Uncertainties in projections of future climate change caused by an increase in greenhouse gas concentrations have been a subject of intensive study in recent years. However, in most cases, uncertainties in parameters and characteristics of models used to obtain those projections, such as climate sensitivity or radiative forcing, are described only by ranges of possible values. The resulting uncertainties in variables describing climate change, such as surface warming or sea level rise, are therefore also given just by ranges of possible values. However, for assessing the possible impact of climate change, it would be more useful to have probability distributions for these variables. There are two significant difficulties in obtaining such distributions. First, it is necessary to know probability distributions for the above mentioned uncertain parameters and model characteristics. Second, existing climate and economics models are computationally too expensive for traditional methods of uncertainty propagation such as Monte Carlo simulation.
        We demonstrate a method for calculating probability distributions for surface air temperature change and sea level rise that result from uncertainties in climate sensitivity and the rate of heat uptake by the deep ocean. These distributions are obtained by applying the Deterministic Equivalent Modeling Method to the MIT climate model. This method provides an effective way of deriving an approximation for the model and allows the propagation of uncertainty. The range and probability distribution of climate sensitivity are based on expert assessments of parameters, while those for the rate of heat uptake are based on the results of simulations with coupled atmosphere-ocean GCMs. As an example of propagating correlated uncertainties, we also show the results of calculations in which the uncertainty in projected increases in forcing is also taken into account. The probability distribution for forcing, associated with an increase in atmospheric CO2 concentrations is calculated based on the distributions for anthropogenic CO2 emissions and the rate of oceanic carbon uptake. The probability distribution for emissions has been calculated in an independent study, while the rate of ocean carbon uptake is assumed to be related to that of heat.