A common question arises when running trajectories...."What is the error associated with
a given trajectory calculation." Overall, from the literature, one can estimate the total error to be
anywhere from 15 to 30% of the travel distance. The total error is composed of four error components:
 physical error due to the inadequacy of the data’s representation of the atmosphere in space and time,
 computational error due to numerical inaccuracies,
 measurement errors in creating the model’s meteorological data fields,
 forecast error if using forecast meteorology.
The physical component of the error is related to how well the
numerical fields estimate the true flow field. There is no way of knowing this error without independent
verification data.
The computational component of the error is composed of the integration
error (part of which is due to truncation) and a data resolution error, i.e., trying to
represent a continuous function, the atmospheric flow field, with gridded data points of limited resolution
in space and time. The integration error can be estimated by computing a backward trajectory from
the forward trajectory endpoint. The error is then 1/2 the distance of the final endpoint and the starting
point. The resolution error can be estimated by starting several trajectories about the initial point
(offset in the horizontal and vertical). The divergence of these trajectories will give an estimate of the
uncertainty due to divergence in the flow field. An initial offset should be used that is comparable to the
estimated integration error. One component of the resolution error that is difficult to estimate relates to
the size and speed of movement of various flow features through the grid. There should be sufficient number
of sampling points (in space and time) to avoid aliasing errors. Typically a grid resolution of
"x" can only represent wavelengths of "4x". This error will be a function
of the meteorological conditions.
Integration Error Example
The integration error component of the numerical error
can be estimated by running a forward and backward trajectory to the origin point. Run
the previous 700 hPA isobaric example. View the previous
tdump endpoints
file, and use the final position (67.796N, 25.527W, 2439.8 m
AGL) as the starting point (on the 23^{th} 0000 UTC)
for a backward trajectory calculation. Insure that the endpoints
file names are different for both the forward and backward calculations
by setting the tdump file to tdumpback for example. 

Then display both trajectories on the same plot by entering both file
names in the Input endpoints: box of the Trajectory
Display GUI using a + symbol (e.g. ./tdump+tdumpback).
Note how the return trajectory is very close to the initial origin point. You can
see that the model automatically returned to the NAM 12 km grid at 0900 UTC on December
20 by viewing the tdumpback endpoints file. 

Resolution Error Example
As mentioned before, a greater source of error, resolution error, is due to
the difficulty in representing atmospheric variables, which are continuous
in space and time, by discrete data points on a grid. This error is difficult to
quantify, but a sense of the error can be determined by running
trajectories using several different sources of meteorological data.
In the adjacent calculation, trajectories have been
computed using meteorological data from NAM(12 km)/GFS (red), RUC/GFS (blue),
and MM545/GFS (green). After the first 36 hours, differences
between trajectories are much greater than the numerical error. Note that the green
trajectory went up near the end because it hit Greenland (HYSPLIT is terrain
following). These calculations are more consistent than most simulations due to
the isobaric assumption.


