Environmental Statistics Study Group

David B. Stephenson

Understanding the changing state of the global climate poses some very interesting and challenging environmental problems that deserve more attention from statisticians. We have selected the two topics below as being of particular interest for the ESSG proposal:

How to characterize trends in temperature time series ?

Observed surface air temperatures vary on all possible time-scales from daily, monthly, to seasonal and longer. There has been much debate about the possible increasing trends in mean temperatures expected from man-made global warming. However, trends can also occur in quantities other than annual and seasonal mean values such as daily temperature extremes. A recent investigation of cold extremes in daily mean Central England Temperatures (CET) revealed that cold extremes exhibit clearer recent increasing trends than those seen in monthly and seasonal averages (Antoniadou et al. 2000).

A monthly mean CET series was originally constructed by the late Professor Gordon Manley, and is now routinely updated by the Hadley Centre. The monthly mean surface air temperatures, for a region representative of the English Midlands, are expressed in degrees Celsius for the period from 1659 to the present (Manley 1973).

A time series of daily mean temperature (defined as the arithmetic mean of the min and max temperatures) is also available for the shorter period of 1772-now. They are described in the article by Parker et al. (1992) and have been used to study extreme cold events by Antoniadou et al. (2000). Both the monthly and daily data are available from http://www.badc.rl.ac.uk/data/cet/

Estimating the probability of atmospheric flow regimes ?

The climate is a non-linear dynamical system having many degrees of freedom. From chaos theory for systems with a small number of degrees of freedom, one expects the system to remain longer in certain regions of state space. These more persistent states are referred to as "regimes" and can be discerned as local maxima in estimates of the probability density for the leading principal components (Corti et al. 1999). The existence (or not!) of such regimes is important for our understanding of climate dynamics and predictability.

Corti et al. (1999) presented evidence for regimes in an analysis of the gridded geopotential height of the 500mb pressure surface over the period 1948-98. Geopotential height at 500mb is a good indicator of the flow patterns in the troposphere. The monthly mean data set consists of height values on a 2.5 degree grid covering the northern hemisphere (p=144x29=4176 variables). Corti et al. (1999) reduced the dimension by projecting onto the first two leading principal components and then examined the p.d.f. in this PCA reduced state space. A Gaussian kernel method was used to make smooth estimates of the p.d.f.

It is not at all clear that this is the best way to reduce this large data set in order to search for persistent regime modes. New methods need to be developed capable of working with the large gridded data sets commonly used in climate research. It is also not clear whether or not the regimes are merely artifacts of poor sampling or are in fact significant structures in state space. The data will be made available on the web site http://www.met.rdg.ac.uk/cag/STATS/.

References

T. Antoniadou, P. Besse, A.-L. Fougeres, C. Le Gall, and D.B. Stephenson, (2000), Balancier atmospherique (NAO) et climat en Atlantique nord, Revue de Statistique Appliqu\'ee, (to appear).

S. Corti, F. Molteni, and T.N. Palmer, (1999), Signature of recent climate change in frequencies of natural atmospheric circulation regimes, Nature, 398, 799-802.

G. Manley, 'Central England Temperatures: monthly means 1659 to 1973', Quarterly Journal of the Royal Meteorological Society, 1974, vol. 100, pp. 389--405.

D.E. Parker, T.P. Legg and C.K. Folland, 'A new daily Central England Temperature series, 1772--1991', International Journal of Climatology, 1992, vol. 12, pp. 317--42.