# Radiometric Method for Determining Canopy Stomatal Conductance in Controlled Environments
## 2 Materials and Methods
### Canopy Aerodynamic Conductance  
In field settings, the log-wind profile approximation allows canopy g\({}_{\rm A}\) to be determined from H provided \(\Delta\)T\({}_{\rm A}\), the aerodynamic canopy-to-air temperature difference (\(\Delta\)T\({}_{\rm A}\) = T\({}_{\rm Aero}\) - T\({}_{\rm air}\)), the displacement height, and the roughness length are known [41]. However, the short fetch (1 m) of the canopies used in this study precludes the use of the log-wind profile approximation for calculating g\({}_{\rm A}\) in controlled-environment chambers. Instead, an analog of [PERSON]'s law (Equation (6)) that relates the surface-to-air temperature difference to the sensible heat loss from the surface was used to describe the energy transfer between the canopy and the chamber air [8]:  
\[\rm H=\varrho^{*}Cp^{*}g_{A}{}^{*}(T_{R}\ -T_{air}) \tag{6}\]  
where \(\varrho\) = density of air (kg m\({}^{-3}\)), \(Cp\) = heat capacity of air at constant pressure (kJ m\({}^{-3}\)\({}^{\circ}\)C\({}^{-1}\)), g\({}_{\rm A}\) = canopy aerodynamic conductance (mol m\({}^{-2}\) s\({}^{-1}\)), and T\({}_{\rm R}\) (\({}^{\circ}\)C) was approximated by T\({}_{\rm canopy,IR}\)-T\({}_{\rm air}\) was measured at the reference height above the canopy, and used to determine the radiometric canopy-to-air temperature difference (\(\Delta\)T\({}_{\rm IR}\) = T\({}_{\rm R}\) - T\({}_{\rm air}\)). Equation (6) assumes that the slope between H and \(\Delta\)T\({}_{\rm IR}\) equals the slope between H and \(\Delta\)T\({}_{\rm A}\), when T\({}_{\rm Aero}\) = T\({}_{\rm R}\). This assumption is valid for fully covered canopies, whereby the contribution to \(\Delta\)T\({}_{\rm IR}\) from the temperature of the surface below the vegetation (e.g., soil or hydroponic tray) is negligible. The canopy leaf boundary layer conductance component depends on leaf shape and size, and the turbulent conductance component depends on wind speed and canopy aerodynamic roughness [8]. Canopy aerodynamic conductances of dense wheat and soybean canopies with distinct canopy architectures were calculated from the slopes of plots of H vs. measured \(\Delta\)T\({}_{\rm IR}\) following Equation (6). Radiometric \(\Delta\)T\({}_{\rm IR}\) and H were varied simultaneously by manipulating chamber CO\({}_{2}\) concentration at constant environmental conditions (wind speed and VPD) over the course of several days. The g\({}_{\rm A}\) measured for each species results from the amount of drag generated by the interaction between canopy architecture and the chamber air recirculating at constant wind speed. Although changes in CO\({}_{2}\) affect H and \(\Delta\)T\({}_{\rm IR}\) through changes in stomatal conductance, g\({}_{\rm A}\) remains constant at a fixed chamber wind speed. The highly turbulent conditions in the chamber ensure that free convection effects are negligible compared to forced convection, so changes in light level should not significantly affect canopy g\({}_{\rm A}\). Estimates of g\({}_{\rm A}\) obtained from the slope of a plot of H vs. \(\Delta\)T\({}_{\rm IR}\) are also insensitive to systematic errors in H (e.g., offset errors in R\({}_{\rm net}\)) because these do not affect the slope. In this context, the canopy g\({}_{\rm A}\) obtained by this radiometric method represents the canopy leaf boundary layer conductance, as well as the conductance for turbulent heat transfer between the leaves at T\({}_{\rm Aero}\) and T\({}_{\rm air}\) measured at the reference height above the canopy. The H vs. \(\Delta\)T\({}_{\rm IR}\) plot is also useful for exploring differences between T\({}_{\rm Aero}\) and T\({}_{\rm R}\). The offset, defined as the value of \(\Delta\)T\({}_{\rm IR}\) when H and \(\Delta\)T\({}_{\rm A}\) are zero (Equation (7)), quantifies this difference because \(\Delta\)T\({}_{\rm IR}\) and \(\Delta\)T\({}_{\rm A}\) are referenced to a common T\({}_{\rm air}\). \[\Delta\)T\({}_{\rm A}=\Delta\)T\({}_{\rm IR}\) + Offset.