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| Titel |
Generalized function of the parameters in the storage-discharge relation for low flows |
| VerfasserIn |
Kazumasa Fujimura, Yoshihiko Iseri, Shinjiro Kanae, Masahiro Murakami |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250104019
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| Publikation (Nr.) |
 EGU/EGU2015-3439.pdf |
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| Zusammenfassung |
| The accurate estimation of low flows can contribute to better water resource management and
more reliable evaluation of the impact of climate change on water resources. For the case of
low flows, the nonlinearity of the discharge Q associated with the storage S was originally
proposed by Horton (1936) as the power function Q=KSN, where K is a constant and N is
the exponent. Although the Q(S) relations for groundwater runoff from unconfined aquifers
have been treated as second-order polynomial functions on the basis of the hydraulic
investigation by Ding (1966), the general power function Q = KNSN was introduced into
the unit hydrograph model for overland flow and the parameters K and N were
calibrated by Ding (2011). According to recent studies, the value of the exponent N is
varied between 1 and 3 or higher by calibration (e.g., Wittenberg, 1994 and Ding,
2011); however, it is currently unclear whether the optimum value of N has the
rule.
Fujimura et al. (2014) applied the general power function Q = KNSN for low flows in
mountainous basins over a period spanning more than 10 years using hourly data, and carried
out sensitivity analysis using a hydrological model for 19Â900 sets of the two parameters K
and N, in which the exponent N was varied between 1 and 100 in steps of 0.5. The results
showed that the optimum relation between N and K could be characterized by the
exponential function K=1/(α Nβ), where α and β are constants. Moreover, the
lowest error in the sensitivity analysis was obtained by using an exponent N of
100.
The aim of this study is to extend the previous study of Fujimura et al. to clarify the
properties of the K(N) relations. A sensitivity analysis is performed efficiently using a
hydrological model, in which the exponent N is varied between 1 and 100Â000 along the
neighborhood of the exponential function K=1/(α Nβ). The hourly hydrological model used
in this study comprises the Diskin-Nazimov infiltration model, groundwater recharge and
groundwater runoff calculations, and a direct runoff component. The study basins are four
mountainous basins in Japan with different climate and geology: the Sameura Dam
basin (472km2) and the Seto River basin (53.7km2) within the Sameura Dam basin,
which are located in western Japan and have variable of rainfall, and the Shirakawa
Dam basin (206km2) and the Sagae Dam basin (233km2), which are located in a
region of heavy snowfall in eastern Japan. The period of available hourly data for the
former two basins is 20 years from 1 January 1991 to 31 December 2010, and the
period for the latter two basins is 11 years and 12 years from 1 October 2003 to 30
September 2014. The analysis is evaluated using the average of daily runoff relative error
(ADRE). The plot of logK against logN with the lowest ADRE yields a straight line,
K=1/(αNβ), in which the value of β is 1.0 and the correlation coefficient of the
line is 1.0 for N values in the range from 100 to 100Â000. We can conveniently
assume the K(N) relation to be K=1/(100α) when N =100. Therefore, the Q(S)
relation can be converted to Q={S/(100α)}100, where only one parameter, α, is
used.
References
Ding, J. Y. (1966) Discussion of “Inflow hydrographs from large unconfined aquifers”
by Ibrahim, H. A. and Brutsaert, W., J. Irrig. Drain. Div., ASCE, 92, 104–107. //
Ding, J. Y. (2011) A measure of watershed nonlinearity: interpreting a variable
instantaneous unit hydrograph model on two vastly different sized watersheds. Hydrol.
Earth Syst. Sci., 15, 405–423. // Fujimura, Y., Iseri, K., Kanae, S. & Murakami, M.
(2014) Identification of low-flow parameters using hydrological model in selected
mountainous basins in Japan, IAHS Publ. 364, 51-56. // Horton, R. E. (1936) Natural
stream channel-storage. Trans. Am. Geophys. Union, 17, 406–415. // Wittenberg, H.
(1994) Nonlinear analysis of low flow recession curves. IAHS Publ. 221, 61-67. |
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