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

비선형 대기 모형에서 수치 해의 시간 간격 민감도

  • Lee, Hyunho (School of Earth and Environmental Sciences, Seoul National University) ;
  • Baik, Jong-Jin (School of Earth and Environmental Sciences, Seoul National University) ;
  • Han, Ji-Young (Korea Institute of Atmospheric Prediction Systems)
  • 이현호 (서울대학교 지구환경과학부) ;
  • 백종진 (서울대학교 지구환경과학부) ;
  • 한지영 ((재)한국형수치예보모델개발사업단)
  • Received : 2012.12.12
  • Accepted : 2013.01.24
  • Published : 2013.02.28

Abstract

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

Acknowledgement

Supported by : 기상청

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