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.