## 1 Introduction  
The Gross Primary Production (GPP) of the terrestrial biosphere is a key quantity in the understanding of the global carbon cycle. GPP is the amount of atmospheric carbon fixed through the process of photosynthesis by living biomass and represents the largest gross flux of CO\({}_{2}\) between the atmosphere and the Earth surface [1]. The interactions between climate, GPP and atmospheric CO\({}_{2}\) result in a strong \"carbon cycle--climate coupling\" [2]. The magnitude of the coupling is a major source of uncertainty in the understanding of future carbon assimilation by crops (impacting the food production), carbon storage in forests (representing a large sink for anthropogenic CO\({}_{2}\)), and climate forcing by CO\({}_{2}\). Estimation of GPP over time at the global scale is therefore of great societal and scientific interest. To date, monitoring of GPP has not been possible at scales beyond that of a single agricultural field or natural ecosystem [3]. At those scales, networks of eddy-covariance towers [4] provide a platform to measure Net Ecosystem Exchange (NEE) of carbon at high temporal resolution. GPP can be estimated from these measurements using various statistical techniques, with estimates differing by up to 10% [5]. Upscaling of eddy-covariance measurements using observation-derived carbon-climate relations and satellite data has been shown to be one of the best methods to estimate GPP at larger scales [6]. Numerical modelling to estimate GPP may employ either a land surface model [7] or approaches that rely on remotely-sensed vegetation indices (VI) combined with mechanistic descriptions of plant photosynthesis [8; 9; 10; 11]. A typical VI is the Normalized Difference Vegetation index (NDVI) [12; 13; 14], which is related to the fraction of Absorbed Photosynthetically Active Radiation (fAPAR) and the Leaf Area Index (LAI). These products are inputs in light-use-efficiency approaches [15] or even in a full Farquhar photosynthesis method [16] that drive several carbon cycle models (e.g., C-Fix [17], and SibCASA [18]). VIs are linked to chlorophyll content and the temporal resolution of spaceborne composite VI products is typically eight days or more. Consequently, short term environmental changes affecting plant productivity (e.g., water availability, temperature, nutrient deficiency, diseases) may not be well accounted for; this can lead to biases in the carbon uptake capacity of vegetation [19; 20]. Hence the use of \"greenness indicators\" tends to return the potential carbon uptake by plants rather than the actual uptake [21; 22]. It is therefore not surprising that the available methods' global GPP estimates have a large range (from 100 to 180 PgC/year [6; 23]). At smaller scales, such as individual ecosystems or plant species, the uncertainty in the level of photosynthesis is likely to be larger, because of differing drought responses, management practices, soil conditions, and nitrogen availability [24]. Photosynthetic activity is tightly related to plant fluorescence by plants in the red and near-infrared wavelength range (see below). Sun-induced fluorescence (SiF) is the re-emission of solar radiation absorbed by leaf chlorophyll at longer wavelengths. It has a distinct spectral shape with one peak at 730-740 nm (far-red fluorescence) and another at 685-690 nm (red fluorescence). This emission varies smoothly with wavelength [25]. SiF can be measured in the field or by airborne remote sensing instruments (e.g., [26; 27]; see also [28] and references therein). Since approximately 1%-2% of the absorbed solar energy by vegetation is released as fluorescence (against typically about 19% released as heat and about 80% used for photosynthesis [29]), capturing the SiF requires sensors with good signal-to-noise ratios (and fine spectral resolutions, see below). At the same time, SiF may potentially interfere with retrieval of other atmospheric properties [30; 31].