## 1 Introduction  
Organic carbon (C), which is fixed through photosynthesis, provides agricultural soils with the quality required to obtain high yields [1]. The most substantial fluxes of C fixed per unit of ground and time (gross primary production (GPP)) [2] occur in the tropics, subtropics, and humid temperate regions, e.g., Eastern North America and Western and Central Europe [3]. In particular, Western Europe has one of the highest cultivated net primary productions in the world (\(>\)1 Kg C/m\({}^{2}\)) [4]. Climatic variables have been widely used to monitor C fixation [5; 6; 7]. In particular, temperature analyses have traditionally dominated C budget studies [8]. Current approaches include other factors, such as CO\({}_{2}\) fertilization, O\({}_{3}\), Nitrogen (N) deposition, and land cover change [9; 10; 11; 12]. However, controlling factors, scale, and the ecosystem's complexity vary among studies and, consequently, the extent to which limiting factors influence C fixation response. In croplands and grasslands, climate, soil type, and land management have been highlighted as important controlling factors of C response [13; 14; 15]. At a global scale, precipitation has been reported as the climatic component with the highest impact on the primary production of croplands and temperate grassland biomes (up to 50 and 70% of the total area, respectively) but the influence varies depending on the characteristics of the studied region [6]. Nitrogen (N) deposition has been highlighted as an important driver of primary production in N-limited ecosystems that also have an impact on biodiversity in alpine grasslands. [PERSON], et al. [9] have pointed out that N deposition drives local grassland primary production better than the mean annual climatic variables and soil conditions on a global scale. Similar results have been reported in a meta-analysis using 32 studies of grasslands located in temperate regions and six in tropical areas [16]. Global model projections revealed N deposition as the third driver with the most significant impact on biodiversity in alpine areas, which also influence primary productivity [17; 18]. Therefore, monitoring N deposition and climatic variables in alpine grasslands could contribute to explaining how these variables drive GPP in areas with complex topography and high species richness. In Switzerland, alpine meadows and pastures cover 12% of the total territory (5139 km\({}^{2}\) out of 42,285 km\({}^{2}\)) and grasslands occupy ca. 71% of the remaining utilized agricultural area [19; 20]. The results of experimental studies in (sub-) alpine areas (1500-3000 m a.sl.) highlight N deposition, temperature, grazing, presence of rocks and stones, and shallow soils as the most limiting factors of biomass production and C storage [21; 22; 23]. However, in these remote areas, studies on large-scale interactions among N deposition, climatic factors, and GPP are lacking. On one hand, coarse spatial resolution datasets are widely used for calibration and validation of Earth system models. On the other hand, the role of N deposition in C uptake is still considered unclear, underestimated, or underexplored [24; 25; 26; 27]. Therefore, analyzing whether observed local interactions between climatic factors, N deposition, and GPP remain true at a large scale is relevant to fostering the use of N deposition datasets in modelling approaches. Available N deposition maps for Switzerland brought along the opportunity to study its impact on GPP response at a national scale for the first time. Remotely sensed GPP datasets are also available to study C dynamics of land cover at global and regional scales [28]. While previous versions of MODIS GPP products have shown underestimated and overestimated trends at high and low production sites, respectively [29; 30], different validation efforts and following improvements in the algorithms have enhanced the reliability of remotely sensed GPP products for multiple applications [31; 32; 33].