Developoment of Limited-Area Spectral Models

成功的数值天气预报不仅取决于通常用偏微分方程表示的物理过程的适当建模和作为输入数据的准确观测，还取决于数值方法的效率和准确性。数值方法基本上可以分为两大类：有限差分法和谱法。利用有限差分法，利用泰勒级数逼近求出在规定点上的时空导数。在谱法中，因变量被表示为具有规定空间结构的函数的和，与每个函数相关的系数通常是时间的函数。光谱技术已被证明在全球大气数值模拟中极具价值，但在有限区域模式中尚未得到广泛应用。在全局模型中，大气被视为一个横向封闭的球壳。相反，有限区域模型中的大气与其周围的大气相互作用。这种开放边界条件是气象有限区域模拟中最困难的方面之一。在这个项目下，将为正压和斜压有限区域模型开发一种使用切比雪夫多项式的谱方法。

Successful numerical weather prediction not only rests upon appropriate modeling of physical processes frequently expressed as partial differential equations and accurate observations used as input data, it also depends on the efficiency and accuracy of the numerical methods. The numerical methods can basically be separated into two groups: finite difference and spectral methods. With the finite difference methods, the spatial and temporal derivatives are evaluated at prescribed points using Taylor series approximations. With the spectral methods, the dependent variables are expressed as the sum of functions that have a prescribed spatial structure and the coefficient associated with each function is generally a function of time. The spectral techniques have been proven extremely worthy in the numerical modeling of the global atmosphere, but have not been used extensively in limited-area models. The atmosphere in a global model is treated as a laterally-closed spherical shell. In contrast, the atmosphere in a limited-area model interacts with its surrounding atmosphere. This open boundary condition is one of the most difficult aspects in limited-area modeling in meteorology. Under this project, a spectral method using the Chebyshev polynomials will be developed for both barotropic and baroclinic limited-area models.