Chapter 9
Field Intercomparison
by Robert E. Livezey
9.1 Introduction
Frequently analyses of climate data, wh ether model-generated or observed,
require the simultaneous assessment of the significance of multiple statistics.
A commonly ocurring situation is the test of a hypothesis for the difference in
means of two fields of data, e.g. the average winter time temperature anomaly
pattern over a net of European stations in each of two sets of GCM simulations. Regardless ofwhether the problem is approached with the multivariate
methods described in Chapter 8 or as a collection of individual or loeal significance tests, the collective or field significance of the results depends crucially
on the number of data points or tests and their interdependence.
In those situations where the sampIe size is at least several (three to five)
times as large as the effective dimensions of the analyzed fields, the prescriptions discussed in Chapter 8 are appropriate. However, often in climate
studies or studies of interannual variability this is not the case. In these instances the permutation and Monte Carlo techniques described in this chapter are generally effective alternatives for hypothesis testing. They also have
the advantage that they can be used when reference distributions of test
statistics cannot be analytically derived or are otherwise unknown, thereby
also permitting the use of innovative statistics (although the design basis for
such statistics should still be sound statistical principles). Generally these
procedures are not difficult to apply.
When, in addition to relatively small sampIe sizes, apriori expectations
of experimental out comes are missing (i.e. "fishing expeditions" ), then the
methods of this chapter may be the only effective alternatives for objective
Field Intercomparison
by Robert E. Livezey
9.1 Introduction
Frequently analyses of climate data, wh ether model-generated or observed,
require the simultaneous assessment of the significance of multiple statistics.
A commonly ocurring situation is the test of a hypothesis for the difference in
means of two fields of data, e.g. the average winter time temperature anomaly
pattern over a net of European stations in each of two sets of GCM simulations. Regardless ofwhether the problem is approached with the multivariate
methods described in Chapter 8 or as a collection of individual or loeal significance tests, the collective or field significance of the results depends crucially
on the number of data points or tests and their interdependence.
In those situations where the sampIe size is at least several (three to five)
times as large as the effective dimensions of the analyzed fields, the prescriptions discussed in Chapter 8 are appropriate. However, often in climate
studies or studies of interannual variability this is not the case. In these instances the permutation and Monte Carlo techniques described in this chapter are generally effective alternatives for hypothesis testing. They also have
the advantage that they can be used when reference distributions of test
statistics cannot be analytically derived or are otherwise unknown, thereby
also permitting the use of innovative statistics (although the design basis for
such statistics should still be sound statistical principles). Generally these
procedures are not difficult to apply.
When, in addition to relatively small sampIe sizes, apriori expectations
of experimental out comes are missing (i.e. "fishing expeditions" ), then the
methods of this chapter may be the only effective alternatives for objective