# Radiometric Method for Determining Canopy Stomatal Conductance in Controlled Environments
## 2 Materials and Methods
### Net Radiation, Evaportranspiration, and Photosynthesis  
The net radiation above the canopy, \(R_{\mathrm{net}}\), was assumed proportional to net input of shortwave radiation and incoming longwave radiation (Equation (3)). \[R_{\mathrm{net}}=\mathrm{PPF}_{\mathrm{abs}}+\mathrm{NPSW}_{\mathrm{abs}}+ \downarrow\mathrm{L}_{\mathrm{g}}-\uparrow\mathrm{L}_{\mathrm{c}} \tag{3}\]  
where \(\mathrm{PPF}_{\mathrm{abs}}\) = absorbed photosynthetic radiation (W m\({}^{-2}\)), NPSW\({}_{\mathrm{abs}}\) = absorbed non-photosynthetic shortwave radiation (W m\({}^{-2}\)), \(\downarrow\mathrm{L}_{\mathrm{g}}\) = longwave radiation emitted by the glass from the water filter and the chamber walls (W m\({}^{-2}\)), and \(\uparrow\)L\({}_{\rm c}\) = longwave radiation emitted by the canopy (W m\({}^{-2}\)). Assuming that the longwave radiation components (\(\downarrow\)L\({}_{\rm g}\)\(-\)\(\uparrow\)L\({}_{\rm c}\) = \(\varepsilon\)\({}_{\rm c}\)\(\downarrow\)L\({}_{\rm g}\)\(-\)\(\varepsilon\)\({}_{\rm c}\)\(\sigma\) T\({}^{4}\)\({}_{\rm R}\) = \(\varepsilon\)\({}_{\rm c}\)\(\sigma\) T\({}^{4}\)Sky\({}^{-}\)\(\varepsilon\)\({}_{\rm c}\)\(\sigma\) T\({}^{4}\)R) nearly canceled each other was acceptable as long as the differences between T\({}_{\rm Sky}\) and T\({}_{\rm R}\) were also small. For example, if T\({}_{\rm glass}\) = 30 \({}^{\circ}\)C, T\({}_{\rm wall}\) = T\({}_{\rm air}\) = 23 \({}^{\circ}\)C, and T\({}_{\rm R}\) = 24 \({}^{\circ}\)C, then T\({}_{\rm sky}\) = 28.6 \({}^{\circ}\)C, and \(\downarrow\)L\({}_{\rm g}\)\(-\)\(\uparrow\)L\({}_{\rm c}\) = 27 W m\({}^{-2}\). Although Equation (3) ignores changes in longwave radiation within the canopy caused by vertical gradients in temperature, it was a better estimate than direct measurements with a net radiometer. Most net radiometers are calibrated for field operation, where the fraction of longwave radiation is much smaller than in these chambers, and the dimensions of the chambers placed the net radiometer close to the top of the foliage, where self-shading led to significant overestimates of the net radiation flux. Net radiometers are preferred in chambers illuminated by solar radiation, but they are affected during cloudy days with highly diffuse radiation. Net radiation in the chamber could be varied by either changing PPF\({}_{\rm o}\) with neutral density filters (window screen filters) or by draining the water filter under the lamps. Shading with neutral density filters does not alter the spectral composition of the incident radiation. In contrast, the water filter under the lamps reduces the amount of longwave radiation impinging on the canopy, thereby increasing the ratio of PPF\({}_{\rm abs}\) to R\({}_{\rm net}\)[39]. Removing the water filter increased \(\downarrow\)L\({}_{\rm g}\) compared to \(\uparrow\)L\({}_{\rm c}\) and added \(\sim\)100 W m\({}^{-2}\) to R\({}_{\rm net}\), as the glass temperature measured with a thermocoule reached 45 \({}^{\circ}\)C. The PAR\({}_{\rm abs}\) to R\({}_{\rm net}\) ratio was 83% of R\({}_{\rm net}\) in a chamber with a water filter below the lamps, but was only 64% of R\({}_{\rm net}\) when the water filter was removed. These changes in surface radiation forcing (R\({}_{\rm net}\)) were used to change canopy temperature and H for studying the relation between T\({}_{\rm Aero}\) and T\({}_{\rm R}\). Chamber ET (mmol m\({}^{-2}\) s\({}^{-1}\)) consisted of canopy transpiration (E\({}_{\rm can}\)) and evaporation (E) from the hydroponic solution through the porous media sustaining the plants (Equation (4)). \[\rm ET=E_{\rm can}+E. \tag{4}\]  
Chamber latent heat flux (LE; W m\({}^{-2}\)) was determined from the product of ET and the heat of vaporization of water (44 kJ mol\({}^{-1}\)). Evaporation from the hydroponic tubs, covered with lids but without a canopy, was small (\(\sim\)2% of R\({}_{\rm net}\) when expressed in W m\({}^{-2}\)).