An idealized model of the one-dimensional carbon dioxide rectifier effect

The net flux of carbon dioxide (CO₂) from the land surface into the atmospheric boundary layer has a diurnal cycle. Drawdown of CO₂ occurs during daytime photosynthesis, and return of CO₂ to the atmosphere occurs during night. Even when the net diurnal-average surface flux vanishes, the diurnal-average profile of atmospheric CO₂ mixing ratio is usually not vertically uniform. This is because of the diurnal rectifier effect, by which atmospheric vertical transport and the surface flux conspire to produce a surplus of CO₂ near the ground and a deficit aloft.
This paper constructs an idealized, 1-D, eddy-diffusivity model of the rectifier effect and provides an analytic series solution. When non-dimensionalized, the intensity of the rectifier effect is related solely to a single 'rectifier parameter'. Given this model's governing equation and boundary conditions, we prove that the existence of the rectifier effect is related to the correlation of CO₂ gradient and transport, and also to the day–night symmetry of transport.
The rectifier-induced near-surface CO₂ surplus ought to be included in inverse calculations that use near-surface CO₂ mixing ratio to infer land–surface sources and sinks of carbon. Such inverse modeling is facilitated by our model's simplicity. To illustrate, we use a 1-D inverse calculation to infer the amplitude of diurnal CO₂ surface flux.