CSI, IGW and Frontogenesis:

Other causes of mesoscale

bands in winter storms

MT417 – Iowa State University – Week 3

Bill Gallus

Conditional Symmetric Instability

(CSI)

• CSI indicates an atmospheric state where slanted convection can develop if saturated air parcels are given a bit of lift

• Frontogenesis is often the process that provides the lift to create mesoscale bands of heavier precipitation in regions where CSI exists

• To understand CSI, we must examine other types of instability

Convective Stability/Instability

(conditional gravitational….)

• This is the term used often on warm summer days to indicate that thunderstorms are possible

• Gravity is the restoring force

• You often evaluate it by using a Skew-T chart and looking to see if the lapse rate is steeper than a moist adiabat

• Can also look at cross-sections to see if Theta-E decreases with height

300

310

320

330

stable

unstable

Inertial stability/instability

• Don’t hear about this much in synoptic courses – usually in dynamics courses

• Coriolis force is the restoring force

• To understand it, use the momentum equations, which can be written as

• DV/Dt = -f k x Va

• The equation shows us that if flow is supergeostrophic, acceleration is to the right toward high pressure to slow down

• If flow is subgeostrophic, acc. Is to right

toward low pressure to speed up

V

Vg Va

V

Vg Va

• Since flow is usually strongly out of the

west, we define momenum (or geostrophic

momentum) as

Mg = ug –fy

And we can plot momentum on a cross-

section

North South

30

40

50

If we take the blue blob with 40 units of momentum and move it to the north, it is

then supergeostrophic (in an environment with only 30ish units) and would

accelerate south – back to where it started. This indicates inertially stable

conditions

Conditional Symmetric

Instability/Stability

• This is a type of baroclinic instability

(requires a temperature gradient)

• Combines what we know about the other

two types of stability/instability

• Formerly was often evaluated using cross-

sections of momentum and Theta-E

North South

30

40

50

270

280

290

Now note that if we push the parcel horizontally, it is

still inertially stable and would go back to its starting

point

North South

30

40

50

270

280

290

And if we push the parcel verticaly, it is still

gravitationally stable and would go back to its starting

point

North South

30

40

50

270

280

290

But if we push the parcel along a path where it conserves its momentum,

it will find itself warmer than its environment (higher theta-E value) and

would continue to accelerate along this slanted path – indicating

instability. We call this CSI

M, Theta-E surface evaluation of

CSI

• If the Theta-E lines slope more than the M-lines, CSI is present

• If the M-lines slope more than the Theta-E lines, we have conditional symmetric stability

• Think about what strongly sloped Theta-E lines mean ….. Strong horizontal temperature gradient (front may be nearby, frontogenesis is likely strong…)

MPV/EPV evaluation of CSI

• In recent years, forecasters have begun using EPV (Equivalent Potential Vorticity) more often to evaluate CSI

• If EPV < 0, the atmosphere must either be

Convectively unstable

CSI

So to evaluate CSI, we want EPV < 0 AND d(Theta-E)/dz > 0 (to rule out convective instability)

What is EPV?

• Absolute vorticity dotted with Theta-E

gradient

• Expansion of terms leads to:

• -dVg/Dz dθe/dx + dUg/dz dθe/dy + (ζ + f)

dθe/dz

• Remember, we want this negative without

dθe/dz < 0

• Thus, the third term will always be positive

since we can’t allow Theta-E to decrease

with height, and absolute vorticity is almost

always positive.

• In first two terms, note that vertical shear

of geostrophic wind appears. Remember

– this is thermal wind, and we know it is

related to horizontal temperature gradients

• Thus, to make environment more

favorable to have CSI, we want

• Strong horizontal temperature gradients

• Strong horizontal moisture gradients

• Straight or anticyclonic isobar curvature (to

keep absolute vorticity small)

• Near-neutral stability (so dθe/dz is small)

Internal Gravity Waves

• Another method of getting mesoscale

bands of heavy precipitation is to have

high-amplitude ducted (trapped) internal

gravity waves occur

• These form in very unbalanced situations

• Can create spectacular pressure changes

of 10 mb or so in 30 minutes, with

thundersnow and 4 inch per hour rates

Environments supporting IGWs

• Poleward of surface front

• Beneath inflection point of upstream trof/downstream ridge

• Jet streak moving through trof (favorable region often in right entrance quadrant of jet streak, and left exit quadrant of geostrophic jet max)

• Low-level inversion to help trap (duct) the wave

More rules…

• Critical level needed in near-neutral stable

layer above inversion (strong wind shear

in/near top of inversion)

• Low-level flow is opposite to IGW motion

Forecasting?

• Can use Lagrangian Rossby Number as

indicator of IGW potential

• RoL = |Va| / |V| >> 0 where Va is

component of ageostrophic wind normal to

height contours

L Jet

Inflection axis

IGW?