## 1 Introduction  
The terrestrial ecosystem offsets approximately 30.5% of the carbon dioxide (CO\({}_{2}\)) released due to anthropogenic activity [1] and plays a prominent role in regulating global carbon cycling [2]. As a quantitative indicator of the total amount of carbon assimilated via photosynthesis, terrestrial gross primary production (GPP) serves as the initial driver of the global carbon cycle [3]. On the continental scale, the terrestrial ecosystems in Europe have been proven to be ecologically fragile and particularly sensitive to climate change [4; 5; 6]. According to long-term-recorded remotely sensed data, the terrestrial ecosystem has demonstrated widespread greening since the 1980s, especially in the Northern Hemisphere [7]. Modeling studies have suggested that the total GPP values for Europe vary in a wide range from 2.5 to 8.7 Pg C yr\({}^{-1}\)[8; 9; 10; 11; 12; 13; 14]. While there are some discrepancies between study regions (e.g., those including or excluding part of Russia), estimates of European GPP are subject to significant uncertainties, hindering our understanding of the role of the European terrestrial ecosystems in mitigating climate change. Attempts to model GPP on a global scale using remote sensing data fall into three general categories. The first is empirical approaches based on statistical models or machine learning. These studies empirically link GPP with the spectral vegetation index [15; 16; 17], leaf area index (LAI) [18], and sun-induced chlorophyll fluorescence (SIF) [19; 20]. Some studies use machine learning methods to estimate local or global GPP [21; 22]. The second category is the widely used light use efficiency (LUE) model [23]. These models assume that GPP is a product of the fraction of absorbed photosynthetic active radiation (APAR) and LUE reduced by modifying factors. Examples are BIOMASS [24], CASA [25], C-Fix [8], 3-PG [26], VPM [27], EC-LUE [28], the P-model [29], and CCW [30] models. The third category is process-based terrestrial biosphere models (TBMs), such as CENTURY [31], TEM [24], Biome-BGC [32], BESS [33], BEPS [34], and FGM [35]. Biologically, GPP is a product of leaf-scale photosynthesis. Thus, GPP is related to both internal and environmental factors, including rapid leaf-level biochemical reactions, stomatal conductance [36], canopy structure [37], climatic factors, soil moisture [38], and slower environmental acclimation processes [39]. However, empirical models, machine learning methods, and LUE models have a limited ability to simulate the response of GPP to complicated environmental and internal biological factors due to their inadequate representation of the mechanisms that regulate the physiological process of photosynthesis. TBMs have proven to be particularly useful for estimating GPP due to their inclusion of the biochemical processes of photosynthesis. TBMs commonly include the mechanistic leaf photosynthesis model developed by [PERSON] et al. (1980). To estimate the spatiotemporal patterns of GPP on a large scale, TBMs require a range of forcing data, such as meteorological data, land cover, the leaf area index, the clumping index, and leaf trait information. Most importantly, the leaf photosynthesis rate simulated by the Farquhar model is particularly sensitive to the parameterization of leaf photosynthetic capacity at 25 \({}^{\circ}\)C (V\({}_{\text{cmax}}\)) (umol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)) [2; 40; 41], reflecting the active amount and kinetic activity of the Rubisco enzyme in leaves. Inadequate constraints on V\({}_{\text{cmax}}\) lead to substantial uncertainties in GPP estimation [42]. Traditionally, V\({}_{\text{cmax}}\) is estimated by measuring the net photosynthesis rate (A\({}_{\text{n}}\)) relative to internal CO\({}_{2}\) pressure (C\({}_{\text{j}}\)) (i.e., A\({}_{\text{n}}\)-C\({}_{\text{i}}\) curve) at different CO\({}_{2}\) concentrations with saturating irradiance or using a modified 'one-point method' [43; 44].