Comparison at constant amount of water vapor

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 $1-\exp(-\ensuremath{a}\tau)$, , 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 $1-\exp(-\ensuremath{a}\tau)$, 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 $\ensuremath{T_\ensuremath{\mathrm{emi}}\ifthenelse{\equal{}{}}{}{^\ensuremath{\... ...rm{}}}}\, \ensuremath{\displaystyle\left[ 1-\exp(-\ensuremath{a}\tau) \right] }$ while $\ensuremath{T_\ensuremath{\mathrm{cal}}\ifthenelse{\equal{}{}}{}{^\ensuremath{\mathrm{}}}}\propto \exp(\ensuremath{a}\tau)$. In other words, while can have close values in both model, this may require very different values of $\tau$. Also, the differences between model results are much more pronounced on $1-\exp(-\ensuremath{a}\tau)$ 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 $\exp(-\ensuremath{a}\tau)$ 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%.