水平气压梯度力差分格式误差的定量分析

Quantitative Analysis of the Discretization Errors of the Horizontal Pressure Gradient Force over Sloping Terrain

通过分析发现地形坐标系中气压梯度力差分格式的计算误差应分为二类，其中，第二类误差在水平坐标面倾斜时出现。这种误差可理解为将水平坐标面上的气压（或位势高度）插回到等高面（或等压面）上的插值误差。构造气压梯度力差分格式的目的正是为了减小这种第二类误差，而不是其他误差。误差分析表明静力扣除法和Ｃｏｒｂｙ格式的第二类误差都很小，比一般方法的误差小约一个量级。分析还表明第二类误差产生的主要原因是由于气压随高度非线性变化。依据这一分析思路，本文改进了ｓ（ｚ）坐标系中的静力扣除法。改进后的方法比改进前的误差小约一个量级。

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.