TRAJECTORIES

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What is a trajectory?

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A trajectory is the time integration of the position of a parcel of air as it is transported by the wind. The parcel's passive transport by the wind is computed from the average of the three-dimensional velocity vectors at the particle's initial-position P(t) and its first-guess position P'(t+dt). The velocity vectors are interpolated in both space and time.

The first guess position is

P'(t+dt) = P(t) + V(P,t) dt,

and the final position is

P(t+dt) = P(t) + 0.5 [ V(P,t) + V(P',t+dt) ] dt

Trajectories may be integrated both forward and backward in time. A measure of the integration error may be obtained by computing a backward trajectory from the end-point-position of its forward counterpart.

In the example below, a forward trajectory was started at 45N, 95W, 1500 m AGL, and returned to 44.62N, 95.17W, 1408 m AGL. The difference between the starting point and endpoint represents an error of about 2% of the total travel distance.

Forward trajectory	Backward trajectory