## 4 Discussion  
Eddy covariance measurements, while they provide the \"gold standard\" for net CO\({}_{2}\) flux measurements, are often affected by a number of problems, including instrumentation malfunctioning or low friction velocity, which can cause long data gaps. For this reason, several methods have been implemented to overcome periods of missing data [52; 53; 54]. The novelty of our approach lies in the particular combination of sensors used and in the comparison of different methods of obtaining NDVI as an input to the LUE model. This demonstrates the possibility of modeling and filling the gaps in a carbon flux dataset using empirical methods based on irradiance and spectral reflectance measurements. We address the data aggregation in the time domain and take advantage of flux station meteorological variables to filter optical measurements, illustrating how one dataset can be used to inform the processing of another. Over the years, NDVI has emerged as a widely used reflectance index for detecting seasonal changes related to photosynthetic activity [37; 55; 56; 57; 58]. The effectiveness of NDVI as a metric of green biomass and as a useful parameter in a simple expression of the LUE model for a grassland ecosystem is confirmed in our study. The strong correlations between NDVI, APAR\({}_{\text{green}}\), and midday CO\({}_{2}\) flux for this prairie grassland provide a strong foundation for using optical measurements to model fluxes and gap-fill eddy covariance data, as proposed by [PERSON] _et al._[54]. Our findings are in agreement with past studies that have shown good correlations between NDVI and green biomass, APAR\({}_{\text{green}}\), or total canopy chlorophyll content for many ecosystems [37; 59; 60; 61]. Strong agreements between NDVI or NDVI-based modeled fluxes and eddy covariance measurements, particularly for ecosystems dominated by annual grasslands, are reported by similar studies [37; 60; 62]. These observations illustrate the utility of combining optical and flux measurements to characterize seasonal photosynthetic patterns. The best relationship with NDVI and green biomass was established with NDVI\({}_{\text{680,800}}\), but similar, strong patterns were found for all NDVI formulations (Figure 6). More work would be needed to understand the slight differences, which are presumably related to the different band formulations, temporal sampling periods, solar angle influence, or footprints of the three NDVI methods. Despite its broad-band formulation, proxy NDVI was able to depict most of the seasonal variability in net CO\({}_{2}\) flux, and had the benefit of continuous sampling (similar to eddy covariance sampling). This outcome highlights the utility of broadband proxy NDVI for monitoring seasonal photosynthetic activity (\"photosynthetic phenology\") using a set of simple, inexpensive optical measurements [43]. These findings confirm that, for the purpose of measuring the seasonal course of photosynthetic activity in grassland ecosystems, broadband dual channel low-cost sensors can replace more complex and expensive hyperspectral sensors at eddy covariance sites when the budget is limited [27; 43; 63; 64]. Of the three NDVI methods used, the proxy NDVI had the most limited sampling footprint (estimated at \(\approx\)100 m\({}^{2}\)), which might explain why it sometimes deviated from the other methods in the depiction of seasonal trends (Figure 5), and why it yielded slightly lower agreement with measured fluxes relative to MODIS NDVI (Figure 7). Further study with mobile sensors or fixed arrays of several proxy NDVI sensors located within the flux tower footprint would possibly improve the agreement with fluxes and clarify this question. Several versions of the LUE model driven by satellite remote sensing of NDVI have been in wide use for many years [24; 65; 66]. While these models can depict broad global patterns, their agreement with local field measurements varies considerably across ecosystems or with different model formulations [67; 68].