The concentration of CO₂ in air near the ground needs to be predicted to assess environmental and health risks from leaking underground storage. There is an exact solution to the advection–diffusion equation describing trace gases carried by wind when the wind profile is modeled with a power-law dependence on height. The analytical solution is compared with a numerical simulation of the coupled air–ground system with a source of CO₂ underground at the water table. The two methods produce similar results far from the boundaries, but the boundary conditions have a strong effect; the simulation imposes boundary conditions at the edge of a finite domain while the analytic solution imposes them at infinity. The reverse seepage from air to ground is shown in the simulation to be very small, and the large difference between time scales suggests that air and ground can be modeled separately, with gas emissions from the ground model used as inputs to the air model.