Diagnosing Lagrangian aspects of the atmospheric circulation by Eulerian tracer advection with relaxation

In the past, one widely used technique to diagnose Lagrangian aspects of the atmospheric circulation has been the computation of trajectories. Trajectories provide detailed information along the pathways of individual parcels, but one has to consider a vast amount of them in order to obtain continuous-in-time, volume-filling information. As a consequence, analysing trajectories can be a painstaking task. To overcome this problem, we developed an alternative method allowing one to continuously diagnose Lagrangian information about the atmospheric circulation on a Eulerian grid. The method is based on the advection of passive tracer fields and includes a relaxation term. One thus obtains accumulated Lagrangian information, such as the recent meridional or vertical parcel displacement or the recent parcel-based diabatic heating, for each grid point at any time step. This convenient output format allows one to analyse large data sets (such as reanalysis data) in a straightforward manner. We suggest our method to be particularly useful in the field of synoptic climatology. Here, we present the underlying idea of the method and motivate its utility on the basis of examples that make use of reanalysis data.