# Trajectory Error

Previous HOME Next 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 est imate 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. measurementerrors in creating the mode l’s meteorological data fields, 4. forecasterror 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 in tegration error (part of which is due to truncation) and a data resolution error, i.e., tryi ng to represent a continuous function, the atmospheric flow field, with gridded data points of limited r esolution in space and time. The integration error can be estimated by computing a backward traject ory from the forward trajectory endpoint. The error is then 1/2 the distance of the final endpoi nt and the starting point. The resolution error can be estimated by starting several trajectories about t he initial point (offset in the horizontal and vertical). The divergence of these trajectories will gi ve an estimate of the uncertainty due to divergence in the flow field. An initial offset should be used that is comparable to the est imated integration error. One component of the resolution error that is difficul t to estimate relates to the size and speed of movement of various flow features through the grid. There should be sufficientnumber of sampling points (in space and time) to avoid aliasing errors. Typicallya grid resolution of " x " can only represent wavelengths of " 4x ". This error will be a function of t he 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 poi nt. 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 23 th 0000 UTC) for a backward trajectory calculation. If performing this calculation using PC HYSPLIT, insure that the trajectory endpoints file names are differentfor both the forward and backward calculations so that both trajectories can be plotted on the same map. Unfortunately, multiple independent 

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6 / 8 /201 5 http://www.arl.noaa.gov/doc uments/workshop/NAQC2007/HT ML_Docs/trajerro.htm ltrajectories 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 indi cating very little integration error. The plot to the right was generated by downloading both trajectory endpoints files and plo tting them on the same map using PC HYSPLIT. You can see that the model automat ically 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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6 / 8 /201 5 http://www.arl.noaa.gov/doc uments/workshop/NAQC2007/HT ML_Docs/trajerro.htm lcontinuous 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 MM 545/GFS (green). After the first 36 hours, differ ences 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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6 / 8 /201 5 http://www.arl.noaa.gov/doc uments/workshop/NAQC2007/HT ML_Docs/trajerro.htm l