Foundational basis for optimal climate change detection from energy-balance and cointegration models

Foundational basis for optimal climate change detection from energy-balance and cointegration models This thesis has critically examined the validity of optimal fingerprinting methods for the detection and attribution (D&A) of climate change trends. The validity is called into question because optimal fingerprinting involves a linear regression of non-stationary time series. Such non-stationary regressions are in general statistically inconsistent, meaning they are liable to produce spurious results. This thesis has investigated, using an idealized linear-response-model framework motivated by energy-balance considerations, whether the standard assumptions of optimal fingerprinting are sufficient to guarantee consistency, and hence whether detected climate trends are likely to be genuine or artefacts of spurious correlation. The principal reasoning tool in the thesis is the linear impulse-response model, familiar to many climatologists when parameterized as an energy-balance model (EBM), a simplified representation of global climate. A rigorous and efficient maximum likelihood method has been developed for estimating parameters of EBMs with any k > 0 number of boxes from CO2-quadrupling general circulation model (GCM) experiments and the method implemented as a free software package. It has been found that a three-box ocean is optimal for emulating the global mean surface temperature (GMST) impulse responses of GCMs in the Coupled Model Intercomparison Project Phase 5 (CMIP5). A new linear-filtering method has also been developed for estimating historical effective radiative forcing (ERF) from time series of GMST. It has been shown that the response of any k-box EBM can be represented as an ARMA(k, k-1) autoregressive moving-average filter and that, by inverting the ARMA filter, time series of surface temperature may be converted into radiative forcing. A comparison with an established method ("ERF_trans"), using historical simulations from HadGEM3-GC31-LL, found that the new method gives an ERF time series that closely matches published results (correlation of 0.83). Applying the new method to historical temperature observations, in combination with HadGEM3, produces evidence of a significant increase in ERF over the historical period with an estimated forcing in 2018 of 1.45 +- 0.504 Watts per square metre. It has been proved, using an idealized linear-response-model framework where forcing is represented as an integrated process, that if standard assumptions hold then the optimal fingerprinting estimator is consistent, and hence robust against spurious regression. Hypothesis tests, conducted using historical GMST observations and simulation output from 13 GCMs of the CMIP6 generation, have produced no evidence that these assumptions are violated in practice. The historical trends in GMST which are detected and attributed using these GCMs are therefore very likely not spurious. Consistency of the fingerprinting estimator was found to depend on "cointegration" between historical observations and GCM output. Detection of such a cointegration for the GMST variable indicates that the least-squares estimator is "superconsistent", with better convergence properties than might previously have been assumed. Furthermore, a new method has been developed for quantifying D&A uncertainty, which exploits the connection between cointegration and error-correction time series models to eliminate the need for pre-industrial control simulations.