A Bayesian approach to reconstructing space-time climate fields from proxy and instrumental time series, applied to 600 years of northern hemisphere surface temperature data

We explore the relationship between the mean and spatial dis persion of Northern Hemisphere surface temperature anomalies over the last 1200 yea rs, an lyzing both instrumental and proxy records. Formal statistical tests applied to 14 an nu lly resolved proxy records identify the period 964-1163 as being both anomalously warm nd anomalously spatially variable, i.e. the Medieval Warm and Variable Period. The ob served increase in mean is unlikely to be an artefact of surface temperatures being mor e va iable during this period. According to the proxy records, the 1906-1990 period is warm er than the medieval period, but the spatial variability is not significantly different w ithin the two periods. Analysis of the Climate Research Unit compilation of instru mental records reveals a positive correlation between the spatial mean and the stand ard deviation over the 20 th Century. There is a suggestion, then, that increases in the spat ial standard deviation consistently accompany increases in the spatial mean. This two moment ana lysis yields a more complete description, or fingerprint, of surface temperature a nomalies during different periods, and indicates that, in the two dimensional space spanned by t he mean and standard deviation, the medieval period can primarily be distinguishe d from the 20th Century, and, likewise, the 1980-2005 period from the 1932-1963 mid 20 th Century warming, on the basis of the mean. While the uncertainties associated with the point estimates of the standard deviations for different warm periods overlap considerabl y, these point estimates do increase with increasing mean temperature. If, as expected, s urface temperatures continue to rise in the future, we expect, based on past trends, that the s patial dispersion of the surface temperature distribution will likely increase as well. 10 Chapter 2 Mean and dispersion

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