## 2 Materials and Methods
### CO\({}_{2}\) Flux Measurements  
Net CO\({}_{2}\) fluxes were measured using the eddy covariance (EC) technique [21]. Identical EC flux towers were deployed at our E3 (50.8672\({}^{\circ}\), \(-\)111.9045\({}^{\circ}\)) and E5 (50.9057\({}^{\circ}\), \(-\)111.8823\({}^{\circ}\)) grassland sites. Sites exhibited uniform vegetation cover (described above), providing measureable fluxes from all wind directions (_i.e._, the flux footprint) except those passing through the tower structures. Each tower was equipped with an open-path infrared gas analyzer (IRGA; LI-7500, LI-COR, Lincoln NE, USA) and a three-dimensional sonic anemometer (CSAT3; Campbell Scientific, Logan UT, USA) to quantify vertical CO\({}_{2}\) fluxes. Each EC sensor was affixed at 2.9 m (E3 site) and 3.0 m (E5 site) above ground level and each IRGA was horizontally separated 15-17 cm from each sonic anemometer. All raw EC fluxes were measured at a sampling rate of 10 Hz. Other sensors to quantify environmental conditions and weather were also fixed to each tower to measure half-hour averages of, for example, air temperature, relative humidity (RH) and soil conditions. All collected data were stored by a datalogger (CR5000, Campbell Scientific).  
EC data were analyzed using the software package EddyPro (LI-COR, v. 5.1) to quality check raw data, remove outliers and apply standard corrections to calculate corrected vertical fluxes of CO\({}_{2}\). Raw 10 Hz CO\({}_{2}\) fluxes were preconditioned by eliminating data spikes greater than 3.5 standard deviations (\(\sigma\)), temporary drop-outs (10% per bin), and heavily-skewed data (+2 \(>\) x \(<\) \(-\)2). Anemometer tilt (mean pitch: E3 = \(-\)1.6\({}^{\circ}\); E5: +1.5\({}^{\circ}\)) was corrected using a double rotation by forcing lateral and vertical wind components to zero. Data were removed when the time lag between measurements of the anemometer and IRGA exceeded \(\pm\)0.4 s. Flux data were further detrended using a block-averaging approach over half-hour time increments. Calculated fluxes were corrected for density fluctuations using the [PERSON] _et al._[46] procedure. High-pass spectral corrections were implemented after [PERSON] _et al._[47], while low-pass spectral corrections, integrating in-situ conditions to determine system cut-off frequencies, were used after [PERSON] _et al._[48]. Fluxes were further rejected when EC sensors malfunctioned or were affected by moisture, when wind passed through the tower before contacting EC sensors, or when friction velocities fell below 0.1 m\(\cdot\) s\({}^{-1}\) (after [PERSON] _et al._[49]). Turbulence tests using the approach of [PERSON] and [PERSON] [50] were used to remove the poorest-quality fluxes (level 2) when they did occur. Half-hour fluxes below \(-\)3\(\sigma\) or above +3\(\sigma\) were considered outliers and removed. Corrections applied to daytime data resulted in the removal of 23.33% of all calculated fluxes across all EC measurements at both sites. For final comparison with optical data and derived biophysical parameters (proxy NDVI and APARgreen), a midday average net CO\({}_{2}\) flux was calculated based on a 5-h average, matching the period of averaging used for optical data (Figure 4).