A Bayesian ANOVA Scheme for Calculating Climate Anomalies, with Applications to the Instrumental Temperature Record

Climate datasets with both spatial and temporal components are often studied after removing from each time series a temporal mean calculated over a common reference interval, which is generally shorter than the overall length of the dataset. The use of a short reference interval affects the temporal properties of the variability across the records, by reducing the standard deviation within the reference interval and inflating it elsewhere. For an annually averaged version of the Climate Research Unit's (CRU) temperature anomaly product, the mean standard deviation is 0.67 degrees C within the 1961-90 reference interval, and 0.81 degrees C elsewhere. The calculation of anomalies can be interpreted in terms of a two-factor analysis of variance model. Within a Bayesian inference framework, any missing values are viewed as additional parameters, and the reference interval is specified as the full length of the dataset. This Bayesian scheme is used to re-express the CRU dataset as anomalies with respect to means calculated over the entire 1850-2009 interval spanned by the dataset. The mean standard deviation is increased to 0.69 degrees C within the original 1961-90 reference interval, and reduced to 0.76 degrees C elsewhere. The choice of reference interval thus has a predictable and demonstrable effect on the second spatial moment time series of the CRU dataset. The spatial mean time series is in this case largely unaffected: the amplitude of spatial mean temperature change is reduced by 0.1 degrees C when using the 1850-2009 reference interval, while the 90% uncertainty interval of (-0.03, 0.23) indicates that the reduction is not statistically significant.