## 1 Introduction  
Terrestrial net primary production (NPP) is the difference between gross primary production (GPP) and the total carbon gain by photosynthesis, and plant autotrophic respiration (Ra) and the loss of carbon to produce energy for growth and maintenance. NPP makes pivotal contributions to the Earth system by transferring solar energy into organic materials. Changes in NPP are tightly connected with atmospheric CO\({}_{2}\) concentrations and climate [1]. Understanding these connections and underlying mechanisms is an intense topic of climate sciences. The manner in which terrestrial NPP responds to increasing atmospheric CO\({}_{2}\) concentrations and CO\({}_{2}\)-induced climate change comprises a net feedback of GPP and Ra, and is co-controlled by multiple drivers. Much evidence has been obtained to show that terrestrial carbon uptake is enhanced because increasing atmospheric CO\({}_{2}\) stimulates photosynthetic activity [2; 3; 4]. For example, [PERSON] et al. (2017) estimated an increase of 31 \(\pm\) 5% in global terrestrial GPP during the twentieth century as a result of the increasing CO\({}_{2}\)[3], and [2] reported an increase of 2.8 \(\pm\) 1.50% in global terrestrial NPP, from 1982 to 2011, because of elevated CO\({}_{2}\)[2]. Some observations, however, reveal lower sensitivities of terrestrial production to elevated CO\({}_{2}\), such as [5] that reported no significant GPP change in a semi-arid grassland in response to elevated CO\({}_{2}\). Moreover, CO\({}_{2}\)-induced climate change, nutrients availability, and ecosystem structures can also have crucial effects on processes of photosynthesis, leading to more uncertainties in the processes. Higher temperatures caused by elevated CO\({}_{2}\) can suppress the CO\({}_{2}\) fertilization effects and negatively influence net ecosystem production [4; 6]. Available nutrients can also exert limitations on CO\({}_{2}\) stimulation [7; 8]. Additionally, rapidly rising CO\({}_{2}\) levels may have less stimulation on vegetation carbon gain than we expected because of the saturating effect [6; 9], since the net photosynthetic rate has a nonlinear relationship with CO\({}_{2}\) concentration [10]. Such evidence illustrates that the response of terrestrial NPP to the rising atmospheric CO\({}_{2}\) is still complex and uncertain, and that climate change and these associated complexities and uncertainties need more investigation for an accurate understanding of climate and environment change. Earth system models (ESMs) are a common tool for investigating the responses on a global or regional scale. ESMs have been successively improved in their representation of physical climate systems and terrestrial biogeochemical processes; therefore, they are fundamentally trustworthy to simulate the terrestrial carbon cycle and its interactions with climate [11; 12]. The Coupled Model Intercomparison Project (CMIP) has proposed standard experimental protocols for model participants [13; 14]. The abruptly quadrupled CO\({}_{2}\) simulation (abrupt-4 \(\times\) CO\({}_{2}\)) is a protocol in which atmospheric CO\({}_{2}\) concentration is fixed as four times that in the pre-industrial simulation (piControl). The fundamental objective of the abrupt-4 \(\times\) CO\({}_{2}\) protocol is to project how much the Earth warms in response to increases in greenhouse gases. One common way is to estimate this is with equilibrium climate sensitivities (ECS), which is defined as global surface temperature change when CO\({}_{2}\) concentration is doubled [15]. ECS ranged from 1.5 to 4.5 K for CMIP models, and from 1.8 to 5.6 K for CMIP6 models. Moreover, the protocol allows for an examination of the overall response of terrestrial NPP to the elevated CO\({}_{2}\) concentration. Studies based on the abrupt-4 \(\times\) CO\({}_{2}\) reported that terrestrial NPP is broadly enhanced due to CO\({}_{2}\) fertilization effects [16]. These protocols and reports provide a common framework and a valuable reference for assessing terrestrial carbon responses to elevated CO\({}_{2}\).