174
Chapter 9: Field Intercomparison
9.4.1 Local Probability Matching
If the eounting norm statistie is used with pp or BP and it is possible to
aecount properly for serial eorrelation in the loeal tests such that the loeal
probabilities of false rejeetions of the null hypothesis are the same for both
the original field sampies to be tested and all of the sampies eonstrueted by
resampling, then the analyst ean proeeed as before. This is what Livezey and
Chen (1983) attempted to do heuristieally for their Ioeal tests.
A eonsiderable amount ofprogress has been made by Zwiers and von Storch
(1994) in solving the problem of dealing with serial eorrelation in loeal tests
of the differenee in means. Thus, matching the Ioeal probabilities mentioned
above should be possible through use of loeal tests for the original sampies
(which are serially eorrelated) that eonsist of, for example, their "table look
up" tests.
9.4.2 Times Series and Monte Carlo Methods
In field test situations that result from a single time series operating on a
fuH grid or field of series, like for example the field of eorrelations between
the SOl and extratropieal Northern Hemisphere 700 hpa heights in Livezey
and Chen (1983), then a viable strategy is to model the single se ries with
autoregressive teehniques and use the resulting model to generate random
Monte Carlo sampies whieh preserve the autoeorrelation strueture of the
original series.
Both Thiebaux and Zwiers (1984) and Trenberth (1984) deseribe pro eedur es for the autoregressive modeling whieh rely heavily on the work of Katz
(1982). Zwiers and H. von Storch (1994) suggest that a simple AR(l) proeess is an adequate approximation for many meteorologie al and dimatological time series with the annual eyde removed. This approximation would
obviously be ineorrect for interannual series (like the SOl) in whieh the quasibiennial oseillation (QBO) is important.
Simultaneous modeling of both spatial and temporal eorrelation for generation of Monte Carlo sampies is eonsiderably more ehallenging, so the use of
this approach for field vs. field problems generally will often be intractable.
9.4.3 Independent Sampies
The most direct remedy for dealing with serial correlation is to eliminate it.
For GCM experiments eareful experimental design ean ensure that sampies
are temporally uneorrelated. In the ease ofreal data studies it is also possible
to eliminate temporal eorrelation but at the price of smaller sampies.
The proeedure for obtaining test sampies without serial eorrelation is simple: Estimate an "effective time between independent sampies" , Ta, and
prune the data aeeordingly. For example, if To is approximately twiee the
sampling interval elimination of all of the even or odd numbered sampies
Chapter 9: Field Intercomparison
9.4.1 Local Probability Matching
If the eounting norm statistie is used with pp or BP and it is possible to
aecount properly for serial eorrelation in the loeal tests such that the loeal
probabilities of false rejeetions of the null hypothesis are the same for both
the original field sampies to be tested and all of the sampies eonstrueted by
resampling, then the analyst ean proeeed as before. This is what Livezey and
Chen (1983) attempted to do heuristieally for their Ioeal tests.
A eonsiderable amount ofprogress has been made by Zwiers and von Storch
(1994) in solving the problem of dealing with serial eorrelation in loeal tests
of the differenee in means. Thus, matching the Ioeal probabilities mentioned
above should be possible through use of loeal tests for the original sampies
(which are serially eorrelated) that eonsist of, for example, their "table look
up" tests.
9.4.2 Times Series and Monte Carlo Methods
In field test situations that result from a single time series operating on a
fuH grid or field of series, like for example the field of eorrelations between
the SOl and extratropieal Northern Hemisphere 700 hpa heights in Livezey
and Chen (1983), then a viable strategy is to model the single se ries with
autoregressive teehniques and use the resulting model to generate random
Monte Carlo sampies whieh preserve the autoeorrelation strueture of the
original series.
Both Thiebaux and Zwiers (1984) and Trenberth (1984) deseribe pro eedur es for the autoregressive modeling whieh rely heavily on the work of Katz
(1982). Zwiers and H. von Storch (1994) suggest that a simple AR(l) proeess is an adequate approximation for many meteorologie al and dimatological time series with the annual eyde removed. This approximation would
obviously be ineorrect for interannual series (like the SOl) in whieh the quasibiennial oseillation (QBO) is important.
Simultaneous modeling of both spatial and temporal eorrelation for generation of Monte Carlo sampies is eonsiderably more ehallenging, so the use of
this approach for field vs. field problems generally will often be intractable.
9.4.3 Independent Sampies
The most direct remedy for dealing with serial correlation is to eliminate it.
For GCM experiments eareful experimental design ean ensure that sampies
are temporally uneorrelated. In the ease ofreal data studies it is also possible
to eliminate temporal eorrelation but at the price of smaller sampies.
The proeedure for obtaining test sampies without serial eorrelation is simple: Estimate an "effective time between independent sampies" , Ta, and
prune the data aeeordingly. For example, if To is approximately twiee the
sampling interval elimination of all of the even or odd numbered sampies