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1

The isentropic potential vorticity (P) is defined as:

2

The isentropic potential vorticity P is a multiplicative function of two factors: 

3

Isentropic potential vorticity is a large positive value when 

cyclonic rotation is strong (n > 0) and/or where static stability is large 

4

Isentropic potential vorticity is a large positive value when cyclonic rotation is strong (n > 0) and/or where static stability is large, representing  

isentropes that are tightly packed in the vertical (-do -O/do p >>0)

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normally, -do -O/do p, such that ................. only occurs when ...............

p<0

n<0

6

positive potential vorticity anomalies 

Localized maxima in isentropic potential vorticity 

7

Localized maxima in isentropic potential vorticity are known as positive potential vorticity anomalies, whereas  ............................................................... are known as negative potential vorticity anomalies

localized minima in isentropic potential vorticity 

8

It can be shown that the isentropic potential vorticity is .......................... following the ...................................................., when .................................

conserved following the motion along an isentropic surface (i.e., under dry adiabatic conditions), when friction is neglected. 

9

  The non-conservation of isentropic potential vorticity following the motion on an isentropic surface thus allows us to 

infer where diabatic heating is occurring and/or where friction is important. 

10

Because IPV is conserved following the flow, if static stability or absolute vorticity change in value, the other must  

change in the inverse in order to keep the value of the IPV constant 

11

Because IPV is conserved following the flow, if static stability or absolute vorticity change in value 

, the other must change in the inverse in order to keep the value of the IPV constant 

12

Because IPV is conserved following the flow, if static stability or absolute vorticity change in value, the other must change in the inverse in order to keep the value of the IPV constant, that is: 

  • If the static stability increases, the absolute vorticity must decrease
  • If the static stability decreases, the absolute vorticity must increase 

13

On the synoptic-scale, IPV anomalies evolve through  

a combination of translation (motion/advection), rotation, and deformation by the synoptic-scale wind field. 

14

On the synoptic-scale, IPV anomalies evolve through a combination of translation (motion/advection), rotation, and deformation by the synoptic-scale wind field. For these processes, IPV is  

conserved following the motion. 

15

For typical mid-latitude, synoptic-scale flow, we can obtain a characteristic valueof P= 

P=1x10-6 m2 Ks-1 kg-1

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.................................................................. we can obtain a characteristic valueofP=1x10-6 m2 Ks-1 kg-1. 

For typical mid-latitude, synoptic-scale flow 

17

For typical mid-latitude, synoptic-scale flow, we can obtain a characteristic valueofP=1x10-6 m2 Ks-1 kg-1.

  For simplicity, we term this value to be equal to 

1 PVU, 

18

For typical mid-latitude, synoptic-scale flow, we can obtain a characteristic valueofP=1x10-6 m2 Ks-1 kg-1.

  For simplicity, we term this value to be equal to 1 PVU, where PVU stands for 

“potential vorticity unit.” 

19

For typical mid-latitude, synoptic-scale flow, we can obtain a characteristic valueofP=1x10-6 m2 Ks-1 kg-1.

  For simplicity, we term this value to be equal to 1 PVU, where PVU stands for “potential vorticity unit.”

  In the troposphere, P is typically  

less than or equal to 1.5 PVU. 

20

For typical mid-latitude, synoptic-scale flow, we can obtain a characteristic valueofP=1x10-6 m2 Ks-1 kg-1.

  For simplicity, we term this value to be equal to 1 PVU, where PVU stands for “potential vorticity unit.”

  In the .................................., P is typically less than or equal to 1.5 PVU. 

troposphere

21

In the stratosphere, where the static stability is  ...............as ........................................................... 

.............. is typically ........................................................

very large as potential temperature rapidly increases with height, P is typically greater than 2.0 PVU. 

22

in ............................where .......................................  is very large as potential temperature rapidly increases with height, P is typically greater than 2.0 PVU. 

In the stratosphere, where the static stability 

23

In the stratosphere, where the static stability is very large as potential

temperature rapidly increases with height, P is typically greater than 2.0 PVU.

  This gives rise to the 

construct of the dynamic tropopause 

24

In the stratosphere, where the static stability is very large as potential

temperature rapidly increases with height, P is typically greater than 2.0 PVU.

  This gives rise to the construct of the dynamic tropopause, which is commonly

represented by  

the 1.5 PVU or 2.0 PVU surface of constant potential vorticity. 

25

Where potential temperature is relatively warm on the dynamic tropopause, the tropopause itself is at a 

relatively high altitude, inferring an upper tropospheric ridge. 

26

where potential temperature is relatively cold on the dynamic tropopause, the tropopause itself is at a 

relatively low altitude, inferring an upper tropospheric trough. 

27

  If we take the dynamic tropopause to be the 1.5 PVU surface, we observe that it is found at 

relatively low altitudes 

28

If we take the dynamic tropopause to be the 1.5 PVU surface, we observe that it is found at relatively low altitudes and on 

relatively cold isentropic surfaces near the poles. 

29

If we take the dynamic tropopause to be the 1.5 PVU surface, we observe that it is found at relatively low altitudes and on relatively cold isentropic surfaces near the poles.

  Conversely, it is found at  

relatively high altitudes  

30

Conversely, it is found at relatively high altitudes and on 

relatively warm isentropic surfaces near the equator.