Construction of the Spherical High-Order Filter for Applications to Global Meteorological Data Cheong, Hyeong-Bin; Jeong, Han-Byeol;
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.
Stability of the Divergent Barotropic Rossby-Haurwitz Wave, Journal of the Korean earth science society, 2016, 37, 2, 107
Bourke, W., 1972, An efficient, one-level, primitiveequation spectral model. Monthly Weather Review, 100, 683-689.
Cheong, H.B., Kwon, I.H., and Goo, T.Y., 2004, Further study on the high-order double-Fourier-series spectral filtering on a sphere. Journal of Computational Physics, 193, 180-197.
Cheong, H.B., Kwon, I.H., Kang, H.G., Park, J.R., Han, H.J., and Kim, J.J., 2011, Tropical cyclone track and intensity prediction with a structure adjustable balanced vortex. Asia-Pacific Journal of Atmospheric Sciences, 47, 293-303.
Cheong, H.B. and Kong, H.J., 2013, Spherical harmonics power-spectrum of global geopotential field of Gaussian-bell type. Journal of Korean Earth Science Society, 34, 393-401.
Cheong, H.B., Kong, H.J., Kang, H.G., and Lee, J.D., 2015, Fourier finite-element method with linear basis functions on a sphere: Applications to elliptic and transport equations. Monthly Weather Review, 143, 1275-1294.
Cheong, H.B. and Park, J.R., 2007, Geopotential field in nonlinear balance with the sectoral mode of Rossby-Haurwitz wave on the inclined rotation axis. Journal of Korean Earth Science Society, 28, 936-946.
Dilts, G.A., 1985, Computation of spherical harmonic expansion coefficients via FFT's. Journal of Computational Physics, 57, 439-453.
Dubos, T., 2009, A conservative Fourier-finite-element method for solving partial differential equations on the whole sphere. Quarterly Journal of the Royal Meteorological Society, 135, 1877-1889.
Durran, D.R., 1999, Numerical methods for wave equations in geophysical fluid dynamics. Springer, NY, USA, 465 p.
Haltiner, G.J. and Williams, R.T., 1980, Numerical prediction and dynamic meteorology. Second ed., Wiley, NJ, USA, 477 p.
Heikes, R.P. and Randall, D.A., 1995, Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: basic design and results of tests. Monthly Weather Review, 123, 1862-1880.
Hortal, J.R. and Simmons, A.J., 1991, Use of reduced Gaussian grids in spectral models. Monthly Weather Review, 119, 1057-1074.
Jakob-Chien, R., Hack, J.J., and Williamson, D.L., 1995, Spectral transform solutions to the shallow water test set. Journal of Computational Physics, 119, 164-187.
Kwon, I.H. and Cheong, H.B., 2010, Tropical cyclone initialization with spherical high-order filter and idealized three-dimensional bogus vortex. Monthly Weather Review, 138, 1344-1367.
Nair, R.D., 2009, Diffusion experiments with a global discontinuous Galerkin shallow-water model, Monthly Weather Review, 137, 3339-3350.
Nehrkorn, T., 1990, On the computation of Legendre functions in spectral models. Monthly Weather Review, 118, 2248-2251.
Swarztrauber, P.N., 1996, Spectral transform methods for solving the shallow-water equations on the sphere. Monthly Weather Review, 124, 730-744.
Tackley, P.J., 2000, Self-consistent generation of tectonic plates in time-dependent, three-dimensional mantle convection simulations 1. Pseudoplastic yielding. An Electronic Journal of The Earth Sciences, 1, 1-45.