Lifting by cold pools (RKW theory)

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Lifting by cold pools(RKW theory)

• AOS C115/C228

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Very rapid recap of CAPE CIN(with some skewed,
qualitative images)
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Environmental temperature profile
Average environmental lapse rate 6.5C/km in
tropopshere
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Lift a parcel
Subsaturated parcel cools _at_ DALR, RH rises
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Saturation reached (LCL)
Note parcel negatively buoyant a push needed
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Further lifting beyond LCL
MALR varies with height
Saturated parcel cools _at_ MALR
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Positively buoyant above LFC
Parcel needed push to get to LFC
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Cloud top (TOC) where buoyancy vanishes
Parcel runs out of vapor and/or reaches
stratosphere
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Convective available potential energy (CAPE)
Energy reservoir feeds strong storm
updrafts positive area
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Convective inhibition (CIN)
Parcel must overcome inhibition to reach LFC --
needs a push
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Shear
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Midlatitudes westerly wind increases with height
in troposphere
Principal reason its colder to the north
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Vertical shear creates spin
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Vertical shear creates spin
Storm moves faster than lower tropospheric winds
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Storm-relative view
Storm moves faster than lower tropospheric winds
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Shear should force downshear tilt
Storm would rain into its own inflow, not a good
situation
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A better storm configuration
Storm avoids raining into its own inflow
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A better storm configuration
Large amount of CAPE, low LFC, little CIN A good
recipe
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A downshear-tilting storm
Storm rains into its own inflow, cooling it
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A downshear-tilting storm
LFC rises, much less CAPE, much more CIN
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A downshear-tilting storm
Unviable and wont live long
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Shear bad (for storm) but it can be good
thing too
Cold pool good (lifting) but it can be bad
thing too
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Horizontal vorticity

• Spin in vertical plane
• Spin axis is horizontal
• Right-hand rule determines sign
• Positive horizontal vorticity illustrated

CW spin positive CCW spin negative
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Creating horizontal vorticity

• Vertical wind shear
• Horizontal temperature gradients

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Creating horizontal vorticity

• Vertical wind shear
• Horizontal temperature gradients

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Creating horizontal vorticity

• Vertical wind shear
• Horizontal temperature gradients

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Creating horizontal vorticity

• Vertical wind shear
• Horizontal temperature gradients

Here CCW spin negative vorticity
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Horizontal vorticity ?

• Boussinesq equations, cross-derive to obtain
• where

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An isolated warm bubble
8 km
16 km
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with wind vectors
Vorticity tendency largest here (largest
horizontal B gradient)
Vorticity largest here
Temperature gradients horizontal vorticity CCW,
CW spins balanced
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Add on some shear?

Add shear to picture -- biased to CW
spin Thermal (cloud) would tilt downshear
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Storm cold pools make negative horizontal
vorticity
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Effect of cold pool vorticity
Air gets lifted but not very well By itself,
cold pool vorticity bad for storm
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Now consider shear vorticity
By itself, shear vorticity is also bad, forcing
downshear tilt
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Now consider shear vorticity
But two wrongs can make a right
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Vorticity balance
Vorticities balanced - get deep lifting, strong
storm
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The optimal state
Optimal strength -- as close to vertical as
possible, without raining into its own inflow
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RKW vorticity balance theory(Rotunno et al. 1988)
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RKWs optimal state where ?u wind speed
difference over cold pool depth (proxy for
vertical shear) c storm speed (proxy for pool
negative vorticity)
Weisman and Rotunno (2004)
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Recap

• Sources of horizontal vorticity vertical shear
  horizontal temperature gradients
• By itself, CW shear vorticity weakens
  (multicell-type) storms
• Forces downshear tilt, rain into inflow
• By itself, CCW cold pool vorticity weakens
  storms
• Provides lifting but its not very deep
• Not an unalloyed good
• Opposing vorticities can balance to produce
  optimal storm strength (Goldilocks!)
• Cold pool vorticity stronger - leans upshear
• Shear vorticity stronger - leans downshear

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Weisman and Rotunno (2004)
RKW emphasized surface-based vertical shear over
cold pool depth. WR2004 addresses objections to
RKW theory by exploring (ii) Shear shifted above
cold pool (iii) Shear extending above cold pool
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No shear case
Observe vertical deformation of tracer lines
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Add some westerly shearover cold pool depth
Max lifting case
upshear side -- downshear side
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Same shear, but elevated
A lot less total lift above x2
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Same shear, deeper layer
Less total lifting - more downshear tilt
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Demonstration
Nice multicell storm Sequence of short-lived
updrafts strong cold pool Storm leans
upshear Cold pool vorticity stronger than shear
vorticity
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Demonstration
Take this storm and destroy its cold pool by
turning off evaporation cooling Cold pool, its
lifting and its vorticity go away What happens?
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Demonstration
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Another demonstration(cold pool collapse in very
strong shear)