RECONSTRUCTING PAST CLIMATE FROM NATURAL PROXIES AND ESTIMATED CLIMATE FORCINGS USING LONG MEMORY MODELS

We produce new reconstructions of Northern Hemisphere annually averaged temperature anomalies back to 1000AD, based on a model that includes external climate forcings and accounts for the long-memory features displayed in the data sets. Our reconstruction is based on two linear models, with the first linking the latent temperature series to three main external forcings (solar irradiance, greenhouse gas concentration, and volcanism), and the second linking the observed temperature proxy data (tree rings, sediment record, ice cores, etc.) to the unobserved temperature series. Uncertainty is captured with additive noise, and a rigorous statistical investigation of the correlation structure in the regression errors motivates the use of long memory fractional Gaussian noise models for the error terms. We use Bayesian estimation to fit the model parameters and to perform separate reconstructions of land-only and combined land-and-marine temperature anomalies. We quantify the effects of including the forcings and long memory models on the quality of model fits, and find that long memory models result in more precise uncertainty quantification, while the external climate forcings substantially reduce the bias and variance of the reconstructions. Validation metrics for the annually resolved reconstruction produced here, which includes both forcings and long memory models, compare favorably to those for the smoothed, decadally resolved reconstructions of Mann et al. (2008a). Finally, we use posterior samples of model parameters to arrive at an estimate of the transient climate response to greenhouse gas forcings of 2.56◦C (95% credible interval of [2.20, 2.95]◦C), in line with previous, climate-model-based estimates. .