A filament was encountered by the ER-2 during a altitude excursions prior to landing in Hawaii on 1996.12.06. Temperature, ozone, N2O are used to characterize the vertical structure of the filament. The ozone/N2O mixing ratio is used to derive an altitude profile of the filament's percentage of ambient versus original air. It is speculated that this filament originated in the Arctic polar vortex. A temperature anomaly is associated with the filament that is consistent with equatorward movement while preserving potential vorticity. This association of tracer and temperature features is similar to several filament encounters on other ER-2 flights.
It may be interesting to compare the temperature field in relation to the filament location. This is shown in the next figure.
Figure 7. Temperature signature of the filament for
three altitude excursions. Circular and rectangular symbols mark the
high and low altitudes of the anomalously high ozone region.
This plot of temperature profiles shows that the filament, as
defined by molecular tracers, is thinner than the layer of air with
anomalously high temperature. One interpretation is that the filament
"dragged" air along as it moved equatorward, and as this expanded layer
moved in latitude it preserved potential vorticity (PV). Preserving PV
during an equatorward movement produces "filament spin-up" that
consists of a vertical compression accompanied by a horizontal
expansion (described in the next section). The vertical compression
causes an adiabatic heating at the upper boundary of the moving layer
of air, and at the lower booundary there may be an adiabatic cooling.
(This pattern has been observed by the MTP on several occasions while
flying between a polar vortex and the tropics.) The above figure does
indeed show an exces of warmth at the top of the filament and a
suggestion of coolling near the bottom. The next section describes
Filament Spin Up Due to PV Conservation
Consider what might happen to a chunk of the vortex edge after it is
dislodged from the vortex by a planetary wave. As it moves equatorward
its slope will change due to differences in wind versus altitude. It
will also be streatched in other directions due to differences in wind
speed versus latitude. In the following figure keep in mind that the
horizontal and vertical axes are greatly different, so imagine that the
chunk of vortex air that is dislodged is really wider than it is
Figure 8. The farther the filament travels toward the equator the more it resembles a "tilted pancake."
If an air parcel moves toward the equator it is traveling to lower latitudes,
and even if it is not subjected to wind field forces that distort its shape
the fact that the air parcel must retain its potenttial vorticity (PV) causes
it to become flatter and more spread out. The governing equation is:
PV = (-dTheta/dP) * ((dV/dx - dU/dy) + 2 * Omega *
where PV = potential vorticity,
Theta = potential temperature = T [K] * (1000 mb * P[mb] ) 0.286
P = pressure [mb],
V = eastward component of horizontal wind,
U = northward component of horrizontal wind,
Omega = earth's rotation rate [radians/second],
Ø = latitude,
x = east-pointing coordinate,
y = north pointing coordinate.
The term dTheta/dP is referred to as
"static stability," the term dV/dx - dU/dy is referred to as "relative
vorticity" and the term 2 * Omega * sin Ø is referred
to as the "coriolis parameter."
PV is a conserved property of an air parcel that does not
undergo irreversible interactions with its surroundings and does not gain
or lose energy through its parcel boundaries. For time scales that characterize
an air parcel's movement from the vortex edge to mid-latitudes it can be
said that the parcel's PV must be conserved unless it undergoes significant
mixing with the surrounding air.
Consider an air parcel that moves toward the equator, which
experiences a decreasing "coriolis parameter".
There are two ways to conserve PV during this latitude change:
1) Increase "relative vorticity" or
2) Increase "static stability."
Figure 9. Depiction of a disk of vortex air being
dislodged from Antarctic vortex and moving equatorward. The disk-shaped air
parcel is shown at three hypothetical times during its motion toward New
Zealand. Flight track for ER-2 flight 1994.05.23 is shown (blue trace).
Figure 10. Depiction of how an air parcel vertically
compresses as it expands horizontally during equatorward movement.
In this figure showing simultaneous horizontal expansion and
vertical compression (preserving air parcel volume) it can be imagined that
the horizontal expansion is associated with a "spin-up" caused by an increase
in "relative vorticity." The vertical compression will increase static stability
since isentrope surfaces will be brought closer together as vertical compression
proceeds. This scenario therefore depicts a situation inwhich both "relative
vorticity" and "static stability" increase to counter the loss of the "coriolis
parameter" value, thus preserving PV.
Figure 11. Two concepts for how the temperature
field could be distorted by the filament's vertical compression. The blue
trace is for no effect on the ambient air whereas the red trace assumes that
nearby ambient air above and below the filament partakes in some of the filament's
Recall our implicit assumption that the vortex chunk of air
will move toward the equator after it is torn off the main vortex. If it
were simply entrained in the mid-latitude air adjoining the vortex edge then
it would only move equatorward as far as the meandering mid-latitude air
during its planetary wave motion, and in this case the air surrounding the
filament would undergo the same PV-conserving vertical compression and horizontal
expansion as the filament. But, if the chunk of vortex air that is destined
to become a mid-latitude filament moves through the mid-latitude air
mass once it has separated from the main vortex, and if this motion is toward
the equator, then the filament will undergo a PV-conserving vertical compression
that the ambient air it moves through does not experience. What could cause
the latter case to exist? Recall that the air in the vortex has a higher
PV than the air at mid-latitudes. PV is proportional to the product of horizontal
vorticity and vertical static stability. Since the static stability within
the vortex is lower than outside, there must be an excess of vorticity for
air within the vortex. It is this anomalously high vorticity of chunks of
vortex air that are torn from the main vortex that must cause the vortex
air to migrate equatorward (help, dynamicist!). Filaments of vortex air at
low mid-latitudes are an observational fact. The only matter in question
is whether the vortex air moves equatorward by a process of moving through
mid-latitude air or a process of being entrained by mid-latitude air that
is on its way toward the equator. Later I will claim that observed temperature
field distortions in relation to tracer-derived filament thickness can be
used to answer this question.
It is not necessary to resolve the question raised in the
previous paragraph to realize that encounters with filaments should be associated
with changes in air temperature. Specifically, the vertical gradient of temperature
should increase during flight within a filament. This is a prediction based
on basic atmospheric physics. The ER-2 has flown many missions in the vicinity
of a winter polar vortex, and these missions included instruments that measure
the tracers necessary to distinguish vortex air from mid-latitude air. Furthermore,
these missions also included the Microwave Temperature Profiler instrument,
which allows for the detection of changes in vertical temperature gradient.
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