## 1 Introduction  
As one of the principal processes controlling land-atmosphere interaction, gross primary productivity (GPP) is a key component of the terrestrial carbon balance [1, 2]. Continuous and accurate monitoring of GPP is necessary for quantifying how the dynamics of carbon cycles at regional to global scales respond to climate variability, and for addressing related issues including the terrestrial carbon sink, vegetation dynamics and ecosystem vulnerability [3, 4, 5], above all in the context of climate change. Forecasted changes in temperature, precipitation and atmospheric CO\({}_{2}\) are likely to lead to changes in terrestrial productivity [6]. The near-infrared reflectance of vegetation (NIRv) has been proposed as a new approach for estimating GPP [7; 8]. NIRv captures the fraction of NIR reflectance attributable to vegetation and addresses the confounding effects of leaf area, background brightness and the distribution of the photosynthetic capacity with depth in canopies. It has been shown to correlate well with GPP throughout the world's biomes [7; 8; 9]. The NIRv approach does not take into account radiation and light-use efficiency, since it assumes that plants allocate resources efficiently, so this measure of plants' investment in capturing light should correlate with their capacity to fix CO\({}_{2}\)[7; 8]. However, radiation plays an important role in linking vegetation greenness to photosynthesis [10] and, despite not usually being the most important limiting factor, radiation does, in fact, constrain vegetation growth over 27% of the Earth's vegetated surface area [11]. In the light-use efficiency (LUE) concept developed by [PERSON] [12], GPP acts as a function of the photosynthetically active radiation (PAR), the fraction of absorbed PAR (fPAR) by plants and the conversion efficiency of absorbed light energy (\(\epsilon\)). Recently, NIRVP [13; 14], defined as the product of the near-infrared reflectance of vegetation and incoming PAR, has been shown to be closely correlated with GPP on different spatial and temporal scales [13; 15; 16]. The benefits of adding incoming PAR to NIRv are also evident in the work of [PERSON] et al. [17]. The effect of radiation on GPP varies with latitude and the time of year. In boreal and temperate European forests, radiation and temperature are the main drivers of the latitudinal gradient and interannual patterns in GPP [18; 19]. Carbon assimilation in many borealiferous forest ecosystems has been shown to be light-limited in autumn [20; 21]. Regarding seasonality, radiation can also affect GPP due to its effect on the phenology of carbon uptake caused by the radiation constraints on photosynthesis, since radiation is a major factor limiting photosynthetic activity during the end of the season [11; 22]. The carbon uptake period is also sensitive to changes in radiation in evergreen forests [23]. Radiation use is related to canopy structures and levels of foliage organization, which vary between vegetation cover types [24]. The clumping index (CI) is a measure of the level of foliage grouping within canopy structures relative to a random distribution [24; 25]. Leaf organizational structures exist for various ecological reasons, and affect radiation interception and distribution within canopies and, consequently, carbon uptake [26]. Neglecting the CI increases the uncertainty of GPP estimates [26; 27]. In fact, the estimation of GPP from sun-induced fluorescence (SIF) improved after accounting for the canopy structure effects [28]. We aimed to explore how radiation as a modulator of NIRv could improve GPP estimates, especially at high latitudes and in the latter part of the year, given that photosynthetic photon flux density (PPFD) drives the GPP of the green biomass. We also hypothesized that the incorporation of information on foliar clumping would provide more accurate estimates of radiation distribution and, therefore, of its use in the canopy.