# A Three-Layer Atmosphere-Ocean Time Series Model of Global Climate Change

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## Abstract

Time series models of global climate change have tended to estimate a low climate sensitivity and a fast adjustment rate to equilibrium. These results appear to be biased by omission of a key variable - heat stored in the ocean. I develop a time series model of the ocean atmosphere climate system where atmospheric temperature moves towards a long-run equilibrium with both radiative forcing and ocean heat content, which is distributed between upper ocean and deep ocean components. The time series model utilizes the notion of multicointegration to impose energy balance relations on an autoregressive model. As there are only around fifty years of observations on ocean heat content I use the Kalman filter to estimate heat content as a latent state variable constrained by the available observations. The estimate of the equilibrium climate sensitivity is 8.4K with a confidence interval of 5.0 to 11.7K. Temperature takes centuries to adjust to an increase in radiative forcing. The transient climate sensitivity at the point of carbon dioxide doubling is 1.7K.

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