Is it possible to detect the amount of $\rm CO_2$ in the atmosphere by observing Northern Lights? From my limited understanding, the different colours observed from the Northern Lights is due to the presence of different gases in the atmosphere. Is it possible to observe the amount of $\rm CO_2$ in the atmosphere using this phenomenon? Also, can it be used to detect changes in the amount of $\rm CO_2$ over time?
 A: Carbon dioxide spectral lines could be observed in the polar auroras, but that would be a terrible way to monitor the Earth's atmospheric $\mathrm{CO_2}$.  The constantly changing nature of the Northern Lights contributes much to their beauty but makes them a dubious scientific instrument.   Any $\mathrm{CO_2}$ blue auroral light would be orders of magnitude weaker than the auroral light from much more common nitrogen and oxygen atmospheric species (i.e. atomic, molecular, and ionic states).
If the tiny $\mathrm{CO_2}$ signal changed, it would be difficult to disentangle the effects of $\mathrm{CO_2}$ concentration, solar activity, geomagnetic activity, upper atmosphere dynamics, the season, the location, …. We have many better ways of monitor atmospheric  $\mathrm{CO_2}$, including ground, airborne, and satellite instruments.
Even if one wants to do radiant spectroscopy of $\mathrm{CO_2}$ in the upper atmosphere, sunlight is a much better excitation source than the high energy charged particles that generate the Northern Lights. Sunlight is more stable, more dependable, excites $\mathrm{CO_2}$  molecules at all latitudes, not just around the poles, and the sunlight excited signal is much, much stronger even near the poles.  For example, SABER-TIMED satellite measurements of 4.3 µm infra-red radiance from $\mathrm{CO_2}$ in the lower thermosphere "show that the daytime signal is more than 2 orders of magnitude larger than the night-time signal in the auroral regions".
The effect of atmospheric $\mathrm{CO_2}$ changes on the Northern Lights would also likely be similar or less than that expected for the related weaker - albeit less fickle and more widespread - phenomena of atmospheric airglow.
Direct visible airglow emissions from $\mathrm{CO_2}$ are negligible, but $\mathrm{CO_2}$ concentration affects the multi-body chemistry that produces the various oxygen and nitrogen species that actually produce the visible airglow. For example:
$CO_2 + O^+ \rightarrow CO + O_2^+ ;\; O_2^+ + e^- \rightarrow  O + O^*;\;  O^* \rightarrow O + \gamma\,(\textrm{6300 nm})$.
The expected effect of $\mathrm{CO_2}$ variations on airglow is an order of magnitude smaller than the changes due to solar cycle variations.
