  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.
