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.

Introduction
Spherical Laplacian Operator and Pole Conditions
Discretization of the Laplacian Operator and High-order Filter
Evaluation of the Fourier-Finite Difference High-order Filter
Summary and Conclusion
Acknowledgments
References

• Hyeong-Bin Cheong(Department of Environmental Atmospheric Sciences, Pukyong National University) Corresponding author
• Han-Byeol Jeong(Department of Environmental Atmospheric Sciences, Pukyong National University)