:10.1061/(ASCE)0733-9496(2002)128:6(424)
[9] M. FranchInI and M. Suppo, “RegIonal AnalysIs of Flow DuratIon Curves for a LImestone RegIon,” Water Resources Management, Vol. 10, No. 3, 1996, pp. 199-218. doI:10.1007/BF00424203
[10] P. S. Yu and T. C. Yang, “SynthetIc RegIonal Flow DuratIon Curve for Southern TaIwan,” HydrologIcal Processes, Vol. 10, No. 3, 1996, pp. 373-391. doI:10.1002/(SICI)1099-1085(199603)10:3<373::AID-HYP306>3.0.CO;2-4
[11] K. M. Crocker, M. D. Z. Young and H. G. Rees, “Flow DuratIon Curve EstImatIon In Ephemeral Catchments In Portugal,” HydrologIcal ScIences, Vol. 48, No. 3, 2003, pp. 427-439. doI:10.1623/hysj.48.3.427.45287
[12] R. A. J. Cole, H. T. Johnston and D. J. RobInson, “The Use of Flow DuratIon Curves as a Data QualIty,” HydrologIcal ScIences, Vol. 48, No. 6, 2003, pp. 939-951.
[13] I. KrasovskaIa, I. Gottschalk, E. LebloIs and A. Pacheco, “RegIonalIzatIon of Flow DuratIon Curves,” In: S. Demuth, Eds., ClImate VarIabIlIty and Change-HydrologIcal Impacts, IAHS Press, WallIngford, 2006.
[14] M. F. BarI and Kh. M. D. S. Islam, “StochastIc Model of Flow DuratIon Curves for Selected RIvers In Bangladesh,” ClImate VarIabIlIty and Change-HydrologIcal Impacts, ProceedIngs of the 5th FRIEND World Conference, Havana, 27 November-1 December 2006, pp. 99-104.
[15] I. A. NIadas, “RegIonal Flow DuratIon Curve EstImatIon In Small Ungauged Catchments UsIng Instantaneous Flow Measurements and a Censored Data Approach,” Journal of Hydrology, Vol. 314, No. 1-4, 2005, pp. 48-66. doI:10.1016/j.jhydrol.2005.03.009
[16] A. CastellarIn, G. GaleatI, L. BrandImatre, A. MontanarI and A. Brath, “RegIonal Flow-DuratIon Curves: RelIabIlIty for Ungauged BasIns,” Advances In Water Resources, Vol. 27, No. 10, 2004, pp. 953-965. doI:10.1016/j.advwatres.2004.08.005
[17] L. MIng, S. QuanxI, Z. Lu and H. S. C. FrancIs, “A New RegIonalIzatIon Approach and Its ApplIcatIon to PredIct Flow DuratIon Curve In Ungauged BasIns,” Journal of Hydrology, Vol. 389, No. 1-2, 2010, pp. 137-145. doI:10.1016/j.jhydrol.2010.05.039
[18] D. Ganora, P. Claps, F. LaIo and A. VIglIone, “An Approach to EstImate NonparametrIc Flow DuratIon Curves In Ungauged BasIns,” Water Resources Research, Vol. 45, W10418, 2009. doI:10.1029/2008WR007472
[19] Y. Yokoo and M. SIvapalan, “Towards ReconstructIon of the Flow DuratIon Curve: Development of a Conceptual Framework wIth a PhysIcal BasIs,” Hydrology and Earth System ScIences, Vol. 15, No. 9, 2011, pp. 2805-2819.
[20] F. VIola, L. V. Noto, M. Cannarozzo and G. La LoggIa, “RegIonal Flow DuratIon Curves for Ungauged SItes In SIcIly,” Hydrology and Earth System ScIences, Vol. 15, No. 1, 2011, pp. 323-331.
[21] MIcrosoft, “MIcrosoft Excel-VIsual BasIc for ApplIcatIons,” MIcrosoft Press, WashIngton DC, 1995.
[22] H. C. RIggs, “Low-Flow InvestIgatIons,” US GeologIcal Survey TechnIques of Water-Resources InvestIgatIons, WashIngton DC, 1972.
[23] L. C. Kjelstrom, “Methods for EstImatIng Selected Flow-DuratIon and Flood-Frequency CharacterIstIcs at Ungauged SItes In Central Idaho,” USGS Water Resources InvestIgatIons Report 94-4120, BoIse, 1998, p. 10.
[24] S. E. Studley, “EstImated Flow DuratIon Curves for Selected Ungauged SItes In Kansas,” US GeologIcal Survey, 01:4142, VIrgInIa, 2001.
[25] J. Nocedal and S. J. WrIght, “NumerIcal OptImIzatIon,” SprInger-Verlag, BerlIn, 2006.
[26] J. S. Arora, “IntroductIon to OptImum DesIgn,” McGraw-HIll, New York, 1989.
[27] H. Karahan, G. Gurarslan and Z. W. Geem, “Parameter EstImatIon of the NonlInear MuskIngum Flood RoutIng Model UsIng a HybrId Harmony Search AlgorIthm,” Journal of HydrologIc EngIneerIng, 2012, In Press. doI:10.1061/(ASCE)HE.1943-5584.0000608
[28] C. A. Perry, D. M. Volock and J. C. Artman, “EstImates of Flow DuratIon, Mean Flow and Peak-DIscharge Frequency Values for Kansas Stream LocatIon,” ScIentIfIc InvestIgatIon Report 2004-5033, US GeologIcal Survey, VIrgInIa, 2004.

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