Knowledge of the sensitivity of climate to external  forcing is critical to our ability to predict the effects  of anthropogenic greenhouse gases.  A recent paper by other  authors examined the cumulative response to a series of  large volcanic eruptions such as those between 1880 and 1920  using energy-balance modelling and concluded that climate  sensitivities of 2.4 degrees for doubled CO2 or more imply volcanic cooling of 0.2 degrees or more continuing well into the 1930s.  This long-term cooling is arguably  inconsistent with the instrumental temperature record for  the first part of this century. If true, this would imply  a climate sensitivity significantly lower than the currently  accepted "best guess" value of 2.5 degrees.
We have performed similar experiments with a series  of large volcanic forcings as input to a simple  upwelling-diffusion climate model.  Our results do not  show the large long-term residual temperature response  seen in the previous diffusion-only model work referred  to above. Our results for the time period 1880-1950 are  reasonably consistent with the temperature record even  for climate sensitivity of  4.5 degrees.  We discuss the  dependence of the model response on model formulation  and choice of model parameters, and the implications of  these uncertainties for estimates of climate sensitivity