全球风场构建涡度、散度的新方法

摘要

Vorticity and divergence can be calculated using wind field in numerical forecast. The issue involves the problem of calculating differentiation using observation data, and it is ill-posed in mathematics. In a limited domain, the one-dimensional numerical differentiation can be used to calculate vorticity and divergence, but the method requires that the data along the boundary be accurate. This paper suggests a new method of calculating vorticity and divergence using the periodical function’s one-dimensional numerical differentiation algorithm, and comparison is made with usually used difference method. The stream function and velocity potential are calculated using vorticity and divergence, and the initial wind field is reconstructed using the stream function and velocity potential. Results show that the algorithm proposed in this paper is stable, feasible, and its accuracy is superior to the difference method. It provides a new idea that the method mag be used in global meteorology data diagnosis analysis and forecast.%目前在数值预报中通常利用风场借助于差分方法来构建涡度和散度场，这个问题涉及到观测资料求微分的问题，从数学上来说，此问题是不适定的。在有限区域上构建时可以采用一维数值微分来实现，但此方法在端点部分的资料必须是精确的，本文提出了新的方法，该方法借助于周期函数的一维数值微分，并用该方法应用到全球风场构建涡度、散度中去，同时与通常的差分方法进行了比较，利用涡度、散度计算了流函数和势函数，然后用流函数和势函数重构初始风场。结果表明，本文提出的方法算法稳定、可行且计算精度比差分方法高，为应用到全球气象资料的诊断分析及预报中提出了新的思路。