Section 8.2: Uni varia te Analysis
143
An alternative way to take serial correlation into ac count is to fit a parametric model to the time series, and then use the fitted model to derive the
variances needed in the asymptotic t-test (Katz, 1982; Thiebaux and Zwiers,
1984).
8.2.3 Field Significance
The interpretation of GeM experiments usually requires evaluating the significance of changes in a field composed of many grid points (and, possibly,
variables). This raises the question of the collective significance of an ensemble of univariate tests, which requires taking into account the multiplicity of
local tests and their interdependency.
Even in the simple case where all the univariate tests are independent, the
overall rate of rejection of the null hypothesis at the a level should be larger
than a for global or field significance, if the number of local tests is finite.
The critical rejection rate can be inferred from the binomial distribution (H.
von Storch, 1982; Livezey and ehen, 1983) and, for a small number of tests,
the threshold for field significance (global rejection of the null hypothesis )
can be large (see Figure 9.2). Furthermore, the interpretation of the results
is difficult because only global decisions about the experiment are possible
(Ho rejected or accepted everywhere), without a way to discriminate between
sub-regions of true or accidental change. For local decisions, one may have to
adopt Madden and Julian's (1971) stringent choice of a very high significance
level in the individual tests (e.g., a = 0.01).
In the more realistic case where the GeM data, hence the local tests, are
not independent but spatially correlated, one observes that Ho tends to be
rejected in "pools" of grid points, rather than at randomly distributed points,
and one expects the critical rejection rate to be larger since the effective number of independent tests is smaller. This number is difficult to estimate, because the tests have complex and poorly known spatial correlations. Livezey
and Chen (1983) have thus suggested to establish field significance by using
permutation techniques, which is costly in computer time but can take properly into ac count the interdependence between the tests (see Chapter 9). An
alternative is to use a multivariate approach, although, as discussed below,
it mayaIso have limitations.
8.2.4 Example: GCM Response
to a Sea Surface Temperature Anomaly
For illustration, consider the SST anomaly experiment of Hannoschöck and
Frankignoul (1985). To evaluate the sensitivity of the GISS 3 GCM Model
I to a North Pacific SST anomaly, three independent runs were performed
in perpetual January conditions: a 15-month and an 8-month control run,
3Goddard Institute for Space Studies.
143
An alternative way to take serial correlation into ac count is to fit a parametric model to the time series, and then use the fitted model to derive the
variances needed in the asymptotic t-test (Katz, 1982; Thiebaux and Zwiers,
1984).
8.2.3 Field Significance
The interpretation of GeM experiments usually requires evaluating the significance of changes in a field composed of many grid points (and, possibly,
variables). This raises the question of the collective significance of an ensemble of univariate tests, which requires taking into account the multiplicity of
local tests and their interdependency.
Even in the simple case where all the univariate tests are independent, the
overall rate of rejection of the null hypothesis at the a level should be larger
than a for global or field significance, if the number of local tests is finite.
The critical rejection rate can be inferred from the binomial distribution (H.
von Storch, 1982; Livezey and ehen, 1983) and, for a small number of tests,
the threshold for field significance (global rejection of the null hypothesis )
can be large (see Figure 9.2). Furthermore, the interpretation of the results
is difficult because only global decisions about the experiment are possible
(Ho rejected or accepted everywhere), without a way to discriminate between
sub-regions of true or accidental change. For local decisions, one may have to
adopt Madden and Julian's (1971) stringent choice of a very high significance
level in the individual tests (e.g., a = 0.01).
In the more realistic case where the GeM data, hence the local tests, are
not independent but spatially correlated, one observes that Ho tends to be
rejected in "pools" of grid points, rather than at randomly distributed points,
and one expects the critical rejection rate to be larger since the effective number of independent tests is smaller. This number is difficult to estimate, because the tests have complex and poorly known spatial correlations. Livezey
and Chen (1983) have thus suggested to establish field significance by using
permutation techniques, which is costly in computer time but can take properly into ac count the interdependence between the tests (see Chapter 9). An
alternative is to use a multivariate approach, although, as discussed below,
it mayaIso have limitations.
8.2.4 Example: GCM Response
to a Sea Surface Temperature Anomaly
For illustration, consider the SST anomaly experiment of Hannoschöck and
Frankignoul (1985). To evaluate the sensitivity of the GISS 3 GCM Model
I to a North Pacific SST anomaly, three independent runs were performed
in perpetual January conditions: a 15-month and an 8-month control run,
3Goddard Institute for Space Studies.