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지형자료의 국지 규모 분리를 위한 라플라시안 연산자의 이용
박자린,최석진 한국기상학회 2021 한국기상학회 학술대회 논문집 Vol.2021 No.10
지형 고도 자료는 수치 모델의 최하층 경계조건으로 항구적인 외부강제력으로 작용하여 대기 운동의 역학적, 물리적 현상의 모의에 직접적인 영향을 주는 요소이다. 또한, 수치 모델은 안정적인 모의를 위해 분해능과 이산 방안 등 사용하는 수치 계에 따라 관측된 지형자료로부터 일정 규모로 평활화된 자료를 사용해야만 한다. 산악 지역이 많은 한반도에서 국지기상 현상의 모의에 수치 지형 고도의 생성 방법과 그 평활화가 미치는 영향이 중요한 이유이다. 육면체구 격자 기반인 한국형 모델(Korean Integrated Model, KIM)의 지형은 전 지구 15초 SRTM(Shuttle Radar Topographic Mission) 지형 고도 자료로부터 격자점 평균 및 Spherical Harmonics(SPH) 스펙트럴 변환을 통해 생성해 왔다. SPH 스펙트럴 변환은 파수 절단으로 전구적으로 균일하게 등방성을 가지도록 평활화된 자료를 만들 수 있다. 그러나 국지 영역별 규모 분리를 하는 데 어려움이 있어 다양한 가변격자 체계에 대한 지형자료 생성을 지원하는 데 한계가 있다. 본 연구에서는 가변격자 체계를 지원하는 상세 지형 생성 도구로서 KIM의 역학코어 내에서 사용되는 라플라시안 연산(▽<SUP>2q</SUP>, q는 차수)을 이용한다. 이 방안은 역학코어와의 일관성을 가지며 라플라시안 계수와 적용 횟수를 통해 선택적 규모 분리와 국지적 상세 지형 묘사가 가능하다. 또한, 고차 라플라시안 연산을 이용함으로써 기존의 라플라시안 기반의 과도한 평활화 문제를 극복하였다. 상세 지형이 국지 기상 현상 모의에 미치는 영향을 보기 위해 8km 고해상도 모델에서 평활화 정도를 달리한 지형을 사용하여 강원지역의 지형성 소낙성 강수 사례를 모의하였다. 산악 지역에서의 상세 지형은 상승류를 발생시켜 강수 증가에 영향을 주었고, 이는 국지 지형성 강수예측 정확도 향상에 효과가 있음을 보인다.
박자린,최석진 한국기상학회 2020 Asia-Pacific Journal of Atmospheric Sciences Vol.56 No.1
This study used the time-split method for higher-order diffusion in a global numerical weather prediction model of the spectral element method on a cubed-sphere grid, and verified its performance compared to those of the explicit and implicit timestep diffusion schemes. Because the spectral element method on a cubed-sphere grid involves intrinsic characteristics of eigenvalues of the Laplacian operator, allowable timestep sizes are more restricted for stable time integration in higher-order diffusion. For example, the 6th-order diffusion significantly limits the timestep size for adequate filtering of small-scale numerical noise during simulation. The time-split scheme can be an alternative to overcome the severe constraints on the timestep size and allow the model a timestep size as large as is potentially acceptable even in higher-order diffusion, while maintaining atmospheric kinetic energy compared to that of the explicit and implicit schemes. During analysis of the amplification factor and numerical simulation of the schemes, it was shown that the time-split scheme has a theoretical response comparable to that of the explicit and implicit schemes. The numerical simulations were conducted using the Korean Integrated Model (KIM) with a 6th-order diffusion operator of three different diffusion schemes at resolutions of 0.25- or 0.125-degree grid spacing. The time-split scheme yields a forecast performance similar to both the explicit and implicit timestep schemes while greatly reducing the computational time.
Spectral Analysis Method for a Limited Area Using the Eigenmodes of the Spherical Laplacian Operator
박자린,정형빈 한국기상학회 2013 Asia-Pacific Journal of Atmospheric Sciences Vol.49 No.5
We propose a spectral analysis method using the eigenmodes of the spherical Laplacian operator on the limited area domain. Two numerical methods are considered for the horizontal discretization: One uses the half-ranged Fourier series for both longitudinal and latitudinal directions, and the other uses the Fourier finite-element method with piecewise linear basis functions for the latitudinal direction. The field variable for the two numerical algorithms is represented as linear combinations of the eigenvectors of the Laplacian operator on the limited area domain; we define the one-dimensional spectrum with the eigenvector coefficients as a function of the indices equivalent to the total wavenumbers of the Laplacian operator on the global domain. The spatial robustness of this method was verified through the self-consistency test comparing the spectra of isotropic Gaussian bells on the sphere. We used the method in the kinetic energy spectral analysis for a limited area with global atmospheric data, and compared the results for different seasons. The kinetic energy spectra represented the well-known characteristics with scale and different powers with season.
정형빈,박자린 한국지구과학회 2007 韓國地球科學會誌 Vol.28 No.7
Analytical geopotential field in balance with the sectoral mode (the first symmetric mode with respect to theequator) of the Rosby-Haurwitz wave on the inclined rotation axis was derived in presence of superrotation backgroundflow. The balanced field was obtained by inverting the divergence equation with the time derivative being zero. Theinversion consists of two steps, i.e., the evaluation of nonlinear forcing terms and the finding of analytical solutions basedon the Poisson’s equation. In the second step, the forcing terms in the form of Legendre function were readily inverteddue to the fact that Legendre function is the eigenfunction of the spherical Laplacian operator, while other terms weresolved either by introducing a trial function or by integrating the Legendre equation. The balanced field was found to beexpressed with six zonal wavenumber components, and shown to be of asymmetric structure about the equator. Inassociation with asymmetricity, the advantageous point of the balanced field as a validation method for the numericalmodel was addressed. In special cases where the strength of the background flow is a half of or exactly the same as therotation rate of the Earth, it was revealed that one of the zonal wavenumber components vanishes. The analyticalbalanced field was compared with the geopotential field which was obtained using a spherical harmonics spectral model.It was found that the normalized diference lied in the order of machine rounding, indicating the reliability of theanalytical results. The stability of the sectoral mode of Rossby-Haurwitz wave and the associated balanced field wasdiscussed, comparing with the first antisymmetric mode........... . : .... .... .. ..... , ... .... .... .... .. ... ... ........... .... (... .. .. .... . .. .. ). ... ... ...... ..... ..... . .