Articles | Volume 16, issue 22
Research article
23 Nov 2016
Research article |  | 23 Nov 2016

Direct inversion of circulation and mixing from tracer measurements – Part 1: Method

Thomas von Clarmann and Udo Grabowski

Abstract. From a series of zonal mean global stratospheric tracer measurements sampled in altitude vs. latitude, circulation and mixing patterns are inferred by the inverse solution of the continuity equation. As a first step, the continuity equation is written as a tendency equation, which is numerically integrated over time to predict a later atmospheric state, i.e., mixing ratio and air density. The integration is formally performed by the multiplication of the initially measured atmospheric state vector by a linear prediction operator. Further, the derivative of the predicted atmospheric state with respect to the wind vector components and mixing coefficients is used to find the most likely wind vector components and mixing coefficients which minimize the residual between the predicted atmospheric state and the later measurement of the atmospheric state. Unless multiple tracers are used, this inversion problem is under-determined, and dispersive behavior of the prediction further destabilizes the inversion. Both these problems are addressed by regularization. For this purpose, a first-order smoothness constraint has been chosen. The usefulness of this method is demonstrated by application to various tracer measurements recorded with the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). This method aims at a diagnosis of the Brewer–Dobson circulation without involving the concept of the mean age of stratospheric air, and related problems like the stratospheric tape recorder, or intrusions of mesospheric air into the stratosphere.

Short summary
We present a method which uses global measurements of stable stratospheric trace species to infer stratospheric circulation. This method finds the circulation vectors which best satisfy the continuity equation for the given measurements. Some of the main disadvantages of more conventional methods are avoided. As a proof of concept, this method has been applied to measurements from the MIPAS instrument. Its adequacy has been proven since the inferred circulation shows the expected features.
Final-revised paper