Geostrophic momentum approximation Q-vector and its application in synoptic charts

Abstract

In this paper, we extend the expression of quasi-geostrophic Q-vector brought forward by Hoskins et al. into the Q-vector equation under the condition of geostrophic momentum approximation, and discuss the method of how to quantitatively estimate vertical motion in synoptic charts with Q-vector expression under geostrophic momentum approximation. Compared with the expression of quasi-geostrophic Q-vector, the Q-vector expression under geostrophic momentum approximation has two more terms which are related to geopotential height extremum and wind velocity extremum. Then, each term of Q-vector under geostrophic momentum approximation is transformed into the expression which is conveniently judged in synoptic charts. The results show that to judge vertical motions in synoptic chart quantitatively, one of the three ways can be used: when contour line presents the form of wave-like trough-ridge and passes through the entrance and exit areas of jet stream, correspondingly use the 1st term of Q-vector under geostrophic momentum approximation (i.e., quasi-geostrophic Q-vector); when there exist a closed pressure system and an angle between contour line and wind velocity, correspondingly use the 2nd term of Q-vector under geostrophic momentum approximation; at the jet streak, correspondingly use the 3rd term of Q-vector under geostrophic momentum approximation.