Saltzman B. (editor) Anomalous Atmospheric Flows and Blocking
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A
CASE
STUDY
OF
EDDY
FORCING DURING
AN
ATLANTIC BLOCKING EPISODE
G.
J.
SHUTTS
Meleorological
Ofice
Bracknell, Berkshire
RG12
2SZ
England
1.
INTRODUCTION
Observed blocking flow patterns are not steady in time and fluctuate with
the passage of baroclinic wave systems causing a weakening, then reintensi-
fication, of blocking anticyclones (Palmin and Newton,
1969).
This replace-
ment/displacement phenomenon has
also
been noted in Southern Hemi-
sphere blocking (Wright,
1974).
As well as amplitude changes, blocking patterns frequently exhibit an
overall zonal translation during their lifetime
-
typically toward the west
though not exclusively. This complicates the problem of splitting fields into
mean and eddy components and is only partially alleviated by time filtering,
which is used to isolate the effect of cyclone waves.
Green
(1 977)
put forward the hypothesis that the shape and orientation of
cyclone waves in the drought summer of
1976
(over western Europe) led to
mean anticyclone vorticity forcing which could, with subsidence, maintain
high pressure at the surface against friction. Austin
(1
980)
describeda simple
quasi-geostrophic model with prescribed vorticity forcing which could ex-
plain the warmth and equivalent barotropic structure of blocking anticy-
clones in the troposphere if the forcing increased sharply with height.
Illari
(1
982, 1984)
calculated the vorticity and quasi-geostrophic potential
vorticity budget over Western Europe and the eastern Atlantic during July
1976
using National Meteorological Center (NMC) analyses and found
eddy forcing terms large (in the sense that the implied spin-up time is much
less than the duration of the block) and spatially organized
so
as to support
the block. Savijarvi
(1
977)
found no coherent pattern of eddy vorticity flux
divergence in his study of a blocking episode. He used height field data
to
calculate geostrophic vorticity and velocity
so
that the eddy vorticity flux
divergence involves many numerical differentiations and is likely to have
large errors.
Hansen and Chen
(1982)
camed out a case study of the energy conver-
sions and transfer between cyclone-scale and ultralong waves in a blocking
135
ADVANCES
IN
GEOPHYSICS, VOLUME
29
0
British
Crown
Copyright
1986
136
G.
J.
SHUTTS
situation. They found strong transfer of energy from baroclinic, cyclone-
scale waves to barotropic, ultralong wave scales
of
motion, particularly in
cases
of Atlantic blocking. The initiation of
a
blocking episode by intense
cyclogenesis was thought to represent such an energy transfer process.
Hansen and Sutera
(1984)
compared the spectral transfer
of
energy and
enstrophy during blocking and nonblocking periods and found a striking
difference in the enstrophy transfer. Ultralong waves (wavenumbers
1
-3)
were normally found to lose enstrophy to smaller scales. In blocking epi-
sodes,
however, enstrophy was transferred upscale to the ultralong waves in
conjunction with a greater rate of expulsion of enstrophy from interme-
diate-scale waves. Their picture of anomalous energy and enstrophy cascade
is consistent with the eddy straining hypothesis outlined in the following
section.
Mahlman
(1980)
studied the evolution of blocks in a general circulation
model and noted the important part played by eddies in their maintenance.
Air of low potential vorticity was observed to flow northward from the
tropics and to
be
deposited on the western flank
of
the blocking anticyclone.
The barotropic experiments
of
Shutts
(
1983)
strongly support this Lagran-
gian picture and show it to be associated with the east
-
west scale compres-
sion of the eddy field immediately
upstream
ofthe block. It
was
hypothesized
that this scale collapse or enhanced enstrophy cascade provides a mean
anticyclonic/cyclonic dipole forcing pattern which strengthens the existing
dipole circulation. Essential to the process is an irreversible folding and
diffusion of potential vorticity contours paralleling the wave breaking mech-
anism discussed by McIntyre and Palmer
(1983)
in connection with sudden
stratospheric warming.
The aim of this article is to verif) the preceding conceptual model of the
interaction of eddies with blocking flow patterns.
2.
THE
EDDY
STRAINING MECHANISM
A
brief review of the energy and potential vorticity arguments which form
the basis of the eddy straining hypothesis
will
be
presented here.
It was suggested that traveling cyclone-scale eddies approaching a split-
jetstream flow pattern suffer a greater rate of deformation than when in a
more typical (less diffluent) flow field and that this provides an enhanced
energy cascade (Kraichnan,
1967;
Rhines,
1979)
to larger scales (i.e., the
block flow field).
Synoptically, depressions become narrow, slow-moving cold frontal
troughs
with meridional orientation. This ensures deep excursions of air
between low and high latitudes and results in strong heat and vorticity
A CASE
STUDY
OF
EDDY
FORCING
137
transport. Subsequently the trough may split into two smaller scale systems
which travel separately around the block in the northern and southern jet-
stream branches.
From a potential vorticity viewpoint, the east
-
west scale compression
corresponds to
an
irreversible cascade of potential entrophy to smaller scales
and ultimately dissipation. Following Holland and Rhines (1980), the equa-
tion for eddy potential enstrophy
is
obtained by multiplying the equation for
conservation ofpotential vorticity
(4)
by the deviation (4’) from a time mean
(4)
and averaging in time giving:
(alathp
+
q‘v‘
vij
+
V
-
v+p
+
V’
v~q‘z
=
~‘q‘
(-)
=
time mean
(1)
where
q
may represent the quasi-geostrophic potential vorticity on an iso-
baric surface or the Ertel potential vorticity on
an
isentropic surface, V is the
nondivergent wind on the appropriate surface, and
F’
is a forcing term due
to irreversible physical processes.
Following Marshall and Shutts
(1
98
I),
if the mean potential
vorticity
is
approximately conserved along the mean streamfunction contours or
4
=
?(@),
where
v/
is the streamfunction and V
=
k
A
Vy
where
k
is the unit
vector pointing vertically upward, then it can be shown that Eq.
(1)
simplifies
to
(2)
-
-
3(d/t.3t)qT
+
(q’V’)*
-
Vq
+
4V’
-
Vq”
=
F’q‘
where
-
-
Note that Div(q’V’).
=
Div(q’V’).
The tendency term in Eq.
(2)
may be neglected for a sufficiently long
averaging period and the triple correlation term will be assumed small. These
assumptions are all formally valid in the linear experiments described in
Shutts
(
1983). Equation
(2)
is then simply
-
--
(q’v’).
*
Vq
=
F‘q‘
(3)
and the so-called residual potential vorticity flux (q’v’). is downgradient if
F’
is dissipative. Illari and Marshall (1983) have used this technique of
subtracting out a rotational component to the vector
q
flux in an analysis of
the 1976 European block. The enhanced enstrophy
-
cascade upstream
of
the
block promotes strong downgradient (q’v’)., which in turn implies a
north- south dipole
of
eddy
q
flux divergence in a sense such
as
to reinforce
the anomalous potential vorticity field.
-
138
G.
J.
SHUTTS
From the Lagrangian viewpoint this is manifest as narrow tongues of high
or low
q
moving southward or northward, respectively, in association with
meridionally oriented eddies.
When the meridional wavelength is long, the time spent by a parcel of air
in any phase of the eddy is inversely proportional to its zonal wavelength
according to the classical Rossby formula. Consequently, large meridional
excursions with respect to the mean flow are possible just upstream of the
block where the deformation rate of the velocity field is greatest.
Enhanced enstrophy cascade at cyclone scales and the support ofthe mean
vorticity field by eddy vorticity transport are consistent with the observed
spectral transfer of enstrophy during blocking episodes found by Hansen and
Sutera (1984). This process
was
investigated in Shutts (1983) by integrating
linear and nonlinear barotropic models in P-plane channel geometry with a
wavemaker to provide a source of eddies. In the linear experiments eddies
were forced
in
a basic state flow field which contained a split jetstream. The
resulting long-term eddy vorticity fluxes, their divergence, and the second-
order correction to the flow induced by the eddy vorticity
flux
divergence
were
all
calculated. Anticyclonic forcing was found on the western side ofthe
blocking high and extending around the northern side
of
the block in the jet
flow. The second-order induced flow clearly showed that the eddies tend to
reinforce the basic state block pattern.
The nonlinear barotropic vorticity equation was integrated with a similar
wavemaker from an initial state of uniform westerly flow. The evolution of
the flow tended toward a statistically steady state due to the inclusion of an
Ekman friction term. For sufficiently weak initial uniform flow, perpetual
blocking ensued downstream of the wavemaker
(Fig.
1).
Blocking was due
entirely to the eddy vorticity
flux
divergence pattern associated
with
the
wavemaker-forced eddies since no other time-rnean forcing terms exist in
the nonlinear barotropic vorticity equations integrated (e.g., orographic
terms). Residual vorticity fluxes
(q‘v’).
are large and down the absolute
BASIC
STATE
HEIGHT FIELD
FIG.
I.
Mean streamfunction
field
with
residual eddy vorticity
flux
vectors;
[Figure
6c
of
Shutts
(1983)].
A CASE STUDY
OF
EDDY FORCING
139
;
______,_......
.-.
._....._.__..
-
FIG.
2.
Time-mean eddy vorticity
flux
divergence. Contour interval:
5
X
lo-"
seP.
[Fig-
ure 6d
of
Shutts
(1983).]
vorticity gradient at the point ofjet splitting,
as
hypothesized. The accompa-
nying eddy vorticity flux divergence field has a strong meridional dipole on
the western side of the block in the sense required to strengthen the blocking
pattern (Fig.
2).
A
trajectory analysis revealed that low absolute vorticity air was being
intermittently swept northward ahead of approaching troughs and into the
center of the mean anticyclone. The circulation comprising the southern
part of the blocking pattern was maintained in
a
similar way by the injection
of high vorticity from the north. Confirmation that these eddy vorticity
transfer processes occur in reality was sought from similar diagnostic analy-
ses of real data.
3.
DATA
MANIPULATION
AND
THE
SYNOPTIC SITUATION
Diagnostic quantities were calculated from global initialized analyses
from the European Centre for Medium Range Weather Forecasts- for the
period 5
-
22
February 1983 inclusive available
at
6-hr intervals- the period
of the forecast -analysis cycle. [For details of the data assimilation scheme
see Lorenc (198
1)
and Lonnberg and Shaw (1983).] Analyzed data are stored
as packed spherical harmonic coefficients with triangular truncation
T80
(i.e., all harmonics of order
80
and less). For the purpose of this case study the
fields are extracted on a 1.875
'
latitude-longitude grid and available at
1000,
850,700,
500,400,
300,250,200,
150, 100,70,50, and
30
mbar.
Vorticity is obtainable directly from the archive
so
that no loss of informa-
tion need result through the use of finite difference expressions for the curl of
the vector wind field. However, the isentropic vorticity required for the
calculation ofErtel potential vorticity is derived by the latter method. Unlike
other studies which use twice-daily datasets (e.g., Savijh, 1977; Illari,
1984), here we sample four times daily. Although most upper air data is
reported at
OOZ
and
122,
much of the small-scale information in an analysis
140
G.
J.
SHUTTS
comes from the 6-hr forecast (first guess field) and it seemed worthwhile to
include the
062
and
182
analyses, particularly in view of the high-frequency
contributions made to the vorticity flux by frontal systems.
Time filtering is used to emphasize the contribution made by traveling
weather systems with time periods of 6 days or less. To this end, a high-pass
filtered flux
(s”Xn,
is
defined such that
1
N-6
-
(S’
V’xip
=
-
c
s;v:
N-
12
i-7
where
Si
denotes the ith 6-hr values of some physical quantity
S
out of a
sequence of
N
analysis values. Although this filter exhibits some undesirable
features such
as
oscillation of the root-mean-square frequency response
about unity, it does attenuate low frequencies effectively (e.g., the root-
mean-square response at periods of 6
days
is
~0.4).
This is particularly
desirable for a short time series of
data
known to be dominated by low-fre-
quency fluctuations (Blackmon
et
al.,
1977).
Spatial smoothing is sometimes desirable since many of the fields of inter-
est have pronounced small-scale structure. The eddy vorticity flux diver-
gence is such a field for which smoothing helps to bring out its contribution
to forcing large-scale circulation anomalies.
A
smoothing scheme similar
to
those suggested by Sardeshmukh and Hoskins (1984) is used. Global field
values are decomposed into
a
sum of orthogonal spherical harmonics with
triangular truncation T80. Coefficients in the expansion with
n
>
n,
,
are
multiplied by exp{-
[(n
-
nl)/(n2
-
n,)Iz)
where
n
is the degree ofthe asso-
ciated Legendre function and
n,
and
n2
are constants taken here to be
20
and
25,
respectively. Sardeshmukh and Hoskins show that such a class
of
filters,
which depend only
on
the total wavenumber
of
each mode through
n,
are
equivalent to an isotropic spatial filter in the spherical domain. It is tacitly
assumed that isotropic smoothing of
a
two-dimensional field is the most
appropriate one for the problem at hand.
The blocking episode began with the building
of
a mid-Atlantic ridge
(30”
W)
on
5
February and
a
sympathetic cyclonic development between
Norway and Scotland.
As
the ridge extended northward to Iceland
on
6
February, the cold trough likewise extended southward into Holland, reach-
ing Italy by 7 February accompanied by an upper cold cut-off vortex. Further
cyclonic activity between Greenland and Norway on 9 and
10
February led
to the establishment ofa strong northerly airstream over the British Isles with
a strong (1042mbar) surface anticyclone at
55
ON
25
W.
A
vigorous depres-
A
CASE
STUDY
OF
EDDY
FORCING
141
sion, which began forming
off
the eastern seaboard ofthe United States on
12
February, had developed to
987
mbar off Newfoundland by
122,13
Febru-
ary.
As
the storm reached its maximum intensity
(975
mbar) south of
Greenland by
122, 14
February,
a
meridional elongation of the associated
upper trough began. Simultaneously, the sea level pressure of the blocking
anticyclone between Scotland and Southern Norway began to rise
(1023
mbar at
122, 13
February to
1030
mbar
24
hr later). By
122,
15
February, the depression
was
centered near southern Greenland with
a
cen-
tral pressure
of
992
mbar and with a trough extending to a separate low
center near
40"
N
30"
W
(see Fig.
7).
At
that time the blocking anticyclone
was centered north
of
Scotland with
a
central pressure of
1037
mbar but
40"
30"
20"N
FIG.
3.
High-pass
Mtered
E
vectors
superimposed
on
the
mean
streamfunction
field
(cen-
tered
at
30"
W).
142
G.
J.
SHUTTS
continued to rise to
1043
mbar by
17
February.
A
further depression devel-
oped
off
the eastern seaboard of the United States on
16
February and
became slow moving in the central Atlantic. The situation remained rather
static until
22
February, by which time the surface anticyclone had moved
into central Europe and cyclonic activity dominated the North Atlantic.
The time-mean block appears as strong mid-Atlantic ridge tilting north-
eastward with a trough extending southward into Europe and thence west-
ward to Iberia.
A
weak broad trough also exists to the south of the main
ridge at
30"
W,
forming the weaker cyclonic component of the block dipole
(Fig.
3).
4.
E
VECTORS
AND
THE
SENSE
OF
MOMENTUM FORCING
The usual concept of eddy momentum forcing as the tensor divergence of
Reynolds stresses arises from splitting the velocity field in the Eulenan form
of the momentum equations into mean and eddy parts and then averaging.
For large-scale atmospheric flow the covariance statistics involving
u
and
u,
the zonal and meridional components of velocity, respectively, are the domi-
nant Reynolds stresses.
Traditionally, the horizontal transport of momentum has been repre-
sented in the zonal-mean sense by
u'u'.
Only recently has the problem of the
local
forcing oflarge-scale circulation
by eddies been considered. Eddies are then conventionally defined as the
deviation from a time mean
so
that momentum forcing becomes a vector
quantity defined atch point in space. Finding
a
vector quantity to general-
ize the notion of
u'v'
as a momentum
flux
has turned out to
be
intimately
related to concepts of group velocity, wave action flux, and wave/mean flow
interaction.
-
Hoskins
et
al.
(1983)
introduced the quasi-vector
E
=
(p
-
sure of the time-mean forcing of westerly momentum exerted by the eddy
field and whose direction
is
related to the direction of the group velocity
vector for Rossby waves.
If
E
makes a small angle with the x-axis (in Carte-
sian P-plane geometry) then this angle is one-half of that made between the
group velocity vector (relative to the mean flow) and the x-axis. Since obser-
vationally, the high-pass filtered velocity covariance statistics typically sat-
is@
the inequality
vX
>
8
>
lu'ull,
the corresponding
E
vectors tend to
point eastward along the storm tracks.
E
can
be
regarded as an effective flux
of
westward
momentum since convergence regions of
E
experience a net
force from east to west.
It is helpful at this point to recall the theoretical motivation for
E.
In
u'2
,
-
E)
I
I
appropriate to Cartesian geometry whose divergence is a mea-
A CASE
STUDY
OF
EDDY FORCING
143
spherical geometry, the equations governing the horizontal motion field in
pressure coordinates are
au
u
au
v
aU
au
uvtan8
-+--
+--+a)--
at acos
8
aa
a
a8
ap
a
la0
a
cos
8
aa
-2LRsin8
-
v+--=0
(4)
av
u
av
v
av
av
u2
tan
8
-+--
+--+a)-+-
dt acostl
aA
a
dB
ap
a
la0
a
a8
+2Rsin8
-
u+--=0
(5)
-+
'('7
'I)+
(6)
aP
acos
8
d3,
where
@
is the geopotential,
8
is
latitude,
3,
is longitude,
a)
is the pseudoverti-
cal velocity of pressure coordinates, and
a
and
l2
are the radius and angular
speed of rotation
of
the earth. It can be shown that the time average of
Eqs.
(4)
and
(5)
give
-
la@
-2Qsin8
-
U+--
-
aii
ztan8
v,
*
vii+a)--
aP
a
acose
aa
and
-
-
-
-av
2
tan
8
1acS
I
auw
v,
'
vv+a)-+
-
+2Qsine
ii+--+--
a
a0
acos8 ad aP
a
1
at+
avw
-
-
tan8
a
ae
ap
a
+
-
-
+
-
+
-
v'2)
-
-
-0
where
V,
=
Ci
+
i7j.
Hoskins et
al.
(1983)
suggest that the boldface terms in
Eq.
(8)
are in
approximate balance (based on observational analysis), the eddy forcing
term a-'(avT/a8) causing a slight departure from geostrophic balance.
Al-
though it is a small term compared with the pressure gradient term, its
influence cannot
be
neglected since unlike the latter it is an important source
of mean vorticity (though not a net source, of course).
We can replace this force in the
j
direction by a conservative force plus a