Determination of optimal order for the full-logged I-D-F polynomial equation and significance test of regression coefficients

Jin Hee Park; Jae Joon Lee

doi:10.3741/JKWRA.2022.55.10.775

All Issue

2022 Vol.55, Issue 10 Preview Page Next Page

Research Article

Determination of optimal order for the full-logged I-D-F polynomial equation and significance test of regression coefficients 전대수 다항식형 확률강우강도식의 최적차수 결정 및 회귀계수에 대한 유의성 검정

31 October 2022. pp. 775-784

PDF XML

Abstract

In this study, to determine the optimal order of the full-logged I-D-F polynomial equation, which is mainly used to calculate the probable rainfall over a temporal rainfall duration, the probable rainfall was calculated and the regression coefficients of the full-logged I-D-F polynomial equation was estimated. The optimal variable of the polynomial equation for each station was selected using a stepwise selection method, and statistical significance tests were performed through ANOVA. Using these results, the statistically appropriately calculated rainfall intensity equation for each station was presented. As a result of analyzing the variable selection outputs of the full-logged I-D-F polynomial equation at 9 stations in Gyeongbuk, the 1^st to 3^rd order equations at 6 stations and the incomplete 3^rd order at 1 station were determined as the optimal equations. Since the 1^st order equation is similar to the Sherman type equation and the 2^nd order one is similar to the general type equation, it was presented as a unified form of rainfall intensity equation for convenience of use by increasing the number of independent variables. Therefore, it is judged that there is no statistical problem in considering only the 3^rd order polynomial regression equation for the full-logged I-D-F.

Keywords

Full-logged I-D-F polynomial equation

Optimal order

Stepwise selection

Statistical significance test

본 연구에서는 임의지속기간의 확률강우량 산정을 위해 실무에서 주로 사용되고 있는 전대수 다항식형 확률강우강도식의 최적차수 결정을 위하여 경상북도 내 9개 지점을 대상으로 확률강우량을 산정하고 전대수 다항식형 강우강도식의 회귀계수를 추정하였다. 추정된 지점별 다항식을 대상으로 단계선택법을 이용하여 각 지점별 다항식의 최적변수를 선정하고 선정된 변수들의 통계적 유의성을 검토하기 위하여 분산분석을 통한 유의성 검정을 실시하였으며, 이들 결과를 이용하여 각 지점별 통계적으로 적절하게 산정된 강우강도식을 제시하였다. 경북 9개 지점의 전대수 다항식형 강우강도식의 변수선정 결과는 6개 지점에서 1~3차식이 최적식으로 나타났고 1개 지점이 불완전 3차식이 최적식으로 나타났다. 그 중 1차는 Sherman 식, 2차는 General 식의 형태와 유사하므로 독립변수의 수를 증가시켜 적합도를 높이고 사용 편의를 위해 통일된 형태의 강우강도식으로 제시한다면 전대수 다항식형 강우강도식은 3차 회귀식까지만 고려하여도 통계학적으로 문제가 없는 것으로 판단된다.

키워드

전대수 다항식형 확률강우강도식

최적차수

단계 선택법

유의성 검정

References

Allen, D.M. (1971). The prediction sum of squares as a criterion for selecting predictor variables. Technical Report no.23, Department of Statistics, University of Kentucky, KT, U.S.

Heo, J.H., Kim, K.D., and Han, J.H. (1999). "Derivation of rainfall Intensity-Duration-Frequency equation based on the approproate probability distribution." Journal of Korea Water Resources Association, Vol. 32, No. 3, pp. 247-254.

Jeong, J.H., Ryu, G.H., and Kim, J.C. (2017). "A practical method for derivation of 'rainfall intensity - Duration' curve." The Magazine of The Korean Society of Hazard Mitigation, Vol. 17, No. 3, pp. 49-54.

Kim, T.S., Shin, J.Y., Kim, S.Y., and Heo, J.H. (2007). "Parameter estimation of Intensity-Duration-Frequency curve using genetic algorithm (I): Comparison study of existing estimation method." Journal of Korea Water Resources Association, Vol. 40, No. 10, pp. 811-821. 10.3741/JKWRA.2007.40.10.811

Lee, J.J., Son, K.I., Lee, W.H., and Lee, K.C. (1981). "A study on the analysis of time-regional distribution of precipitation frequency and rainfall intensity in Korea." Journal of Korean Association of Hydrological Sciences, KWRA, Vol. 14, No. 4, pp. 53-72.

Lee, W.H. (1967). "A study on rainfall characteristics and determination of probability rainfall amount at various district in Korea." Journal of the Korean Society of Civil Engineers, KSCE, Vol. 15, No. 3, pp. 28-38.

Lee, W.H. (1980). "A stochastic analysis on determination of design precipitation for planning of urbanized stream & sewerage." Journal of the Korean Society of Civil Engineers, KSCE, Vol. 28, No. 4, pp. 81-94.

Lee, W.H., and Byeon, K.J. (1969). "Study of the rainfall intensity probability formula required for designing city sewerage and river plans." Journal of the Korean Society of Civil Engineers, KSCE, Vol. 16, No. 4. pp. 1-11.

Lee, W.H., Park, S.D., and Choi, S.Y. (1993). "A derivation of the typical probable rainfall intensity formula in KOREA." Journal of the Korean Society of Civil Engineers, KSCE, Vol. 13, No. 1, pp.115-120.

Ministry of Environment (ME) (2019). Standard guidelines for flood estimation.

Ministry of Land, Transport and Maritime Affairs (MLTMA) (2011). Study of improvement and supplement of probability rainfall.

Ministry of Land, Transport and Maritime Affairs (MLTMA) (2012). Design flood calculation tips.

Ministry of the Interior and Safety (MOIS) (2021). Consultation on assessment of accidental impact, etc. Practical Guidelines.

National Emergency Management Agency (NEMA) (2010). A study for setting urban disaster prevention performance goals in consideration of climate change.

Park, J.H., and Lee, J.J. (2022). "Temporal distritution analysis of design rainfall by significance test of regression coefficients" Journal of Korea Water Resources Association, Vol. 55, No. 4, pp. 257-266.

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 :10
Pages :775-784
Received Date : 2022-09-15
Revised Date : 2022-09-26
Accepted Date : 2022-09-27
DOI :https://doi.org/10.3741/JKWRA.2022.55.10.775

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

All Issue