Potential vorticity

Randel, W. J., and F. Wu, TOMS Total Ozone Trends in Potential Vorticity Coordinates, Geophys. Res. Lett., 22, 683-686 (1995). 

In this study we will present aspects of STE in relation with the budget and concentrations of ozone in the troposphere, specifically in the Northern Hemisphere. Firstly, we present ozone observations in the tropopause region from the measurement campaign MOZAIC, and discuss their correlation with potential vorticity. The results have been used to improve the parameterization of stratospheric ozone in a coupled tropospheric chemistry - general circulation model. We will show examples of the performance of the model regarding the simulation of ozone in the tropopause region, and present the simulated seasonality of cross-tropopause ozone transport in relation to other tropospheric ozone sources and sinks. Finally, we will examine and compare the influence of cross-tropopause transports to surface ozone concentrations for simulations with contemporary, pre-industrial, and future emission scenarios. 

Examination of ozone observations from MOZAIC and potential vorticity... 

Figure 1. Subset of observed ozone concentrations (ppbv) and potential vorticity (pvu) from the MOZAIC database for April 1996. The linear regression is given by the solid line.

Figure 2. Comparison of simulated ozone (ppbv) and potential vorticity (pvu) with MOZAIC data for the flight from Frankfurt (Germany) to New York (USA) on March 15, 1996 (a) simulated horizontal ozone distribution at approximately 10 km altitude (03 in ppbv) solid line denotes the flight path (b) simulated vertical ozone distribution along the flight path solid line denotes the model tropopause, dashed line denotes the flight altitude (c) ECMWF (dotted) and modeled (solid line) potential vorticity along the flight path (d) observed (dotted) and modeled (solid line) ozone concentrations along the flight path.

Danielsen, E.F., Hipskind, R.S., Gaines, S.E., Sachse, G.W., Gregory, G.L., and Hill, G.F. (1987) Three-dimensional analysis of potential vorticity associated with tropopause folds and observed variations of ozone and carbon monoxide, J. Geophys. Res. 92,2103-2111. 

Beekmann, M., Ancellet, G., and Megie, G. (1994) Climatology of tropospheric ozone in southern Europe and its relation to potential vorticity, J. Geophys. Res. 99,12841-12853. 

Strong vortex The vortex is strong, when c area of EPV values (>105 PVU(= Potential Vorticity Unit = km2kg ls l 10 6) for 550 K, >48 PVU for 475 K and >32 PVU for 435 K.) characterising the vortex interior is unified and compact and the temperature inside the vortex has at some point been below 195 K. 

Figure 1. Left Flight track of the FALCON aircraft and contour lines of the ECMWF Potential Vorticity at the 475 K level of Potential Temperature ( 20 km altitude) on February 28,1996. Right Flight track of the FALCON aircraft and contour lines of the ECMWF 475 K-PV on March 6,1996.

Figure 2 Scatter plot of potential vorticity (PV) values versus NjO mixing ratios for different years at the 475 K level of potential temperature as an indication of the descent and position of the measured air parcel in die vortex...

Figure 1 represents the potential vorticity map at 435K obtained with the PV advection model MIMOSA developped in the Service d Aeronomie. This PV map shows also a passage of filament over the OHP station, In figure 2, the lidar ozone profile (vmr) at OHP on the same day is compared to the monthly mean profile. In this case study of a METRO alert, it is clear that a filament overpass correspond to a positive anomaly at 435K. 

The aim now, is to identify all the filament events over OHP during the three winters 96-97,97-98 and 98-99 and understand their effect on the ozone amount. To detect the filament events, we choose a potential vorticity threshold corresponding to the lower edge of the vortex We use the equivalent latitude to represent the PV and the PV threshold is calculated from the first and seconde derivative of the PV as a function of equivalent latitude.lt corresponds to the closest position between the value of the full width half maximum of first derivative and maximum of the second derivative. 

FIGURE 3. the temporal evolution of the potential vorticity (in blue), the PV threshold (in black) and the ozone daily deviation during winter 96-97 (in black under) (01 november to 30 april)... 

To differentiate a filament from a vortex intrusion case, we use a method based on the evolution of the potential vorticity along the cross-section between the OHP station and the vortex center defined from the PV maximum. 

The final objective of the study is to show a possible decrease in the ozone amount in the filaments as a function of time when ozone destruction takes place inside the vortex. Clearly, the number of events at the OIIP station is too small to detect such a behaviour. But the perspective is to use more ground based stations and more height levels in the potential vorticity advection model MIMOSA as well as to include the REPROBUS chemistry scheme in the advection model in order to understand the role of filaments in ozone depletion at mid-latitude. 

Korty RL, Schneider T (2007) A climatology of the tropospheric thermal stratification using saturation potential vorticity. J Climate (in press)... 

In the 1960s, the start of application of computers to the practice of marine research gave a pulse to the development of numerical diagnostic hydrodynamic models [33]. In them, the SLE (or the integral stream function) field is calculated from the three-dimensional density field in the equation of potential vorticity balance over the entire water column from the surface to the bottom. The iterative computational procedure is repeated until a stationary condition of the SLE (or the integral stream function) is reached at the specified fixed density field. Then, from equations of momentum balance, horizontal components of the current vector are obtained, while the continuity equation provides the calculations of the vertical component. The advantage of this approach is related to the absence of the problem of the choice of the zero surface and to the account for the coupled effect of the baroclinicity of... 

If these vortices are considered as potential vortices, then the induced perturbation velocity in the inviscid part of the flow is given by,... 

Danielsen E.F., Stratospheric tropospheric exchange based on radioactivity, ozone, and potential vorticity. J. Atmos. Sci., 25, 4495-4498 (1968). 

For a large class of scale of motions, the primitive equations (which are rather expensive to solve numerically) can be replaced by approximate equations for the vorticity or the potential vorticity. Relative vorticity can be thought of as a measure of the rotation of the fluid with respect to a coordinate sytem fixed to the Earth. Its vertical component is defined in spherical coordinates as... 

A more general form of the vorticity is provided by Ertel s potential vorticity (Rossby, 1940 Ertel, 1942). In the log-pressure coordinate system, this quantity is defined by... 

As indicated earlier, atmospheric motions are often advantageously represented in an isentropic coordinate system. In this case, Ertel s potential vorticity is defined by... 

Apart from the absolute vorticity ( +f), the Ertel s potential vorticity varies in the vertical as 09/2 (see Lait, 1994). It is therefore useful to define a modified potential vorticity... 

Figure 3.9. Zonally averaged distribution of the modified potential vorticity (unbroken lines in 10-4K m2s-1kg-1) from the surface to approximately 30 km altitude (10 hPa). The potential temperature (K) is represented by dashed lines and the tropopause by a dotted line. From Appenzeller (1994).

Figure 3.10. Global distribution of the potential vorticity on the 850 K isentropic surface during a wintertime planetary wave event. The shaded region over the Pacific ocean with a weak gradient is characterized by nonlinear wave dissipation and strong quasi-horizontal mixing. This region is referred to as the surf zone . Wind vectors are also indicated and provide information about large-scale transport. Courtesy of A. O Neill, University of Reading, UK.

Finally, it is interesting to note that, since potential vorticity is a conserved quantity, air parcels that are displaced to an area with different PV values develop a differential motion which tends to restore them to their original PV area. Thus, strong PV gradients act as dynamical barriers to transport. Barriers against horizontal mixing are observed in the lower stratosphere near the polar vortex and at the boundary between tropical and extratropical air masses. Wave events distort PV surfaces often leading to the formation of thin filaments which are pulled away from the barriers. 

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