chapter 3 Flashcards
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:
- 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 m2 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 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
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.
Figures a and b, demonstrate
the link between potential temperature anomalies on the dynamic tropopause and troughs and ridges on upper tropospheric isobaric charts
Figures a and b, demonstrate the link between potential temperature anomalies on the dynamic tropopause and troughs and ridges on upper tropospheric isobaric charts, that is:
- lower values of …………………………………………. imply…………………………………………………..
potential temperature on the dynamic tropopause imply lower tropopause heights and upper tropospheric troughing
Figures a and b, demonstrate the link between potential temperature anomalies on the dynamic tropopause and troughs and ridges on upper tropospheric isobaric charts, that is:
- Lower values of potential temperature on the dynamic tropopause imply lower tropopause heights and upper tropospheric troughing and
- Higher values of ……… . . . .. . . . . .
potential temperature on the dynamic tropopause imply higher tropopause heights and upper tropospheric ridg
A positive potential vorticity anomaly is associated with
A negative potential vorticity anomaly is associated with
locally large anticyclonic absolute vorticity (η < 0) and reduced static stability with weakly-packed isentropes in the vertical (-∂θ/∂p > 0).
We first examine the structure of a ………………. potential vorticity anomaly, as depicted in Figure. A positive potential vorticity anomaly is associated with
positive
a depressed height of the dynamic tropopause.
We first examine the structure of a positive potential vorticity anomaly, as depicted in Figure. A positive potential vorticity anomaly is associated with a depressed height of the dynamic tropopause.
Accompanying this is
upper tropospheric cyclonic rotation
We first examine the structure of a positive potential vorticity anomaly, as depicted in Figure. A positive potential vorticity anomaly is associated with a depressed height of the dynamic tropopause.
Accompanying this is upper tropospheric cyclonic rotation. Isentropes are
tightly packed in the vertical direction through the positive potential vorticity anomaly,
Accompanying this is upper tropospheric cyclonic rotation. Isentropes are tightly packed in the vertical direction through the positive potential vorticity anomaly, indicative of
high static stability.
Thus, relatively warm potential temperature is found in
the stratosphere above the positive anomaly
relatively cold potential temperature is found in
the middle to upper troposphere below the positive anomaly.
A B C
D E F G H
I J K L
The following figure represents
The structure of an idealized upper tropospheric positive PVA
Likewise, above and below the positive potential vorticity anomaly (PVA), isentropes become
less tightly packed in the vertical direction
Likewise, above and below the positive potential vorticity anomaly (PVA), isentropes become less tightly packed in the vertical direction. This is indicative of
weaker static stability at such altitudes
above and below the negative potential vorticity anomaly, isentropes become
more tightly packed in the vertical direction
In a similar way, above and below the negative potential vorticity anomaly, isentropes become more tightly packed in the vertical direction. This is indicative of
stronger static stability at such altitudes
A B
C J
D E F G H
I K L
The following represents
The structure of an idealized upper tropospheric negative PVA
To assess the surface IPV anomalies, we need a relationship called
thermal vorticity relationship
…………………………………….. we need a relationship called thermal vorticity relationship
To assess the surface IPV anomalies
To assess the surface IPV anomalies, we need a relationship called thermal vorticity relationship, between
the geostrophic vorticity and potential temperature
The above equation states that under the constraints of quasi-geostrophic balance, the …………………………………………………………. is a function of
under the constraints of ……………………….the vertical derivative of the geostrophic relative vorticity with respect to is a function of the Laplacian of the potential temperature .
quasi-geostrophic balance
Since h is
positive
Since h is positive, given the known proportionality implied by the
Laplacian on the RHS of (3)
Since h is positive, given the known proportionality implied by the Laplacian on the RHS of (3), we know that ∂عg/∂p is a
local maximum
Since h is positive, given the known proportionality implied by the Laplacian on the RHS of (3), we know that ∂/∂p is a local maximum where -O is
a local maximum
Since h is positive, given the known proportionality implied by the Laplacian on the RHS of (3), we know that ∂عg/∂p is a local maximum where -O is a local maximum. Similarly, ∂عg/∂p is …………………………. where -O is
a local minimum where is a local minimum
Therefore, since do p < 0, -O is a local maximum where there is
cyclonic geostrophic relative vorticity at the surface
Therefore, since do p < 0, is a local maximum where there is cyclonic geostrophic relative vorticity at the surface and -O is a
local minimum where there is anticyclonic geostrophic relative vorticity at the surface.
Therefore, since < 0, is a local maximum where there is cyclonic geostrophic relative vorticity at the surface and is a local minimum where there is anticyclonic geostrophic relative vorticity at the surface.
With this relationship, now we can assess
the structure of IPV anomalies at the surface from the potential temperature anomalies.
as shown in the image
due to the thermal vorticity relationship, a ………………………………. is associated with
warm surface potential temperature anomaly
with cyclonic rotation ع > 0 at the surface.
Because potential temperature generally increases
with height
Because potential temperature generally increases with height, a warm surface potential temperature anomaly implies
a downward bowing of the near-surface isentropes.
Because potential temperature generally increases with height, a warm surface potential temperature anomaly implies a downward bowing of the near-surface isentropes. This leads to
relatively strong static stability at and just above the surface and relatively weak static stability at higher altitudes.
…………………………. increases with height, a warm surface potential temperature anomaly implies a downward bowing of the near-surface isentropes. This leads to relatively strong static stability at and just above the surface and relatively weak static stability at higher altitudes.
Because potential temperature generally
Because potential temperature generally increases with height, a ………………………………………………….. implies a downward bowing of the near-surface isentropes. This leads to relatively strong static stability at and just above the surface and relatively weak static stability at higher altitudes.
warm surface potential temperature anomaly
The combination of cyclonic rotation and relatively strong static stability at the surface thus suggests
that warm surface potential temperature anomalies are conceptually equivalent to positive potential vorticity anomalies.
…………………………………………………………………….. thus suggests that warm surface potential temperature anomalies are conceptually equivalent to positive potential vorticity anomalies.
The combination of cyclonic rotation and relatively strong static stability at the surface
In a similar way, the combination of anticyclonic rotation ع< 0 and relatively weak static stability at the surface thus suggests that
cold surface potential temperature anomalies are conceptually equivalent to negative potential vorticity anomalies.
……………………………………………….. thus suggests that cold surface potential temperature anomalies are conceptually equivalent to negative potential vorticity anomalies.
the combination of anticyclonic rotationع < 0 and relatively weak static stability at the surface
A positive IPV anomaly in an easterly flow is associated with:
These are associated with
middle-tropospheric descent and ascent, respectively.
consider ………………………………………………….. as a consequence, we can express the isentropic potential vorticity as:
Consider an atmosphere with no pre-existing relative vorticity (ζ = 0) and no background flow
Since f increases in magnitude with
increasing latitude
Since f increases in magnitude with increasing latitude, P is larger in magnitude toward
the poles
Since f increases in magnitude with increasing latitude, P is larger in magnitude toward the poles and smaller in magnitude toward
the equator
Let us now superimpose a series of alternating positive and negative upper tropospheric isentropic potential vorticity anomalies upon the distribution of P highlighted in Figure 1.
The result of doing so along the latitude where
P = P
By definition, positive upper tropospheric isentropic potential vorticity anomalies are associated with
cyclonic flow
…………………………………………………………….. are associated with cyclonic flow
positive upper tropospheric isentropic potential vorticity anomalies
By definition, positive upper tropospheric isentropic potential vorticity anomalies are associated with cyclonic flow. Likewise, negative upper tropospheric isentropic potential vorticity anomalies are associated with
anticyclonic flow
………………………………………………………………. are associated with anticyclonic flow.
negative upper tropospheric isentropic potential vorticity anomalies
The advection of P by the
alternating cyclonic and anticyclonic vortices
The advection of P by the alternating cyclonic and anticyclonic vortices results in ………………………………………………… and ………………………………………..
positive P advection to the west of a positive isentropic potential vorticity anomaly and
negative P advection to the west of a negative isentropic potential vorticity anomaly.
The advection of P by the alternating cyclonic and anticyclonic vortices results in positive P advection to the west of a positive isentropic potential vorticity anomaly and negative P advection to the west of a negative isentropic potential vorticity anomaly.
This results in
westward movement of the upper tropospheric trough/ridge pattern
he advection of P by the alternating cyclonic and anticyclonic vortices results in positive P advection to the west of a positive isentropic potential vorticity anomaly and negative P advection to the west of a negative isentropic potential vorticity anomaly.
This results in westward movement of the upper tropospheric trough/ridge pattern associated with
the alternating positive and negative upper tropospheric isentropic potential vorticity anomalies.
This results in westward movement of the upper tropospheric trough/ridge pattern associated with the alternating positive and negative upper tropospheric isentropic potential vorticity anomalies.
This westward propagation is more rapid for
larger-scale isentropic potential vorticity anomalies (e.g., longwaves)
This westward propagation is more rapid for larger-scale isentropic potential vorticity anomalies (e.g., longwaves) and less rapid for
smaller-scale isentropic potential vorticity anomalies (e.g., shortwaves).
The combination of this westerly flow and the westward motion of the pattern that results from isentropic potential vorticity advection allows us to state the following:
- Longwave troughs retrogress to the west, against the large-scale flow, or move eastward at a relatively slow rate of speed.
- Shortwave troughs move to the east at a rate of speed that is equal to or somewhat less than that of the large-scale westerly flow
The concept of the movement of surface cyclones and anticyclones is very similar to that associated with
the upper tropospheric trough/ridge pattern
The concept of the movement of surface cyclones and anticyclones is very similar to that associated with the upper tropospheric trough/ridge pattern.
In this case, however, we consider ………………………………………. instead of
the background meridional potential temperature distribution at the surface instead of meridional isentropic potential vorticity distribution.
In this case, however, we consider the background meridional potential temperature distribution at the surface instead of meridional isentropic potential vorticity distribution.
Areas near the equator are
warmer
In this case, however, we consider the background meridional potential temperature distribution at the surface instead of meridional isentropic potential vorticity distribution.
Areas near the equator are warmer, while areas near the poles are
colder
Areas near the equator are warmer, while areas near the poles are colder. The resultant background potential temperature distribution at the surface is depicted
Areas near the equator are warmer, while areas near the poles are colder. The resultant background potential temperature distribution at the surface is depicted in Figure 3.
Let us now superimpose a series of alternating warm and cold
surface potential temperature anomalies upon the distribution of -O
Warm surface potential temperature anomalies are associated with
cyclonic flow
Warm surface potential temperature anomalies are associated with cyclonic flow and cold surface potential temperature anomalies are associated with
anticyclonic flow.
The advection of potential temperature by the induced cyclonic and anticyclonic vortices results in
warm potential temperature advection east of warm surface potential temperature anomalies
and cold potential temperature advection east of cold surface potential temperature anomalies.
……………………………………………….. result in warm potential temperature advection east of warm surface potential temperature anomalies and cold potential temperature advection east of cold surface potential temperature anomalies.
The advection of potential temperature by the induced cyclonic and anticyclonic vortices results in
he advection of potential temperature by the induced cyclonic and anticyclonic vortices results in warm potential temperature advection east of warm surface potential temperature anomalies and cold potential temperature advection east of cold surface potential temperature anomalies.
As a result, surface cyclones and anticyclones move
eastward
