Abstract
Unit hydrograph identification by the parametric approach is based on the assumption of a proper analytical form for its shape, using a limited number of parameters. This paper presents various suitable analytical forms for the instantaneous unit hydrograph, originated from known probability density functions or transformations of them. Analytical expressions for the moments of area of these form versus their definition parameters are theoretically derived. The relation between moments and specific shape characteristics are also examined. Two different methods of parameter estimation are studied, the first being the well-known method of moments, while the second is based on the minimization of the integral error between derived and recorded flood hydrographs. The above tasks are illustrated with application examples originated from case studies of catchments in Greece.
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Abbreviations
- A :
-
catchment area
- a,b,c :
-
definition parameters (generallya is a scale parameter, whileb andc are shape parameters)
- C v :
-
coefficient of variation
- C s :
-
skewness coefficient
- D :
-
net rainfall duration
- f( ):
-
probability density function (PDF)
- F( ):
-
cumulative (probability) distribution function (CDF)
- g( ):
-
objective function
- H :
-
net rainfall depth
- H 0 :
-
unit (net) rainfall depth (=10 mm)
- I(t):
-
net hyetograph
- i(t):
-
standardized net hyetograph (SNH)
- I n :
-
n th central moment of the standardized net hyetograph
- Q(t):
-
surface runoff hydrograph
- q(t):
-
standardized surface runoff hyrograph (SSRH)
- Q n :
-
n th central moment of the standardized surface runoff hydrograph
- S D (t):
-
S-curve derived from a unit hydrograph of durationD
- s(t):
-
standardizedS-curve (SSC)
- t :
-
time
- T D :
-
flood duration of the unit hydrographU D (t)
- T 0 :
-
flood duration of the instantaneous unit hydrographU 0(t) (= right bound of the functionU 0(t))
- t U :
-
IUH lag time (defined as the time from the origin to the center of area of IUH or SIUH)
- t I :
-
time from the origin to the center of the area of the net hyetograph
- t Q :
-
time from the origin to the center of the area of the surface runoff hydrograph
- t p :
-
time from the origin to the peak of IUH (or SIUH)
- U D (t):
-
unit hydrograph for rainfall of durationD (DUH)
- U o (t):
-
instantaneous unit hydrograph (IUH)
- u(t):
-
standardized instantaneous unit hydrograph (SIUH)
- U n :
-
nth central moment of area of IUH
- U′ n :
-
nth moment of IUH about the origin
- U″ n :
-
nth moment of IUH about the right bound (when exists)
- V :
-
surface runoff volume
- V 0 :
-
volume corresponding to the unit hydrograph
References
Koutsoyiannis, D., Vassilopoulos, E., and Karalis, E., 1982,Hydrological Study of the Iliolousto Dam (in Greek), Greek Ministry of Public Works.
Kumaraswamy, P., 1980, A generalized probability density function for double bounded random variables,J. Hydrol. 46, 79–88.
Nash, J. E., 1959, Systematic determination of unit hydrograph parameters,J. Geophys. Res. 64, 111–115.
O'Donnell, T., 1986, Deterministic catchment modelling, in D. A. Kraijenhoff and J. R. Moll (eds.),River Flow Modelling and Forecasting, D. Reidel, Dordrecht.
Sutcliffe, J. V., 1978,Methods of Floof Estimation, A Guide to Flood Studies Report, Institute of Hydrology, Report No. 49.
Xanthopoulos, Th., Koutsoyiannis, D., Roti, S., and Tzeranis, J., 1988,Hydrological Investigation of the Thessalia Water Basin, Report on Design Floods (in Greek), Nat. Tech. Univ. of Athens.
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Koutsoyiannis, D., Xanthopoulos, T. On the parametric approach to unit hydrograph identification. Water Resour Manage 3, 107–128 (1989). https://doi.org/10.1007/BF00872467
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DOI: https://doi.org/10.1007/BF00872467