Water Resources Management

, Volume 3, Issue 2, pp 107–128

On the parametric approach to unit hydrograph identification

Authors

  • Demetris Koutsoyiannis
    • Department of Civil Engineering, Division of Water ResourcesNational Technical University of Athens
  • Themistocle Xanthopoulos
    • Department of Civil Engineering, Division of Water ResourcesNational Technical University of Athens
Article

DOI: 10.1007/BF00872467

Cite this article as:
Koutsoyiannis, D. & Xanthopoulos, T. Water Resour Manage (1989) 3: 107. doi:10.1007/BF00872467

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.

Key words

Unit hydrographinstantaneous unit hydrographidentificationprobability density functionprobability distribution functionmethod of momentsoptimization

Notations

A

catchment area

a,b,c

definition parameters (generallya is a scale parameter, whileb andc are shape parameters)

Cv

coefficient of variation

Cs

skewness coefficient

D

net rainfall duration

f( )

probability density function (PDF)

F( )

cumulative (probability) distribution function (CDF)

g( )

objective function

H

net rainfall depth

H0

unit (net) rainfall depth (=10 mm)

I(t)

net hyetograph

i(t)

standardized net hyetograph (SNH)

In

nth central moment of the standardized net hyetograph

Q(t)

surface runoff hydrograph

q(t)

standardized surface runoff hyrograph (SSRH)

Qn

nth central moment of the standardized surface runoff hydrograph

SD(t)

S-curve derived from a unit hydrograph of durationD

s(t)

standardizedS-curve (SSC)

t

time

TD

flood duration of the unit hydrographUD(t)

T0

flood duration of the instantaneous unit hydrographU0(t) (= right bound of the functionU0(t))

tU

IUH lag time (defined as the time from the origin to the center of area of IUH or SIUH)

tI

time from the origin to the center of the area of the net hyetograph

tQ

time from the origin to the center of the area of the surface runoff hydrograph

tp

time from the origin to the peak of IUH (or SIUH)

UD(t)

unit hydrograph for rainfall of durationD (DUH)

Uo(t)

instantaneous unit hydrograph (IUH)

u(t)

standardized instantaneous unit hydrograph (SIUH)

Un

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

V0

volume corresponding to the unit hydrograph

Copyright information

© Kluwer Academic Publishers 1989