利用C3连续双三次曲面拟合了全球数值模式地形曲面； 讨论构建了有复杂地形数值模式引入地形追随高度坐标（坐标）后， 同时引入包含定常斜率、 曲率和挠率的双三次曲面地形， 又进一步讨论了双三次曲面地形模式大气的水平气压梯度力计算问题。结果表明， 对坐标模式大气的压、 温、 湿场， 通过做经、 纬向三次样条拟合， 求得地形斜率“静力平衡”气压差， 从而插值（反演）任一水平面（海平面）上的气压场， 同时可以求得时变的参考大气， 则计算水平气压梯度（力）的精度， 完全依赖于插值（反演）对应的水平面（海平面）气压场的计算精度。并指出， 理论上可按三次样条的曲率判断， 做变量场（地形）的局域或单点平滑。
In the numerical analysis of weathey prediction(NWP) model, the cubic spline function consists of cubic spline, bicubic surface and tri-cubic (3-D cubic) cube, all of which possess the 2-order differentiable ‘convergence’ and ‘optimality’ of the mathematical laws. In this paper, fitting a C3-continuous bicubic surface to topography in a global numerical model was studied, on which the height-based terrain following coordinates ( coordinates) be set for the bicubic terrain has its stationary slopes, curvatures and torsions. Then, horizontal pressure gradient force (HPGF) of the atmosphere model based on the bicubic terrain in the coordinates was studied. It is on the bicubic mountains that reduce level pressure field to every horizontal Z-plane of a one-to-one correspondence of every -plane, where the Z= , for instance, the sea level is the plane of Z=0, by means of integrating the fitted, meridional and zonal cycle splines of log pressure differences on ‘hydrostatic balance’ along the mountain slopes horizontally with using the temperature and moisture fields at each corresponding -plane, in fact, it′s just a time-dependent reference atmosphere mapped in the dynamic model atmosphere. The calculation accuracy of HPGF totally depends on the pressure fields interpolated to every Z-plane (sea level). In principle, it is suitable for judging reasonable local areas (single point) to be smooth, according to their curvatures of fitting splines to a variable field, so dose the bicubic terrain.
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