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ISSN : 1225-6692(Print)
ISSN : 2287-4518(Online)
Journal of the Korean earth science society Vol.34 No.1 pp.51-58
DOI : https://doi.org/10.5467/JKESS.2013.34.1.51

비선형 대기 모형에서 수치 해의 시간 간격 민감도

이현호1·백종진1,*·한지영2
1서울대학교 지구환경과학부, 151-742, 서울특별시 관악구 관악로 1
2(재)한국형수치예보모델개발사업단, 156-849, 서울특별시 동작구 신대방2동 395-65
대기 모델링 연구에서 시간 간격을 적절하게 결정하는 것은 중요한 문제이다. 본 연구에서는 비선형 대기 모형에서 수치 해의 시간 간격에 대한 민감도를 조사하였다. 이를 위해 간단한 무차원화된 역학 모형을 사용하여 시간 간격과 비선형성 인자를 바꾸어가며 수치 실험을 수행하였다. 실험 결과, 비선형성 인자가 영향을 줄 만큼 크지 않고 절단 오차를 무시할 수 있는 경우에는 수치 해가 시간 간격에 민감하지 않았다. 그러나 비선형성 인자가 큰 경우에는 수치 해가 시간 간격에 민감한 것으로 밝혀졌다. 이 경우, 시간 간격이 감소할수록 공간 필터의 강도가 증가하여 작은 규모의 현상이 약하게 모의되었다. 이는 일반적으로 시간 간격이 감소하면 절단 오차가 감소하여 더 정확한 수치 해가 도출된다는 사실과 상충한다. 이러한 충돌은 비선형 모형의 수치 해를 안정하게 하기 위해 공간 필터가 반드시 필요하기 때문에 피할 수 없다.

Sensitivity of Numerical Solutions to Time Step in a Nonlinear Atmospheric Model

*Corresponding author: jjbaik@snu.ac.kr

Tel: +82 2 880 6990

Fax: +82 2 883 4972
, Hyunho Lee1, Jong-Jin Baik1,*, and Ji-Young Han2

1School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Korea
2Korea Institute of Atmospheric Prediction Systems, Seoul 156-849, Korea

Abstract

An appropriate determination of time step is one of the important problems in atmospheric modeling. In thisstudy, we investigate the sensitivity of numerical solutions to time step in a nonlinear atmospheric model. For thispurpose, a simple nondimensional dynamical model is employed, and numerical experiments are performed with varioustime steps and nonlinearity factors. Results show that numerical solutions are not sensitive to time step when thenonlinearity factor is not influentially large and truncation error is negligible. On the other hand, when the nonlinearityfactor is large (i.e., in a highly nonlinear regime), numerical solutions are found to be sensitive to time step. In thissituation, smaller time step increases the intensity of the spatial filter, which makes small scale phenomena weaken. Thisconflicts with the fact that smaller time step generally results in more accurate numerical solutions owing to reducedtruncation error. This conflict is inevitable because the spatial filter is necessary to stabilize the numerical solutions of thenonlinear model.

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