The spline format is a no-linear, second-order derivative one, its linear segment is that of the second-order central difference. In this paper, we give a derivation proof of that the space truncation error, phase velocity and group velocity errors of the second-order center differential is halved that of the first-order center differential under a hypothesis of genuine solution of simple harmonic wave. So, we draw lessons from the idea of the dynamic core of spectral model, the semi-implic semi-Lagrangian integration scheme with 2D spectral spherical harmonic function transform on the Gussion grid, to introduce a new explicit quasi-Lagrangian integration scheme with cubic spline function transform on guasi-uniform latitude-longitude grid (called "spline model"). Adopting original atmospheric equations of motion, which includes that in the North Pole and the Sorth Pole, a general forecast equation of spline format of space-time second-order differential remainder is derived, then obtain the hydrostatic pressure and temperature forecast eqations of conservation of the atmospheric mass. Based on uniform latitude-longitude grid, we harmonize two quasi-uniform ones, which must be quasi-uniform latitude space, and on which cubic spline function transformation (transformation=fitting+interpolation) must be done for variables of pressure, temperature, moisture, winds and general Newtonian force acting to unit air mass on rotating earth (acceleration), which made all of them second-order derivative, to solve the track of an upstream point, but the upstream air parcel goes alone just "cubic path" of fitting their slopes, curvatures and torsions of the variable fields to "bicubic surface in horizontal + cubic spline in vertical". It is with a path of uniform acceleration motion to forecast wind field, and with fitting splines to the paths of the 3D hydrostatic advection and getting its implicit average divergence in one time step, to forecast increments of pressure and temperature fields in the adiabatic process. We give two integration cases that testify to the dynamic core of global spline model.
GU Xuzan
,
ZHAO Jun
,
TANG Yonglan
. A Quasi-Lagrangian Integration of Conservation of Atmospheric Mass with Unify Scheme of Cubic Spline Function Transformating on Quasi-uniform Latitude-longitude Grid and Its Integration Cases[J]. Plateau Meteorology, 2017
, 36(4)
: 1091
-1105
.
DOI: 10.7522/j.issn.1000-0534.2016.00069
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