## 1 Introduction  
Grasslands are among the most widespread vegetation types worldwide, covering between 14% and 26% of the earth's surface [1; 2]. They play an important role in the carbon (C) cycle, as they store about 23% of the global soil C [3] and, given the contribution of grasslands in mitigating climate change, it is important to monitor their C sequestration potential. The Eddy Covariance (EC) method permits to measure, at an ecosystem scale, the atmosphere-ecosystem exchange of water, energy and CO\({}_{2}\) fluxes [4]. It provides a reliable direct measurement of different gas compounds together with meteorological variables, at high temporal detail, making it possible to ascertain the influence of climate drivers or other disturbances/stress factors on fluxes at ecosystem scale [5]. The EC measurements represent fluxes in an area around the tower (named footprint) whose size and shape depend on the set-up of the equipment, the structure and height of the canopy and wind direction and speed. This spatial limitation raises the necessity to estimate C fluxes outside the footprint of an EC tower, since it would be costly and unfeasible to install towers to cover all areas of interest. The net ecosystem exchange (NEE) is the balance between two components, the respiration of the ecosystem (R\({}_{\text{eco}}\)) and the gross primary production (GPP), which represents the amount of carbon fixed through photosynthesis [6; 7]. A possible approach to estimate GPP outside the limits of the footprint of an EC tower is the use of remotely sensed information [8]. Light-use efficiency (LUE) models are the most frequently applied to estimate GPP from spectral vegetation indices (VIs) remotely retrieved [9]. The LUE concept states that GPP is directly related to the absorbed photosynthetically active radiation (APAR) and photosynthetic efficiency by Photosynthetically Active Radiation (PAR) unit, which can be reduced under environmental stresses such as low temperatures or water stress [10; 11]. Thanks to the empirical relationship that exists between the fraction of absorbed photosynthetically-active radiation (fAPAR) and VIs [10; 11; 12], the latter are used in many studies as proxies of GPP. The most widely used VIs to that end are the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI), which are empirically known to be good metrics of green biomass [8; 9; 13; 14]. NDVI is more sensitive to background reflectance and tends to saturate at high leaf area, which makes EVI a good alternative, as it is less sensitive to these limitations [14; 15]. Some VIs similar to NDVI and EVI have also been used, such as the Green Normalized Difference Vegetation Index (GNDVI) which is more sensitive to chlorophyll content in plants than NDVI [16; 17], and the Soil-Adjusted Vegetation Index (SAVI) which is derived from NDVI by including a soil-adjustment factor [18]. In grasslands, several greenness-related VIs demonstrated their suitability as proxies of GPP. The MERIS Terrestrial Chlorophyll Index (MTCI) was found to provide the best estimates of GPP in subalpine grasslands [19; 20], EVI and SAVI were the best predictors of GPP in a temperate-alpine grassland [14], MTCI, PSRI (Plant Senescence Reflectance Index) and GNDVI revealed their suitability in a Mediterranean grassland [17]. Other studies revealed the usefulness of water-related vegetation indices. In this regard, other VIs used to depict the water content in plants such as Normalized Difference Surface Water Index (NDSWI), Land Surface Water Index (LSWI) and Modified Normalized Difference Water Index (MNDWI) [13; 21; 22] could also be useful, since they are more sensitive to drought than greenness-related VIs, which makes them likely the best VIs in the estimation of C fluxes in ecosystems undergoing seasonal drought [23]. In most studies, the selection of VIs [14; 17; 19] is limited by the availability of remote information from satellite platforms. An important input of LUE models is the LUE term.