  Atmospheric carbon dioxide concentrations are being closely monitored by
remote sensing experiments which rely on knowing line intensities with an
uncertainty of 0.5% or better. We report a theoretical study providing
rotation-vibration line intensities substantially within the required accuracy
based on the use of a highly accurate {\it ab initio} dipole moment surface
(DMS). The theoretical model developed is used to compute CO$_2$ intensities
with uncertainty estimates informed by cross comparing line lists calculated
using pairs of potential energy surfaces (PES) and DMS's of similar high
quality. This yields lines sensitivities which are utilized in reliability
analysis of our results. The final outcome is compared to recent accurate
measurements as well as the HITRAN2012 database. Transition frequencies are
obtained from effective Hamiltonian calculations to produce a comprehensive
line list covering all $^{12}$C$^{16}$O$_2$ transitions below 8000 cm$^{-1}$
and stronger than 10$^{-30}$ cm / molecule at $T=296$~K
