## 1 Introduction
Measuring one A\({}_{\text{n}}\)-Ci curve can take up to one hour, generating only one V\({}_{\text{cmax}}\) value based on a small number of leaf samples. Thus, field measurements of V\({}_{\text{cmax}}\) on the leaf scale [45] are laborious, time-consuming, and, most importantly, mismatched with the footprints (\(\sim\)100 m-450 m) of eddy covariance (EC) flux towers [46]. Due to the lack of spatiotemporal information on V\({}_{\text{cmax}}\), the state-of-the-art TBMs generally assume a constant V\({}_{\text{cmax}}\) for a specific plant functional type (PFT). More specifically, PFT-specific V\({}_{\text{cmax}}\) values are typically parameterized using two types of data: (1) optimal V\({}_{\text{cmax}}\) data calibrated from a GPP derived from eddy covariance flux tower measurements [35; 47; 48]; and (2) empirical V\({}_{\text{cmax}}\) compiled from field measurements reported in the literature [49]. However, many studies have proven the existence of variations inV\({}_{\text{cmax}}\) with space and time, even for plants with the same PFT [50; 51; 52; 53; 54]. Consequently, the conventional parameterization methods that fix V\({}_{\text{cmax}}\) as a PFT-specific constant can lead to substantial bias in GPP estimations. In addition, previous studies have mostly been conducted on the global scale, and TBMs with parameters calibrated based on all flux tower observations worldwide may have limited accuracy on the regional scale, as in Europe. Thus, European GPP could possibly be improved by including spatially and temporally explicit V\({}_{\text{cmax}}\) values combined with a model calibration method based on EC observations based in Europe alone. Recent advances in remote sensing have made it possible to derive dynamic V\({}_{\text{cmax}}\) information on a global scale [55]. Global V\({}_{\text{cmax}}\) products are generally estimated based on the strong correlation between V\({}_{\text{cmax}}\) and two major biochemistry properties (i.e., the leaf chlorophyll content (LCC) and leaf nitrogen content) [56], which can be estimated from remotely sensed hyperspectral land surface reflectance and solar-induced chlorophyll fluorescence (SIF) data. For example, two V\({}_{\text{cmax}}\) products are estimated from GOME-2 SIF data [57] and GOME-2/OCO-2 SIF data [51]. However, the spatial resolution of SIF-derived V\({}_{\text{cmax}}\) products is generally too coarse (i.e., 36 km-1\({}^{\circ}\)) for regional studies. In contrast, the V\({}_{\text{cmax}}\) products derived from LCC have a higher spatial resolution (i.e., 500 m to 1\({}^{\circ}\)) [58; 59]. While some LCC-based V\({}_{\text{cmax}}\) products have a relatively low update frequency and a short accumulation time (i.e., less than a decade with a one-month interval) [58], a few LCC-based V\({}_{\text{cmax}}\) products provide approximately twenty years of comprehensive V\({}_{\text{cmax}}\) estimation at a 500 m spatial resolution and 8-day temporal resolution [59]. Thus, the newly developed remote sensing V\({}_{\text{cmax}}\) products provide an opportunity to improve the estimation of GPP in Europe by including spatial and temporal variations in V\({}_{\text{cmax}}\). While a high value has been placed on the modeling of V\({}_{\text{cmax}}\) dynamics on a global scale, the concomitant increase in our understanding of the V\({}_{\text{cmax}}\) change effect on GPP has only partially been realized. This brings us to the crux of our study: the quantitative analysis of uncertainties in GPP using the conventional constant V\({}_{\text{cmax}}\) parameterization in TBMs. In this study, we hypothesize that by considering changes in V\({}_{\text{cmax}}\), we can improve the estimation of spatial and temporal variations in GPP. Specifically, we address the following three scientific questions: (1) How much carbon has been assimilated by the terrestrial ecosystem in Europe? (2) Can GPP estimation be improved by including the spatiotemporal dynamics of V\({}_{\text{cmax}}\) compared with the conventional method of fixing V\({}_{\text{cmax}}\) as a PFT-specific constant?