Lifting by cold pools (RKW theory) A&OS C115/C228

Very rapid recap of CAPE & CIN (with some skewed, qualitative images)

Environmental temperature profile Average environmental lapse rate: 6.5˚C/km in tropopshere

Lift a parcel Subsaturated parcel DALR, RH rises

Saturation reached (LCL) Note parcel negatively buoyant… a push needed

Further lifting beyond LCL Saturated parcel MALR MALR varies with height

Positively buoyant above LFC Parcel needed push to get to LFC

Cloud top (TOC) where buoyancy vanishes Parcel runs out of vapor and/or reaches stratosphere

Convective available potential energy (CAPE) Energy reservoir feeds strong storm updrafts; “positive area”

Convective inhibition (CIN) Parcel must overcome inhibition to reach LFC -- needs a push

Shear

Midlatitudes: westerly wind increases with height in troposphere Principal reason: it’s colder to the north

Vertical shear creates spin

Storm moves faster than lower tropospheric winds

Storm-relative view Storm moves faster than lower tropospheric winds

Shear should force “downshear” tilt Storm would rain into its own inflow, not a good situation…

A “better” storm configuration Storm avoids raining into its own inflow

A “better” storm configuration Large amount of CAPE, low LFC, little CIN: A good recipe

A downshear-tilting storm Storm rains into its own inflow, cooling it

A downshear-tilting storm LFC rises, much less CAPE, much more CIN

A downshear-tilting storm Unviable… and won’t live long…

Shear == bad (for storm) … but it can be good thing too Cold pool == good (lifting) … but it can be bad thing too

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

Creating horizontal vorticity Vertical wind shear Horizontal temperature gradients

Creating horizontal vorticity Vertical wind shear Horizontal temperature gradients

Creating horizontal vorticity Vertical wind shear Horizontal temperature gradients

Creating horizontal vorticity Vertical wind shear Horizontal temperature gradients Here: CCW spin & negative vorticity

Horizontal vorticity  Boussinesq equations, cross-derive to obtain –where

An isolated warm bubble 16 km 8 km

…with wind vectors Temperature gradients = horizontal vorticity CCW, CW spins balanced Vorticity largest here Vorticity tendency largest here (largest horizontal B gradient)

Add on some shear? Add shear to picture -- biased to CW spin; Thermal (cloud) would tilt downshear +

Storm cold pools make negative horizontal vorticity

Effect of cold pool vorticity Air gets lifted… but not very well… By itself, cold pool vorticity bad for storm

Now consider shear vorticity By itself, shear vorticity is also bad, forcing downshear tilt

Now consider shear vorticity But two “wrongs” can make a “right”

Vorticity balance Vorticities balanced - get deep lifting, strong storm

The “optimal state” Optimal strength -- as close to vertical as possible, without raining into its own inflow

RKW vorticity balance theory (Rotunno et al. 1988)

Weisman and Rotunno (2004) RKW’s “optimal state” where: ∆u = wind speed difference over cold pool depth (proxy for vertical shear) c = storm speed (proxy for pool negative vorticity)

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

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

No shear case Observe vertical deformation of tracer lines

Add some westerly shear over cold pool depth upshear side -- downshear side Max lifting case

Same shear, but elevated A lot less total lift above x=+2

Same shear, deeper layer Less total lifting - more downshear tilt

Demonstration Nice multicell storm Sequence of short-lived updrafts; strong cold pool Storm leans upshear Cold pool vorticity stronger than shear vorticity

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?

Demonstration

Another demonstration (cold pool collapse in very strong shear)