显式自由表面模型时间分裂格式的一个积分方案

讨论了有关显式自由表面模型的时间分裂格式中的分裂误差。在传统的积分方案中，由于采用蛙跳格式，斜压动量方程具有三层的时间离散结构，但是，正压动量方程在相应的时间层上只有二层的离散结构。因此，正压方程与斜压方程的时间离散结构是不相容的。分析结果表明，这是导致分裂误差的原因。本提出一种能保持时间离散结构相容的正压和斜压方程的时间积分方案。该积分方案的分裂误差很小因此特别适合于需要长期积分的气候研究。该方案在北太平洋的一个自由表面模型中得到了应用。

A proper time integration with split stepping for the explicit free-surface modeling

Errors due to split time stepping are discussed for an explicit free-surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three-time-level structure because of leapfrog scheme. The barotropic one, however, has two-time-level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long-term integration for climate studies. It is applied to a free-surface model for the North Pacific Ocean.