Figures in Appendix B displays an exhaustive comparison of
the influence on the calibration of the different modeling by ATM 1985 and
ATM 2009. The columns of these figures display
,
,
and
as a function of the frequency. There are two
figures per frequency band of the EMIR generation of receivers at Pico
Veleta: one at medium elevation (*i.e.* 45 deg) and one at low elevation
(*e.g.* 20 deg) were the differences between models will be maximum. For
each band, realistic values of
,
,
and
values
were used. The top rows displays the results for ATM 1985, the middle rows
displays the results for ATM 2009 and the bottom rows displays the relative
difference, *i.e.* (ATM 1985 - ATM 2009)/ATM 2009 in percentage. The
computations (and in particular the relative differences) are done for one
value of water vapor at a time in the range between 0.1 and 8 mm.

The first fact arising from the comparison, is that both models have
clearly different behaviors as a function of frequency: ATM 1985 have a
much simpler dependency on the frequency than ATM 2009. This comes mainly
from the inclusion of water isotopologue lines (*e.g.* the large line at
about 105 Ghz) and ozone lines (the many narrow lines) in ATM 2009 but also
from a finer modeling of water lines by ATM 2009.

Another general trend is that the differences between models for
,
and
decreases when the amount of
water vapor increases. This points toward a good consistency of the
treatment of water vapor in both models but a very different treatment of
the dry continuum emission/absorption of the atmosphere. However, this
result is inversed on
, *i.e.* the differences on
increases
when the amount of water vapor increases. This surprising result probably
comes from the fact that
while
.
In other words, while
can have close values in both model, this may
require very different values of . Also, the differences between
model results are much more pronounced on
and
than on
and
. The reason of the decrease of the
differences between
and
comes from the fact that the loss
term added in
is independent of the ATM model while it represents a
significant fraction of the
value. We guess that the large
differences in modeling between ATM versions have finally a relatively
small impact on
comes from the fact that
and
consistently cancel the modeling impact of ATM. Hence
at 45 deg of elevation, the relative difference in
is almost always
smaller than 5%, while at 20 deg of elevation, this relative difference is
of the order of 10%.