Accuracy of trajectories as determined from the conservation of meteorological tracers

Dynamical structures as well as transport processes are often investigated using trajectories. Several alternative techniques are currently in use to calculate trajectories, which may produce significantly different results. In this study, three‐dimensional, isentropic, isobaric and isoeta (terrain‐following coordinate surfaces) trajectories are calculated. In the case of the isentropic trajectories, both the kinematic and the dynamic calculation method are applied. Using a tracer that is conserved along the real three‐dimensional trajectories, it is possible to determine which of these trajectories are the most accurate. Here, conservative meteorological quantities, namely potential vorticity, specific humidity and potential temperature, are used. As these tracers are conserved only in the absence of diabatic processes, regions of the atmosphere where these processes are important, i.e. the boundary layer and moist regions, are excluded. Tracer conservation along the different trajectories is studied to find the most accurate trajectory type. It is found that three‐dimensional trajectories are the most accurate ones, and kinematic isentropic trajectories, affected more by dynamical inconsistencies between meteorological fields, are the second best in the troposphere. In the stratosphere, three‐dimensional and isentropic trajectories may be of similar accuracy. Isobaric and isoeta trajectories are much less accurate, both in the troposphere and in the stratosphere. Dynamic trajectories tend to perform unrealistic inertial oscillations and thus give clearly worse results than any of the kinematic trajectories. Since there exists no direct relationship between the average errors in tracer conservation and average spatial position errors of the trajectories, a transformation of the tracer conservation errors into spatial position errors is difficult.