Saltzman B. (editor) Anomalous Atmospheric Flows and Blocking

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104

ANTHONY

HANSEN

22-4

500

mbor

Ir'

-40

-20 0

Amplitude

(gpm)

FIG.

The

frequency

distribution

histogram of the amplitude of the wave packet formed

from

zonal

wavenumbers

-4,

[Z,-,].

See

text for details.

Alternatively, an area-averaged wave amplitude indicator was also calcu-

lated

follows:

where the latitudinal variation of the 500-mbar height is not averaged prior

to the Fourier analysis. Applying the same filtering discussed above results in

a time series that also yields a bimodal frequency distribution. Generally,

differences between the two methods

calculating the wave amplitude are

minor, but the area-average approach systematically places more days in the

large-amplitude mode than

does

the procedure outlined earlier. However,

the

particular method

computing the wave amplitude

does

not affect the

budget

results

to be presented in any substantial way. We will employ the

former method in what follows.

shown by Sutera (1986), the striking

aspect

of the histograms is the

bimodality in the

[Z2-,]

histogram. The zonal-mean wind exhibits a unimo-

dal distribution (Sutera, 1986). The obvious question of the statistical signifi-

cance of the minimum in the

[Z2-,]

histom

has been discussed in detail

by Sutera (1986). Nonparametric estimates

the probability density using

the maximum

penalized

likelihood method

(Good

and Gaskins,

1980),

based on

these

data

and using mesh spacings comparable to our bin widths,

yield probability density distributions that look quite similar to our histo-

grams. Probability density distributions of

[Z2-,]

for the individual winters

each exhibit similar bimodal characteristics.

bimodal probability density

estimation based on the sample histogram provides much greater statistical

confidence in the fit than does a Gaussian estimate of the distribution. These

ATMOSPHERIC PLANETARY WAVE CHARACTERISTICS

105

TABLE

FREQUENCY

VARIATION

[Z,J

Mode

day9

Mode

days

1980/ 198

47 (52%) 43 (48%)

1981/1982

(53%)

42 (47%)

1982/1983 48 (53%) 42 (47%)

1983/ 1984

(58%)

(42%)

Total

195

(54%)

165 (46%)

The number

days

from each winter belonging

each ensemble. The number

parentheses

the

percentage

days

each

year

the

total

the

years

belonging

each ensemble.

results are discussed in greater detail by Sutera. The main purpose of the

present study is to illustrate that by

stratifying

the data based upon the two

modes in the

[Z,-,]

probability distribution, we find consistent, systematic

differences in various diagnostic quantities. These results add confidence in

the physical significance of the bimodality and provide insight into the

dynamics involved.

Henceforth, days for which the value of

[Z,-,]

is less than the minimum in

Fig.

will be referred to

Mode

days, and those for which

[Z2-4]

greater

than the minimum will be called Mode

days. We get

195

Mode

days (54%

of the total) and 165 Mode

days (46% of the total). The breakdown for the

individual years is given in Table

The average duration of both Mode

and

Mode

events is roughly

days, with transitions between modes taking 4

days on the average. Individual events persist anywhere from a few days to

over

weeks.

WAVE STRUCTURE

THE

Two MODES

The large-scale structure of the wave pattern for the two modes is illus-

trated by constructing maps of the mean 500-mbar heights for each mode

(Fig. 2a and b). The mean 500-mbar height for Mode

has a very zonal

appearance, while the Mode

pattern exhibits a prominent ridge over the

eastern Pacific and deep troughs over the western Pacific and eastern North

America. The climatological mean stationary 500-mbar pattern is a

weighted average of the patterns associated

with

the two modes and depends

upon the asymmetry in the statistics of the

two

modes.

By synthesizing the 500-mbar pattern represented by zonal wavenumbers

2-4, denoted

Z2-4

(Fig.

and b),

clearer picture

presented of the

differences between the two modes. Comparing the resulting 500-mbar

106

ANTHONY

HANSEN

FIG.

Average heights of the

500-mbar

surface

in meters for

(a)

all

Mode

days

from the

four

winters

and

(b)

all

Mode

days.

The

contour

interval is

ATMOSPHERIC PLANETARY WAVE CHARACTERISTICS

107

FIG.

Mean 500-mbar heights synthesized from zonal wavenumbers

2-4,

22-4,

for

(a)

Mode

(b)

Mode

and (c)

AZ,-,,

the difference between the Mode

and

Mode

Zz-4

maps.

The contour interval is 50 m.

108

ANTHONY

HANSEN

FIG.

3c.

See

legend

107.

height fields indicates that for Mode

the western Pacific trough, the eastern

Pacific ridge, and the Hudson Bay trough

sharply amplified compared to

their Mode

counterparts. The difference between these two fields (Fig. 3c)

highlights the major differences in 500-mbar heights that extend eastward

from eastern Asia to the east coast of North America. The difference in the

total height field between the

two

modes is represented largely by the differ-

ences in wavenumbem 2-4 (not shown).

Inspection

of maps of the difference in

Z2-.,

for the two modes (Mode

minus Mode

for each of

the

individual years shows that the differences

between the modes extend farther downstream in the form of a ridge over the

Atlantic Ocean or Europe. This feature is not prominent in the 4-yr mean

field, however, because the phase of

this

ridge, relative to the surface of the

earth

is variable from

year

to year. For example, in 1980/ 198

(Fig. 4a) the

Mode2Atlanticridgeaxisisalong2O0W,

whilein 1981/1982(Fig. 4b)it is

along

1O"E.

These two winters exhibit gridpoint differences in

Z2-4

500

mbar

over

100

m for the eastern Pacific ridge, the western Pacific trough,

and the

North American trough. The 198211983 winter (Fig. 4c) exhibited

lower amplitude planetary waves and thus smaller differences in the synthe-

sized 5Wmbar heights,

Z2-4,

between the two modes. The overall pattern in

1982/1983

was

similar

to the other years except the western Pacific

low

did

ATMOSPHERIC PLANETARY WAVE CHARACTERISTICS

109

FIG.

4. The difference between the Mode 2 and Mode

maps

Z2-,

for

each

the

individual winters:

(a)

1980/1981,

(b)

1981/1982,

(c)

1982/1983, and (d) 1983/1984.

110

ANTHONY

HANSEN

FIG.

and

See

legend

109.

ATMOSPHERIC PLANETARY

WAVE

CHARACTERISTICS

111

not experience the same deepening for Mode 2 that it did in the other years.

The generally lower amplitude of the midlatitude quasi-stationary waves

during this winter may have been connected with the El Nifio event in

progress at the time. In 1983/1984, the western Pacific low and the eastern

Pacific ridge experienced sharp amplification for Mode 2 (greater than

100

m) with a lesser deepening of the North American low (Fig. 4d). Height

increases for Mode 2 also existed along 40”E, but these are not

well defined

as the analogous feature in the other 3 years. These results give a general

impression of the interannual variability in the wave patterns associated with

the bimodality. It is also evident that the differences between the two modes

extend over

large portion of the Northern Hemisphere midlatitudes.

superposing the wavenumber

field on top ofthe

Z2-4

patterns (Fig. 5a

and b), the overall mean planetary-wave fields for each mode are illustrated.

Since the amplitude and phase of wavenumber

is nearly identical in each

case, the greatest contrast in patterns lies over western North America and

the eastern Pacific, with the pattern elsewhere being similar in phase for the

two modes but of greater amplitude for Mode 2.

To see the temporal variation of the 500-mbar pattern for the wave-

number 2-4 ensemble as it intermittently switches between Mode

and

Mode 2 behavior, consider the longitude- time section of the synthesized

ZZe4

height field averaged between 20” and 80”N for 1981/1982 as an

example (Fig.

6).

The time periods designated as belonging to Mode

are

indicated by the brackets on the right-hand side of the figure. Note that for

the three major Mode 2 events during this winter,

fairly consistent pattern

characterized by a western Pacific trough, eastern Pacific ridge, eastern

North American trough, and Atlantic- European ridge is present.

Synoptically, the Mode 2 events manifest themselves as what Rex

(

1950)

would call “amplified wave” patterns. Rex drew a distinction between this

type of pattern and what is now called “Rex blocking,” in which a split

westerly jet, with an easterly flow between and the familiar high-low doublet

pattern, exists. The Mode 2 events in general do

not

include Rex-type block-

ing events. Inspection of daily synoptic charts indicates that Mode 2 episodes

can be identified quite well without knowledge of the wave amplitude indi-

cator by searching for patterns characterized by hemispheric-scale amplified

waves. On the other hand, regionally isolated Rex-type blocking patterns are

uniformly

not

included in the Mode 2 category. These events have quite

different characteristics than do the Mode

events. This aspect will be

discussed further in Section 5.

The overall impression is lefl that rapid transitions are occurring between

large and small wave amplitudes for fixed-phase waves. Next consider the

mean spectral energy and enstrophy budgets of the two modes to determine

112

ANTHONY

HANSEN

FIG.

Mean

500-mbar

heights

synthesized

from

zonal

wavenumbers

1-4,

Z,-,,

for

(a)

Mode

and

(b)

Mode

ATMOSPHERIC PLANETARY WAVE CHARACTERISTICS

113

20-80'11 1981-82

22-4

I I

9Q"E

100

90%

90'E

Long

ude

FIG.

The longitude-time section of

Z2-,

averaged between

20"N

and

80"N

for

1981/1982.

The brackets along the right-hand side

the

figure

indicate the time periods

belonging to Mode

The contour interval

The zero contour has been removed for

clarity.

what processes supply energy and enstrophy toward the maintenance

the

large-amplitude waves.

ENERGETICS

AND

ENSTROPHY

BUDGETS

FOR

THE

Two

MODES

Data

Before proceeding with the analysis, let us briefly discuss the data sets

being employed. The data used in this study are the initialized fields

for

the

operational model of the European Center for Medium Range Weather

Forecasts. We obtained the data for the horizontal wind, vertical velocity,

geopotential height, and temperature at 10 levels in the troposphere (1000,

850,700,500,400,300,250,200,150, and 100 mbar) interpolated to a 2.5

2.5"

latitude-longitude

grid.

The fields for 0000

GMT

December

through 28 February of the years 1980/1981, 1981/1982, 1982/1983, and