### We calculated three isentropic back trajectories simultaineously for the same latitude and longitude, but for three different altitudes. Then we calculated one back trajectory by itself. To my surprise the results are different. Why are the back trajectories different if you calculate them jointly or separately?

The “correct” trajectory is the first plot with three trajectories. This is not something that can be easily fixed. The method used to compute the vertical motion, this would be true for any of the secondary methods (isentropic, constant density, and isobaric) computes the velocity required to keep the trajectory on the surface. The computation uses the horizontal gradient of the field, which is computed as a “centered difference.” To save on computer time, trajectories are only computed with meteorological data on a subgrid that follows the trajectory. However the center gradients cannot be computed on the edge of the grid, where we use a standard forward difference. Under some circumstances the trajectory may approach the edge of the subgrid prior to the subgrid being shifted, hence the calculation would use the forward difference rather than the centered difference. In your case, the three simultaneous trajectories required a larger subgrid, hence no trajectory ever approached the edge and all used the centered difference method. In the single trajectory case, the subgrid was smaller and hence on occasion it would have used the forward difference method at the same times that in the 3-trajectory case it would have used a centered difference. Hence you get a slightly different vertical motion and slightly different trajectories. You can check this by increasing the size of the minimum subgrid size using PC HYSPLIT, in the advanced configuration menu, from the default 10, to say 100. You will then get the same single trajectory as in the 3-trajectory simulation.

All this raises a larger question. When the trajectories are sensitive to such small variations, then you should have much less confidence in any single trajectory when using them for source attribution. In your case the trajectories have substantial twists and turns, which suggest changes in air mass and other discontinuities that are not consistent with the isentropic assumption. I would suggest you use the “data” option for vertical motion, using the vertical velocity fields that are produced by the meteorological model, rather than one of the internal HYSPLIT vertical velocity options.

Roland Draxler