When I ran a foward trajectory from a location on a previously computed backward trajectory, I did not return to the starting location of my backward trajectory. Why?


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