Saltzman B. (editor) Anomalous Atmospheric Flows and Blocking

74

HEINZ-DIETER

SCHILLING

I

VB6VBIn

mNB VB6VBI

II

IU

NB VBSVEI

II

mNQ

m2/s2

po

KZ

110

'3

4

90

To

10

14.4.

-

25.4.73

m2t.

I

KE

15.5. -23.5.73

1

,,,,,

I

VEIIIIUNB VE-5

VEX

I

IENB VBInIIINB

FIG.

I.

See

legend

on

p.

73.

mbar high with at least one closed contour (in a representation with 4-gpdm

increments) which

(b)

is persistent for at least

5

days, and (c) lies in the region

70"

W

5

15

70"E

and

50"

5

q

I

80".

Additionally (d) the high cell is em-

bedded in a split jet with branches of about equal masses. (e)

If

criteria (a -c)

are fulfilled at least for

5

consecutive days and there exists a further day,

fulfilling (a), (c), and (d) but separated from the other blocking days by a day

with arbitrary 500-mbar flow, this entire

period

is taken as

one

blocking case.

Out of this revised Atlantic/European blocking catalog selected cases are

ON

ATMOSPHERIC

BLOCKING

TYPES

AND

NUMBERS

75

3.1.- 15.1. 74

KE

KZ

26.8.-

1.9.74

I

VBI LmNB

VBI

IIIUNBNIM*

NONELOCKING

PERIODS

40

20

3.5. -11. 5. 73

LO

:."

3

8.12.-17. 12.73

i\"

::

K,

20

KT

1-5

I

IIIUUk5"

1-5

1

JfIUllk5'

FIG.

1.

See legend

on

p.

73.

given in Appendix

C.

The complete catalog is available from the author

upon request.

In this section we are interested in several stages of evolution:

VB,

the

5-day period before onset;

I,

11, and 111, which constitute three equal subdivi-

sions of the block; and

NB,

the 5-day period following the block. For

KE,

KT,

patterns as displayed in Fig.

1

are similar in almost every case, but for

K,

the

similarities are not as striking (see also Lejenas,

1977).

Therefore we exclude

the latter from further consideration.

We introduce parameters describing the observed jet-splitting tendency

and the dominance of larger scales in the zonal Fourier spectrum of pertur-

bations. This is done by kinetic energy weighted averages of the respective

wavenumbers of appropriate height field decompositions (e.g., zonal Fourier

components

m

with

rn

#

0

or order numbers

n

of normal modes of the

Laplacian

V2

on the sphere, having eigenvalues

xf

(see Appendix A).

M

rn=

1

m-

1

76

HEINZ-DIETER

SCHILLING

B,

=

n/K,

(2b)

The kinetic energy of zonal wavenumber

rn

is

denoted by

K,;

icn

and

U,,

are the wavenumber and amplitude of the meridional decomposition

of

U,

the zonal-mean

flow.

Other symbols are defined in Appendix

A

if not ex-

plained in the text. These parameters show reasonably good response to

blocking conditions. The tendency for jet splitting is chararacterized by

smaller than normal values of

B,

and the dominance of ultralong waves by

larger than normal values of

L,

.

This

can be seen for the

20

examples in Fig.

2

(averaged over the

20

cases).

The time evolution

of

the measure

of

static stability

L$,

=

dooo/fZ(qC);

0

=

[-

l/pXa

ln6/ap)]E:#

(3)

is shown also in Fig.

2.

It exhibits almost no variations during blocks and

seems to

be

quite unaffected by the transformation of

flow.

It cannot be expected that each of the components of the set

C

=

(KE,

KT,

L,,

B,)

will respond with constant reliability. Sometimes only a subset of Cis

well developed and the rest is masked.

5100'

64

.............

............

LCrlt (winter

)

_..'

.'-.

L,,it

(summer)

................

I

:.-:.,,,

,

1300

/

~,(summeri

L'

VB

I

II

E

N0

FIG.

2.

L,,

B,,

and

L,,

averaged over several

stages

of

Atlantic

blocking

(20

cases).

See

text

for

definitions.

Winter,

I

Oct

to

31

Maq

summer,

1

Apr

to

30

Sep.

ON

ATMOSPHERIC BLOCKING

TYPES

AND

NUMBERS

77

18-

1.7-

1.6-

1.5

1.4..

1.3-

1.2-

1.1..

1.0-

3.

BLOCKING

NUMBERS

It is quite attractive to form a single blocking number out of the foregoing

parameters. By doing

so,

it is hoped that weak development of one or two

parameters will be compensated by other strongly developing ones.

We decided

to

arrange the parameters in a such

way

as

to obtain the largest

values of the number during the mature stage of blocking. However, there

are different possibilities for the definition:

BII

=

KELi/(KTBz)

(4)

BI

=

K,Lf/(K,L&J

(5)

The latter was motivated

by

the fact that

B,

sometimes exhibits an erratic

behavior. Moreover, it seems that the above-mentioned set Cof characteris-

tics is redundant. This is because

B,

tends to decrease whenever

L,

increases,

as can

be

shown in simple models (e.g., barotropic ones conserving energy

and enstrophy). Figure

3 justifies Eq.

(5),

showing that this criterion per-

forms as well as

Eq.

(4)

on average. However,

B1

is smoother than

BI1

in single

cases.

In view

of

A.

Hansen's (see this volume) amplitude index

[Z2-J,

which is

restricted to zonal wavenumbers

m

=

2,3,

and

4,

a more selective version of

Bl

was tested

(6)

B12-4

=

B1

'

Kz-4/KE

Here,

K2-4

means the kinetic energy of zonal wavenumbers

rn

=

2,3,

and

4,

averaged over the same latitudinal belt as before

(52.5

"N

5

v,

5

82.5'

N).

E,

I

1

VB

I

JINe

VBI

11

DNB

FIG.

3.

Same

as

Fig.

2,

except for

BZ,

and

BZ

as

normalized

with the

value

of

period

VB.

78

HEINZ-DIETER

SCHILLING

2.66

2.34

BI

1.78

'6

7

TIME

'67 '72

TIME

'7

3

2.34

1.78

-

-w-rV

.

. . .

.

. .

.

. .

.

. . .

.

,

.

. .

.

. . .

.

...

....

..

...

....

..

. .

.

,

.

. .

.

...

....

..

....

_.

....

..

....

_.

..

....

.,

...

...,_

,.

....

._

. .

.

. .

. . .

.

. . . .

.

. .

. . . .

..

....,.

. .

.

. .

..

......

,.

.....

.

. .

. . .

. .

..

.....

I::

::::

:

,

. .

t

.

. .

~

-zz

!::

:"'

'

0-4

2.66

2.34

BI

1.78

'70

TIME

'71

'76

TIME

'7

6

FIG.

4.

BI

curves

for

selected periods during 1967

-

1976. Nonlinear ordinate scale.

Blocking

cases

are

indicated by dotted

areas.

Solid lines,

B12-4/(B12-,)m0n;

dashed lines,

Bl/(Bl)mon.

Values above 2.5

1

were cut

o&

I

20

FIG.

5.

Frequency distribution

ofB12-4/(B12-4)mon

being

averaged over one

blocking

period

except

for

periods

>

15

days. Such long

cases

were split into

two

halves, each one an entry. The

distribution

for

all Atlantic/European

as

well

as

Pacific

cases

during 1967- 1976 is indicated

by

dotted area. The distribution

for

nonblocking periods longer than

4

days

is

given (dashed lines),

with averaging analogous to block

cases.

ON

ATMOSPHERIC BLOCKING TYPES

AND

NUMBERS

79

To eliminate the seasonal variation of those numbers, they were normalized

by their long-term monthly means (BI)mon or (B12-4)mon, taken only over

nonblocking days. Some examples are given in Fig.

4

to show how the

normalized Bland

B12-4

behave during selected periods in 1967- 1976.

Blocking periods (dotted areas in Fig.

4)

are taken from the author's

catalog of Atlantic/European cases (see Appendix

C),

or in the case of Pacific

blocks from Treidl

et

al.

(

198 1) (some Pacific cases are also given in Appen-

dix

C).

The overall response of Bl to Atlantic/European cases is not signifi-

cantly different from that to Pacific cases (not shown).

Many events are marked by a well-developed Bl or

B12-4

number. Those

clearly have circumpolar characteristics strong enough to justify the use of

circumpolar energetics in their study. According to Fig. 5, about 30% of the

blocks show relatively small B12,4 averages, comparable to those recorded for

the majority (70%) of nonblochng periods. Those blocks definitely require a

local description.

Since strong development

of

BI generally coincides with strong develop-

ment of B12-4 (see Fig.

4)

we can expect that many of the well-developed

circumpolar cases are dominated by the zonal waves

m

=

2,3, and

4.

This

finding is confirmed by Fig. 6a and b. The 500-mbar stream field, consist-

ing of

m

=

1

-

5 (and defined on a regular grid), wascorrelated with blocking

numbers for a 2-yr period. In both (a) and (b) it can

be

seen first that

m=

2 is

dominating the response with relatively fixed phase, and second that

a

leao

FIG.

6. (a) Pointwise correlation

of

ty'

in

500

mbar (consisting

of

waves

m

=

1,

. .

,5)

with

BI/(BI),,,o,,

for

the period mid-1969 to mid-1971 (720 days). (b) Same

as

(a) except

for B12-4/

(B12-4)mon.

80

HEINZ-DIETER

SCHILLMG

FIG.

6b.

See

legend

on

p.

79.

“blocks” (given by peaking

BI

or

B12-4

curves) influence remote regions

(compare with dotted

95%

significance areas).

We are interested now in how the dynamics varies according to the block-

ing numbers. This question is answered in the next section. Also, what can

be

concluded from the increase

ofl,

during blocking events? At least in the case

of

relatively long-lived blockings the longer waves should have enhanced

baroclinic activity. This is necessary since the ever-present differential heat-

ing has

to

be

balanced by eddy heat fluxes in a long-term sense. Whenever the

“synoptic” wave regime’s baroclinic activity is reduced during strong block-

ing (this reduction is documented in Fig. 7d for

rn

=

5

-

8),

the longer waves

have to perform this

task,

at least partially.

4.

KINETIC

ENERGY

BUDGET

AND

BLOCKING

NUMBERS

We now examine the kinetic energy budget in the blocked latitude belt

using statistical methods. Our starting point is the quasi-geostrophic version

of

the vorticity equation with linear damping. The spectral kinetic energy

tendency consistent with this equation reads

-

dK,/dt

=

-

k,K,

+

BTP,

+

BCL,

+

ORO,

+

NLLS,

+

NLLL,

+

BOUND,

(7)

ON

ATMOSPHERIC

BLOCKING

TYPES

AND NUMBERS

81

A

B

_____

m

=

1

__

rn

=

2-4

.3

{

_._._

rn

=

5-8

.3

1

.3!

d

3-i

FIG.

7.

Time-lagged

correlations

of

BI2-,/(Bl2-,)-

with energy

fluxes

defined

in

the text.

Solid

lines,

m

=

2-4;

dashed

lines,

m

=

1;

dashdotted

lines,

m

=

5-8.

Arrows

indicate the

95%

significance

levels;

7

<

0,

BI

lags

the

fluxes;

7

>

0,

BI

leads

the

fluxes.

A, Summer

(1

Apr to

30

Sep);

B,

winter.

a,

NLW,

b,

NLLL;

c,

BTP;

d,

BCL,

e,

TOP.

-1

BTP,

=

-

82

HEINZ-DIETER SCHILLING

The term Eq.

(1

1)

is introduced by the vertical integration

of

the divergence

term in the vorticity equation and the lower boundary condition involving

orography

h.

In the derivation

of

this term the lower boundary condition for

the eddies was linearized (see Appendix B). The upper boundary condition

was simply

o

=

0.

Moreover, it

was

assumed that the zonal-mean flow at the

lower boundary can be computed geostrophically by an extrapolation for-

mula for

&q).

All terms, Eqs. (9)

-

(

14), are possible candidates for providing suitable

energy input during blocking episodes. Indeed, there have been many sug-

gestions for blocking mechanisms based on one or more types of energy

conversion; for example (a) barotropic instability BTP, (Thompson, 1957);

(b) baroclinic instability BCL, (Chen and Shukla, 1983; Hansen and Chen,

1982); (c) baroclinic instability BCL, plus nonlinear interaction

NLLL,

between longer waves (Schilling, 1982); (d) mountain torque induced con-

version

ORO,

(Egger, 1978; Charney and Devore, 1979); (e) nonlinear

interaction of longer with shorter scales NLLS, (Fischer, 1984; Hansen and

Chen, 1982).

A

first step in studying the relevance of those inputs to blocking dynamics

is to correlate the above-mentioned energy fluxes with blocking numbers.

To

this end we should remove the nonstationarity associated with the trivial

seasonal trend. Therefore fluxes and energies are normalized to give zero

mean and variance

1:

tjJ

is

thejth day of the Ith month continuously counted during the 10 years

1967- 1976;

(

),

is a

10

yr monthly mean related to the Ith month.

Figure 7a-

c

shows the seasonally stratified response of some of the energy

fluxes to variations of

B12-4

(and vice versa). Interestingly, we find a signifi-

ON

ATMOSPHERIC BLOCKING TYPES AND NUMBERS

83

cant signal for the nonlinear interactions with synoptic scales

NLLS2-,

and

the barotropic instability

BTP2-,

.

On the other hand, topographically induced energy input seems to have

nothing to do with the circumpolar type of blocking (Fig. 7e). The same is

true for

BOUND,

(not shown).

The most prominent result for seasonally stratified and time-la ed

BZ2-4

correlations (Fig.

7d)

is that with the flux

BCL,

,

a

substitute of

&,

,

given

bY

-

(a

as before). It was found that

BCL,

and

BCL,

are well correlated for

rn

2

2,

especially during episodes of large energies

K,

(Schilling,

1986).

Figure 7d shows the strong response of blocking numbers to the baroclinic

activity of ultralong waves. Here

r

<

0

means a leading flux. Above normal

baroclinic activity of

m

=

2

-4

results in above normal

BIZ-4

1

or

2

days later.

On the other hand above normal

results generally in below-normal

baroclinic fluxes

1

or

2

days later. The wave group

rn

=

5

-

8

tends to sup-

press baroclinic activity during episodes of large

BZ

(compare

with

A.

Hansen,

this

volume)!

We discuss now these results in more detail by scaling arguments related to

the baroclinic part

BCL.

If

A,

=

(1/2a)[(@/ap

-

@&I)’]

is the available potential energy

of

the

zonal flow we note that

(d/dt)A,

=

-

BCL,

+

other terms

m

We introduce some scale quantities

((

)

is a time average) for the zonal

stream and the eddies separately:

Zonal stream: for velocity

(KT)lIZ,

geopotential

(@/dp)p,,

-

foBc(KT)1/2,

resulting in

A,

-

B,Z(K,)/L&,

and length scale

B,.

Eddies of wave group

m:

for velocity

(Km)lD,

geopotential

4L-

f,Lc(K,)lIZ,

and length scale

L,.

Since the APE

of

the eddies

A,

is found to

be

of

the same order

as

K,,

we obtain for

(d&/ap)p,,

-

mf,L&p

We can estimate now the order of magnitude for

BCL,:

(K,)(KT)’lz

BCL,

-

r

L&t

Since longer waves are characterized by longer time scales,

To

=

(L&/

L,)(KE)-l’Z

is

a

characteristic time of the system. The magnitude of

BCL

Saltzman B. (editor) Anomalous Atmospheric Flows and Blocking

Подождите немного. Документ загружается.