模拟地球物理集合预报和集合资料同化中不确定性的时空随机模式generator
A spatio-temporal stochastic pattern generator for simulation of uncertainties in geophysical ensemble prediction and ensemble data assimilation
摘要：
提出了一种时空伪随机高斯场的生成器，它满足“尺度比例”性质（Tsyroulnikov，2001）。该发生器是基于一个三阶的时间随机微分方程与伪微分空间算子定义在有限区域的二维或三维域中的笛卡尔坐标系。所产生的伪随机场在时空中是均匀和各向同性的（具有缩放的垂直和时间坐标）。任何时空方向上的关联函数都属于Matérn类。时空相关性是不可分离的。一个频谱空间数值求解器的实现和加速利用现实世界的地球物理场的属性，特别是，他们的空间频谱的平滑度。该生成器被设计为创建加法或乘法或其他时空扰动，这些扰动代表了地球物理学数值预测模型中的不确定性。生成器的程序代码是公开可用的。
英文摘要：
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a pseudo-differential spatial operator defined on a limited area 2D or 3D domain in the Cartesian coordinate system. The generated pseudo-random fields are homogeneous and isotropic in spacetime (with the scaled vertical and temporal coordinates). The correlation functions in any spatio-temporal direction belong to the Matérn class. The spatio-temporal correlations are non-separable. A spectral-space numerical solver is implemented and accelerated exploiting properties of real-world geophysical fields, in particular, smoothness of their spatial spectra. The generator is designed to create additive or multiplicative, or other spatio-temporal perturbations that represent uncertainties in numerical prediction models in geophysics. The program code of the generator is publicly available.
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