Links internal to this web page:

    Filament Behavior and Potential Vorticity
    Flight of 1994.05.23
    Flight of 1995.05.08
    Flight of 1996.12.06
    Conclusions

Filament Behavior and Potential Vorticity

Introduction

The Microwave Temperature Profiler mounted in a NASA ER-2 atmopsheric research aircraft, the MTP/ER2, has measured altitude temperature profile distortions associated with molecular tracer filaments on several occasions. In every case the pattern of temperature distortion compared with non-filament air obeys the rule: "warmer above, colder below." In two cases it was possible to compare the altitude thickness of the layer having distorted temperature with the thickness of the layer having anomalous tracer values. In each case the distorted temperature layer was thicker than the tracer layer.

The tracer/tracer signatures for these filaments can be explained by assuming the filament air is moving toward the equator from a point of origin that is likely the polar vortex edge. Conservation of potential vorticity requires that a layer of air will undergo vertical compression as it moves toward the equator. This vertical compression should produce an adiabatic heating at the top of the layer and an adiabatic cooling at the bottom, assuming that the average temperature of the layer determines its buoyancy in relation to the air mass that it penetrates. This argument can explain the "warm above/cold below" temperature structure associated with filaments. However, the greater thickness of the temperature distortion in relation to the thickness of the tracer anomaly requires that some additional physical process must be invoked that accompanies the filament's equatorward journey. I will suggest that friction between the original filament's upper and lower surfaces entrain ambient air and cause it to share in the temperature distortion as potential vorticity is conserved.

The goal of this web page is to report observations that make the case that filaments have different thicknesses using the temperature field distortion and tracer measures. I hope someone with a theoretical
background in atmospheric physics will be challenged to give an account of the observations.

Filament Basics

Consider the northern hemisphere winter situation. Air over the polar region receives no sunlight for long periods of time except for an occasional latitude excursions beyond the arctic circle. Polar air parcels cool due to thermal radiation to space that is greater than their absorption of terrestrial surface thermal radiation. As the air cools, it contracts and descends. This diabatic descent is accompanied by adiabatic heating, but the net effect is for polar air to be cooler over time, and to be cooler than air at the same altitude outside the vortex. By late winter the air at 20 km has descended several kilometers, and near the bottom of the vortex the air has descended by a slightly smaller amount.

Since ozone and N₂O concentrations do not change significantly over time scales of a few months vortex air has relatively high ozone concentrations and low N₂O concentrations compared to air at the same altitude outside the vortex. Thus, level flight through the vortex edge into the vortex is accompanied by a rise in ozone and a fall in N₂O concentrations.

As depicted in the next figure the vortex has a larger latitude extent at higher altitudes. The vortex edge is tilted by a greater angle than appears in the figure, as can be imagined by expanding the horizontal scale by the factor 700 (needed to achieve the same scale vertically as horizontally).

Figure 1. Latitude cross-section of typical winter hemisphere showing location of vortex. Tropopause and jets are also indicated, using symbols STJ for sub-tropical jet, PJ for polar jet and VJ for vortex jet. 

A wind maximum occurs near the vortex edge, and is associated with the large latitude gradient of potential vorticity that acts as a barrier to air parcel movement across the vortex edge. Imagine a mid-latitude air stream with latitude excursions (planetary waves). At its northern most excursion it will increase the horizontal wind gradient, and with sufficient force it could "tear off" a chunk of vortex air and entrain it in to mid-latitude air.  This is depicted in the next figure.

Figure 2. Depiction of tearing off of chunk of vortex air by mid-latitude winds.

The altitude extent of this air might be 1 km, but the horizontal extent could be many kilometers. The air chunk appears to be vertically larger than its horizontal extent in the figure, but this appearance is due to the 700-fold difference in vertical and horizontal scales.

If the chunk of vortex air moves toward the equator it has many opportunities to be streatched horizontally because winds at neighboring altitudes are rarely the same. Horizontal gradients also exist, and will add to the horizontal spreading of the original vortex air parcel. Whereas there are two important contributors to a horizontal spreading, there are essentially none that cause the air vertical dimention to change. Thus, as time passes the vortex air will become flatter in shape. The closer to the equator an air parcel is found, the longer it is likely to have travelled, and the flatter in shape it is likely to be. This is depicted in the next figure.

Figure 3. The farther the filament travels toward the equator the more it resembles a "tilted pancake."

In this figure the tilt of the vortex air is so large that it may be considered to be a very large "pancake" that is essentially horizontal. The longer a filament is embedded in mid-latitude air, and the greater the horizontal gradients of wind at these mid-latitudes, the more likely it is for the filament to break up into isolated pieces. Thus, the depiction of the filament in the above figure could just as well be represented as a series of smaller filamentary strands. Of course, the longer and more turbulent the air, the greater is the mixing of vortex air with mid-latitude air at the vortex air boundaries.

Filament Spin Up Due to PV Conservation

There's one more factor that can produce a horizontal expansion of the filament. But of greater significance for this article this factor also is predicted to produce a vertical compression.  It's the vertical compression of the air parcel that is detectable by the MTP instrument because the vertical compression creates a "warm above/cold below" temperature distortion of the filament.

If an air parcel moves toward the equator it is traveling to lower latitdues, 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  causes it to become flatter and more spread out in order to preserve potential vorticity, PV. The governing equation is:

    PV = (-dTheta/dP) * ((dV/dx - dU/dy) + 2 * Omega * sin Ø)

        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."

It is not clear from the theory how this partitioning should occur. This is a job for the observationalist, and this article presents evidence that at least the "static stability" component changes as an air parcel moves equatorward. To illustrate this situation let's shift our imagination to the southern hemisphere, in aniticipation of a key MTP observation, and consider that a chunk of the Antarctic vortex is torn off by mid-latitude winds that "bang into" the vortex edge during a planetary wave meander.

Figure 4. 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).

In the above figure the disk-shaped air parcel is shown as expanding horizontally with time. As it undergoes this horizontal expansion it also undergoes a vertical compression, as shown in the next figure.

Figure 5. 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.

It would be observationally difficult to detect a horizontal expansion, or even the wind speed changes associated with the spin-up, but it is easy for an MTP to detect the increase in static stability associated with vertical compression. The following figure shows two concepts for what might happen to the temperature field in the vicinity of the vertically compressing disk-shaped vortex filament.

Figure 6.  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 vertical compression.

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. The remainder of this article is devoted to descriptions of tracer and temperature field observations during three vortex filament encounters.

MTP Instrument

The Microwave Temperature Profiler, or MTP, is a passive microwave radiometer than scans through a range of elevation angles every few seconds and records brightness temperature versus elevation angle. Since brightness temperature at the two MTP operating frequencies are dominated by oxygen molecule thermal emission, the measurement of brigthness temperature versus elevation angle can be converted to plots of air physical temperature versus altitude with respect to the aircraft. The two (local oscillator) operating frequencies are 56.66 and 58.80 GHz, and for a typical flight altitude of 20 km the oxygen absoprtion at these two frequencies is 0.42 and 0.90 Nepers per km (average of IF band passes).  Hence, the measured brightness temperature comes from ranges of ~2.4 and 1.1 km (assuming certain things).

A statistical retrieval procedure is used to extract temperaature versus altitude information from the set of MTP measured observations of brightness temperature versus elevation angle. For flight at 20 km the accuracy of retrieved profiles is <1.0 K from 19 to 21.5 km, <2.0 K from 17.2 to 24.2 km and <3.0 K from 16 to 26 km. The altitude resolution is ~150 meters (full-width half-max) near flight level, and degrades to ~600 meters at altitudes that are 1.0 km above or below the aircraft. T(z) profiles are obtained every 20 seconds.

Flight of 1994 May 23

Flight of 1995 May 8

Flight of 1996 December 6

It may be interesting to compare the temperature field in relation to the filament location. This is shown in the next figure.

 Figure 13. 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."

Conclusions

For each of the three filament encounter flights the same temperature pattern was found to exist: the top of the filament was warmer than neighboring altitudes and the lower part of the filemnt was cooler. This is consistent with a prediction based on the filament preserving potential vorticity as it moves equatorward.

Acknowledgements

References

This site opened:  April 9, 2004.  Last Update:  June 29, 2006