An Analytical Model for the Distribution of CO2 Sources and Sinks, Fluxes, and Mean Concentration Within the Roughness Sub-Layer

Abstract

A one-dimensional analytical model that predicts foliage CO2 uptake rates, turbulent fluxes, and mean concentration throughout the roughness sub-layer (RSL), a layer that extends from the ground surface up to 5h, where h is canopy height, is proposed. The model combines the mean continuity equation for CO2 with first-order closure principles for turbulent fluxes and simplified physiological and radiative transfer schemes for foliage uptake. This combination results in a second-order ordinary differential equation in which soil respiration (R) and CO2 concentration well above the RSL are imposed as lower and upper boundary conditions, respectively. An inverse version of the model was tested against datasets from two contrasting ecosystems: a tropical forest (h = 40m) and a managed irrigated rice canopy (h = 0.7m), with good agreement noted between modelled and measured mean CO2 concentration profiles within the entire RSL. Sensitivity analysis on the model parameters revealed a plausible scaling regime between them and a dimensionless parameter defined by the ratio between external (R) and internal (stomatal conductance) characteristics controlling the CO2 exchange process. The model can be used to infer the thickness of the RSL for CO2 exchange, the inequality in zero-plane displacement between CO2 and momentum, and its consequences on modelled CO2 fluxes. A simplified version of the solution is well suited for being incorporated into large-scale climate models. Furthermore, the model framework here can be used to a priori estimate relative contributions from the soil surface and the atmosphere to canopy-air CO2 concentration, thereby making it synergetic to stable isotopes studies.