It's good that you did the backward/forward comparision. Not many users go
to the trouble. You discovered the precision/accuracy limitation. Over
the integration time interval there is an accumulation of numerical error.
It can be reduced by reducing the integration time step but we felt that
the current time step gives an acceptable level of precision (about 1% per
day) considering the number of users and their typical application. An
interesting aspect of a trajectory integration is that as the error
accumlates and moves the trajectory into adjacent grid points, the errors
can really grow quickly. The numerical uncertainty of your calculation is
half of the distance between your return point and start point.
One reason we don't get too excited about the precision error is that the
accuracy is even worse - that may be as high as 5% per day. The
trajectory calculation is an integration using discrete data points
(gridded values in space and time) to represent a continuous function.
How well the gridded data can be used to represent the flow depends upon
the size of the flow features and their speed through the domain versus
the number of grid points that sample those features. Too coarse data in
space and time adds the greatest uncertainty to the calculation.
One test of this would be to rerun your trajectory, but offset the
starting point by 0.1 degrees, you will find your endpoint after 10 days
to be different by almost 15 deg longitude.
Roland Draxler