If we assume that a particle passively follows
the wind, then its trajectory is just the integration of the particle
position vector in space and time. The final position is computed
from the average velocity at the initial position (P) and firstguess
position (P').

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

P'(t+
Δ
t) = P(t)
+ V(P,t)
Δt

The integration time step is variable:
V_{max}
Δt < 0.75
The meteorological data remain on its native horizontal
coordinate system. However, the meteorological data are interpolated
to an internal terrainfollowing (σ) vertical
coordinate system:
σ =
( Z_{top} –
Z_{msl} ) / ( Z_{top} –
Z_{gl} )
Z_{top }
top of the trajectory model’s coordinate system
Z_{gl} 
height of the ground level
Z_{msl } height of the internal coordinate
The model’s internal heights can be chosen at any interval, however
a quadratic relationship between height and model level is specified,
such that each level’s height with respect to the model’s internal
index, k, is defined by
Z_{agl}
= ak^{2} + bk +c
The constants are automatically defined such that the model’s internal
resolution has the same or better vertical resolution than the input
data.
