Theoretical analysis of quantification of drought frequency inflow series via K-water cumulative difference method

Jiheun Kim; Jae Hwang Lee; Young-Oh Kim

doi:10.3741/JKWRA.2022.55.9.701

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2022 Vol.55, Issue 9 Preview Page

Technical Note

Theoretical analysis of quantification of drought frequency inflow series via K-water cumulative difference method 누가차분법을 통한 가뭄 빈도유입량 산정에 관한 이론적 고찰

30 September 2022. pp. 701-705

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Abstract

Reliable drought inflow scenarios are required to plan reservoirs in response to the present severe drought-like conditions. However, the previously developed method for generating drought inflows, the K-water cumulative difference method (KCM), is considered inadequate owing to its potential for negative inflow, reversal phenomena, and overestimation. Nevertheless, the occurrence of these aspects has not been theoretically analyzed. Hence, this study employed the quantile function and frequency factor for log-normal and Gumbel distributions to quantify the contributing factors of these limitations. Consequently, it was found that the negative inflows are generated when the difference in the location parameters, during the accumulation process, exceeds that of the scale parameters. In addition, as the standard deviation decrease during the accumulation process, the reversal phenomena, and inflated values prevailed.

Keywords

K-water cumulative difference method

Drought inflow

Drought frequency analysis

Quantile function

Frequency factor

이상기후로 가뭄이 빈번해짐에 따라 수자원 시설의 가뭄대응력 산정에 대한 필요성이 커지고 있다. 이를 위해서는 신뢰할 수 있는 갈수빈도 유입량 추정 연구가 선행되어야 한다. 본 연구는 기존 K-water의 가뭄 빈도유입량 추정방법인 누가차분법의 세 가지 한계, 즉 음의 값과 역전현상, 그리고 평년 이상으로 과대 산정되는 문제의 발생조건에 대해 각각 2변수 log-normal 분포와 Gumbel 분포를 적용하여 이론적 고찰을 실시하였다. 그 결과, 음의 값은 누가 과정에서 scale parameter보다 location parameter의 변화가 커지는 경우 발생함을 확인하였고, 역전현상 및 평년보다 큰 가뭄유입량은 누가 과정에서 표준편차가 감소하는 경우 발생하는 것으로 분석되었다.

키워드

누가차분법

가뭄유입량

갈수빈도분석

분위수 함수

빈도계수법

References

Chow, V.T. (1951). "A general formula for hydrologic frequency analysis." Eos, Transactions American Geophysical Union, Vol. 32, No. 2, pp. 231-237. 10.1029/TR032i002p00231

Jung, Y., Nam, W., Shin, H., and Heo, J. (2012). "A study on low-flow frequency analysis using dam inflow." Journal of the Korean Society of Civil Engineering, Vol. 32, No. 6B, pp. 363-371. 10.12652/Ksce.2012.32.6B.363

Kenney, J.F. (1951). Mathmetics of statistics. Pt. 2, 2nd ed. Princeton, Van Nostrand, NJ, U.S., p. 123.

Kim, H.S., Kim, H.S., Jeon, G.I., and Gang, S.U. (2016). "Assessment of the 2014-2015 drought in Korea." Water for Future, Vol. 49, No. 7, pp. 61-75.

K-water (2016). Improvement of the frequency estimation method on dam inflow for the optimal reservoir operation. Publication No. KIWE-WRRC-16-01, Korea Water Resources Corporation, Deajeon, Republic of Korea, pp. 11-14.

Ryoo, K., Lee, H.-G., Park, J.-H., and Hur, Y-T. (2009). "Improvement of estimation method on the low flow frequency inflow for the optimal reservoir operation." Proceeding of 2009 Conference, KWRA, pp. 1287-1291.

Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 55
No :9
Pages :701-705
Received Date : 2022-08-24
Accepted Date : 2022-08-31
DOI :https://doi.org/10.3741/JKWRA.2022.55.9.701

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

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