## 1 Introduction  
During the last few decades, the Earth's ecosystems have absorbed one-third of human CO\({}_{2}\) emissions [1]; much of this absorbance occurs via carbon accumulation in forest biomass and soils [2]. The terrestrial gross primary productivity (GPP) and ecosystem respiration (ER) are the two largest fluxes in the global carbon cycle. GPP, which represents the total ecosystem carbon uptake via photosynthesis [3], tends to increase, mostly due to increased photosynthetic CO\({}_{2}\) absorption [4]. Overall, this terrestrial uptake relieves the human increase in atmospheric CO\({}_{2}\) levels by inducing negative feedback in the climate and carbon cycle systems [5]. It is critical to examine in what range, how long, and in which ecosystem this negative feedback and net CO\({}_{2}\) absorption will continue. GPP is considered one of the primary mechanisms that drives climate regulation, carbon sequestration, and carbon storage. In addition, it is seen as a key proxy for a variety of ecosystem services such as food, fiber, and fuel production, as well as the management of Earth's habitability [1; 3]. However, future predictions of ecosystem reactions and consequently the feedback strength are exceedingly unknown and uncertain. Nonetheless, recent evidence suggested that significant tropical CO\({}_{2}\) absorption has been identified that is roughly offsetting net deforestation and demonstrating significant negative global feedback to atmospheric CO\({}_{2}\) and climate [6]. On the contrary, the occurrence of extreme events such as droughts, heatwaves, or rainstorms, as well as the related disruptions, can partially balance carbon sinks or even cause net losses in carbon stocks, thereby releasing CO\({}_{2}\) into the atmosphere [7; 8; 9]. For example, droughts can impact the global carbon balance by limiting vegetation development at different stages or within a wide range of tree mortalities and ecosystem fires [7]. Since climate extremes can produce rapid and delayed reactions in ecosystems, it is expected that even minor changes in the frequency or severity of climate extremes might significantly diminish carbon sinks and result in significant positive feedbacks to climate change [10; 11; 12]. Net ecosystem exchange (NEE) is commonly measured at the ecosystem scale using data from eddy covariance (EC) flux towers. NEE is defined as the sum of GPP (representing net photosynthesis) and ER (total energy return), both of which are positive in nature. Although nighttime ER can be quantified via the EC approach, daytime GPP or ER cannot be directly observed by the EC. Rather, it can be separated at the ecosystem scale by using flux-partitioning methods based on night- and daytime NEE data [13; 14]. Since EC flux towers have a comparatively tiny footprint and are distributed randomly across the terrestrial ecosystems, it is crucial to create global gridded data for the GPP. In recent years, several types of models have been developed (see Table 1) that are widely used to assess the spatio-temporal trends of GPP [15; 16]. Overall, these methods can be classified into three major categories. The first category is _the EC flux data-driven models_ based on random measurements at flux tower sites. These models account for the relationships between the inferred GPP and other explanatory factors at the site level in order to estimate GPP. These covariates can then be upscaled into gridded data using machine learning algorithms [17; 18]. The second category is _the satellite-based models_, of which the light-use-efficiency (LUE) model is a representative example [19; 20; 21; 22; 23; 24]. The third category is _the process-based models_, which simulate the interactions between various ecosystem synthesizers [5; 25] such as biochemical and physiological processes that characterize vegetation's response to climatic and environmental conditions [15; 26; 27; 28].