Validation of 3D semi-geostrophic equation as the vanishing Froude/Rossby number limit of the 3D Euler equation, in the class of smooth solutions

半地转(SG)方程是著名的大尺度地球物理流体动力学偏微分方程模型。通过研究它的有效性，特别是严格量化它作为欧拉方程的近似精度，我们获得了对SG捕捉到的地球天气的“主要特征”的重要洞察，如天气锋面和潮湿对流。这一理论研究也为新天气代码的数值模拟和检验提供了指导。来自英国气象局和雷丁大学的研究人员参与了这一项目，这有助于其产生更广泛的影响

Semi-geostrophic (SG) equation is a well-known partial differential equation model of large scale geophysical fluid dynamics. By studying its validation and especially rigorously quantifying its accuracy as an approximation of the Euler equation, we gain important insight into the *main features* of the Earth weather that are captured by SG, such as weather fronts and moist convection. This theoretical study also provides guidance for numerical simulation and testing of new weather code. Researchers from the Met Office and University of Reading are connected to this project, which facilitates its wider impact