One of the largest sources of uncertainties in modelling of the future global climate is the response of the terrestrial carbon cycle. Studies have shown that it is likely that the extant land sink of carbon will weaken in a warming climate. Should this happen, a larger portion of the annual carbon dioxide emissions will remain in the atmosphere, and further increase global warming, which in turn may further weaken the land sink. We investigate the potential sensitivity of global terrestrial ecosystem carbon balance to differences in future climate simulated by four general circulation models (GCMs) under three different CO2 concentration scenarios. We find that the response in simulated carbon balance is more influenced by GCMs than CO2 concentration scenarios. Empirical orthogonal function (EOF) analysis of sea surface temperatures (SSTs) reveals differences among GCMs in simulated SST variability leading to decreased tropical ecosystem productivity in two out of four GCMs. We extract parameters describing GCM characteristics by parameterizing a statistical emulator mimicking the carbon balance response simulated by a full dynamic ecosystem model. By sampling two GCM-specific parameters and global temperatures we create 60 new "artificial" GCMs and investigate the extent to which the GCM characteristics may explain the uncertainty in global carbon balance under future radiative forcing. Differences among GCMs in the representation of SST variability and ENSO and its effect on precipitation and temperature patterns explain the majority of the uncertainty in the future evolution of global terrestrial ecosystem carbon in our analysis. We suggest that the characterisation and evaluation of patterns and trends in simulated SST variability should be a priority for the further development of GCMs, in particular as vegetation dynamics and carbon cycle feedbacks are incorporated.