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）方程是一个著名的大尺度地球物理流体动力学偏微分方程模型。通过研究它的验证，特别是严格量化其作为欧拉方程近似的准确性，我们获得了重要的洞察地球天气的主要特征，如天气锋和潮湿对流。该理论研究也为数值模拟和新天气规则的检验提供了指导。英国气象局和阅读大学的研究人员与这个项目有联系，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