The isentropic potential vorticity (P) is defined as:

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

Isentropic potential vorticity is a large positive value when

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

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)

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

p<0

n<0

positive potential vorticity anomalies

Localized maxima in isentropic potential vorticity

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

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.

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.

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

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

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:

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

On the synoptic-scale, IPV anomalies evolve through

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

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.

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

P=1x10^{-6} m^{2} Ks^{-1} kg^{-1}.

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

For typical mid-latitude, synoptic-scale flow

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,

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.”

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.

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

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.

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

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

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.

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

relatively high altitude, inferring an upper tropospheric ridge.

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

relatively low altitude, inferring an upper tropospheric trough.

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

relatively low altitudes

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.

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

Conversely, it is found at relatively high altitudes and on

relatively warm isentropic surfaces near the equator.