## 1 Introduction  
Sustainable development is the core path to maintaining the health of ecosystems [1,2]. Over the past few decades, air pollution and climate change caused by global warming have been threatening the health of ecosystems [3,4]. Tropospheric ozone (O\({}_{3}\)) is the most damaging air pollutant for plants [5,6]. Ozone damages ecosystem vegetation carbon sequestration, carbon allocation, nutrient supply, biodiversity and other aspects [7,8]. As plants play a vital role in regulating the ambient environment, ozone-induced damage in plants may further accelerate environmental degradation, with severe consequences for human and ecosystem health. The few studies that have considered the effects of ozone on the carbon cycle still lack simulations of the interaction of ozone with various global change factors. As a result, we know little about the interaction of multiple global change factors on ecosystem carbon cycles. The interaction mechanism of global change factors is very complex. Climate change affects the carbon cycle of terrestrial ecosystems directly or indirectly by changing temperature, precipitation and other factors [9, 10, 11, 12, 13]. CO\({}_{2}\) fertilization not only increases the photosynthetic rate of plants but also reduces the risk of drought by reducing stomatal conductance [14,15]. Many previous studies have reported that CO\({}_{2}\) fertilization offsets the possible negative effects of climate change [16]. This is because the effect of CO\({}_{2}\) fertilization increases the leaf intercellular concentration of carbon dioxide and stimulates the photosynthesis of plants [17,18]. Although fossil records and experiments show that high concentrations of CO\({}_{2}\) reduce stomatal pore size and total stomatal number per unit leaf area, this reduction in stomatal conductance does not affect the high intercellular CO\({}_{2}\) concentration during vegetation photosynthesis, which is even higher than predicted by most models [19, 20, 21]. However, emissions of CO\({}_{2}\) are usually accompanied by O\({}_{3}\) precursors, which have driven a rise in tropospheric ozone ([O\({}_{3}\)]) [22]. O\({}_{3}\) forms reactive oxygen species (ROS) within cells, causing damage to plant tissues and reduced photosynthesis [23, 24, 25]. In addition, ozone exposure altered the content of abscisic acid and K+ ions in plant stomatal cells, causing expansion pressure and abnormal signaling in plant guard cells [26,27]. Ozone disrupts plant photosynthesis, reduces gas exchange, induces early leaf senescence, and inhibits the growth of natural vegetation and crops [28, 29, 30, 31, 32, 33, 34, 35]. It can be seen that the effects of [CO\({}_{2}\)] and [O\({}_{3}\)] on plants are very complex, although some scholars believe that the increase in [CO\({}_{2}\)] can reduce the impact of [O\({}_{3}\)] on vegetation [36]. However, few models take the synergistic effects of CO\({}_{2}\), O\({}_{3}\) climate change and other factors into consideration in the simulation [37]. Because the effects of different factors on vegetation are very complicated, it is difficult to express them by simple functions. Process-based ecosystem models can help us understand the response and adaptation of vegetation under the influence of global change factors by simulating the physiological change process of vegetation and output intermediate variables [38,39]. Therefore, it is necessary to consider multifactor modeling and reveal the interaction of global change factors based on the model. In China, studies based on multiple variability factors have mostly focused on the effects of O\({}_{3}\) and CO\({}_{2}\) changes on crop yields [36], and research on carbon sinks in terrestrial ecosystems is lacking [40,41]. Refs. [42,43] simulated the net primary productivity (NPP) and net carbon exchange (NCE) of terrestrial ecosystems in China and showed that the rise in O\({}_{3}\) led to a 7.7% decrease in carbon storage in China and an average 4.5% decrease in national NPP.