Possible climate change caused by an increase ingreenhouse gas concentrations, despite having been asubject of intensive study in recent years, is stillvery uncertain. Uncertainties in projections ofdifferent climate variables are usually described onlyby the ranges of possible values. For assessing thepossible impact of climate change, it would be moreuseful to have probability distributions for thesevariables. Obtaining such distributions is usuallyvery computationally expensive and requires knowledgeof probability distributions for characteristics ofthe climate system that affect climate projections. A fewstudies of this kind have been carried out with energybalance/upwelling diffusion models. Here wedemonstrate a methodology for performing a similarstudy with a 2 dimensional (zonally averaged) climatemodel that reproduces the behavior of coupledatmosphere/ocean general circulation models morerealistically than energy balance models. Thismethodology involves application of the DeterministicEquivalent Modeling Method to derive functionalapproximations of the model's probabilistic response.Monte Carlo analysis is then performed on theapproximations. An application of the methodology isdemonstrated by deriving the uncertainty in surfaceair temperature change and sea level rise due tothermal expansion of the ocean that result fromuncertainties in climate sensitivity and the rate ofheat uptake by the deep ocean for a prescribedincrease in atmospheric CO₂ concentration. Wealso demonstrate propagation of correlateduncertainties through different models, by presentingresults that include uncertainty in projected carbonemissions.

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