본 연구에서는 지역 영역 기상 수치 예보 모델의 여러 수평 영역 및 수평 해상도에 따른 이상적인 열대저기압 의 진로와 베타자이어의 민감도를 조사하였다. 모델의 이상적인 초기 조건은 경험적인 함수로 생성된 3차원 축대칭 모 조 소용돌이와 허리케인 활동 시기의 평균 대기 조건으로 구성된다. 이때 모델 설정에 따른 이상적인 열대저기압의 변 화를 분석하기 위하여 배경 흐름은 제거되었다. 수치 모델의 수평 영역 및 수평 해상도에 따른 이상적인 열대저기압의 민감도 실험을 수행하기 위해, 지역 영역 수치 모델로서 W RF (Weather Research a nd F orecasting) 모델을 사용하였다. 모의된 열대저기압의 바람장으로부터 베타자이어를 추출하기 위해, DFS (Double-Fourier Series) 국지 영역 고차 필터 를 사용하였다. 모델의 수평 영역의 크기가 감소할수록 베타자이어의 구조와 강도가 약해졌으며, 이는 열대저기압 진로 의 차이를 발생시켰다. 수평 영역의 크기를 본 연구의 실험에서 가장 작은 영역인 3,000 km3,000 km로 설정하였을 경 우에 베타자이어 통풍류의 서진 성분이 크게 감소하였으며, 수평 영역을 더 넓게 설정한 실험들에 비해 열대저기압의 진로가 동쪽으로 편향되었다. 본 결과는 열대저기압과 관련된 바람장 전체를 포함하지 못할 정도로 매우 작은 수평 영 역을 사용할 경우, 열대저기압의 진로가 적절히 모의 될 수 없음을 시사한다. 반면, 5,000 km5,000 km와 6,000 km 6,000 km의 수평 영역에서는 그 민감도가 매우 작게 나타났다. 수평 해상도가 감소할수록 이상적인 열대저기압의 진 로는 매우 서쪽으로 편향되었다. 베타자이어의 크기와 강도도 수평 해상도가 감소할수록 크고 더 강하게 나타났다.

Tropical cyclone scale vortices and associated Rossby waves were investigated numerically using high-resolution barotropic models on the global domain. The equations of the barotropic model were discretized using the spectral transform method with the spherical harmonics function as orthogonal basis. The initial condition of the vortex was specified as an axisymmetric flow in the gradient wind balance, and four types of basic zonal states were employed. Vortex tracks showed similar patterns as those on the beta-plane but exhibited more eastward displacement as they moved northward. The zonal-mean flow appeared to control not only the west-east translation but also the meridional translation of the vortex. Such a meridional influence was revealed to be associated with the beta gyre and the Rossby wave, which are formed around the vortex due to the beta effect. In the case of the basic zonal state of climatological mean, the meridional translation speed reached the maximum value when the vortex underwent recurving.

The impact of vertical grid-nesting on the tropical cyclone intensity and track forecast was investigated using the Weather Research and Forecast (WRF) version 3.8 and the initialization method of the Structure Adjustable Balanced Bogus Vortex (SABV). For a better resolution in the central part of the numerical domain, where the tropical cyclone of interest is located, a horizontal and vertical nesting technique was employed. Simulations of the tropical cyclone Sanba (16th in 2012) indicated that the vertical nesting had a weak impact on the cyclone intensity and little impact on the track forecast. Further experiments revealed that the performance of forecast was quite sensitive to the horizontal resolution, which is in agreement with previous studies. The improvement is due to the fact that horizontal resolution can improve forecasts not only on the tropical cyclone-scale but also for large-scale disturbances.

Effect of the nonuniform grid on the two-dimensional transport equation was investigated in terms of theoretical analysis and finite difference method (FDM). The nonuniform grid having a typical structure of the numerical weather forecast model was incorporated in the vertical direction, while the uniform grid was used in the zonal direction. The staggered and non-staggered grid were placed in the vertical and zonal direction, respectively. Time stepping was performed with the third-order Runge Kutta scheme. An error analysis of the spatial discretization on the nonuniform grid was carried out, which indicated that the combined effect of the nonuniform grid and advection velocity produced either numerical diffusion or numerical adverse-diffusion. An analytic function is used for the quantitative evaluation of the errors associated with the discretized transport equation. Numerical experiments with the non-uniformity of vertical grid were found to support the analysis.

Two dimensional finite element method with quadrilateral basis functions was applied to the spherical high order filter on the spherical surface limited area domain. The basis function consists of four shape functions which are defined on separate four grid boxes sharing the same gridpoint. With the basis functions, the first order derivative was expressed as an algebraic equation associated with nine point stencil. As the theory depicts, the convergence rate of the error for the spherical Laplacian operator was found to be fourth order, while it was the second order for the spherical Laplacian operator. The accuracy of the new high order filter was shown to be almost the same as those of Fourier finite element high order filter. The two-dimension finite element high order filter was incorporated in the weather research and forecasting (WRF) model as a hyper viscosity. The effect of the high order filter was compared with the built-in viscosity scheme of the WRF model. It was revealed that the high order filter performed better than the built in viscosity scheme did in providing a sharper cutoff of small scale disturbances without affecting the large scale field. Simulation of the tropical cyclone track and intensity with the high order filter showed a forecast performance comparable to the built in viscosity scheme. However, the predicted amount and spatial distribution of the rainfall for the simulation with the high order filter was closer to the observed values than the case of built in viscosity scheme.

전구영역 수치모델을 이용하여 순압 로스비-하우어비츠 파동의 안정성을 조사하였다. 본 연구에서 조사한 로스 비-하우어비츠 파동은 강체 회전하는 동서 기본류와 유한한 진폭을 가지는 구면조화 파동으로 구성된다. 로스비-하우어 비츠 파동은 강체 회전하는 동서 평균류의 강도에 따라 정상 또는 비정상의 구조로 나타난다. 수치 실험을 통해 임의 의 다른 두 시간에서 섭동장의 진폭을 비교하여 파동의 안정성뿐만 아니라 성장률을 결정하였다. 로스비-하우어비츠 파 동의 불안정 모드는 다양한 동서 파수 성분이 결합된 형태로 나타났다. 파동의 속도가 느린 지역에서 와도 섭동장은 불연속적인 형태를 보이는데, 이는 모델의 수평 해상도와 관계가 없는 것으로 밝혀졌다. 푸리에-유한 요소 모델에서 더 이른 적분 시간에 불안정 모드가 나타났는데, 이는 구면조화 스펙트럴 모델 대비 더 낮은 수치 정확도를 가지기 때문 인 것으로 보인다. 모델의 전체적인 정확도를 고려하여, 불안정 모드가 구면 조화 파동을 전체적으로 지배하기 시작하 는 시간을 추정하였다.

The high-order Laplacian-type filter, which is capable of providing isotropic and sharp cut-off filtering on the spherical domain, is essential in processing geophysical data. In this study, a spherical high-order filter was designed by combining the Fourier method with finite difference-method in the longitude and latitude, respectively. The regular grid system was employed in the filter, which has uniform angular spacing including the poles. The singularity at poles was eliminated by incorporating variable transforms and continuity-matching boundary conditions across poles. The high-order filter was assessed using the Rossby-Haurwitz wave, the observed geopotential, and observed wind field. The performance of the filter was found comparable to the filter based on the Galerkin procedure. The filter, employing the finite difference method, can be designed to give any target order of accuracy, which is an important advantage being unavailable in other methods. The computational complexity is represented with 2n-1 diagonal matrices solver with n being the target order of accuracy. Along with the availability of arbitrary target-order, it is also advantageous that the filter can adopt the reduced grid to increase computational efficiency.