Atms 4320 / 7320 Lab
On the use of isentropic maps in weather analysis and forecasting.

On the use of isentropic maps in weather analysis and forecasting.
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Concept of potential Vorticity (Pedlosky pp34 ff):
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Start with the N-S equation (x,y,z,t coords): d V

3 dt
 
1


3 p

2
 
V


 g


F


On the use of isentropic maps in weather analysis and forecasting.
►
Take the curl of the momentum equation to get the 3-dimensional vorticity equation: d
 dt
 w a
 
V

 w a
 
V


 


2
 p
  

F

►
(A) (B) ( C) (D)
► w a in this case is the 3-dimentional vorticity:

On the use of isentropic maps in weather analysis and forecasting.
► w a in this case is the 3-dimentional vorticity w a
  i
ˆ   ˆ j
  k
ˆ

On the use of isentropic maps in weather analysis and forecasting.
► term (A) is vortex tilting term -- variation of velocity v perpendicular to the vorticity filaments
► term (b) vortex stretching term
► term (c) baroclinic production term (source of vorticity)
► term (d) diffusive effects of Friction

On the use of isentropic maps in weather analysis and forecasting.
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Use Continuity equation to combine terms
(a and b) to get: d dt w

 w
 a
 

V
3

 


3
 p
  


F
2
►
Consider a scalar that has this form: d
 dt
 
, d
 dt

0

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On the use of isentropic maps in weather analysis and forecasting.
 
► to get a potential vorticity equation: d dt 

 w a


 



 w
 a
      


 


3
 p



 
 


F
 



On the use of isentropic maps in weather analysis and forecasting.
►
Now potential vorticity conserved if:

 w a


  
 is
►
 is conserved for each(adiabatic process)
► frictional force is negligible
► the fluid is barotropic, or  (  ,p):

On the use of isentropic maps in weather analysis and forecasting.
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Potential Vorticity, given the proper balance conditions, can be inverted to recover the
“balanced” height field, wind field, temperature field, etc. (Hoskins, 1985
QJRMS)
►
Potential Vorticity in Pressure Coords (No longer conserved!)

On the use of isentropic maps in weather analysis and forecasting.
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The expression (see Lupo and Bosart, 1999)
PV
  g


 k



 
V

 p
  



  a
 
 p 


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How good an assumption is this? See Bosart and Lackmann (1995, MWR,) Bosart and
Lupo (1999, QJRMS), Burkhardt and Lupo
(2005, JAS).

On the use of isentropic maps in weather analysis and forecasting.
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PV maps: Usually we interpolate data to the x,y,  coordinate system. Then we can examine PV on surfaces of Kelvin (potential temperature). Most commonly choose, 315 K, 300 K, 280 K, etc.
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Also, Eady postulated (1957), that surface disturbances grow and decay due to disturbances on the upper “lid” (tropopause).

On the use of isentropic maps in weather analysis and forecasting.
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This is the idea behind defining a tropopause based on Potential Vorticity values. (Dynamic tropopause) (as the 2 PVU surface typically), and examining quantities on that.
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This is as opposed to a “thermodynamic tropopuase” defined as an isothermal layer by the WMO.

On the use of isentropic maps in weather analysis and forecasting.
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Modern isentropic analysis involves examining
Pressure, potential temperature, on a potential vorticity surface (Lupo and Bosart, 1999 chose the
2 PVU surface). Read Nielsen-Gammon and
Lefevre (1996, JAS). Read Hoskins (1985, QJRMS)
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I’ll pass out Morgan, M, and Nielsen-Gammon,
J.W., (1998). This is a comprehensive guide for the use of these maps in the NH. In the SH, see Lupo et al. (2001, MWR).

On the use of isentropic maps in weather analysis and forecasting.
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The maps

On the use of isentropic maps in weather analysis and forecasting.
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Maps!

On the use of isentropic maps in weather analysis and forecasting.
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Low pressure and trough regions tend to show up as areas of high tropopause pressure and “cold” potential temperatures.

On the use of isentropic maps in weather analysis and forecasting.
High pressure and ridges tend to show up as areas of low tropopause pressure and
“warm” potential temperatures.

On the use of isentropic maps in weather analysis and forecasting.
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At the surface, the opposite is true.
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Jet maxima tend to show up where the isotherms, or isobars are “packed”
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Visit: www.atmos.albany.edu/deas/nwp.html

On the use of isentropic maps in weather analysis and forecasting.
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The End!

On the use of isentropic maps in weather analysis and forecasting.

On the use of isentropic maps in weather analysis and forecasting.