Quantitative Analysis of the Discretization Errors of the Horizontal Pressure Gradient Force over Sloping Terrain
水平气压梯度力差分格式误差的定量分析

The analysis has demonstrated that the discretization errors of the horizontal pressure gradient force in terrain-following coordinate models should be divided into two kinds, one of which, the second kind Error-II, appears while the horizontal coordinate surface is inclined. Error-II can be regarded as the error for extrapolating pressure (or geopotential) from horizontal coordinate surfaces back to the constant height (or pressure) surface. It is the error that we construct special schemes to reduce. Analytical expressions are derived for Error-II and show that the errors induced by the scheme of Corby et al. and by the method of subtracting out of a reference atmosphere are about one order of magnitude smaller than that by general schemes. It is pointed out that Error-II is caused mainly by the nonlinearity between the pressure and height. At last, we improved the scheme with subtracting out of a reference atmosphere in s(z) coordinate models. Error-II for the improved scheme is only one-tenth of that for the original.