## 2 Materials and Methods
### NDVI Measurements  
#### 2.4.1 \(\text{NDVI}_{\text{680,800}}\)  
Narrow-band reflectance measurements were obtained with a dual channel spectrometer (UniSpec-DC, PP-Systems, Amesbury, MA, USA), which has a spectral range of 305-1130 nm and a \(\approx\)3 nm nominal bandwidth (10 nm full width at half maximum). The spectrometer was fitted with two optical fibers, one looking upward and one looking downward, enabling simultaneous sampling of downwelling irradiance and target radiance and correction for variable sky conditions [45]. The upward-looking detector was fitted with a hemispherical cosine head (UNI435, PP Systems, Amesbury MA, USA) and sampled downwelling radiation; the downward-looking detector was fitted with a fiber optic (UNI684, PP Systems, Amesbury MA, USA) and field-of-view restrictor (hypotube, UNI688, PP Systems, Amesbury MA, USA) and sampled upwelling radiation with a nominal field-of-view of approx. 20 degrees from a distance of approx. 2 m.  
The spectrometer sampling procedure involved walking a series of transects across a 1-hectare grid centered on the flux tower, with each sample approximately 10 m apart (Figure 2). This grid sampling was completed approximately every 20 days during the growing season within one hour of solar noon. This allowed us to calculate the NDVI\({}_{\text{680,800}}\) of an area approximating the flux footprint and to compare the field spectral measurements with those derived from the MODIS satellite sensors. A separate study [41] demonstrated that, due to the uniformity of the landscape, the NDVI values of these different sampling regions were very similar, with an error of 4% or less. In addition to the grid sampling, the field spectrometer was also used to measure spectral reflectance at exactly the samelocation of each aboveground biomass sampling site for the purpose of NDVI-biomass calibration (numbered circles, Figure 2). Spectral processing software (Multispec, [[http://specnet.info](http://specnet.info)]([http://specnet.info](http://specnet.info))) was used to calculate raw reflectance values, calculated as the ratio between upwelling surface radiance (\(R_{\text{target}}\)) and downwelling solar irradiance (\(I_{\text{downwelling}}\)):  
\[\text{Raw reflectance}\,=\,R_{\text{target}}/I_{\text{downwelling}} \tag{7}\]  
The next step was to calculate a cross-calibration value comparing downwelling solar irradiance (\(I_{\text{downwelling}}\)) to a 99% reflective white standard panel (\(R_{\text{panel}}\)) (Spectralon, Labsphere Inc., North Sutton, NH, USA):  
\[\text{Cross-calibration}\,=\,I_{\text{downwelling}}/R_{\text{panel}} \tag{8}\]  
This cross-calibration was then used to calculate a corrected reflectance value as follows:  
\[\text{R}_{\text{corrected}}\,=\,(R_{\text{target}}/I_{\text{downwelling}})\times (I_{\text{downwelling}}/R_{\text{panel}}) \tag{9}\]  
This application of the cross-calibration was corrected for optical differences among sensors and for changing irradiance [45]. Both target and panel readings were taken under similar illumination and sun angle conditions. White panel measurements were taken at the beginning and ending of every grid sampling procedure. For NDVI\({}_{680,800}\) calculations, reflectance was interpolated to 1-nm wavebands. NDVI\({}_{680,800}\) was obtained from spectrometer grid data using the 680 nm waveband for the red region of the spectra and the 800 nm waveband for the infrared region, and was calculated using the following formula:  
\[\text{NDVI}_{680,800}\,=\,(\rho_{800}\,-\,\rho_{680})/(\rho_{800}\,+\,\rho_{680}) \tag{10}\]  
where \(\rho\) represents the reflectance at a given waveband, and subscripts indicate the wavelength values used. NDVI\({}_{680,800}\) was compared to green biomass and \(f\text{APAR}_{\text{green}}\) (see Sections 2.2 and 2.3), but because of the low sampling frequency (about every 20 days) was not compared to daily flux values or used directly in the LUE model.