## 3 Results
### Parameterization of the LUE Model Using Proxy NDVI, MODIS NDVI and APAR\({}_{green}\)  
Figures 7 and 8 present the different approaches in flux-optical comparison, LUE model testing, and subsequent gap-filling of the flux dataset using optical datasets, including results based on proxy NDVI (panel a), MODIS NDVI (panel b), or APAR\({}_{green}\) derived from proxy NDVI (panel c). For this purpose, only results from the E3 site during 2012 were selected because this site and year had the fewest gaps in the optical measurements. To explore the possible effect of hysteresis in our datasets,  
Figure 6: Correlations between green biomass and (**a**) NDVI\({}_{680,800}\); (**b**) proxy NDVI (5 h averaged) and (**c**) MODIS NDVI for both E3 (black dots) and E5 sites (white dots) in 2012 and 2013. Error bars for green biomass are expressed as standard error of the mean. Resulting equations and correlations (\(R^{2}\) values) are indicated for each fit above.  
relationships between flux and NDVI (or APARgreen) are presented for the whole season (single fit) and for the green up phase and the maturity phase separately (separate fits). In this analysis, we used the peak flux value of the season to separate the season in the two parts. Better model estimates (higher \(R^{2}\) values) were obtained when separate equations were used for the two parts of the season (Figure 7), indicating seasonal hysteresis in the flux-NDVI and flux-APARgreen relationships. Flux model estimates derived from MODIS NDVI or APARgreen (based on proxy NDVI) yielded slightly better agreement with measured fluxes than the estimates based on proxy NDVI (Figure 7).  
Figure 7: Relationship between proxy NDVI (5 h average, panel **a**); MODIS NDVI (panel **b**); APARgreen (panel **c**) and filtered net CO2 fluxes (5 h average) for the E3 site in 2012. Fits are shown for the whole season (dashed line), for the green-up phase (black dots, solid line), and for the senescence phase (white dots, solid line). \(R^{2}\) values are reported for each panel considering the whole season (dashed line), the green-up phase (black dots) and the senescence phase (white dots). \(p\) values are \(<\)0.001 for all the relationships.  
The resulting time trends of modeled and measured fluxes using these two approaches (whole-season _vs._ two halves) are shown in Figure 8. Regardless of the model formulation, a single fit for the whole season tended to underestimate fluxes in the first half of the season and overestimate them in the second, and separate fits improved the agreement (Figure 8). In our final exercise, we used APAR\({}_{\text{green}}\) as independent variable and net CO\({}_{2}\) flux as a dependent variable to derive a modeled flux (Figures 7c and 8c). Unlike NDVI, APAR\({}_{\text{green}}\) also explicitly considers the dynamic variation in PAR irradiance (_i.e._, PPFD), and thus incorporated hourly and day-to-day variation in illumination. Relative to the proxy NDVI (from which it was derived), the APAR\({}_{\text{green}}\)-based model yielded a better fit with measured fluxes. The APAR\({}_{\text{green}}\)-based model also yielded more dynamic patterns of flux measurements relative to NDVI-based models (_cf._ Figure 8c to Figure 8a,b).  
Figure 8: Time series of observed and modeled net CO\({}_{2}\) fluxes based on proxy NDVI (panel **a**); MODIS NDVI (panel **b**); and APAR\({}_{\text{green}}\) (panel **c**). The original fluxes are shown as solid lines. Fluxes modeled using a single fit are shown as dashed lines, and fluxes modeled using two separate fits are shown as dotted lines. All results are for the E3 site in 2012.