Section 8.3: Multivaria.te Ana.lysis
151
c) Observed Anomaly Patterns
In some cases, one may want to verify the consistency of a GCM response
with observed anomaly patterns. Of course, this requires the expected response to the prescribed anomaly to be well-documented. To a large extent,
this is the case for the atmospheric response to the warm SST anomaly appearing in the equatorial Pacific during EI Niiio. Thus, H. von Storch and
Kruse (1985) have used the 500 hPa height anomaly observed in January
1983 (Figure 8.4 left), during the most intense EI Niiio on record, as guess
vector for the response of the T21 ECMWF4 GCM to the composite warm
EI Niiio SST anomaly of Rasmusson and Carpenter (1981), as well as to an
anomaly of reverse sign. Nine independent J anuary means were available,
plus three anomaly J anuaries in each SST anomaly case. The mean anomaly
response of the model to the positive SST anomaly (Figure 8.4 right) seems
rather similar to the observed pattern. This was confirmed by the multivariate test, although the guessed pattern was shown to only explain part of
the GCM signal. Note that H. von Storch and Kruse (1985) used permutation procedures to establish significance, but similar results would have been
found with a parametric test. On the other hand, the null hypothesis was
accepted in the cold anomaly case (Le., the amplitude of the guess vector
was not significantly different from zero), suggesting that the atmospheric
response is not linear. This is of interest, but the test gives no other clues on
the GCM response to the cold anomaly.
Although useful, the use of observed patterns as guess vectors also has limitations, which are easily discussed in the context of this experiment. Indeed,
the "observed signal" may have been strongly affected by the noise associated
with the natural variability of the atmosphere, especially since it was derived
from a single monthly mean. Furthermore, the prescribed SST anomaly was
not exactly that observed in 1983 (nor could it be, because of observational
uncertainties), and SST anomalies outside the tropical Pacific, or other external forcings, may have contributed to the observed change. Thus, the GCM
forcing was an approximation to the true one, and the guess vector only a
noisy, and possibly biased, guess of the true signal. An improved procedure
would be to base the guess vector on observed anomaly composites, thereby
decreasing its noise level, and furthermore to take into account its statistical
uncertainty in the testing procedure. This could be done by specifying not
only the guess vector but also its error covariance matrix, as discussed below
in the context of ocean model testing.
d) Summary
The multivariate approach is a very powerful tool to interpret the results
of response and sensitivity studies with atmospheric GCMs. It is easy to
implement, but its usefulness is limited by the difficulty, or the subjectivity,
'European Centre for Medium Range Weather Forecast.
151
c) Observed Anomaly Patterns
In some cases, one may want to verify the consistency of a GCM response
with observed anomaly patterns. Of course, this requires the expected response to the prescribed anomaly to be well-documented. To a large extent,
this is the case for the atmospheric response to the warm SST anomaly appearing in the equatorial Pacific during EI Niiio. Thus, H. von Storch and
Kruse (1985) have used the 500 hPa height anomaly observed in January
1983 (Figure 8.4 left), during the most intense EI Niiio on record, as guess
vector for the response of the T21 ECMWF4 GCM to the composite warm
EI Niiio SST anomaly of Rasmusson and Carpenter (1981), as well as to an
anomaly of reverse sign. Nine independent J anuary means were available,
plus three anomaly J anuaries in each SST anomaly case. The mean anomaly
response of the model to the positive SST anomaly (Figure 8.4 right) seems
rather similar to the observed pattern. This was confirmed by the multivariate test, although the guessed pattern was shown to only explain part of
the GCM signal. Note that H. von Storch and Kruse (1985) used permutation procedures to establish significance, but similar results would have been
found with a parametric test. On the other hand, the null hypothesis was
accepted in the cold anomaly case (Le., the amplitude of the guess vector
was not significantly different from zero), suggesting that the atmospheric
response is not linear. This is of interest, but the test gives no other clues on
the GCM response to the cold anomaly.
Although useful, the use of observed patterns as guess vectors also has limitations, which are easily discussed in the context of this experiment. Indeed,
the "observed signal" may have been strongly affected by the noise associated
with the natural variability of the atmosphere, especially since it was derived
from a single monthly mean. Furthermore, the prescribed SST anomaly was
not exactly that observed in 1983 (nor could it be, because of observational
uncertainties), and SST anomalies outside the tropical Pacific, or other external forcings, may have contributed to the observed change. Thus, the GCM
forcing was an approximation to the true one, and the guess vector only a
noisy, and possibly biased, guess of the true signal. An improved procedure
would be to base the guess vector on observed anomaly composites, thereby
decreasing its noise level, and furthermore to take into account its statistical
uncertainty in the testing procedure. This could be done by specifying not
only the guess vector but also its error covariance matrix, as discussed below
in the context of ocean model testing.
d) Summary
The multivariate approach is a very powerful tool to interpret the results
of response and sensitivity studies with atmospheric GCMs. It is easy to
implement, but its usefulness is limited by the difficulty, or the subjectivity,
'European Centre for Medium Range Weather Forecast.