10-day gap is sometimes not enough to ensure

at much less than the 1% signi¬cance level.

independence.9

The estimated signal, obtained by multiplying

The ˜full™ signal, that is, the overall 500 hPa

the guess patterns by the change in the

height ˜El Ni˜ o minus control™ difference ¬eld,

n

mean coef¬cient (not shown) is very similar

is shown in Figure 7.3. The equality of means

to the full signal (Figure 7.3). A test was

hypothesis was tested with the permutation test

also performed to see if there was a signal

[6.6.12] after projecting the data onto a set of guess

orthogonal to the guess pattern (see [6.5.4]).

patterns [6.5.6].

This was done using the EOF method

Three different sets of guess patterns were used.

described above. The null hypothesis that a

8 A ˜spin-up period™ is the time needed for a model to

10 The eddy component of a random ¬eld Z is the deviation

travel through its phase space from the initial conditions to —

from the zonal mean, Z = Z’[Z], where [·] denotes the zonal

quasi-equilibrium; that is, the time needed by the model to

T

averaging operator. Here [Z] = Z 1/m, where m is the number

˜forget™ the initial conditions.

9 For example, when there is ˜blocking,™ the memory of the of elements in Z and 1 is the m-dimensional vector of units. See

atmosphere might be a few weeks. also [7.2.1].

7.3: Identi¬cation of a Signal in Observed Data 133

component of the signal lies in a direction

orthogonal to the guess pattern was not

rejected.

3 Observed Fields as Guess Patterns

The GCM experiment was conducted to sim-

ulate the atmospheric response to anoma-

lous SST conditions in the tropical Paci¬c.

Therefore, the January mean 500 hPa height

anomaly ¬elds observed during three El Ni˜ on

events (1973, 1977, and 1983) were used as

guess patterns. A separate univariate test was

performed with each guess pattern.

The January 1973 guess pattern successfully

extracted part of the signal, although the

change in pattern coef¬cient was negative

rather than positive, as in the previous item.

The estimated signal, obtained by multiplying

the guess pattern with the change in its

coef¬cient (Figure 7.4, top), had about half of

the strength of the signal obtained by splitting

the GCM data. The most variance was

contained in a sector covering the Atlantic

and Eurasia. The part of the full signal that

appeared in the direction of the guess patterns

was actually weaker than the components that

were orthogonal to the guess pattern.

The January 1977 guess pattern successfully

captured a large fraction of the GCM

signal. There was strong evidence against

the null hypothesis, and the strength of the

Figure 7.4: GCM experiment on the extratropical

projection was about 75% of the value found

atmospheric response to tropical El Ni˜ o SSTn

through splitting the GCM data. The parallel

anomalies. Statistically signi¬cant projections of

component (Figure 7.4, bottom) was very

the full 500 hPa height signal (Figure 7.3) on the

similar to the full signal (Figure 7.3). The

January 1973 guess pattern (top: note that the

orthogonal part of the full signal (not shown)

signal is almost zero in the Paci¬c sector, where the

was still signi¬cantly nonzero.

El Ni˜ o related signal is expected to be strongest)

n

The last guess pattern, January 1983, repre-

and on the January 1977 guess pattern (bottom).

sented the observed atmospheric response to

Units: dkm. From von Storch [386].

the most intense ENSO event on record up

to 1997. Analysis of observational data has

shown that the January 1983 Northern Hemi- circulation anomaly from January 1977, but

sphere extratropical 500 hPa height ¬eld was largely orthogonal to the observed January 1973

substantially different from ˜normal™ January and 1983 anomalies.

mean height ¬elds [385]. None the less, this

¬eld failed to capture the simulated ENSO

signal when it was used as a guess pattern. In 7.3 Identi¬cation of a Signal in

Observed Data

fact, the GCM output was almost orthogonal

to the January 1983 500 hPa height anomaly.

7.3.1 General. Dramatic events sometimes

The major conclusion drawn from this statistical take place in the global environment, such as

analysis [386] was that the El Ni˜ o SST anomalies the appearance of large-scale ENSO sea-surface

n

excite a statistically signi¬cant response in the temperature anomalies of 1982/83 (Figure 7.2)

extratropical atmospheric circulation. The model or the injection of large amounts of aerosols

simulated a response similar to the observed into the stratosphere by an erupting volcano such

7: Analysis of Atmospheric Circulation Problems

134

as the Pinatubo in 1992 (see, e.g., McCormick, given month of the year are independent, that the

Thomason, and Trepte [268] or Pudykiewicz and realizations during the 1967“81 period all come

Dastoor [324]). The large events can be viewed as from random vectors with the same distribution,

natural sensitivity experiments, so it is of interest and that the covariance structure during the

to know whether the state of the atmosphere 1982/83 ENSO was the same as that during the

during, and after, the event is different from preceding 15 years. Clearly these assumptions are

that of the undisturbed, ˜normal™ climate. The not all satis¬ed. None the less, the analysis based

observations that represent the normal climate on this model is useful, even if it is not fully

are regarded as independent realizations of a precise.

˜control™ climate state vector X. The observation The data were available on a 576 point grid. The

taken during the event of interest is labelled guess patterns used in this study are the surface

spherical harmonics, written as P jm (φ) cos(m»)

y1 , and the null hypothesis: ˜y1 is drawn

from X™ is examined. If the null hypothesis is and P jm (φ) sin(m»), where φ is latitude, » is

¯

rejected, y1 ’ x is regarded as an informative, longitude, P jm is the corresponding associated

but uncertain, estimate of the effect of the Legendre polynomial, for j = 0, 1, . . . , ∞

event.11 and m = 0, . . . , j [15]. The surface spherical

harmonics are orthonormal12 functions. The index

j speci¬es the spatial scale, that is, any two

˜

7.3.2 The 1982/83 El Nino and its Impact on

surface spherical harmonics with the same index

the Extratropical Circulation. In Section 7.2

j share the same spatial scale whereas a larger j

we described an analysis of a simulated response to

indicates a smaller scale. Only functions with odd

a prescribed tropical Paci¬c SST anomaly. In this

˜two-dimensional wavenumbers™ m + j are needed

subsection we describe the analysis of observed

to represent a hemispherical ¬eld. There is only

response.

one function for each (m, j) combination when

Hense [174] examined monthly anomalies of

m = 0, but there are two functions, one displaced

Northern Hemisphere stream function for the

π

zonally 2m radians relative to the other, when m is

period January 1982 to September 1983, a period

nonzero. The cosine form of the (1, 1) and (1, 2)

containing the largest ENSO event on record (until

spherical harmonics are shown in Figure 7.5.

1997). The monthly anomalies used in the study

A hierarchy [6.5.8] was chosen as shown in

were obtained by subtracting the 1967“81 mean

Figure 7.6: the hierarchy with K = 1 element

appropriate to the month from each monthly mean

contains only the function P1 (φ); the hierarchy

0