  Various interpretations of the notion of a trend in the context of global
warming are discussed, contrasting the difference between viewing a trend as
the deterministic response to an external forcing and viewing it as a slow
variation which can be separated from the background spectral continuum of
long-range persistent climate noise. The emphasis in this paper is on the
latter notion, and a general scheme is presented for testing a multi-parameter
trend model against a null hypothesis which models the observed climate record
as an autocorrelated noise. The scheme is employed to the instrumental global
sea-surface temperature record and the global land-temperature record. A trend
model comprising a linear plus an oscillatory trend with period of
approximately 60 yr, and the statistical significance of the trends, are tested
against three different null models: first-order autoregressive process,
fractional Gaussian noise, and fractional Brownian motion. The linear trend is
significant in all cases, but the oscillatory trend is insignificant for ocean
data and barely significant for land data. By means of a Bayesian iteration,
however, using the significance of the linear trend to formulate a sharper null
hypothesis, the oscillatory trend in the land record appears to be
statistically significant. The results suggest that the global land record may
be better suited for detection of the global warming signal than the ocean
record.
