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Reduced complexity climate models are useful tools for quantifying decision-relevant uncertainties, given their flexibility, computational efficiency, and suitability for large-ensemble frameworks necessary for statistical estimation using resampling techniques (e.g., Markov chain Monte Carlo). Here we document a new version of the simple, open-source, global climate model Hector, coupled with a 1-D diffusive heat and energy balance model (Diffusion Ocean Energy balance CLIMate model) and a sea level change module (Building blocks for Relevant Ice and Climate Knowledge) that also represents contributions from thermal expansion, glaciers and ice caps, and polar ice sheets. We apply a Bayesian calibration approach to quantify model uncertainties surrounding 39 model parameters with prescribed radiative forcing, using observational information from global surface temperature, thermal expansion, and other contributors to sea level change. We find the addition of thermal expansion as an observational constraint sharpens inference for the upper tail of posterior equilibrium climate sensitivity estimates (the 97.5 percentile is tightened from 7.1 to 6.6 K), while other contributors to sea level change play a lesser role. The thermal expansion constraint also has implications for probabilistic projections of global surface temperature (the 97.5 percentile for RCP8.5 2100 temperature decreases 0.3 K). Due to the model's parameterization of thermal expansion as an uncertain function of global ocean heat, we note a trade-off between two ways of incorporating thermal expansion information: Ocean heat data provide a somewhat sharper equilibrium climate sensitivity estimate while thermal expansion data allow for constrained sea level projections.

Plain Language Summary Global warming poses considerable climate risks, such as increasing sea level and temperature extremes. Constraining the upper bounds of these salient and decision-relevant aspects of climate change can provide important information for assessing vulnerabilities and risk and adaptation planning. Simple climate models that are both flexible and computationally efficient can be constrained by historical observations to statistically estimate key uncertain climate parameters and characterize climate upper bounds. Previous studies have shown that statistical estimates of the global temperature response to atmospheric CO2 depend on both global surface temperature and ocean heat content observational constraints. Here we use the Hector simple climate model to statistically estimate the temperature response to CO2 using several different sets of observational constraints, including several contributors to sea level. We find that the inclusion of thermal expansion tightens estimates of the temperature response to atmospheric CO2 and the upper bounds of temperature projections, while other contributors to sea level play a lesser role.