Lagrangian characterization of heat waves by Eulerian tracer advection with relaxation

Diagnostics of Lagrangian information about the atmospheric flow are usually obtained through 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 flow on a Eulerian grid. The method is based on the advection of passive tracer fields and includes a relaxation term. Thus, it provides a field-based view on Lagrangian properties of the flow. The convenient output format allows one to analyse large data sets such as reanalysis data in a straightforward manner. Here, we make use of this method to quantify the processes of horizontal advection, downwelling, and diabatic heating associated with heat waves in Europe. More specifically, we compute the recent meridional and vertical parcel displacement and the recent parcel-based diabatic heating for each grid point at any time step to correlate these to the occurrence of temperature anomalies in Europe. In this way, we characterize European heat waves in terms of their Lagrangian bevahior. The analysis focuses on the recent decade, which experienced several severe heat waves in Europe, and encompasses case studies of recent major European heat waves as well as a more comprehensive statistical analysis. Our study furthers our knowledge on important mechanisms and drivers of European heat waves, which in turn will help to improve their forecasts.