## 1 Introduction
Satellite remote sensing combined with weather data have been used to model global carbon exchange for many years now, but these current models often disagree with local field measurements due to the coarse scale of their optical and meteorological inputs [24]. For effective carbon policy, fine-grained measurements are needed to match the scale of local land management practices. Recent advances in automation and low-cost optical sensors are making a local-scale optical sensing approach increasingly attractive. Recent studies show that the combined application of remote and proximal optical sensors provide the opportunity to monitor productivity across a wide range of spatial and temporal scales and offer thepossibility to relate remote sensing measurements with carbon fluxes as a foundation for modeling and upscaling [25]. Networks such as SpecNet and EUROSPEC have been exploring the possibility of combining flux and spectral reflectance measurements for a more complete assessment of ecosystem function [26; 27; 28]. These collaborations have increased the availability of both optical and flux data, allowing for improved models linking remote sensing measurements and carbon fluxes. A crucial first step is to quantitatively evaluate optical methods in comparison to flux methods to enable proper model parameterization. The most widely applied model for combining carbon fluxes and optical measurements is the Light Use Efficiency (LUE) model. Originating with the work of [PERSON] [29; 30], more recent parameterizations have been used to estimate gross primary productivity (GPP) based on the equation:  
\[\mathrm{GPP}\;=\;\varepsilon\times\mathrm{APAR}_{\mathrm{green}} \tag{1}\]  
where \(\mathrm{APAR}_{\mathrm{green}}\) (absorbed photosynthetically active radiation) represents the amount of radiation absorbed by green vegetation, and \(\varepsilon\) represents the efficiency with which that absorbed light is used by vegetation to fix carbon. To obtain annual GPP, the equation terms can be integrated (summed) over the full growing season [24; 31]. \(\mathrm{APAR}_{\mathrm{green}}\) can be further defined or measured as the product of \(f\mathrm{APAR}_{\mathrm{green}}\) (the fraction of photosynthetically active radiation absorbed by green vegetation) and PAR (photosynthetically active radiation, also called the photosynthetic photon flux density, or PPFD):  
\[\mathrm{APAR}_{\mathrm{green}}\;=\;f\mathrm{APAR}_{\mathrm{green}}\times \mathrm{PAR} \tag{2}\]  
[PERSON] _et al._[32] reported that, especially in cropland and grassland, canopy structure and APAR covary in time during a seasonal cycle. Partitioning between photosynthetic and non-photosynthetic components of vegetation in APAR calculations significantly improves estimation of ecosystem productivity with respect to models driven by total \(f\mathrm{APAR}\)[33; 34]. \(\mathrm{APAR}_{\mathrm{green}}\), a measure of green vegetation structure closely linked to green biomass or leaf area index, plays a dominant role in the model for most grassland ecosystems. The confusion of methods and LUE model definitions in the literature has led to uncertainty when comparing model results [34]. To clarify the terminology and to emphasize the role of green (not total) vegetation in driving light absorption for photosynthesis and productivity, we adopted the terminology recommended by [PERSON] and [PERSON] [34] and included the subscript \"green\" when referring to \(f\mathrm{APAR}\) and APAR. Light use efficiency (\(\varepsilon\)) relates to vegetation physiology, and is presumably less important in determining seasonal GPP patterns for grasslands and other annual systems where canopy growth dominates the seasonal phenological signals detectable with remote sensing [35]. Consequently, most of the variability in grassland productivity can be explained by changes in \(\mathrm{APAR}_{\mathrm{green}}\)[36] when the ecosystem is not stressed [33; 35; 37]. For this reason, we adopted the hypothesis of a constant \(\varepsilon\) over the season (May-October) in our study.