Using data from CanESM2, the second generation Earth System Model of the Canadian Centre for Climate Modelling and Analysis (CCCma), we analyze the impact of two atmospheric processes-elevated atmospheric CO₂ concentration and climate change through temperature and precipitation-on spatiotemporal change of the terrestrial ecosystem during the period 1850-1989. The results show that the elevated atmospheric CO₂ concentrations enhance the carbon fluxes, with increases of 117.1 gC m^-2 a^-1 for net primary production (NPP), 98.4 gC m^-2 a^-1 for soil respiration (Rh), and 18.7 gC m^-2 a^-1 for net ecosystem production (NEP). Increased linear trends of NPP and Rh of about 0.30 and 0.25 PgC/a², respectively, occur across the whole terrestrial ecosystem, whereas for climate change impact, NPP has a reduced trend of -19.3 gC m^-2 a^-1. The soil respiration reduces by -8.5 gC m^-2 and NEP varies by about -10.8 gC m^-2. For the whole terrestrial ecosystem, linear decreased trends of NPP and Rh are approximately -0.07 PgC/a² and -0.04 PgC/a² (P<0.05). Regions show large differences of NPP distribution in response to climate change. Low latitudes and the Southern Hemisphere exhibit decreased NPP, while NPP is somewhat increased in the mid and high latitudes of the Northern Hemisphere. Enhanced vegetation growth due to the lengthened growing season associated with global warming is probably responsible for such an increase. The response of Rh to warming is consistent with that of NPP. The magnitude of increased Rh is larger than that of NPP in the high latitudes of the Northern Hemisphere. Permafrost soils in these high latitudes, which contain an enormous quantity of organic carbon, may melt with the increasing temperature, which is expected to cause increased Rh due to more dissolved organic carbon. Change in atmospheric CO₂ concentration is a dominant driving factor in the spatiotemporal pattern of carbon fluxes of the terrestrial ecosystem, and its impact significantly supersedes the effects of climate change. It should be noted that the model neglects the impact of nitrogen limitation, and thus the effects of elevated CO₂ on carbon fluxes might be overestimated. In addition, the contribution of climate change is not negligible, particularly in the Amazon basin, because reduction in precipitation and soil moisture can result in decreases in NPP and Rh. In this region, the model estimates that, in response to both rising CO₂ concentration and climate change, the total NPP and Rh decrease by approximately -1.8 gC m^-2 a^-2 and 1.6 gC m^-2 a^-2, respectively. NEP also shows a decreased trend, but most areas of NEP change are not statistically significant at the 5% level. In this region, NEP change is closely related to the variation of temperature, precipitation and soil moisture, and the change correlates more to soil moisture than the other two variables. This indicates that drought is key factor driving NEP changes in this region. The terrestrial carbon fluxes are also driven by multiple factors, e.g. radiation, and the processes involved are complicated. Land use and the effect of aerosol are not considered in this paper. These factors should be incorporated into longer-term simulations to investigate the mechanisms involved in the response of the terrestrial carbon fluxes to CO₂ concentration and climate change.