NUMERICAL INTEGRATION OF A NINE-LEVEL GLOBAL PRIMITIVE EQUATIONS MODEL FORMULATED BY THE BOX METHOD

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Abstract
Based on the box method, finite-difference versions of a system of primitive equations in spherical coordinates are formulated for a spherical grid. Non-linear computational instability cannot occur in time integrations of these equations. Conservation of total mass is guaranteed by the finite-difference form of the continuity equation. The proposed scheme yields no fictitious sources of energy in the derivation of the difference formula for the budget of the total energy over the entire domain. The finite-difference equations for the budget of the relative and absolute angular momentum are not exact analogs of the continuous forms but nevertheless are very accurate. This system of primitive equations for a nine-level general circulation model of the atmosphere has been numerically integrated for 50 forecast days. The network of grid points covers the entire globe with nearly uniform spacing and has no artificial horizontal boundaries. The initial data were latitude-height-dependent zonal mean winds and pressures and zonal mean temperatures perturbed slightly by random numbers. The time integration was carried out without any finite-difference computational problems and baroclinic waves developed and propagated.