Saltzman B. (editor) Anomalous Atmospheric Flows and Blocking
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94
HEINZ-DIETER SCHILLING
a
FIG.
11.
(a)
BCL,-BTP+,
projection of
flux
space
distribution
of
all
blocking
points
1967-
1976
with
NLLS,,,
S
0.37;
subscript
rn
stands
for the dominant wavegroup
of
the
case.
(b)
Same
as
(a), except for
blocking
points
with
NLLS,
>
0.37.
(Units
in
percentage.)
are unaffected by changing details of our procedure. The clusters, however,
are not
so
pronounced that the boundaries between types can
be
considered
as
very well defined.
7.
CONCLUSIONS
Our goal has been
to
characterize blocking
cases
by a small number
of
circumpolar energetic indices. We have found that
as
a first step, five or six
numbers would
be
sufficient. These are a blocking number, characterizing
the longitudinal extent ofthe influence ofblocked zones, thedominant zonal
wavenumber(s), and three or four circumpolar averaged energy fluxes re-
lated to the dominant wavegroup. It
was
found
also
that the baroclinic
instability of the ultralong waves plays an important role in the energy
budget of the blocking waves. The explanation of this fact by current linear
baroclinic instability theories is only possible if some steady forcing is con-
sidered to provide for a standing wave response
as
part of the mean flow. It
has been demonstrated that initial perturbation amplitudes needed for ob-
served rapid amplifications are
no
less than the upper bound
of
values
compatible with the linear assumption. That nonlinear barociinic instability
prevails is demonstrated by the observed cooperation with nonlinear wave
-
wave interaction
as
well.
There are many cases with dominant energy inputs from barotropic inter-
actions accompanied by
a
below-normal baroclinic activity. Therefore, it
ON ATMOSPHERIC BLOCKING
TYPES
AND NUMBERS
95
seems that barotropic models can give considerable information on the
formation of certain kinds of blocks. However, models which crucially de-
pend on large mountain torques should be used with caution for explaining
blocking activity. There is no counterpart for this mechanism in blocking
energetics as long as the blocked latitude belt is considered. Nevertheless,
strong signals from the orographic terms can be extracted out of model data
(Fischer,
1985)
as well as from observational data (Metz,
1985)
taken from
south of the blocked zone, although they can not serve
as
direct input to the
blocking waves.
Local blocking numbers have been defined previously in the literature
(Elliott and Smith,
1949;
Namias,
1964),
but
Bl
and
B12-4
are the first
circumpolar ones. They perform well in many cases and serve as measure of
the circumpolar character of the blocked regime.
Bl,
and even more
so
B12-4,
respond most to the amplifying wavegroup
m
=
2-4,
a characteristic they
have in common with the amplitude index
[Z,-,]
of
A.
Hansen (this vol-
ume).
In general,
m
=
2-4
is the dominant wavegroup (about
50%).
However,
m
=
1
or
m
=
5
-
8
cases are not seldom. On the other hand about
75%
ofthe
m
=
5
-
8
cases are characterized by
Bl
<
1.32,
whereas such small
B1
num-
bers occur in
52%
of the
m
=
1
cases and
33%
of the
m
=
2
-4
cases. Accord-
ingly the dominant wavenumber(s) may indicate the circumpolar extent of
blocking activity, but it is not quite reliable in doing that.
This
is
so
because
dominance of one wavegroup does not necessarily imply the unimportance
of the other ones. The
Bl
number is not redundant in giving the desired
information.
Last but not least we tried to classify blocking cases by means of energy
inputs. We found a tendency toward clustering in flux space which is based
on cooperation patterns. Many of these types can be related to an observa-
tion or model result
as
reported in the literature. However, the structure of
blocking energetics is too complex to give sharp boundaries between types.
On the other hand, the energetics of blocks is not dispensable in the study
of
events, since in many cases the energy inputs are much larger than normal.
Even ensemble and time averages could show relative abnormal values and
therefore strong signals.
It is hoped that this study will help to initiate the discussion on appropriate
classification criteria for blocking events.
A
broad agreement on this issue
will certainly be the basis for better structuring further studies on blocking
dynamics.
ACKNOWLEDGMENTS
I
would like
to
thank
Dr.
A.
R.
Hansen for
his
helpful comments
on
the text.
This
work
was
partly
supported
by the Fraunhofer Gesellschafl, Miinchen, Federal Republic
of
Germany.
96
HEINZ-DIETER SCHILLING
a
JK
Y)lm
APPENDIX
A
Latitude, longitude
Zonal-mean
x-x
X'
restricted
to
zonal
wave
m(or
a wave group
speciiied
in
the text)
Zonal and meridional components
of
the geostrophic wind,
w
=
dp/df
v'
at 1000-mbar level
X
at lower boundary
&potential
Average over the latitude band
pIS~B(pz
and troposphec depth
loo0
mbar
2
p
z
300
mbar
-
cfm1
Ap~(~,,cospkX(k,pj))/
(XL,
cos
pk
);
J
=
2
for
a,
BCL,
BQ
J=
3
for
BTP,
NLLS, NLLL,
K,,
A,,
BOUND
Time average over
10
years
for
each
month
separately
Time average
Amplitude
of
an eigenmode
of
the
discrete
Laplacian
V2=
modes
are
vectors
Y
related
to
an
equidistant
grid and
obeying
vzY,
=
-
K~Y,;
V2,
matrix
of
entries
V2.
The
dar
ii
is
given
on
the same
gridpoints(Q,k"pl+~dQ,K,,withk=O,.
.
.
,K;A~,=5'andp,=
lO0N,p~==90"N)by[E(p1),
. . .
,E(pK)JT=XB
E,Y,.TocomputeY,,
it
was assumed
a,Y,
=
0
for
pl,
pK
with
a,
as
a discrete
Q,
derivation
cos
p-l[(ax/aAxaY/*)
-
(a~/a~xax/*)]l,,,
=
projection
of
J
on
to
cos
B-
laQ,cc"
~,)ip-&,
wkng
cos
p-
wwm
pww).
Eigen-
Radius
of
earth
wave
m
w2>
-
(x)')
((XY)
-
(X>(
Y>!/((X'>
-
(Q2I1W
Y2)
-
(
y)2)1'2
Latitude
c-
'c
for
blocked
zone,
pC
=
60',
say
Coriolis
parameterfat
pc
Density,
pressure, temperature
T(
Prooo/P)R/~
lo00
mbar
a-laJ*
Eartb
gravity
constant
Kinetic energy
of
wave
m
[see
&.
(S)]
%-1KIR
w/m;::
+[(&i/t3p)%lp2]:$-:f;
Ap
=
200
or
500
mbar
ON
ATMOSPHERIC
BLOCKING
TYPES AND
NUMBERS
97
APPENDIX
B
The mountain-induced energy flux stems from the vertical averaging
of
the baroclinic term in the kinetic eddy energy equation
-
[foV/’dW’/dPI
=
-
[fo(~/aP)(V’o’)l+ [foo’dv’/dPl
h-r
The last term denotes the transformation
BCL,.
With
w’
=
0
at the upper
boundary, the second term is transformed into
-
[h(a/dPxv’o’),7
=
(fo/g)wfiG*
(average over
1,p)
with
pfi
=
q’(p
=_p~);
6
=
o’(p
=
p~).
Let
o,
=
-PBgJ(v, h)with
orogra-
phy
h(L,
p),
and
h
=
0.
A
linear approximation of the boundary condition gives
-
[fo(d/dPxv’w’)l~
-fo[&CB(!&i/a
c0.9
qxah’/d2)1,7
(B1)
Since we can establish a quadratic interpolation formula for
&p)
and three
levels, we can do
this
for
~(p)
too:
(with
wj
=
~(p
=
pj);9nx,
=
200
mbar, etc). Using
Eq.
(B2)
we are able
to compute
pB
=
-
(&#+3p)g1,
Ug
,
vfi
for
p
=
p~.
The linearized hydrostatic
relation gives (with
5
=
0)
-
pf,
=
-ghh’
We have therefore
and for the zonal mean
y~fi(dh‘/iM)~
=
w;m(ah/dL)A
=
~’,~(dh/dA)
(B5)
after Eqs.
(B4)
and
(B3).
Using this relation and computing
ZB,
&
after
Q.
(B2)
for
p
=
p~
gives the mountain-induced flux,Eq.
(1 1).
98
HEINZDIETER SCHILLING
APPENDIX
C
ATLANTlC/EUROPEAN BLOCKINGS
Period Dominant Overlapping with
(from-to)”
Fig.
1
(51)
wavegroup Pacific
block?
Type
12.09. -21.09.67
Y~s
18.11-22.11.67
03.04. -08.04.68
03.08.- 12.08.68
15.01.
-2 1.01.69
06.02. -04.03.69
20.05.-29.05.69
Yes
22.09.-26.09.69
25.12.-05.01.69
13.01 .-3 1.01.70
2 1.02.-27.02.70
09.09.- 16.09.70
22.12.-3 1.12.70
1
1.01.
-
15.01.7
1
24.04,-28.04.71
25.01. -07.02.72
19.02.-07.03.72
Yes
05.01
.-23.01.73
03.01.- 18.01.74
Yes
27.01. -09.02.75
14.09.
-
29.09.76
12.10. -29.10.76
12.12.-31.12.76
2.15
2.1
1
2.09
2.74
2.43
2. I6
1.24
2.08
2.37
2.15
I
.87
2.0
I
3.0
1
2.9
I
2.74
4.03
2.22
4.57
3.03
1.32
2.46
1.10
5.13
3.46
2.77
I
.73
2.24
1.41
2.13
2.32
2-4
2-4
2-4
2-4
1
5-8
1
2-4
1
I
2-4
2-4
2-4
1
1
2-4
5-8
2-4
2-4
2-4
2-4
2-4
2-4
2-4
2-4
2-4
2-4
1
2 -4
2
-4
PdY
Partly
PdY
Yes
Yes
Yes
Yes
Yes
BCL/BTP
+
BCL
BCL
NLLS
BTP
+
BCL/BTP
+
BCL
NLLS
NLLS/BCL
NLLSJBTP
+
None
None
NLLS
NLLS/BTP
+
BCL/BTP+
BCL/BTP+
None
NLLS
BCL/BTP
+
BTP
+
BCL/BTP
+
BTP
+
BCL/BTP+
None
None
NLLS
BTP
+
BTP
+
BTP
+
NLLS/BTP+
*
Periods
are
given
as
day, month, year; e.g.,
12.09. -2 1.09.67
is
12
September to
2
1
September
1967.
ON ATMOSPHERIC BLOCKING TYPES
AND
NUMBERS
99
PACIFIC
BLOC KINGS^
Period Dominant wave Overlapping with
(from-to)b
(Bl)
or wavegroup Atlantic blocking? Type
07.08.- 16.08.68 3.36 2-4
PdY
NLLS
19.01.-28.01.69 2.15
1
PdY
None
12.10.-17.10.69 2.24 2 -4
YeS BCL/BTP+
09.01.-16.01.71 3.14 2-4
Yes BCL/BTP
+
21.02.-29.02.72 3.1
1
2-4
Yes BTP
+
02.12.- 12.12.72 2.03 2-4
BCL
02.1 1.-09.11.73 2.52
1
BTP
+
28.12.-09.01.73 3.46 2-4
BCL/BTP
+
12.01.-19.01.74 2.77 2-4
Yes None
04.02.-09.02.75 3.07 2-4
Yes BTP
+
3.24 2-4
None
a
From Treidl
el
a/.,
198 1.
Periods aregiven asday, month, year; e.g.,
12.09.-21.09.67
is
12
September to
21
September
1967.
REFERENCES
Charney,
J.
G., and DeVore,
J.
G.
(
1979).
J.
Atmos.
Sci.
36, 1205
-
12 16.
Charney,
J.
G., Shukla,
J.,
and Mo,
K.
C.
(1981).
J.
Atrnos.
Sci.
38,762-779.
Chen, T.-C., and Shukla,
J.
(1983).
Mon.
Weather
Rev.
111,3-22.
Dickson, R. R.
(1967).
Mon.
Weather
Rev.
95, 143- 152.
Dickson, R.
R.
(1969).
Mon.
Weather
Rev.
97,830-834.
Egger,
J.
(1978).J.
Atmos.
Sci.
35, 1788-1801.
Elliott, R. D., and Smith, T. B.
(1949).
J.
Meteorol.
6,67-85.
Fischer, G.
(1984).
Contrib. Phys.
Atmos.
57, 183-200.
Fischer, G.
(1985).
Contrib. Phys. Atmos.
58,291
-303.
Green,
J.
S.
A.
(1970).
Q.
J.
R.
Meteorol.
SOC.
96, 157- 185.
Hansen,
A.
R., and Chen, T.-C.
(1982).
Mon.
Weather
Rev.
110,1146- 1165.
Legras,
B., and Ghil, M.
(1985).
J.
Atmos.
Sci.
42,433-471.
LejenAs,
H.
(1977).
Atmosphere-Ocean
15, 89- 113.
Metz,
W.
(1985).
J.
Atmos.
Sci.
42, 1880-1892.
Namias,
J.
(1964).
Tellus
16,394-407.
Reinhold, B. B., and Pierrehumbert, R. T.
(1982).
Mon.
Weather
Rev.
110, 1105- 1145.
Sasamori, T., and Youngblut, C. E.
(1981).
J.
Atmos. Sci.
38,87-96.
Schilling, H.-D.
(1981).
Dynamik und Energetik blockierender Wellen in der Atmosph&re.
Schilling,
H.-D.
(1982).
J.
Atmos.
Sci.
39,998- 1017.
Schilling, H.-D.
(1984).
Contrib. Phys. Atmos.
57,
150-
168.
Schilling, H.-D.
(1986).
Mon.
Weather
Rev.,
submitted.
Speth P., and Meyer, R.
(1984).
Contrib. Phys. Atmos.
57,463-476.
Stark,
L. P.
(1965).
Mon.
Weather
Rev.
93, 337-342.
Taubensee,
R.
E.
(1975).
Mon.
Weather
Rev.
103,562-566.
Thompson,
P.
D.
(1957).
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C.,
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19, 1-23.
Dissertation, Universiat Hamburg, FRG. Hamburger Geophys. Einzelschr.
50
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OBSERVATIONAL CHARACTERISTICS
OF
ATMOSPHERIC PLANETARY WAVES WITH
BIMODAL AMPLITUDE DISTRIBUTIONS
ANTHONY
R.
HANSEN
Meteoro/ogy Research
Center
Control Data
Corporation
Minneapolis, Minnesota 55420
1.
INTRODUCTION
Persistent, large-scale circulation anomalies and “blocking” have been
topics
of
great interest in recent years. The connection between quasi-sta-
tionary blocking ridges and stationary forcing due to the
earth’s
topography
and surface thermal contrasts, and the question of whether blocking is
a
regional or global phenomenon, are central issues in the investigation. It has
long been known that the long-term mean waves found in Northern Hemi-
sphere midlatitudes owe their existence
to
the zonally asymmetric distribu-
tion of the earth’s topography and land-sea thermal contrasts (Charney and
Eliassen,
1949;
Smagorinsky,
1953).
Recently, much interest has been gener-
ated by the work of Charney and DeVore
(1979)
and
Hart
(1979),
which
suggested for given forcing parameters, multiple stable steady states of the
zonal-mean wind and planetary wave amplitude were possible due to oro-
graphically induced instability in a simple barotropic model. Other work
illustrated similar possibilities in baroclinic models (e.g., Charney and
Strauss,
1980;
Pedlosky,
1981).
In these models, one stable steady state
corresponds to a relatively strong zonal flow while another corresponds to a
state with a weak zonal flow and
a
wave pattern reminiscent of blocking.
Bimodality in the probability density distribution
of
the zonal wind is pre-
dicted by these theories (e.g., Benzi
et
al.,
1984).
An extension of the Charney
-
DeVore idea to a barotropic model includ-
ing nonlinear wave
-
wave interaction by Benzi
et
al.
(1
986)
shows that the
presence of the wave- wave interaction causes the orographically forced
wave amplitude resonance in Charney and DeVore’s model to become a
“folded” resonance in which, for a given value of the zonal wind, more than
one stable planetary-scale wave amplitude is possible. This folding
of
the
resonance is due simply to the presence of the anharmonic terms in the
governing equations of the model. Sutera
(1986)
has shown that the proba-
bility density distribution of the amplitude
of
the planetary-scale wave
101
Copyright
0
1986 by
Academic
Ress,
Inc.
All
rights
of
repduction
in
my
form
reserved.
ADVANCES
IN
GEOPHYSICS,
VOLUME
29
102
ANTHONY
R.
HANSEN
packet formed by zonal harmonic wavenumbers
2-4
is bimodal. This
wavenumber band
was
chosen because it represents waves with wavelengths
near the resonant wavelength for the
earth’s
topography and observed values
of the zonal wind. Conversely, the zonal-mean wind exhibits a unimodal
distribution.
In the present observational study, we examine stationary wave structure
and mean spectral energy and enstrophy budgets to establish whether con-
sistent, systematic differences appear between these statistics computed for
the two modes. We wish to provide further confidence in the significance of
the observed planetary-wave bimodality based on physical consistency
rather than simply on statistical
tests.
An analysis ofthis kind cannot by itself
provide definitive explanation of the dynamics of these circulation regimes.
However, the information provided by this approach can indicate suitable
directions to pursue in formulating theoretical understanding of the dy-
namics of these important components of the general circulation.
Our results highlight a particular class of persistent quasi-stationary wave
phenomenon in which stationary baroclinic forcing plays an apparently
central role and for which the attendant wave pattern appears more nearly
hemispheric rather than regional in character. The synoptic patterns
asso-
ciated with the large-amplitude wave mode generally correspond to what
Rex
(1950)
termed “amplified waves.” We will contrast this pattern with
what appears to be another distinct blocking phenomenon for which the
wave pattern appears more regional and for which the stationary forcing
appears secondary compared to interactions between
this
pattern and tran-
sient cyclone-scale waves.
Our study differs
from
many previous studies of circulation anomalies
because we use a global measure of wave amplitude rather than the local
departure of the 500-mbar height from climatology. The studies of Dole and
Gordon
(
1983)
and Charney
ef
al.
(1 98 l),
for example, used local, gridpoint
departures of the 500-mbar height from climatology or the average departure
along meridians, whereas we use the global measure of planetary-wave am-
piitude. However, we should note that the two modes found in the wave
amplitude probability density estimation are not “anomalous” circulations.
Rather, they apparently were fundamental
aspects
of the general circulation
during the four winters considered.
Our analysis is
based
on
data
archived at the European Center for Medium
Range Weather Forecasts (ECMWF) from the winters of
1980/1981,
1981/1982, 1982/1983,
and
1983/1984,
where winter is defined by the pe-
riod
from
l
December
through
28
February. We
will
first consider the
frequency distribution of the planetary-wave amplitude in a manner similar
to that used by Sutera
(1
986).
Based
on the bimodal wave amplitude distri-
bution, we then examine the stationary wave structure and construct ensem-
ATMOSPHERIC PLANETARY WAVE CHARACTERISTICS
103
ble mean spectral energy and enstrophy budgets of the two wave modes to
illustrate the important physical processes occurring during each. Finally, we
consider another class of blocking phenomenon with quite different budget
characteristics from those in the large-amplitude wave mode.
2.
FREQUENCY
DISTRIBUTION
OF
THE
PLANETARY-WAVE
AMPLITUDE INDICATOR
First consider the frequency distribution of an indicator of the planetary-
wave amplitude. We will proceed in a manner very similar to that used by
Sutera
(1986).
The data used to construct the histograms and probability
density estimates are daily 500-mbar geopotential heights compiled at
ECMWF on a
5.625"
latitude-longitude grid from
1
March
1980
through
31
May
1984.
For each day, we compute a wave amplitude indicator by
averaging the gridpoint 500-mbar heights,
z(A,+)
with respect to latitude,
4,
from
22.5"N,
to
78.5"N,
and Fourier decompose the result in the zonal
direction. Then, we compute the wave amplitude indicator for the planetary
waves synthesized from wavenumbers
2
-
4
as follows:
To
be precise,
[Z,-,]
is the square root
of
the wave
2-4
height variance, not
the amplitude. The actual amplitude is given by multiplying [Z,-,] by
a.
In
this equation,
2,
denotes the Fourier coefficient for wave
rn.
The wave-
number band
m
=
2
-
4
is chosen because this range represents the topo-
graphically resonant wavelengths for the observed values of the zonal wind
based upon Rossby's two-dimensional formula, This procedure will select
planetary waves of broad latitudinal extent over those with more compli-
cated structure in the meridional direction.
The resulting time series is then filtered to remove high-frequency varia-
bility with periods
of
5
days and less, and low-frequency variability asso-
ciated with the seasonal cycle and interannual variability. It
is
especially
important to remove the interannual variability. This was done by perform-
ing a Fourier transform of the time series of [Z,-,], zeroing the unwanted
frequencies, and resynthesizing the filtered time series. Periods longer than
170
days were removed to eliminate the interannual variability as well as
annual through semiannual periods. The histogram in Fig.
1
was con-
structed from the winter data
of
the filtered
[Z,-,]
time series.
A
similar
procedure was used to obtain
a
histogram of the zonal-mean wind
[u,]
[see
Sutera
(1986)
for these results].