Long-range memory in Earth surface temperatures: spatial scale dependence and land-sea differences

The use of long-range memory models as a description of the noise in Earth surface temperatures has increased the recent years, and as a measure of the persistence for such time series we have the Hurst exponent. It is known that sea surface temperatures are more persistent than land temperatures, and that global temperatures are more persistent than local temperatures. We also know that the persistence is higher for lower latitudes than for higher latitudes. My results confirm these observations, and in addition they reveal what the Hurst exponents are for spatial scales between local and global. This is done by performing spatial averaging over gridded temperature data to obtain new time series in more coarse-grained grid boxes. To find an explanation for the increase in Hurst exponent that is seen when increasing the spatial scale, I have studied how the autocovariance function for a large grid box depends on the spatial cross-covariances within the box. If these are strong compared to the autocovariances in that area they will have an impact on the Hurst exponent. Scale free long-range memory models are found to give a good description for global temperature and many of the local temperatures on time scales from a few months to ten years. The largest deviations are observed in the eastern equatorial Pacific where ENSO is a very dominating process