## 4 Discussion
In fact, the selection of input to key parameters (e.g., PAR, _f_/APAR, APAR, _e_) or their precise definitions (e.g., whether APAR and _f_/APAR are based on total or green canopy material) can broadly affect the results [34; 69]. Site-specific studies incorporating proximal optical measurements can offer insights into these causes of variation. Several recent studies have focused on estimation of carbon dioxide fluxes using proximal optical measurements as proxies for CO\({}_{2}\) fluxes [54; 60; 63]. However, a universal LUE model parameterization to estimate fluxes from proximal optical measurements for all ecosystems, while often discussed, does not yet exist [34; 35]. Despitethese limitations, it is clear that simple models that use linear relationships between fluxes and greenness indices such as those used in our study can successfully be used to estimate seasonal patterns of CO\({}_{2}\) flux for certain ecosystems [70]. In our study, we compared the estimates of carbon fluxes using different predictor variables (proxy NDVI, MODIS NDVI and APAR\({}_{\text{green}}\) derived from proxy NDVI), which reproduced the seasonal net CO\({}_{2}\) flux patterns with varying degrees of fidelity. This experiment allowed us to show that the APAR\({}_{\text{green}}\)-based method improved the estimates over NDVI alone. The proxy and MODIS NDVI methods could not explain all flux variability since they could not capture high-frequency flux changes due to irradiance dynamics. Unlike NDVI, APAR\({}_{\text{green}}\) is not only influenced by canopy structure, but also incorporates PAR irradiance (PPFD) [34]. Consequently, the incorporation of PAR irradiance (PPFD) in the relationship better captures the light dynamics affecting fluxes. This is probably one of the main reasons why the APAR\({}_{\text{green}}\)-based model provided a more accurate representation of day-to-day variation in net CO\({}_{2}\) fluxes than NDVI alone (Figure 8). While similar findings have been reported in some cases [71], other studies [64] have sometimes reported the opposite, finding that incorporation of PAR to yield APAR degrades agreement with CO\({}_{2}\) fluxes relative to NDVI or \(f\)APAR alone. The reasons for these discrepancies deserve further consideration, and could partly result from methodological differences, or the degree of stress (and variation in light-use efficiency), which can be assessed by the shape of the APAR\({}_{\text{green}}\)-flux curve. Additionally, the period of data aggregation could also affect these relationships, as the effects of including PAR are often more readily visible at fine scales (Figure 8). In general, while validation of modeled productivity using _in situ_ measurements provides essential information on model performance, sampling strategies and methodological differences in data collection complicate comparability [72]. One benefit of the proxy NDVI method used here is that it can provide an objective and repeatable sampling method that removes much of the subjective choices often used in field sampling. On the other hand, a limitation of this proxy NDVI method is its relatively limited footprint, which could be addressed by networking multiple sensors. The simple regression approach used in our study appears to work particularly well in ecosystems characterized by strong seasonal dynamics in above-ground green biomass such as grasslands and croplands [63; 37; 59; 60; 62]. In our grassland ecosystem, where seasonal CO\({}_{2}\) fluxes largely scaled with canopy development (e.g., as measured by green, above-ground biomass, Figures 5 and 6), an APAR\({}_{\text{green}}\)-based model assuming constant efficiency yielded good agreement with fluxes (Figures 7 and 8), despite our ignoring the efficiency (\(\epsilon\)) term in the LUE model. In the literature, there is not a universal agreement on implementing \(\epsilon\), and this lack of a standard approach or definition for \(\epsilon\) has recently been addressed by [PERSON] and [PERSON] [34].