As anyone who has spent a wee bit of time reviewing the theoretical method of determining how much radiation is absorbed/re-emitted by CO2 can tell you, the method is spectacularly complicated. It is not feasible for daily calculations. In most fields, an approximation of the solution is used. The Path Length Method is the method 0f choice for engineers, in particular combustion engineers. I’ll not get into the development of this method. It dates back a long way (at least 1950, possibly earlier).
Anyway, if I’ve done this right, this should link to the paper.