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      이중 푸리에 급수 분광법 역학코어의 정확도와 계산 효율성 평가 = Evaluation of Accuracy and Efficiency of Double Fourier Series (DFS) Spectral Dynamical Core

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      https://www.riss.kr/link?id=A108727490

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      다국어 초록 (Multilingual Abstract)

      The double Fourier series (DFS) spectral dynamical core is evaluated for the two idealized test cases in comparison with the spherical harmonics (SPH) spectral dynamical core.
      A new approach in calculating the meridional expansion coefficients of DFS, which was recently developed to alleviate a computational error but only applied to the 2D spherical shallow water equation, is also tested. In the 3D deformational tracer transport test, the difference is not conspicuous between SPH and DFS simulations, with a slight outperformance of the new DFS approach in terms of undershooting problem. In the baroclinic wave development test, the DFS-simulated wave pattern is quantitatively similar to the SPH-simulated one at high resolutions, but with a substantially lower computational cost. The new DFS approach does not offer a salient advantage compared to the original DFS while computation cost slightly increases. This result suggests that the current DFS spectral method can be a practical and alternative dynamical core for high-resolution global modeling.
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      The double Fourier series (DFS) spectral dynamical core is evaluated for the two idealized test cases in comparison with the spherical harmonics (SPH) spectral dynamical core. A new approach in calculating the meridional expansion coefficients of DFS,...

      The double Fourier series (DFS) spectral dynamical core is evaluated for the two idealized test cases in comparison with the spherical harmonics (SPH) spectral dynamical core.
      A new approach in calculating the meridional expansion coefficients of DFS, which was recently developed to alleviate a computational error but only applied to the 2D spherical shallow water equation, is also tested. In the 3D deformational tracer transport test, the difference is not conspicuous between SPH and DFS simulations, with a slight outperformance of the new DFS approach in terms of undershooting problem. In the baroclinic wave development test, the DFS-simulated wave pattern is quantitatively similar to the SPH-simulated one at high resolutions, but with a substantially lower computational cost. The new DFS approach does not offer a salient advantage compared to the original DFS while computation cost slightly increases. This result suggests that the current DFS spectral method can be a practical and alternative dynamical core for high-resolution global modeling.

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      참고문헌 (Reference)

      1 Hortal, M., "Use of Reduced Gaussian Grids in Spectral Models" 119 : 1057-1074, 1991

      2 Robert, A. J., "The integration of a low order spectral form of the primitive meteorological equations" 44 : 237-245, 1966

      3 Williamson D. L, "The evolution of dynamical cores for global atmospheric models" 85B : 241-269, 2007

      4 Boyd, J. P., "The choice of spectral functions on a sphere for boundary and eigenvalue problems: A comparison of Chebyshev, Fourier and associated Legendre expansions" 106 : 1184-1191, 1978

      5 구명서 ; 송강현 ; 김정은 ; 손석우 ; 장은철 ; 정지훈 ; 김형준 ; 문병권 ; 박록진 ; 예상욱 ; 유창현 ; 홍송유, "The Global/Regional Integrated Model System (GRIMs): an Update and Seasonal Evaluation" 한국기상학회 59 (59): 113-132, 2023

      6 홍성유 ; 박훈 ; 정형빈 ; 김정은 ; 구명서 ; 장지현 ; 함수륜 ; 황승오 ; 박병권 ; 장은철 ; Haiqin Li, "The Global/Regional Integrated Model System (GRIMs)" 한국기상학회 49 (49): 219-243, 2013

      7 Sela, J. G., "Spectral modeling at the National Meteorological Center" 108 : 1279-1292, 1980

      8 Yee, S. Y. K., "Solution of Poisson’s equation on a sphere by truncated double Fourier series" 109 : 501-505, 1981

      9 Yoshimura, H., "Improved double Fourier series on a sphere and its application to a semi-implicit semi-Lagrangian shallow water model" 15 : 2561-2597, 2022

      10 Cheong, H. -B., "High-order harmonic spectral filter with the double Fourier series on a sphere" 177 : 313-335, 2002

      1 Hortal, M., "Use of Reduced Gaussian Grids in Spectral Models" 119 : 1057-1074, 1991

      2 Robert, A. J., "The integration of a low order spectral form of the primitive meteorological equations" 44 : 237-245, 1966

      3 Williamson D. L, "The evolution of dynamical cores for global atmospheric models" 85B : 241-269, 2007

      4 Boyd, J. P., "The choice of spectral functions on a sphere for boundary and eigenvalue problems: A comparison of Chebyshev, Fourier and associated Legendre expansions" 106 : 1184-1191, 1978

      5 구명서 ; 송강현 ; 김정은 ; 손석우 ; 장은철 ; 정지훈 ; 김형준 ; 문병권 ; 박록진 ; 예상욱 ; 유창현 ; 홍송유, "The Global/Regional Integrated Model System (GRIMs): an Update and Seasonal Evaluation" 한국기상학회 59 (59): 113-132, 2023

      6 홍성유 ; 박훈 ; 정형빈 ; 김정은 ; 구명서 ; 장지현 ; 함수륜 ; 황승오 ; 박병권 ; 장은철 ; Haiqin Li, "The Global/Regional Integrated Model System (GRIMs)" 한국기상학회 49 (49): 219-243, 2013

      7 Sela, J. G., "Spectral modeling at the National Meteorological Center" 108 : 1279-1292, 1980

      8 Yee, S. Y. K., "Solution of Poisson’s equation on a sphere by truncated double Fourier series" 109 : 501-505, 1981

      9 Yoshimura, H., "Improved double Fourier series on a sphere and its application to a semi-implicit semi-Lagrangian shallow water model" 15 : 2561-2597, 2022

      10 Cheong, H. -B., "High-order harmonic spectral filter with the double Fourier series on a sphere" 177 : 313-335, 2002

      11 Cheong, H. -B., "Further study on the high-order double-Fourier-series spectral filtering on a sphere" 193 : 180-197, 2004

      12 Asselin, R., "Frequency filter for time integrations" 100 : 487-490, 1972

      13 Orszag, S. A., "Fourier series on spheres" 102 : 56-75, 1974

      14 Suda, R., "Fast spherical harmonic transform routine FLTSS applied to the shallow water test set" 133 : 634-648, 2005

      15 Tygert, M., "Fast algorithms for spherical harmonic expansions, II" 227 : 4260-4279, 2008

      16 Lauritzen, P. H., "Evaluating advection/transport schemes using interrelated tracers, scatter plots and numerical mixing diagnostics" 138 : 906-918, 2012

      17 Cheong, H. -B., "Double Fourier series on a sphere : applications to elliptic and vorticity equations" 157 : 327-349, 2000

      18 Koo, M. -S., "Double Fourier series dynamical core with hybrid sigma-pressure vertical coordinate" 65 : 19851-, 2013

      19 Kanamitsu, M., "Description of the NMC global data assimilation and forecast system" 4 : 335-342, 1989

      20 Ullrich, P. A., "DCMIP2016 : a review of non-hydrostatic dynamical core design and intercomparison of participating models" 10 : 4477-4509, 2017

      21 Cheong, H. -B., "Application of double Fourier series to shallow water equations on a sphere" 165 : 261-287, 2000

      22 Merilees, P. E., "An alternative scheme for the simulation of a series of spherical harmonics" 12 : 224-227, 1973

      23 Cooley, J. W., "An algorithm for the machine calculation of complex Fourier series" 19 : 297-301, 1965

      24 Hoskins, B. J., "A multi-layer spectral model and the semi-implicit method" 101 : 637-655, 1975

      25 Diamantakis, M., "A fast converging and concise algorithm for computing the departure points in semi-lagrangian weather and climate models" 148 : 670-684, 2022

      26 Cheong, H. -B., "A dynamical core with double Fourier series: Comparison with the spherical harmonics method" 134 : 1299-1315, 2006

      27 Nair, R. D., "A class of deformational flow test cases for linear transport problems on the sphere" 229 : 8868-8887, 2010

      28 Jablonowski, C., "A baroclinic instability test case for atmospheric model dynamical cores" 132 : 2943-2975, 2006

      29 Suk-Jin Choi ; Song-You Hong, "A Global Non-Hydrostatic Dynamical Core Using the Spectral Element Method on a Cubed-Sphere Grid" 한국기상학회 52 (52): 291-307, 2016

      30 Park, H., "A Double Fourier Series (DFS) Dynamical Core in a Global Atmospheric Model with Full Physics" 141 : 3052-3061, 2013

      31 Ullrich, P. A, "2012: Dynamical core model intercomparison project (DCMIP) test case document"

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