Journal of Korean Society of Disaster and Security (한국방재안전학회논문집)

Korean Society of Disaster & Security (한국방재안전학회)
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Convolution Interpretation of Nonparametric Kernel Density Estimate and Rainfall-Runoff Modeling

비매개변수 핵밀도함수와 강우-유출모델의 합성곱(Convolution)을 이용한 수학적 해석

  • 이태삼 (경상대학교 토목공학과 ERI)
  • Received : 2015.05.20
  • Accepted : 2015.06.12
  • Published : 2015.06.30
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Abstract

In rainfall-runoff models employed in hydrological applications, runoff amount is estimated through temporal delay of effective precipitation based on a linear system. Its amount is resulted from the linearized ratio by analyzing the convolution multiplier. Furthermore, in case of kernel density estimate (KDE) used in probabilistic analysis, the definition of the kernel comes from the convolution multiplier. Individual data values are smoothed through the kernel to derive KDE. In the current study, the roles of the convolution multiplier for KDE and rainfall-runoff models were revisited and their similarity and dissimilarity were investigated to discover the mathematical applicability of the convolution multiplier.

수문학에서 사용되는 강우-유출 모델의 경우 선형적인 시스템을 기반으로 유효강수량으로부터 시간적 지연을 통해서 유출량이 결정되는데 그 양은 강우량의 선형적인 비로 표현되어서 결국 합성곱을 통해 해석되게 된다. 또한 자료에 대한 확률론적 분석에 많이 이용되는 비매개변수 핵밀도함수의 경우, 핵(Kernel)의 의미자체가 합성곱에서 나온 것으로서 개개의 자료를 바탕으로 핵을 통해 매끄러운 확률밀도함수를 구하게 된다. 본 연구에서는 합성곱을 바탕으로 강우-유출 모델과 비매개변수 확률밀도함수를 해석하는 방법에 대해서 되짚어 보고 그 공통적인 특성과 다른 점을 수학적으로 나타내 줌으로써 사용되는 합성곱 함수의 유용성에 대해서 논하였다.

Keywords

References

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