Comparative study on the regression equation of Huff time distribution for design rainfall

Yoohyun Beck; Minseok Park; Jaehyun Ahn

doi:10.3741/JKWRA.2025.58.5.425

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2025 Vol.58, Issue 5 Preview Page Next Page

Research Article

Comparative study on the regression equation of Huff time distribution for design rainfall 설계강우량 Huff 시간분포 회귀식에 관한 비교연구

31 May 2025. pp. 425-438

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Abstract

The temporal distribution of design rainfall is a key parameter in hydraulic structure design; however, the conventional 6th polynomial regression method has practical limitations, including rainfall reversal and underestimation of cumulative rainfall at 100% duration. To address these issues, this study proposes an improved methodology that introduces an additional arbitrary duration beyond 100%, with zero rainfall, ensuring the cumulative rainfall percentage accurately reaches 100%. Three regression techniques were applied: monotonic polynomial regression, modified logistic growth regression, and cubic spline interpolation. The derived regression equations were visualized as hyetographs to support practical application. Results confirmed that all methods satisfied the total rainfall condition of 100%. Monotonic polynomial regression showed superior practical applicability, with an average R²of 99.87% and MAPE of 9.69%. The modified logistic growth regression achieved an average R²of 99.72% and MAPE of 13.93%, providing a simplified equation and stable hyetograph. Cubic spline interpolation yielded perfect statistical performance (R²=100.0%, MAPE=0.00%), but required segmented regression equations, limiting its practicality. This study demonstrates that the proposed approaches effectively address the limitations of conventional polynomial regression and offer reliable alternatives for accurate and practical estimation of rainfall temporal distribution.

Keywords

Design rainfall

Polynomial regression

Monotonic polynomial regression

Modified growth logistic regression

Cubic spline regression

설계강우량의 시간분포는 수공구조물 설계의 핵심 요소로, 기존 6차 다항 회귀식은 강우 역전현상과 시간 100%에서 무차원 강우량 미달 등 실무적 한계를 드러내고 있다. 이를 해결하기 위해 본 연구에서는 무차원 누가지속기간 100% 이후에 강우량이 0 mm인 100%를 초과하는 지속기간을 추가하는 새로운 방법을 적용한 단조 다항 회귀분석과 수정 성장형 로지스틱 회귀분석 및 3차 스플라인 기법을 활용하여 Huff 누가강우백분율의 회귀식을 산정하고 이를 우량 주상도로 시각화했다. 각 회귀분석 방법별로 산정한 회귀식을 이용하여 설계강우량을 시간분포한 결과 총 강우량이 모두 100% 만족하는 것으로 나타났다. 통계량은 단조 다항식의 경우 결정계수 평균 99.87%와 MAPE 평균 9.69%로 우수한 통계적 성능과 높은 실무 적합성을 보였으며, 수정 성장형 로지스틱은 결정계수 평균과 MAPE 평균이 99.72%와 13.93%로 분석되면서 간결한 회귀식과 이상적인 주상도를 제공했다. 3차 스플라인은 결정계수 100.0%, MAPE 0.00%로 통계적으로 완벽했으나, 구간별 개별 회귀식 필요로 인해 실무 적용에서 복잡성이 높게 평가됐다. 본 연구는 기존 다항 회귀분석의 한계를 극복할 대안으로 세 가지 회귀 기법의 유효성을 입증했으며, 강우 시간분포 산정의 정확성과 실무 활용성을 높이는 새로운 대안을 제시했다.

키워드

설계강우량

다항 회귀분석

단조 다항 회귀분석

수정 성장형 로지스틱 회귀분석

3차 스플라인

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Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 58
No :5
Pages :425-438
Received Date : 2025-01-08
Revised Date : 2025-02-21
Accepted Date : 2025-03-25
DOI :https://doi.org/10.3741/JKWRA.2025.58.5.425

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

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