To compute air concentrations it is necessary to
follow all the particles needed to represent the pollutant distribution
in space and time. This can be done explicitly by following the
trajectory of each particle, where a random component is added
to the mean velocity (from the meteorological model), to define
the dispersion of the pollutant cloud. In the horizontal, the
computations can be represented by the following equations:
X(t + Δt) = X_{mean}(t + Δt) + U'(t + Δt)Δt,
U'(t + Δt) = R(Δt) U'(t) + U''(1  R(Δt)^{2})^{0.5},
R(Δt) = exp(Δt/T_{Lx}),
U'' = σ_{u}λ
where λ is a random number with 0 mean and σ of 1. 
The computations can be simplified, if instead of
modeling the motion of each particle, we compute the trajectory
of the mean particle position and the particle distribution. The
standard deviation of the particle distribution could be computed
from all the particles,
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σ^{2} = (X_{i}X_{m})^{2}
or it can be computed without following individual
particles by assuming a distribution shape (puff) and relationship
to the local turbulence. Many different formulations can be found
in the literature.
dσ_{h}/dt = √2 σ_{u}
σ_{u} = (K_{x} / T_{L})^{0.5}
These computations are set
in the Advanced / Configuration Setup / Concentration menu, which creates the
SETUP.CFG file.
