Trajectory Error

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HIGHLIGHTS

• Trajectory computational error

• Plot multiple trajectories on map

• Estimate meteorological error

Total Trajectory Error

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: 

1. physical error due to the inadequacy of the data’s representation of the atmosphere in space and 

time,

2. computational error due to numerical inaccuracies,

3. measurement errors in creating the model’s meteorological data fields,

4. 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. See Example 3 Powerpoint (Ex3_hysplit.ppt)

or,

view the previous 700 hPA isobaric 

example trajectory endpoints file, 

and use the final position (69.866N, 

16.833W, 2797.8 m AGL) as the 

starting point (on the 23th 0000 UTC) 

for a backward trajectory calculation. 

If performing this calculation using PC 

HYSPLIT, insure that the trajectory 

endpoints file names are different for 

both the forward and backward 

calculations so that both trajectories 

can be plotted on the same map. 

Unfortunately, multiple independent 

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trajectories cannot be plotted on the 

same map using HYSPLIT-WEB.

The plot on the left below is the backward trajectory. Note how the return trajectory endpoint is very 

close to the initial origin point indicating very little integration error. The plot to the right was generated 

by downloading both trajectory endpoints files and plotting them on the same map using PC HYSPLIT. 

You can see that the model automatically switched from the GFS back to the NAM 40 km grid at 0600 

UTC on December 20 by viewing the backward 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 

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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.

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