ISSN : 1225-6692(Print)
ISSN : 2287-4518(Online)
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
DOI : https://doi.org/10.5467/JKESS.2013.34.1.51
비선형 대기 모형에서 수치 해의 시간 간격 민감도
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
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.
time step,nonlinear atmospheric models,numerical solutions,small scale phenomena,spatial filter,시간 간격,비선형 대기 모형,수치 해,작은 규모의 현상,공간 필터
- 0124-01-0034-0001-5.pdf2.01MB
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2.Baik, J. J. and Chun, H. Y., 1996, Effects of nonlinearity on the atmospheric flow response to low level heating in a uniform flow. Journal of the Atmospheric Sciences, 53, 1856 1869.
3.Betz, V. and Mittra, R., 1992, Comparison and evaluation of boundary conditions for the absorption of guided waves in an FDTD simulation. IEEE Microwave Guided Wave Letter, 2, 499 501.
4.Chun, H. Y., Choi, H. J., and Song, I. S., 2008, Effects of nonlinearity on convectively forced internal gravity waves: Application to a gravity wave drag parameterization. Journal of the Atmospheric Sciences, 65, 557 575.
5.Han, J. Y. and Baik, J. J., 2012, Nonlinear effects on convectively forced two dimensional mesoscale flows. Journal of the Atmospheric Sciences, 69, 3391 3404.
6.Lorenz, E.N., 1963, Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130 141.
7.Mishra, S.K., Srinivasan, J., and Nanjundiah, R.S., 2008, The impact of the time step on the intensity of ITCZ in an aquaplanet GCM. Monthly Weather Review, 136, 4077 4091.
8.Navon, I.M. and Riphagen, H.A., 1979, An implicit compact fourth order algorithm for solving the shallow water equation in conservation law form. Monthly Weather Review, 107, 1107 1127.
9.Pandya, R. and Durran, D.R., 1996, The influence of convectively generated thermal forcing on the mesoscale circulation around squall lines. Journal of the Atmospheric Sciences, 53, 2924 2951.
10.Pielke, R.A, Sr., 2002, Mesoscale meteorological modeling, 2nd edition. Academic Press, London, UK, 676 p.
11.Teixeira, J., Reynolds, C.A., and Judd, K., 2007, Time step sensitivity of nonlinear atmospheric models: Numerical convergence, truncation error growth, and ensemble design. Journal of the Atmospheric Sciences, 64, 175 189.
12.Williamson, D.L. and Olson, J.G., 2003, Dependence of aqua planet simulations on time step. Quarterly Journal of the Royal Meteorological Society, 129, 2049 2064.
13.Xue, M., 2000, High order monotonic numerical diffusion and smoothing. Monthly Weather Review, 128, 2853 2864.