Keppenne, Christian L., Dettinger, Michael D., Ghil, Michael, Journal of the American Statistical Association
Like many recent studies of instrumental climatological records (see, for example, Ghil and Vautard 1991; Jones et al. 1986; Karl 1985; and Karl, Heim, and Quayle 1991), Handcock and Wallis's work aims to identify possible variations of the earth's climate over the last century. Their use of a rigorous Gaussian random field (GRF) approach to model surface air temperatures over part of the northwestern United States is new. The stochastic structure of time series of winter average temperatures at 88 sites belonging to the U.S. Historical Climatology Network (HCN) is characterized by this approach, and a temporally stable spatial structure--with little evidence of temporal dependence--is found. As a corollary, they derive posterior distributions of the areal mean temperature over time. This application of their random model indicates that, given a scenario of a gradual increase of 5[degrees]F over 50 years, it would take 30-40 more winters of data over this region, for the change to become discernible from natural temperature variations.
The limited geographical area and short time span (50 years) considered are dictated by the nature of the HCN data and GRF model. They restrict somewhat the scope of Handcock and Wallis's conclusions, without invalidating the approach chosen. The analysis is confined to a region extending longitudinally from eastern Montana through the Dakotas and meridianally from northern Nebraska to the Canadian border. This area was chosen because experiments with atmospheric general circulation models (GCM's; see, for example, Schlesinger and Mitchell 1987) agree in unanimously predicting future warming in the corresponding latitude belt, on the one hand, and because the data are relatively homogeneous over it, on the other. But temperature variations observed in this region are not representative of global variability or even of changes over the entire North American region. Attempting to draw general conclusions, applicable to the assessment of global warming, may not have been Handcock and Wallis's prime objective, and their approach seems appropriate for studying the time evolution of the areal-mean temperature over the region in question.
In the remainder of this discussion, we present an alternative approach that is well suited for the study of inhomogeneous temperature data over regions larger than the correlation length scale of interannual and interdecadal climatology, which is of the order of several thousands of kilometers. Analysis of larger spatial scales would presumably permit inferences as to what part of the long-term signal is regional and what part characterizes larger areas (Peixoto and Oort 1984). Moreover, most temperature changes over the last century have been confined to a relatively short period between 1910 and 1940 (Ghil and Vautard 1991), which predates the time interval studied by Handcock and Wallis.
Over the past half century, the characterization of the earth's climate has shifted from climatology to climate dynamics, from a description of the climatological mean--with random fluctuations about it--to a treatment of the climate system as a forced nonlinear oscillator responding dynamically to various deterministic and random forces, active over a wide range of time scales (Ghil and Childress 1987). When deviations from the time or space mean of some arbitrarily long interval are the focus of a climatological characterization, longer-period phenomena can be perceived as trends even though they may be purely periodic. A more realistic approach could be to shift attention to shorter-period phenomena of which several cycles are present within a given record. To a reasonable approximation, the theory of nonlinear dynamical systems allows us to linearize the system about its time mean over some long interval, to study variability over the shorter time scales, as forcing mechanisms at very different time scales are uncoupled. Results for the shorter time scales provide insights to eventually model the dynamics on the longer time scales. …