Transcript Potential vorticity and the dynamic tropopause

Potential vorticity and the
dynamic tropopause
John R. Gyakum
Department of Atmospheric and
Oceanic Sciences
McGill University
E-mail:
[email protected]
Phone: 514-398-6076
Outline
•
•
•
•
•
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Motivation (why use potential vorticity??)
Isentropic coordinates
Potential vorticity structures
Potential vorticity invertability
Dynamic tropopause analyses
Comparison of potential vorticity analyses
with traditional quasi-geostrophic analyses
Motivation (why use potential
vorticity??)
PV = g(-q/p)zaq
g is gravity,
zaq is the component of absolute vorticity
normal to an isentropic surface, and
-q/p is the static stability
• It is conserved in adiabatic, frictionless
three-dimensional flow
Consider the following animation
of PV on the 325 potential
temperature surface:
QuickTime™ and a
GIF decompressor
are needed to see this picture.
What are the units of PV?
PV = g(-q/p)zaq
typical tropospheric values:
-q/p = 10K/100 hPa
zaq≈f=10-4 s-1
and
PV=10 m s-2(10K/100 hPa)(1 hPa(100 kg m s-2m-2)-1)10-4s -1
=10-6 m2 s -1 K kg-1= 1.0 Potential Vorticity Unit (PVU)
Values of PV less than 1.5 PVUs are typically associated with tropospheric air and
values greater than 1.5 PVUs are typically associated with stratospheric air
Now, we are prepared to
appreciate the cross sections
that we viewed at the end of
this morning’s lecture!
1 PVU= 10-6 m2 s-1K kg-1
The shaded zone illustrates that the
1-3PVU band lies within the
transition zone between the upper
troposphere’s weak stratification
and the relatively strong stratification of the lower stratosphere
(Morgan and Nielsen-Gammon
1998).
Non-conservation of PV is often associated
with interesting diabatic effects in explosive
cyclones (Dickinson et al. 1997)
Isentropic coordinates
(potential temperature is the vertical
coordinate)
• Air parcels will conserve potential
temperature for isentropic processes
• Vertical motions can be visualized
• moisture transports can be better visualized
than on pressure surfaces
• Isentropic surfaces can be used to diagnose
potential vorticity
Consider the comparison of the
cross sections we have been
viewing:
temperature cross section
potential temperature cross
section:
isentropes slope up to cold air
and downward to warm air
high/low pressure on a theta
surface corresponds to warm/
cold temperature on a pressure
surface
700 hPa heights (m; solid) and
Temperature (K; dashed)
292 K Montgomery stream function
((m2 s-2 /100) solid) and pressure
(hPa; dashed)
Potential vorticity structures
•
•
•
•
surface cyclone
surface anticyclone
upper-tropospheric trough
upper-tropospheric ridge
Surface cyclone (warm ‘anomaly’)
PV = g(-q/p)zaq
• warm air is associated
with isentropes
becoming packed near
the ground (more PV)
• surface cyclone is
associated with a
warm core with no
disturbance aloft (zT=
zgu- zgl=0-zgl<0
200
Pressure
(hPa)
cold
0
warm
cold
more stable
distance (km)
1000
4000
Surface anticyclone (cold ‘anomaly’)
PV = g(-q/p)zaq
• cold air is associated
with isentropes
becoming less packed
near the ground (less
PV and smaller static
stability)
• surface anticyclone is
associated with a cold
core with no
disturbance aloft (zT=
zgu- zgl=0-zgl>0
200
Pressure
(hPa)
warm
0
cold
warm
less stable
distance (km)
1000
4000
Upper-tropospheric trough (positive PV ‘anomaly’)
PV = g(-q/p)zaq
• cold tropospheric air is
associated with
isentropes becoming
200
more packed near the
warm
cold
cold Pressure
tropopause (more PV
more
(hPa)
stable
and greater static
warm
warm
cold
stability)
• upper tropospheric trough
is associated with a cold
core cyclone with no
disturbance below (zT=
zgu- zgl= zgu-0>0
less stable
0
distance (km)
1000
4000
Upper-tropospheric ridge (negative PV ‘anomaly’)
PV = g(-q/p)zaq
• warm tropospheric air
is associated with
isentropes becoming
200
warm
less packed near the
warm
cold
Pressure
tropopause (less PV
less
(hPa)
and smaller static
stable
cold
cold
stability)
warm
• upper tropospheric ridge is
associated with a warm
core anticyclone with no
disturbance below (zT=
zgu- zgl= zgu-0<0
more
stable
0
distance (km)
1000
4000
Potential vorticity invertability
• If we know the distribution of isentropic
potential vorticity, then we also know the
wind field
• The wind field is ‘induced’ by the PV
anomaly field
• The amplitude of the induced wind
increases with size of the anomaly and with
a reduction in static stability
Potential vorticity inversion may be used
to understand the motions of troughs and
ridges:
• Potential vorticity
maxima and minima
N
max
N
• instantaneous winds
min
max
min
Consider a PV reference state:
• Consider the PV
contours at right with
increasing PV
northward (owing
primarily to increase
of the Coriolis
parameter)
larger PV
N
PV+2dPV
PV+dPV
PV
PV-dPV
Consider the introduction of alternating
PV anomalies:
• The sense of the wind
field that is induced by
the PV anomalies
• There will be a
propagation to the left
or to the west (largest
effecct for large
anomalies
• This effect is opposed
by the eastward
advective effect
larger PV
N
L
+
-
PV+2dPV
PV+dPV
+
PV
East
The application of PV inversion to the
problem of cyclogenesis (Hoskins et al. 1985)
Dynamic tropopause analysis; What
is the dynamic tropopause?
• A level (not at a constant height or pressure)
at which the gradients of potential vorticity
on an isentropic surface are maximized
• Large local changes in PV are determined
by the advective wind
• This level ranges from 1.5 to 3.0 Potential
vorticity units (PVUs)
Consider the cross sections that we have
been viewing:
• Our focus is on the
isentropic cross section
seen below
• the opposing slopes of
the PV surfaces and the
isentropes result in the
gradients of PV being
sharper along isentropic
surfaces than along
isobaric surfaces
Dynamic tropopause pressure: A
Relatively high (low pressure)
Tropopause in the subtropics, and a
Relatively low (high pressure)
Tropopause in the polar regions; a
Steeply-sloping tropopause in the
Middle latitudes
Tropopause potential
temperatures (contour interval
of 5K from 305 K to 350 K) at
12-h intervals (from Morgan and
Nielsen-Gammon 1998)
The appearance of the 330 K
closed contour in panel c is
produced by the large values of
equivalent potential temperature
ascending in moist convection
and ventilated at the tropopause
level;
as discussed earlier, this is an
excellent means of showing the
effects of diabatic heating, and
verifying models
the sounding shows a tropopause
fold extending from 500 to 375
hPa at 1200 UTC, 5 Nov. 1988
for Centerville, AL,
with tropospheric air above and
extending to 150 hPa.
The fold has descended into
Charleston, SC by 0000 UTC,
6 November 1988 to the 600-500
hPa layer. The same isentropic
levels are associated with each fold
Coupling index:
Theta at the tropopause
Minus the equivalent
Potential temperature at
Low levels
(a poor man’s lifted index)
December 30-31, 1993 SLP
And 925 hPa theta
An example illustrates the detail
of the dynamic tropopause (1.5
potential vorticity units) that is
lacking in a constant pressure
analysis
250 and 500-hPa analyses showing the respective
subtropical and polar jets:
250-hPa z and winds
500-hPa z and winds
Dynamic tropopause map shows the properlysharp troughs and ridges and full amplitudes of
both the polar and subtropical jets
QuickTime™ and a
GIF decompressor
are needed to see this picture.
QuickTime™ and a
GIF decompressor
are needed to see this picture.
QuickTime™ and a
GIF decompressor
are needed to see this picture.
The dynamic tropopause
animation during the 11 May
1999 hailstorm:
QuickTime™ and a
GIF decompressor
are needed to see this picture.
An animation of the dynamic
tropopause for the period from
December 1, 1998 through
February 28, 1999:
QuickTime™ and a
GIF decompressor
are needed to see this picture.
Comparison of potential vorticity
analyses with traditional quasigeostrophic analyses
• Focus is on the PV perspective of QG
vertical motions and the movement of high
and low pressure systems
OK, but what about PV????
Consider a positive PV anomaly (PV maximum) aloft in a
westerly shear flow:
z
+ PV anomaly
0
x
Now, consider a reference frame of the PV anomaly
in which the anomaly is fixed:
Consider the quasi-geostrophic
Vorticity equation in the reference
Frame of the positive PV anomaly
z
0= -vg(zg
+ PV anomaly
>0
CVA; d>0
0
<0
AVA; d<0
x
+ f)-df0
Now, consider the same PV anomaly in which the
anomaly is fixed from the perspective of the
thermodynamic equation:
z
+ PV anomaly
cool
0
x
+ PV anomaly
z
>0
0
0 = -vg  T + s(p/R)
cool
CA
WA
x
<0
Consider vertical motions in the vicinity of a warm surface
potential temperature anomaly (surrogate PV anomaly) from
the vorticity equation:
0= -vg(zg
z
CVA
d>0
AVA
d<0
>0
0
<0
x
+ PV
+q
+ f)-df0
Consider vertical motions in the vicinity of a warm surface
potential temperature anomaly (surrogate PV anomaly) from
the thermodynamic equation:
0 = -vg  T + s(p/R)
z
y
cold
<0
>0
WA
CA
warm
+ PV
+q
Movement of surface cyclones and anticyclones on
level terrain:
Consider a reference state of potential temperature:
North
q-q
q
q+q
Consider that air parcels are displaced alternately poleward
and equatorward within the east-west channel. Potential
temperature is conserved for isentropic processes
Since =0 at the surface, potential temperature changes
Occur due to advection only
q-q
North
-
+
L/4
q
L/4
q+q
The previous slide shows the maximum cold advection
occurs one quarter of a wavelength east of cold potential
temperature anomalies, with maximum warm advection
occurring one-quarter of a wavelength east of the warm
potential temperature anomalies. The entire wave travels
(propagates), with the cyclones and anticyclones propagates
eastward.
Just as with traditional quasi-geostrophic theory, surface cyclones
Travel from regions of cold advection to regions of warm advection.
Surface anticyclones travel from regions of warm advection to regions
Of cold advection.
Orographic effects on the motions of surface
cyclones and anticyclones
Consider a statically stable reference state in the vicinity of
mountains as shown below, with no relative vorticity on a potential
Temperature surface
z
q+q
q
q-q
x
Note that cyclones and anticyclones move with
higher terrain to their right, in the absence of any
other effects.
q+q
q-q
q
N
+
Mountain
Range
References
• Bluestein, H. B., 1993: Synoptic-dynamic meteorology in
midlatitudes. Volume II: Observations and theory of weather
systems. Oxford University Press. 594 pp.
• Dickinson, M. J., and coauthors, 1997: The Marcch 1993
superstorm cyclogenesis: Incipient phase synoptic- and
convective-scale flow interaction and model performance. Mon.
Wea. Rev., 125, 3041-3072.
• Hoskins, B. J., M. McIntyre, and A. Robertson, 1985: On the
use and significance of isentropic potential vorticity maps.
Quart. J. Roy. Meteor. Soc., 111, 877-946.
• Morgan, M. C., and J. W. Nielsen-Gammon, 1998: Using
tropopause maps to diagnose midlatitude weather systems.
Mon. Wea. Rev., 126, 2555-2579.