## 2 Materials and Methods
### NDVI Measurements
#### 2.4.2 Proxy NDVI Measurements  
Each site was monitored with an optical phenology station consisting of a data logger (H21-001, Onset Computer Corporation, Bourne, MA, USA) and two-band radiometer mounted on a boom and tripod, 3 m above the ground, placed approximately 10 meters southwest of each tower. The sensors detected incoming light (irradiance) and reflected light from the canopy. One band consisted of two PAR sensors (S-LIA, Onset Computer Corporation) that measured the photosynthetic photon flux density (PPFD) within the PAR band (400-700 nm), and the other band consisted of two PYR sensors (S-LIB, Onset Computer Corporation) measuring irradiance or radiance across a spectral range from 300 to 1100 nm. Both up- and down-looking sensors had cosine (nominally 180 degree) foreoptics, allowing us to sample a relatively large area (\(\approx\)100 m\({}^{2}\)) immediately adjacent to the flux tower, but restricted to a small portion of the total flux footprint (typically \(>\)1 ha, with variations depending on windspeed and wind direction) [41]. This phenology station provided a continuous, high temporal resolution proxy NDVI by means of continuous broad-band reflectance in both PAR and PYR bands sampled every 1-min during the whole growing season and logged as 15-min averages, thus monitoring seasonal changes in the vegetation photosynthetic phenology [43]. Additionally, temperature and relative humidity were monitored via appropriate sensors (RH; S-THB-M002, OnsetComputer Corporation) allowing rainy-day optical data to be identified and filtered from the dataset (see Section 2.6, below). To derive proxy NDVI values, each sensor pair had been previously cross-calibrated against one another by comparing both upward- and downward-looking sensors in an upward-looking (irradiance) configuration, yielding a coefficient that corrected for any sensor differences (typically less than 5%). These coefficients were then applied to each sensor pair (PAR and PYR) prior to calculating proxy NDVI. Subsequent analyses used the 15-min averages (aggregated over different time periods from 1 to 5 h) to calculate midday average APARgreen and proxy NDVI values for comparison with midday average net CO2 flux from the eddy covariance tower (Figure 3). Since 5-h aggregation periods yielded the highest correlation with CO2 flux (see Supplementary Materials), and fully encompassed the overpass times of the MODIS Aqua and Terra sensors, we chose that aggregation period for all subsequent analyses.  
The phenology station data were used to compute a proxy NDVI [27; 43] following the formula:  
\[\text{proxy NDVI}\,=\,(\rho_{\text{PYR}}-\rho_{\text{PAR}})/(\rho_{\text{PYR} }\,+\,\rho_{\text{PAR}}) \tag{11}\]  
where \(\rho_{\text{PYR}}\) is the reflectance of the solar radiation (PYR band), calculated as the ratio of the reflected solar radiation to the incoming solar radiation and \(\rho_{\text{PAR}}\) is the reflectance of the photosynthetically active radiation (PAR band) calculated as the ratio between the reflected PAR and the incoming PAR. This provided a continuous proxy NDVI, which was then averaged over a 5-h midday period (Figures 2 and 3) for comparison with the daily flux measurements. Using the calibration derived from the harvest sites (Equation (5)), the proxy NDVI time series was used to derive \(f\text{APAR}_{\text{green}}\) for the LUE model (Figure 3).  
Figure 3: Experimental design, summarizing steps used in derivation of NDVI and APARgreen (arrows), for comparisons with net CO2 fluxes (double lines). As indicated, APARgreen was estimated from the different NDVI metrics by regression of measured \(f\text{APAR}_{\text{green}}\) against proxy NDVI, and multiplying \(f\text{APAR}_{\text{green}}\) with PAR (photosynthetic photon flux density, measured with PAR sensors). Because the proxy NDVI provided continuous measurements, it was used to derive APARgreen for comparison against Net CO2 flux. Further explanation can be found in the text.