Long Range Memory in Time Series of Earth Surface Temperature

Abstract

Long-range memory (LRM) has been found in numerous natural data records, both in geophysics and other fields. In this thesis LRM in surface temperature time series is studied, and comparison with short-range memory (SRM) models performed.

Trends are important in climate studies, but the trend definition is ambiguous. Two different approaches are included here: the trend described as a function with parameters estimated from the data, and a response model to external forcing. The most commonly used trend function is the linear trend, often used as a measure of anthropogenic effects on global warming. The significance of the trend is dependent on the noise model assumed to describe the data, and here AR(1) and fractional Gaussian noise (fGn) are used.

Some methods for investigating SRM and LRM are described and applied to some selected examples. Comparison of SRM and LRM models is also included.

The thesis also includes a literature review. In the scientific literature mostly local temperature records have been analysed with regards to LRM. Global and hemispheric temperature means are far less studied, so this has been the main focus in this thesis. Three papers are included where the LRM properties of local and global instrumental records, temperature reconstructions and simulated temperature from climate model experiments are studied. In Paper I and II, a trend analysis is also performed.

The overall conclusion that can be drawn from the present work is that long-range persistence on time scales from years to centuries is ubiquitous in observed Earth surface temperature records, and that similar persistence is present in the most advanced climate models to date. This persistence weakens the significance of observed temperature trends, but not enough to render the rising temperature trends throughout the last century statistically insignificant.