<html>
<head>
<title>AWIPS potential vorticity</title>
<meta name="Agency" content="COMET">
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="Author" content="Kevin Fuell">
<meta name="Keywords" content="potential vorticity, vorticity">
</head>
<body bgcolor="#FFFFFF" background="images/backtile.gif">
<div align="center">
<h1> <font face="Arial, Helvetica, sans-serif">Potential Vorticity</font></h1>
</div>
<div align="left">
<p><font face="Arial"><font size="5">1) Definition</font></font></p>
<p><font face="Arial, Helvetica, sans-serif">The potential vorticity is the
product of <a href="abs_vort.htm">absolute</a></font><a href="abs_vort.htm"><font face="Arial">
vorticity</font></a><font face="Arial"> and the static stability. The "potential"
in potential vorticity relates to the value the relative vorticity would have
if a parcel is moved adiabaticly to a standard latitude and static stability.</font></p>
</div>
<div align="left">
<p><font face="Arial"> Huschke, R. E., Ed., 1959: <i>Glossary of Meteorology</i>.
Amer. Meteor. Soc. 638 pp. </font></p>
<p> </p>
<p><font face="Arial"><font size="5">2) How to Calculate</font></font></p>
<p><font face="Arial">In AWIPS potential vorticity can be plotted using a pressure
surface, potential temperature (theta) surface, or a pressure layer. In actuality,
all three of these uses a layer to do its calculations.</font></p>
<p><font face="Arial, Helvetica, sans-serif">For isentropic potential vorticity
the AWIPS calculation is:</font></p>
<p><img src="images/awips/pvisen1a.gif" width="261" height="70"></p>
<div align="left">
<p><font face="Arial, Helvetica, sans-serif">where:</font></p>
</div>
<ul>
<li>
<div align="left"><font face="Arial, Helvetica, sans-serif"> avor_up = absolute
vorticity of the upper level of the layer (1/s)</font></div>
</li>
<li><font face="Arial, Helvetica, sans-serif">avor_low = absolute vorticity
of the lower level of the layer (1/s)</font></li>
<li><font face="Arial, Helvetica, sans-serif">p = pressure (mb)</font> </li>
<li><font face="Arial, Helvetica, sans-serif"><img src="images/theta.gif" width="11" height="17">
= potential temperature (K)</font></li>
</ul>
</div>
<div align="left">
<p> </p>
</div>
<div align="left">
<div align="left">
<p><font face="Arial, Helvetica, sans-serif">For isentropic potential vorticity
the GEMPAK calculation is:</font></p>
</div>
</div>
<div align="left">
<div align="left"></div>
</div>
<div align="left">
<p><img src="images/gempak/pvisen1g.gif" width="298" height="35"></p>
<div align="left">
<p><font face="Arial">where:</font></p>
</div>
</div>
<div align="left">
<div align="left">
<ul>
<li>
<div align="left">
<div align="left">
<div align="left"><font face="Arial">0.01 = conversion from millibars
(Mb) to Pascals (Pa)</font></div>
</div>
</div>
</li>
<li>
<div align="left">
<div align="left">
<div align="left"><font face="Arial">g = acceleration due to gravity
~9.8 (m/s)</font></div>
</div>
</div>
</li>
<li><font face="Arial">avor = absolute vorticity calculated using the average
u and v wind components of the layer. (1/s)</font></li>
</ul>
<p> </p>
<p><font face="Arial, Helvetica, sans-serif">To plot potential vorticity on
a pressure surface or layer, a transformation from isentropic to isobaric
coordinates is added to the equation. For isobaric potential vorticity the
AWIPS calculation is:</font></p>
</div>
<p><img src="images/awips/pvisob1a.gif" width="410" height="73"></p>
<p><font face="Arial, Helvetica, sans-serif">where:</font></p>
</div>
<ul>
<li>
<div align="left">
<div align="left"><font face="Arial, Helvetica, sans-serif">u = wind component
in east-west direction</font></div>
</div>
</li>
<li>
<div align="left">
<div align="left"><font face="Arial, Helvetica, sans-serif">v = wind component
in north-south direction</font></div>
</div>
</li>
<li>
<div align="left">
<div align="left"><font face="Arial, Helvetica, sans-serif">x = distance
in east-west direction</font></div>
</div>
</li>
<li><font face="Arial, Helvetica, sans-serif">y = distance in north-south direction</font></li>
</ul>
<div align="left">
<div align="left">
<div align="left"></div>
</div>
<p> </p>
<p><font face="Arial, Helvetica, sans-serif">For isobaric potential vorticity
the GEMPAK calculation is:</font></p>
</div>
<div align="left">
<p><img src="images/gempak/pvisob1g.gif" width="404" height="73"></p>
<p> </p>
</div>
<div align="left">
<p> </p>
</div>
<div align="left">
<p align="left"><font face="Arial"><font size="5">3)
Validation</font></font></p>
<p>
<p><font face="Arial">Model: Eta<br>
Level: 500mb<br>
</font><font face="Arial">Time: 18 May 2000, 12 UTC, 0 hr fcst<br>
</font></p>
<font face="Arial">
<p><font face="Arial">Documentation:<br>
</font><font face="Arial">Potential vorticity (PV) is always calculated using
a layer even if you just ask for the 500mb level in the 'Planes' section of
the Volume Browser.</font><font face="Arial"> As far as PV on a pressure surface,
AWIPS will use the next level above the requested pressure surface to form
the layer. So in our example below with the Eta model, the 500mb plot from
AWIPS can be duplicated with GEMPAK by requesting PV in the 500mb-450mb layer.
Note that for the AVN model, however, that the 500mb plot from AWIPS would
be <font face="Arial">duplicated with GEMPAK by requesting PV in the 500mb-</font>400mb
layer. When plotting PV with AWIPS in a pressure layer (i.e., 500-300mb),
it was found that an error in the calculation method was occurring (see <a href="4.1.htm#pv_pres_layer">Archive
Issues</a>). The problem was corrected and re-tested by AWIPS developers at
FSL. The fix for this should appear in AWIPS version 5.0.<br>
</font><font face="Arial">For a plot of PV on an isentropic surface, AWIPS
again uses the <font face="Arial">next level above the requested</font> isentropic
surface to form the layer. Because AWIPS isentropic surfaces are every 5K
and GEMPAK can only plot PV on 10K increments, no plots on an isentropic surface
were able to be compared to GEMPAK. However, the transformation from isentropic
to isobaric coordinates was examined and it appears to be correct in the AWIPS
code. PV on a pressure surface was examined over several model runs of the
Eta and AVN using AWIPS D2D and GEMPAK. The plots look very similar.</font></p>
<p align="center"><font face="Arial"><b>GEMPAK</b><br>
</font><img src="images/gempak/potvor_g.gif" width="832" height="665"><br>
</p>
<p align="center"> </p>
<p align="center"> <b>AWIPS</b> <br>
<img src="images/awips/potvor_a.gif" width="856" height="726"> </p>
<p> </p>
</font></div>
</body>
</html>