Observations of gradients in the total CO₂ column, ⟨CO₂⟩, are expected to provide improved constraints on surface fluxes of CO₂. Here we use a general circulation model with a variety of prescribed carbon fluxes to investigate how variations in ⟨CO₂⟩ arise. On diurnal scales, variations are small and are forced by both local fluxes and advection. On seasonal scales, gradients are set by the north-south flux distribution. On synoptic scales, variations arise due to large-scale eddy-driven disturbances of the meridional gradient. In this case, because variations in ⟨CO₂⟩ are tied to synoptic activity, significant correlations exist between ⟨CO₂⟩ and dynamical tracers. We illustrate how such correlations can be used to describe the north-south gradients of ⟨CO₂⟩ and the underlying fluxes on continental scales. These simulations suggest a novel analysis framework for using column observations in carbon cycle science.