final_program_abstracts[1]

11 IMSC Session Program
Bayesian ANOVA for the calculation of climate anomalies
Monday - Parallel Session 9
Martin P. Tingley
SAMSI, USA
Harvard University, USA
For the purposes of studying climate, space-time variables such as temperature are
generally analyzed only after the the mean over some reference time interval has been
removed from each time series. For example, the Climate Research Unit's temperature
compilation is composed of a grid of monthly time series of deviations from a 1961-
90 base period. While climate fields will generally display complex structures,
including strong dependencies on latitude and orography, the anomalies might
reasonably be expected to be dominated by larger scale spatial features, which
facilitates the identification of trends and patterns.
Given the underlying assumption that the field is changing through time, a common
interval must be used to calculate the mean of each time series. In general, the time
series under analysis have different amounts of missing data, resulting in a reference
interval shorter than the length of the data set. As a result, the variance across the
estimated anomaly time series (i.e. spatial variance) is reduced within the reference
interval, and inflated elsewhere.
We present an alternative approach to calculating climate anomalies, based on
maximizing the length of the reference period and accounting for the increased
uncertainty that results from the missing values. In this context, the standardization
problem is framed as a Bayesian multi-factor ANOVA analysis, with the factors being
location and year. The climate anomalies then result from removing the location
effects from each time series. Within the Bayesian framework, the missing values in
the data set are treated as additional parameters that must be estimated, while the
posterior distributions of the year and location effects account for the uncertainty
introduced by the missing observations.
We apply the Bayesian ANOVA scheme to two well known data sets: the northern
hemisphere temperature reconstructions over the last 1.3ky plotted in Figure 6.10 of
the IPCC Fourth Assessment report, and the Climate Research Unit's gridded
instrumental compilation. These data sets are both presented as anomalies from a
1961-1990 reference period, and we discuss the impact that extending the reference
period to the length of each data set has on each.
Abstracts 69