a location poleward (solid line) and equatorward

Sutera [162].

(dotted) of the Paci¬c stormtrack. From Nakamura

and Wallace [287].

cut off from the family of streamlines that trace out

with sequences of two or more nodes of op- the westerly circumpolar ¬‚ow, the anomaly is freed

posite signs indicating that a substantial part of from the effect of advection and can remain stationary

the month-to-month variability in the extratropical for a long time relative to the time scale of baroclinic

midtropospheric height ¬eld could originate from waves. Such cut off ¬‚ow con¬gurations are identi¬ed

standing oscillatory modes. The nodes in the pat- with blocking anticyclones in high latitudes and cut

terns are sometimes named centres of action. off lows in lower latitudes. . . . [We] suspect that

Barnston and Livezey [27] extended Wallace the primary contributions to the observed skewness

and Gutzler™s study by analysing data from all come from these anomalous circulations that occur

seasons. By using rotated EOFs (Section 13.5) relatively infrequently.

they were able to reproduce Wallace and Gutzler™s

results and increase the number of characteristic

midtropospheric patterns. 3.1.9 Bimodality of the Planetary-Scale Cir-

culation. Even though the nonlinearity of the

3.1.8 Extratropical 500 hPa Height: Skewness. dynamics of the planetary-scale13 atmospheric

Nakamura and Wallace [287] analysed 30 years circulation was well known, atmospheric scientists

of daily anomalies (i.e., deviations from the mean only began to discuss the possibility of two or more

annual cycle) of Northern Hemisphere 500 hPa stable states in the late 1970s. If such multiple

height and derived frequency distributions for all stable states exist and are well separated, it should

grid points and for two different time scales. The be possible to ¬nd bi- or multimodal distributions

˜high-frequency™ variations, ranging from two to in the observed data.

six days, are generally normally distributed; the Hansen and Sutera [162] identi¬ed a bimodal

˜low-frequency™ variations, beyond six days, are distribution in a variable characterizing the energy

not normal (Figure 3.10). North of the Paci¬c of the planetary-scale waves in the Northern

and North Atlantic ˜stormtracks,™ the skewness γ1 Hemisphere winter (DJF). Daily amplitudes for

(see [2.6.7]) is negative, but equatorward of the the zonal wavenumbers k = 2 to 4 for 500 hPa

stormtracks the skewness is positive (Figure 3.11). height were averaged for midlatitudes. These were

Nakamura and Wallace suggest that the dynamical used to derive a ˜wave-amplitude indicator™ Z

reason for this pattern is by subtracting the annual cycle and ¬ltering out

all variability on time scales shorter than ¬ve

. . . that quantities such as temperature and potential days. The probability density function f Z was

vorticity exhibit large meridional contrasts across the

13 Often, the spatial scales of the atmospheric circulation

. . . stormtracks, as if there were two different ˜air

are discussed in terms of wavenumber k in a zonal Fourier

masses™ facing each other. It is conceivable that a

decomposition along latitudes. Long waves, for instance k =

piece of one air mass could become cut off to form 1, . . . , 4, represent planetary scales while shorter waves, k ≥ 5,

an isolated vortex within the other air mass. . . . Once are called baroclinic scales.

3: Distributions of Climate Variables

62

estimated by applying the so-called maximum

penalty technique to 16 winters of daily data. The

resulting f Z has two maxima separated by a minor

minimum near zero (Figure 3.12).14

Hansen and Sutera conclude from the bimodal-

ity of their distribution that the nonlinear dynamics

of the atmospheric general circulation yield two

stable regimes. The ˜zonal regime,™ with Z < 0,

exhibits small amplitudes of the planetary waves.

The ˜wavy regime,™ with Z > 0, is characterized

by enhanced planetary-scale zonal disturbances.

The mean 500 hPa height ¬eld for the 62% of

all days when the system is in the ˜zonal™ regime

is indeed almost zonal (Figure 3.13a). The mean

¬eld for the ˜wavy™ regime, derived from the

remaining 38% of all days, exhibits marked zonal

asymmetries (Figure 3.13b).15

3.1.10 Biological Proxy Data. The effects

of variation in, for example, temperature or

precipitation, are often re¬‚ected in biological

variables such as the width of tree rings (a detailed

discussion of this type of data is offered by

Briffa [65]), or the arrival of migrating birds.

Records of plant ¬‚owering dates or similar events

constitute phenological data.

An unusual example is the ¬‚owering date of

wild snow drops in the rural town of Leck

(northern Germany), which are plotted against the

14 There is an interesting story associated with Hansen and

Sutera™s bimodality:

Figure 3.13: Averages of 500 hPa Northern

Hansen and Sutera [162] conducted a ˜Monte Carlo™

Hemisphere height ¬elds in winter (DJF). Contour

experiment to evaluate the likelihood of ¬tting a bimodal

sample distribution to the data when the true distribution interval: 100 m. From [162].

is unimodal with the maximum penalty technique. It was

a) The ˜zonal™ regime: Z < 0.

erroneously concluded that the probability of such a mis¬t is

b) The ˜wavy™ regime: Z > 0.

small. The error in this conclusion was not at all obvious.

Nitsche, Wallace, and Kooperberg [295] did a careful step-

by-step re-analysis of the original data to ¬nd that the Monte

Carlo experiments were inconsistent with the analysis of the

coef¬cient of the ¬rst EOF (Empirical Orthogonal

observational data.

Function; see Chapter 13) of Northwest European

This is a very educational example, demonstrating a

frequent pitfall of statistical analysis. Basic inconsistencies are winter mean temperature in Figure 3.14. The

sometimes hidden in a seemingly unimportant detail when

¬‚owering date varies between Julian day 16

sophisticated techniques, like the maximum penalty technique,

(16 January) and 80 (21 March). The two

are used. The error was found only because J. Wallace

variables, ¬‚owering date and the ¬rst EOF

suspected that the ¬nding could not be true.

Nitsche et al. reproduced the sample distribution shown coef¬cient, are well correlated as indicated by the

in Figure 3.12, but showed that about 150 years of daily

regression line in Figure 3.14. Thus, the ¬‚owering

data would be required to exclude, with suf¬cient certainty,

date of wild snow drops at Leck is a proxy of

the possibility that the underlying distribution is unimodal.

Essentially, then, reasonable estimates were made but the test regional scale winter mean temperature.

of the null hypothesis ˜The sample distribution originates from

There are other proxy data, some of them

a unimodal distribution™ was performed incorrectly. However,

derived from historical archives, such as the yield

even without having rejected the null hypothesis, the possible

implications incorporated in Figure 3.12 indicate that there of wine harvests or reports from courts and

could be two different stable atmospheric states.

monasteries (e.g., Zhang and Crowley [436]), and

15 Compare with the monthly mean ¬elds shown in

others from tree rings (Briffa [65]), geological

Figure 1.1. January 1971 belongs to the zonal regime whereas

data such as sediments (e.g., van Andel [378]),

January 1981 belongs to the wavy regime.

3.2: Some Other Climate Variables 63

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Sea Level (mm)

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-2 -1 0 1 2

EOF Coefficient

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