Estimating trends in the global mean temperature record
  Given uncertainties in physical theory and numerical climate simulations, the historical temperature record is often used as a source of empirical information about climate change. Many historical trend analyses appear to deemphasize physical and statistical assumptions: examples include regression models that treat time rather than radiative forcing as the relevant covariate and time series methods that account for internal variability nonparametrically. However, given a limited record and the presence of internal variability, estimating radiatively forced historical temperature trends necessarily requires assumptions. Ostensibly empirical methods can involve an inherent conflict in assumptions: they require data records that are short enough for naive trend models to apply but long enough for internal variability to be accounted for. In the context of global mean temperatures, methods that deemphasize assumptions can therefore produce misleading inferences, because the twentieth century trend is complex and the scale of correlation is long relative to the data length. We illustrate how a simple but physically motivated trend model can provide better-fitting and more broadly applicable trend estimates and can address a wider array of questions. The model allows one to distinguish, within a single framework, between uncertainties in the shorter-term versus longer-term response to radiative forcing, with implications not only on historical trends but also on uncertainties in future projections. We also investigate the consequence on inferred uncertainties of the choice of a statistical description of internal variability. While nonparametric methods may seem to avoid making explicit assumptions, we demonstrate how even misspecified parametric methods, if attuned to important characteristics of internal variability, can result in more accurate statements about trend uncertainty. 
Andrew Poppick, Elisabeth J. Moyer, and Michael L. Stein
stat.AP