Symmetric instability

Sources:•Texts:

– Martin p. 224-228– Holton p. 277-281

•Meted modules:– homework assignment: an operational approach to slantwise convection : highly recommended (by Kent Johnson), 28 min

• Try the case exercise (location: BC)

– listen to in class: heavy banded snow (by J. Moore), 34 min • This is a survey of conveyor belts, trowal, and (in section 3) symmetric instability

– CSI pitfalls: the use and misuse of CSI : more advanced (by David Schultz), 33 min• Required reading material

•Real-time charts (PV and SI):– Canadian maps (chart description)

Symmetric instability outline

1. examples2. static and inertial instability3. SI as inertial instability on isentropic surfaces4. basic state energy release in an SI exchange5. a computational method to determine SI (PV)

Example

What causes this precip?

N. DakotaS. Dakota

Example 2

E. Nebraska

Jet

PSI?

M

rela

tive h

um

idit

y (

%)

PV min

Jet

0

0

rela

tive h

um

idit

y (

%)

pvor (thte,wnd)

Banded precipitation

• Single- and multiple-banded clouds and precipitation are common, esp. in frontal systems

• They are often aligned with the thickness contours (thermal wind) and occur where they are tightly packed.

• possible cause: symmetric instability with moisture (PSI/MSI/CSI)

• PSI and frontogenesis commonly co-exit– PSI requires EPV<0– frontogenetic circulation requires (geostrophic) PV>0 (ellipticity condition for Sawyer-Eliassen eqn)

• SI is often ‘blamed’ a posteriori, it is not prognosed well (b/o inadequate model-resolution)

Condition for moist or potential SI (MSI):

e lines steeper than M linesor: de/dz < 0 along M linesor: dM/dx <0 along e linesor: equivalent PV (EPV) < 0

But: MSI only occurs if the atmosphere is potentially and inertially stable

Example:

Rimoist Emanuel (1983)

zf

y

u

x

v

yz

u

xz

v

zf

y

u

x

v

yx

w

z

u

xz

v

y

w

kfP

eee

eee

ee

)ˆ(

PV (EPV)

note: the condition for conditional instability: de

/dz <0

MSI: an intuitive explanation

M = fy-ug

70

60

4030

dM/dy>0

M = absolute zonal momentum

see also: Jim Moore’s meted module on frontogenetic circulations & stability)

-

-

-

-

-

-

-

-

--

Dash: e

Solid: Mg

Potential Symmetric Stability Potential Potential Symmetric INstability

Where does MSI occur?

EPVg

Also important for the effective release of the instability: moisture Overlay RH

And frontogenesis … why?

Mapping PI, PSI, frontogenesis, and RH

900-700 mb

Dt

DF

p

EPVg

EPVg

Characteristics of bands due to the release of MSI

1. Two-dimensional, aligned nearly along the thermal wind.

2. Condition for MSI is met in the region of the bands.

3. This region should be close to saturation. MSI by itself is not a sufficient condition for banded precip. MSI is ubiquitous, as is upright PI. We need e to be close to e

*, or RH close to 100%.

4. Bands should move at the speed of the flow at the level of MSI, in the cross-band direction.

5. Spacing of bands is proportional to the depth of unstable layer/slope of moist isentropes.

6. Ascent should be nearly along the moist adiabats.

Bandedness vs MSI

• Byrd 1989: 27 events in OK-KS• 80% of banded cases had

EPV<0 and high RH

• Xu 1992: numerical study• Initial EPV anomaly small: Single band develops

• Initial EPV anomaly larger: Multiple bands develop

Frontal boundary

MSI predictability

• Bands ~ 5-40 km wide, spacing ~twice that much

• grid spacings of at most 10 km are required to capture the most unstable MSI mode (Knight and Hobbs 1988, Persson and Warner 1993)

mesoscale models, incl the current ETA (12 km), should be able to capture most MSI-induced circulations (as well as frontogenetical flow)

• Even high-resolution models tend to underpredict the rainfall variability, and also the integrated amount of rainfall

• 1. The existence of SI alone is not sufficient to initiate convection (need moisture)

• 2. SI is not a forcing mechanism for slantwise ascent over a front (frontogenesis is … SI leads to slantwise convection within the frontogenetic circulation)

• 3. The terms slantwise convection and SI are not interchangeable

• 4. Upright convection always prevails over slantwise convection

Conclusion: some words of caution about CI