Diabatic dispersion depends on the statistics of the large-scale horizontal
eddy motion as well as on the spatial structure,
be it steady or
time varying,
of the diabatic heating field.
The trajectory statistics suggest that the polar vortex, winter hemisphere
surf zone, tropics, and extratropical summer hemisphere are
to varying extents
isolated from each other by eddy transport barriers. The character and
magnitude of the diabatic dispersion for parcels that stay within each of
these four regions is distinctly different. The diabatic dispersion
in both the surf zone and southern hemisphere extratropics is
initially advective, with potential temperature variance (dtheta(t)²)
increasing like t² as time t increases.
After about one month,
on the 500K isentropic surface,
the dispersion becomes
diffusive. Strictly this would be better as "quasi-diffusive"
in the sense that (dtheta(t)²) ~ 2K_ss t
and with a diffusivity K_ss in the range 2-6 K² day^(-1),
roughly equivalent to
K_zz ~ 0.1-0.2m² s^(-1)
on the 500K isentropic surface.
The emergence of a diffusive regime is discussed in terms
of loss of memory of diabatic heating along parcel paths,
as measured by the decay of the Lagrangian autocorrelation function.
Diabatic dispersion within the tropics and polar vortex over the
two month period is more than an order of magnitude
smaller, and is less clearly diffusive.
Some parcels do not remain within any of the four regions defined above, and
show entirely different dispersion characteristics. The diabatic
dispersion of parcels moving poleward out of the tropics into either hemisphere
is faster than either differential advection or diffusion, and is consistent
with a transient shear dispersion model in which (dtheta(t)²)
increases like t³.
For the total ensemble of all parcels,
the potential temperature variance
increases like t²,
consistent with
global-scale differential advection by the mean diabatic circulation.
This is inconsistent, at least
on the two-month timescale considered here, with
a one-dimensional diffusive model of
global-scale vertical diffusive dispersion.