Developoment of Limited-Area Spectral Models

成功的数值天气预报不仅依赖于 物理过程的适当建模，通常表示为 偏微分方程和精确的观测值， 输入数据，这也取决于效率和准确性， 数值方法 数值方法基本上可以分为 分为两类：有限差分法和谱方法。 与 有限差分方法，空间和时间导数是 使用泰勒级数近似在规定的点进行评估。 使用谱方法，因变量表示为 具有规定空间结构的函数和 与每个函数相关联的系数通常是下式的函数： 时间 光谱技术已被证明是非常有价值的， 全球大气的数值模拟，但尚未使用 在有限区域的模型中广泛使用。 全球模式中的大气 被视为横向封闭的球壳。 而反观 有限区域模式中的大气与周围环境相互作用 气氛 这种开放边界条件是最重要的边界条件之一。 在气象学有限区域建模的困难方面。 在这个项目下，使用切比雪夫谱方法 将发展正压和斜压的多项式 有限区域模型

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.