Saltzman B. (editor) Anomalous Atmospheric Flows and Blocking

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244

ALFONSO

SUTERA

probability density. Moreover, by projecting the phase space of a complex

dynamical system (such

the atmosphere) onto a particular direction (as in

our

representation of the large-scale features), any possible fine structure

(such as fractal dimensionality or more exotic features) of the true density

has been distorted and discarded in favor of gross representation into

two

global maxima. On the other hand, the unequivocal information that can be

deduced by our density estimation is that some instability is present in

large-scale atmospheric flow, which has induced the

minimum

ofthe density

distribution. Hence, the correct interpretation of the results, as presented

thus far, is that there exists an instability in the complete phase space, leading

to the fact that its projection

our coordinate axes induces a minimum in

the probability density. (In other words, the property shared by the multidi-

mensional probability density and our projection estimation

the mini-

mum rather than the two maxima.) In fact, the regression equation that

would have our density distribution

an asymptotic property is

y,)(x

y3)

€1’2

(10)

where

yz,

and

are the values of the density at the first maximum,

minimum, and second maximum, respectively; the instability is self-evi-

dent. These further aspects of the interpretation of our results will be ad-

dressed in a forthcoming paper.

Second, at the present stage we cannot conclude that the instability de-

tected is global (spatially) in its nature. In fact, the preparation of the dataset

fie., averaging over latitude and especially using the spatial Fourier projec-

tion) might have smeared out any local property of the instability into a

global feature. The only evidence in favor of the interpretation of the insta-

bility

a global property comes from the difference maps presented in the

previous section. There an educated inspection could reveal a global wave

train intensifLing

the region of exit of the jet. On the other hand, some

support on behalf of the local nature of the instability could come from the

very same maps that show a weaker wave train in the Atlantic sector than

that seen in the Pacific sector. Since this feature is less evident than the

previous one, we would opt with no firm commitment to the global interpre-

tation.

Finally, it is possible that the same density would be explained by a ran-

dom interference between stationary waves and westward-propagating

global free Rossby waves

(R.

Lindzen, this volume). Since we have not

separated the standing part of the waves contributing to the indicator

(A}

from the traveling contribution, we cannot disregard this alternative inter-

pretation. However, an argument (weak, and not conclusive) against this

Wiener’s process

DENSITY DISTRIBUTION

ATMOSPHERIC

FLOW

245

interpretation can be produced on the following basis. If it is the interference

between stationary and free westward- propagating Rossby waves that pro-

duces the bimodal density, then some memory of the time periodicity of

these traveling waves should be detected in the data; not exact, of course, but

the duration

the events should be, at least, Gaussian around the period

the Rossby wave. As already mentioned, we did not find any spectral peak

for frequency shorter than

days. This excludes the exact periodicity re-

quirement.

In disfavor of the Gaussian distribution, we present the following prelimi-

nary evidence. In Fig.

is shown the density distribution of the duration of

the events in Mode

and Mode

deduced from considering the same

indicator here

discussed for the

winters spanning

1966

1979

(Benzi

and Speranza,

1986).

Apparently, this density fails to show any sign of

Gaussian nature, while it would fit very well the Poisson distribution. It has

been proven (see Benzi and Sutera,

1985)

that the distribution of the persist-

ence in a basin of attraction

a fixed point follows a Poisson distribution.

Hence, we would conclude that the observations do not lend support to the

previously mentioned interpretation. Of course, the density just mentioned

has not been carefully estimated and a more thorough analysis could very

well prove that other distributions might fit the data.

- -

*--

*I--*

DURATION

(DAYS)

FIG.

Density distribution (histogram)

the

duration

events in Mode

for statistics

winters (1966-1979). (After Benzi

al.,

1984.)

246

ALFONSO

SUTERA

8. THE

ZONAL

WIND

mentioned in Section

CDV

theory predicts that the zonal wind must

bimodal also. In the next section, using the same methods developed

far, we will address this question.

We present in Table

the results of the density estimation for the variable

Figs.

8a- 8d we present the corresponding densities that satisfy the

95%

confidence level.

is evident that no sign of bimodality is present in any of

the estimations considered. The density distributions are always unimodal

and strongly resemble Gaussian, slightly skewed density distributions. How-

ever, it appears that the skewness

the distribution varies from one year to

another. It implies that

we were to consider the distribution of the four

winters together, as we have done for the variable

we might obtain a

spurious bimodal distribution. In fact, in this case, the correct interpretation

would be that the bimodal nature

the density is a consequence of the

interannual variability-i.e., of time scales much longer than the one here

considered (periods shorter than

days). Of course, this variation of the

zonal wind is

worthy

offurther investigation, and we hope to do it in the near

future with a larger sample. However, on the basis of the yearly individual

density, a regression equation, with such an asymptotic density deduced

from the data, is

where

is the decorrelation time for

(about

days). At the stationary state

(possible only if

were

see Sutera,

198

for example) we will have

U*.

If we plot this relationship in the same phase plane of the

CDV

resonance

dU=

-j(U

U*)

E’”

TABLE

Iv.

CONFIDENCE

LEVELS

THE

KOLMOGOROV-SMIRNOV

TEST

(pK)

FOR

lJa

1981 1982 1983 1984

0.1

lo4 0.9 0.99 0.98 0.99

0.4

lo3

0.8

0.96 0.94 0.99

0.1

lo3

0.7

0.8 0.8

0.75

0.6

lo2

0.55

0.7 0.5

0.3

0.2

lo2

0.5

0.2

0.005

0.1

lo2

0.4

0.3

0.07

0.015

0.4

10’

0.20

0.1

0.02 0.013

0.1

10’

0.05

0.002

0.005

0.6

100

0.03

0.01

O.OOO1

0.0008

The behavior

function

the

hyper-

parameter

for

the

variable

DENSITY

DISTRIBUTION

ATMOSPHERIC

FLOW

247

0.4

0q3py

0.2

LOn3in.;

0.2

0.1

I-'

0.1

,,/

-3-2-1

FIG. 8a-d.

Figs.

2a-d

for

the

variable

curve, we see that for

10 m (i.e., the mean value deduced from obser-

vations), only one intersection between Eq. (1 1) and the resonance curve is

possible. This result would not allow any interpretation of the observed wave

instability discussed in the previous section

being consistent with the

orographic instability of the model proposed by CDV. However, we can note

that if the resonance curve were a multivalued function of Uin the region of

the Uvariability, the consistency could be restored. In Benzi

al.

(1986) and

Speranza (this volume), by including nonlinear effects in a CDV formula-

tion of the barotropic orographic instability, it is demonstrated that such a

multivalued resonance curve can be deduced by an appropriate folding of

the resonance curve.

9. CONCLUSIONS

We have studied the essential behavior ofa measure ofthe large-scale wave

amplitude as deduced from the 500-mbar analysis for the last four winters

(the only analyses available from the European Centre for Medium Range

Weather Forecasts). Our findings are as follows:

The amplitude of the waves has a highly statistically significant bimo-

dal distribution.

The presence of a large-scale instability mechanism is implied.

This instability is consistent with a theory which connects the instabil-

ity with an orographic effect [in the sense discussed in Benzi

al.

(1986)],

248

ALFONSO SUTERA

although an alternative explanation might be advocated (see Lindzen, this

volume).

We are aware of the possibility that our results might

dependent on

the sample size. Extension of the present study to more years is required and

we hope to do it in the near future.

Other limitations of the present study have been discussed, particularly

in assessing the nature of the multidimensional probability density induced

by atmospheric motion. This has led us to

cautious in interpreting the

modes of the probability density

a sign of the existence of stable steady

states.

Apparently the modes can

identified with atmospheric patterns

resembling high-index and amplified large-scale wave patterns.

The zonal wind failed to show any bimodality.

a consequence of item

we emphasize the role of the nonlinear

processes ifthe instability found in the data has its theoretical counterpart in

the orographic instability mechanism.

ACKNOWLEDGMENTS

my pleasure

thank

Dn.

Bengtsson and

Bumdge and the staff‘ofECMWFfor their

hospitality and frequent discussions on the topic addressed in this article. Professor B. Saltzman

and a reviewer helped in improving the manuscript.

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(1985).

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and Climate Theory’’

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Benzi,

R.,

Malguzzi,

P., Speranza,

A.,

and Sutera, A.

(1986).

The statistical propertiesofgeneral

atmospheric circulation: Observational evidence and a minimal theory ofbimodality.

Meteorol.

Soc.,

in press.

Benzi,

R.,

and

Speranza,

(1986).

The

statistical

properties of

low

frequency variability in the

Northern Hemisphere.

Mon.

Weather

Rev.,

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Charney,

G.,

and

DeVore,

(1979).

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G.,

and Eliassen,

(1949).

numerical method for pedicting the perturbation of

the middle latitude westerlies.

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Charney,

G.,

Shukla,

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and

Mo,

(1981).

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Dole,

M.,

and Gordon,

(1983).

Persistent anomalies

the extratropical Northern

Hemisphere wintertime circulation: Geographical distribution and

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1567- 1586.

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ATMOSPHERIC

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Hartmann,

L. and Ghan,

980).

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Moritz,

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Priestley, M.

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Academic Press, New York.

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W.,

Tapia, R. A., and Thompson,

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STATIONARY PLANETARY WAVES,

BLOCKING, AND INTERANNUAL

VARIABILITY

LINDZEN

Center for Meteorology and Physical Oceanography

Massachusetts Institute

Technology

Cambridge, Massachusetts

021

39,

and

Physical Research Laboratory

Ahmedabad,

380

009,

India

INTRODUCTION

This paper is a somewhat didactic discussion of various current trends in

the study of large-scale planetary waves and their anomalies. The intensity of

current activity on this topic stems from the belief that the anomalies can be

unusually long lived and may, therefore, represent particularly predictable

features of weather. The word “blocking” is sometimes associated with these

anomalies. Much of the present activity stems from the winter of 1976/ 1977,

when the period December to mid-February was, on the average, unusually

cold; this

was

associated with a stationary wave pattern that was significantly

amplified over its climatological mean (Namias, 1978).

seems to me that much of the current approach is unbalanced at best.

Far more work is being devoted to accounting for anomalies than to account-

ing for the climatology itself. Moreover, the contention that the anomalies

are persistent may itself be misleading.

persistence

suppose is meant

slow time variation compared to the expected periods of oscillation of the

atmosphere, Such persistence,

hope to show, accounts for a relatively small

part

the planetary-wave anomalies.

will begin, in Section

by examining some aspects of the observed time

behavior of anomalies. It appears that there is some modest interannual

variability of stationary wave patterns, but little evidence of unusual persist-

ence in the larger anomalies. Indeed it appears that a significant part of

interannual variability is simply a statistical residue of short-period anoma-

lies.

Given the above conclusions, it is awkward to discuss the various explana-

tions put forward to account for the allegedly persistent anomalies. How-

ever, the observational picture is not yet convincingly clear. There is some

1986

Academic

Press,

Inc.

All

rights

reproduction in

any

form

reserved.

ADVANCES

GEOPHYSICS,

VOLUME

252

LINDZEN

evidence, that on rare occasions, long-lived

month) significant anoma-

lies do occur. The period

1962

1963

is sometimes cited in this regard (Tung

and Lindzen,

1979).

(Even in such events it seems possible that we are simply

dealing with shorter events “running into each other.”) Two approaches

have been particularly popular: multiple equilibria, and teleconnections

between the tropics and midlatitudes. The former, which is amply repre-

sented in this volume, considers the possibility that stationary wave patterns

have several equilibrium configurations and that persistent anomalies arise

when the atmosphere passes from one equilibrium state to another.

multi-

ple-equilibria theories were correct, then the nonexistence of persistent

anomalies would be a problem. As

will

show in Section

the most com-

mon multiple-equilibria theories appear inappropriate to the atmosphere.

The role

teleconnections

more complicated. Horel and Wallace

(

198

noted that patterns of geopotential heights involving both the tropics

and midlatitudes accounted for significant (about

20%)

portions of the

winter variability

monthly means. Thus, it was conjectured that tropical

occurrences like

Niiio should have anticipatable midlatitude conse-

quences. Given the modest role of this pattern it

difficult to believe that it

can offer much improvement in long-term forecasts. Certainly, it does not

appear to be a mechanism for the prominent short-period anomalies. In

Section

will simply note the poor correlation between El Niiio years and

North American winter climate.

will show some recent data analyses by

Plumb

985)

which appear to suggest a very small role for the tropics in

forcing the climatological stationary waves

northern midlatitudes. The

clear conclusion that one is forced to is that the tropics are certainly not the

major factor in determining midlatitude stationary waves, though they may

be one contributor among others to interannual variability. This is consist-

ent with the recent work of

Lau

and Phillips

(1984)

and Dole

(1983,

who

found that composites

planetary-wave anomalies in midlatitudes showed

no evidence

a tropical precursor. On the contrary, there was a suggestion

of tropical response (i.e., time lag). Nevertheless, a large number of theoreti-

cal papers have purported to find large midlatitude responses to tropical

forcing-duplicating the Horel- Wallace teleconnection pattern.

will

discuss the theoretical papers in Section

where, however,

concentrate on recent results by Jacqmin and Lindzen

(1984)

on the clima-

tological stationary wave pattern and its sensitivity to changes in both the

zonally averaged flow and in the thermal forcing.

Finally, in Section

some recent work on the atmosphere’s free transient

Rossby waves is described. It has been found that these oscillations are

planetary in scale, of significant amplitude, and characterized by periods of

10-

days

periods not unlike those identified with unusual persistence.

PLANETARY WAVES, BLOCKING, AND VARIABILITY

253

How PERSISTENT ARE ANOMALIES?

Although it is commonly taken for granted that anomalies of unusually

long persistence are an important feature of weather,

would like to suggest

that this may, in fact, be untrue. Consider Fig.

taken from the

New York

Times

January

1983,

which summarizes New York City’s weather in

1982

(there was no particular reason for choosing

1982

other than the conve-

nient availability of this figure).

always, the temperature vacillates above

and below the “normal” range. Of particular note is December

1982,

unusually warm month. Note that the warmness ofthe month

a whole was

due to a sequence of warm episodes, none of which lasted longer than a week.

Note also that this warm month also had episodes ofbelow-normal tempera-

ture. The point is perhaps obvious: namely, a warm month does not repre-

sent an anomaly which persisted for a month.

This is consistent with Fig.

taken from Dole and Gordon

(

1983).

This

figure shows number of anomalies (for different anomaly thresholds) versus

duration. We see that the expected duration of any anomaly, once observed,

is less than

days.

To be sure, there are times when

days seems anomalously long. How-

ever, for persistence to have a physical meaning, “long” must be long com-

pared to the normal time scales for transiency. The most obvious compari-

son, here, is with the time scales of the free

planetary-scale

Rossby waves. As

we shall describe in Section

such waves are prominent in the data and

commonly have periods of from

days, consistent with the theory of

such waves. In comparison with these periods, the persistence time scales are

certainly not long.

While the bulk of planetary-wave anomalies are not “persistent” in

physically meaningful way, there is in fact some significant interannual

variability in “stationary” waves. Figure

from van Loon

aI.

(1973)

shows

1000

800

60’

40’

200

FIG.

Temperature

New York City

function

time

for

1982. (From

New

York

Times

January

1983.)