Hyeong-Bin Cheong

The Global/Regional Integrated Model system (GRIMs)

A multiscale atmospheric/oceanic model system with unified physics, the Global/Regional Integrated Model system (GRIMs) has been created for use in numerical weather prediction, seasonal simulations, and climate research projects, from global to regional scales. It includes not only the model code, but also the test cases and scripts. The model system is developed and practiced by taking advantage of both operational and research applications. This article outlines the history of GRIMs, its current applications, and plans for future development, providing a summary useful to present and future users.

Tropical Cyclone Initialization with a Spherical High-Order Filter and an Idealized Three-Dimensional Bogus Vortex

Abstract A tropical cyclone initialization method with an idealized three-dimensional bogus vortex of an analytic empirical formula is presented for the track and intensity prediction. The procedure in the new method consists of four steps: the separation of the disturbance from the analysis, determination of the tropical cyclone domain, generation of symmetric bogus vortex, and merging of it with the analysis data. When separating the disturbance field, an efficient spherical high-order filter with the double-Fourier series is used whose cutoff scale can be adjusted with ease to the horizontal scale of the tropical cyclone of interest. The tropical cyclone domain is determined from the streamfunction field instead of the velocities. The axisymmetric vortex to replace the poorly resolved tropical cyclone in the analysis is designed in terms of analytic empirical functions with a careful treatment of the upper-layer flows as well as the secondary circulations. The geopotential of the vortex is given in suc...

A Dynamical Core with Double Fourier Series: Comparison with the Spherical Harmonics Method

Abstract A dynamical core of a general circulation model with the spectral method using double Fourier series (DFS) as basis functions is presented. The model uses the hydrostatic balance approximation and sigma coordinate system in the vertical direction and includes no topography. The model atmosphere is divided into 25 layers with equal sigma depths. Prognostic equations for the vorticity, divergence, temperature, and logarithmic surface pressure are solved by the DFS spectral-transform method with the Fourier filtering at middle and high latitudes. A semi-implicit time-stepping procedure, which deals with the eigendecomposition and inversion of the 3D Helmholtz equation associated with the gravity wave terms, is incorporated for the gravity wave–related terms. The DFS model is tested in terms of the solution of the 3D Helmholtz equation, balanced initial state, developing baroclinic waves, and short- and long-term Held–Suarez–Williamson simulations for T42, T62, T84, and T106 resolutions. It is found ...

Fourier-series representation and projection of spherical harmonic functions

Computations of Fourier coefficients and related integrals of the associated Legendre functions with a new method along with their application to spherical harmonics analysis and synthesis are presented. The method incorporates a stable three-step recursion equation that can be processed separately for each colatitudinal Fourier wavenumber. Recursion equations for the zonal and sectorial modes are derived in explicit single-term formulas to provide accurate initial condition. Stable computations of the Fourier coefficients as well as the integrals needed for the projection of Legendre functions are demonstrated for the ultra-high degree of 10,800 corresponding to the resolution of one arcmin. Fourier coefficients, computed in double precision, are found to be accurate to 15 significant digits, indicating that the normalized error is close to the machine round-off error. The orthonormality, evaluated with Fourier coefficients and related integrals, is shown to be accurate to O(10−15) for degrees and orders up to 10,800. The Legendre function of degree 10,800 and order 5,000, synthesized from Fourier coefficients, is accurate to the machine round-off error. Further extension of the method to even higher degrees seems to be realizable without significant deterioration of accuracy. The Fourier series is applied to the projection of Legendre functions to the high-resolution global relief data of the National Geophysical Data Center of the National Oceanic and Atmospheric Administration, and the spherical harmonic degree variance (power spectrum) of global relief data is discussed.

Excitation of the 5-day Wave by Antarctica

Abstract The 5-day wave has been detected in composite maps of geopotential height fields of European Centre for Medium-Range Weather Forecasts dataset for 7 years (1984–91, except 1985) and shows a characteristic northwest–southeast meridional phase tilt in the Southern Hemisphere. A numerical integration of Laplace’s tidal equations with periodic forcing of zonal wavenumber 1 only produced the meridional phase tilt when the forcing is located in high latitudes. Such a forcing is created through coupling of the time-fluctuating westerlies with the topography of Antarctica. Numerical simulations that incorporated this mechanism reproduced the observed meridional phase tilt of the 5-day wave, which suggests that Antarctica is responsible for the observed phase tilt through the process of resonance. A linear theory on the meridional phase tilt is given with a nondivergent barotropic model that includes both forcing and dissipation.

Excitation of the 10-Day and 16-Day Waves

Abstract The composite analysis of the 10-day and 16-day waves, the observational counterparts of the second antisymmetric and symmetric rotational Hough mode with the zonal wavenumber 1, respectively, were performed as an extension of Cheong and Kimura’s study in order to investigate the global structure and the excitation mechanism. At the 700-hPa level, the composited waves showed a northwest–southeast phase tilt and northward propagation of the wave energy in the Northern Hemisphere (NH) summer, as was the case for the 5-day wave in Cheong and Kimura, while these features are less conspicuous in the NH winter. At the 10-hPa level, no systematic phase variation with latitude was shown due to high level of noise. Consistent to the previous studies, however, it is found that the amplitude in the winter hemisphere is much larger than that in the summer hemisphere. Responses of shallow water model on the sphere (Laplace’s tidal equations) with the zonal-mean flow to the topographic and/or thermal forcing w...

Geopotentinl Field in Nonlinear Balance with the Sectoral Mode of Rossby-Haurwitz Wave on the Inclined Rotation Axis

Analytical geopotential field in balance with the sectoral mode (the first symmetric mode with respect to the equator) of the Rossby-Haurwitz wave on the inclined rotation axis was derived in presence of superrotation background flow. The balanced field was obtained by inverting the divergence equation with the time derivative being zero. The inversion consists of two steps, i.e., the evaluation of nonlinear forcing terms and the finding of analytical solutions based on the Poisson`s equation. In the second step, the forcing terms in the from of Legendre function were readily inverted due to the fact that Legendre function is the eigenfunction of the spherical Laplacian operator, while other terms were solved either by introducing a trial function or by integrating the Legendre equation. The balanced field was found to be expressed with six zonal wavenumber components, and shown to be of asymmetric structure about the equator. In association with asymmetricity, the advantageous point of the balanced field as a validation method for the numerical model was addressed. In special cases where the strength of the background flow is a half of or exactly the same as the rotation rate of the Earth it was revealed that one of the zonal wavenumber components vanishes. The analytical balanced field was compared with the geopotential field which was obtained using a spherical harmonics spectral model. It was found that the normalized difference lied in the order of machine rounding, indicating the reliability of the analytical results. The stability of the sectoral mode of Rossby-Haurwitz wave and the associated balanced field was discussed, comparing with the flrst antisymmetric mode.

A Double Fourier Series (DFS) Dynamical Core in a Global Atmospheric Model with Full Physics

AbstractThis study describes an application of the double Fourier series (DFS) spectral method developed by Cheong as an alternative dynamical option in a model system that was ported into the Global/Regional Integrated Model System (GRIMs). A message passing interface (MPI) for a massive parallel-processor cluster computer devised for the DFS dynamical core is also presented. The new dynamical core with full physics was evaluated against a conventional spherical harmonics (SPH) dynamical core in terms of short-range forecast capability for a heavy rainfall event and seasonal simulation framework. Comparison of the two dynamical cores demonstrates that the new DFS dynamical core exhibits performance comparable to the SPH in terms of simulated climatology accuracy and the forecast of a heavy rainfall event. Most importantly, the DFS algorithm guarantees improved computational efficiency in the cluster computer as the model resolution increases, which is consistent with theoretical values computed from a dr...

High-Order Spectral Filter for the Spherical-Surface Limited Area

AbstractA high-order spectral filter for the spherical-surface limited-area domain, either window or sector type, is presented, where the window domain is finite both in longitude and latitude and the sector domain is finite in longitude, but is ranged from Pole to Pole in latitude. The data given in the physical domain are extended to either extended window or sector domain by padding artificial data that are appropriate for spectral decomposition with half-ranged Fourier series. The high-order filter equation of Laplacian operator type was split into first- or second-order spherical elliptic equations as in the global domain high-order spectral filter. Each low-order elliptic equation is discretized using half-ranged Fourier series both in longitudinal and latitudinal direction. Since the domain is of the spherical geometry, the window domain spectral filter consists of full matrices for each zonal wavenumber and thus performs filtering with O(N3) operation for N × N grids. On the other hand, the sector...

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

Abstract A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss–Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O ( N g ) operations, where N g is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix–vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.