Inverting the Sawyer-Eliassen Circulation Equation in a Synoptic Meteorology Lab Course at UW-Madison

At the crux of any course in synoptic meteorology is an investigation of the dynamics contributing to the production of vertical motions, and subsequently, sensible weather in the mid-latitude atmosphere. One particularly notable structure that is routinely characterized by linear bands of vertical motions, and the subject of extensive study in the classroom, is the mid-latitude front. While geostrophic deformation can produce bands of considerable baroclinicity, only ageostrophic processes can account for the production of the characteristic convergence and horizontal wind shear that accompanies such fronts. Consequently, the retention of ageostrophic motions in the momentum and thermodynamic equations in the vicinity of the front, specifically in the across-front direction, describes a more complete picture of the process of frontogenesis. The Sawyer (1956)-Eliassen (1962) circulation equation retains these terms and provides a means to diagnose the transverse ageostrophic circulations associated with active fronts.

Traditionally, students of synoptic meteorology are, at best, exposed to conceptual models for these circulations, which are associated with different regimes of geostrophic deformation in the vicinity of fronts. However, given the complex nature of this second-order differential equation, students rarely have an opportunity to solve this equation using real-time data. Consequently, a full understanding of the diagnostic power of this equation is difficult for students to obtain. This presentation discusses the development of software through which students can invert the Sawyer-Eliassen Circulation Equation using real-time data as part of synoptic-dynamic meteorology laboratory activities at UW-Madison. Details on the utility of the software and feedback from students will be presented to motivate its future use in other synoptic laboratory environments.