Theoretical Basis of Weather Forecasting: Quasi-Geostrophic Theory Summary and Operational Applications

The quasi-geostrophic (QG) theory is the dynamic basis that forecasters must master to establish a clear idea of weather forecasting. In this paper, from the two fundamental issues of weather forecasting that are the diagnosis of vertical movement and the development of weather systems, the origin of the QG theory is introduced. It is pointed out that it is a historical inevitability of the modern atmospheric dynamics developing from the atmospheric long-wave theory to the multi-level baroclinic atmospheric numerical model. The inference of the QG equations shows that the QG theory is a complete theoretical system of atmospheric dynamics, based on rigorous mathematical derivation and physical insight and built on top of the three laws of physics (conservations of momentum, energy, and mass), so it is the core of the atmospheric dynamics. The forced terms of omega equation and the geopotential tendency equation show that temperature advection and vorticity advection are the most basic predictors, which lead to the destruction of geostrophic balance, and make geostrophic equilbrium restored (ie, geostrophic adjustment process) through the associated secondary circulation, so that large-scale circulation in the slow-changing always maintains the quasi-level and quasi-geostrophic equilibrium. The QG theory also revealed that the temperature advection is the basic reason for the development of backward tilted baroclinic disturbance, yet the vertical circulation associated with the vorticity advection has led to changes in the thermal structure of large-scale circulation systems. Finally, some qualitative rules in conventional weather maps can be used directly as a QG theory application in the operational weather forecasting.