**1. Introduction**

Climate change caused by increasing atmospheric carbon dioxide (CO2) concentrations has been extensively studied in the context of global warming, and the land carbon cycle feedback is recognized as one of the biggest sources of uncertainty in climate projection [1]. Global warming is proceeding with a greening trend of the Earth, as shown by satellite and ground observations of increases in leaf area index [2,3], canopy cover [4], and biomass [5]. A greening Earth has significant consequences for the terrestrial carbon sink, the integrity of ecosystem, and climate [6,7]. Numerous mechanisms appear to underlie the observed greening, including changes in the climate system [8,9]. Among the mechanisms supporting the greening Earth, CO2 fertilization is considered the dominant factor in enhancing vegetation, with evidence from free-air CO2 enrich (FACE) experiments [10], satellite observations [2,4], and ground observations [11]. Climate change is also substantially contributing to the increase in global vegetation productivity because of the indirect effect of increasing CO2 concentrations [9]. For instance, global warming is enhancing vegetation growth in high latitudes [12,13]. As such, each mechanism contributing to vegetation growth has been scrutinized independently, but, in contrast to climate change studies, the global factors affecting vegetation response have not been well studied and summarized. Therefore, the combination and interactions of multiple different climatological and biophysical mechanisms make it difficult to predict the future growth of vegetation at the global scale. As a result, the big discrepancy between modeled and observed sensitivity to CO2 concentrations is always a source of controversy in the prediction of the future carbon cycle [14]. If climate constrains increase, climate change can cancel the positive effects of CO2 or of other biogeochemical fertilization (e.g. nitrogen deposition) on vegetation, and possibly accelerate global warming. Therefore, understanding the relative strength of climate variables or increasing CO2 concentrations, leading to greening or browning of the Earth, is imperative for future projections.

We firstly summarized and analyzed the trends in climate and vegetation responding to increasing CO2 concentrations from the subset of the Coupled Model Intercomparison Project Phase 5 (CMIP5). The CMIP5 dataset includes present run and future projection data produced by Earth system models following several experimental scenarios. Future vegetation growth depends on the type, magnitude, and seasonal timing of climatic changes and their interactions with vegetation physiology. To simplify the understanding of these complex mechanisms, we divided the vegetated areas into three categories, namely temperature-limited, water-limited, and radiation-limited areas, following Nemani et al. [9].

Then, we decomposed the mechanisms enhancing vegetation growth into three factors: CO2 concentration fertilization effect, radiative climate change, and local climate feedback by vegetation growth. By assessing these three factors quantitatively, we can answer the question as to whether increasing CO2 concentrations will tighten or relax climate constrains on vegetation at the global scale. Friedlingstein et al. [1] evaluated the strengths of the effects of CO2 fertilization and temperature increase on land vegetation carbon storage. Lemordant et al. [15] decomposed the climate effects on evapotranspiration into net radiation, precipitation, and vapor pressure deficit (VPD). However, none of them counted the local climate feedback effect at the global scale. Therefore, contradicting results of vegetation growth by different mechanisms made future predictions confusing. For instance, it is hard to discuss the regional trend in precipitation [16–18] and the changes in water use efficiency [11] at the same time without knowing which mechanism is relatively stronger. Finally, we discussed the validity of the findings through the analysis of historical observations.

#### **2. Materials and Methods**
