Statistical significance of rising and oscillatory trends in global ocean and land temperature in the past 160 years

Abstract. 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 70 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 parameters of the null models are estimated from the instrumental record, but are also checked to be consistent with a Northern Hemisphere temperature reconstruction prior to 1750 for which an anthropogenic trend is negligible. The linear trend in the period 1850–2010 AD is significant in all cases, but the oscillatory trend is insignificant for ocean data and barely significant for land data. However, by using the significance of the linear trend to constrain the 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.