The successful application of simple statistical methods in economic modelling suggest that similar methods could provide insight into global climate. We apply an autoregressive method to observed time series to determine the dependence of atmospheric CO2 concentration on carbon emissions and, in turn, the dependence of globally averaged temperature on atmospheric CO2 concentration. We ascribe physical meaning to the regression parameters in terms of first order differential equations describing the diffusion of CO2 and temperature between reservoirs, viz.: the diffusion of CO2 between the atmosphere and the deep ocean and the transport of heat from the mixed layer. A strong feature of regression models is their built-in mechanism for deciding when a model provides an adequate description of the given data. Two implications of this statistically robust approach are that CO2 diffuses from the atmosphere within a time scale of decades and that global average temperatures are unlikely to exceed 2 deg C above pre-industrial values.

The impulse response of CO2 concentration due to variation in CO2 emissions was estimated from observed time series using the ARX method augmented by testing residuals for self-correlation. It was found to be a simple exponential with a half-time of 43 years with no remnant component. The longer half times and large remnant fraction of the impulse response derived from ocean circulation models is attributed to the failure of these models to account for turbulent mixing in the deep ocean.

The impulse response of CO2 concentration due to variation in CO2 emissions was estimated from observed time series using the ARX method augmented by testing residuals for self-correlation. It was found to be a simple exponential with a half-time of 43 years with no remnant component. The longer half times and large remnant fraction of the impulse response derived from ocean circulation models is attributed to the failure of these models to account for turbulent mixing in the deep ocean.