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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)

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Symmetric instability

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## 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

Real-time charts (PV and SI):

### Symmetric instability outline

• examples

• static and inertial instability

• SI as inertial instability on isentropic surfaces

• basic state energy release in an SI exchange

• a computational method to determine SI (PV)

Example

What causes this precip?

N. Dakota

S. Dakota

Example 2

Jet

M

PSI?

relative humidity (%)

Jet

relative humidity (%)

0

PV min

0

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)

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

• Condition for moist or potential SI (MSI):

• e lines steeper than M lines

or: dqe/dz < 0 along M lines

or: dM/dx <0 along qe lines

• or: equivalent PV(EPV) < 0

Rimoist

Emanuel (1983)

PV (EPV)

Example:

• note: the condition for conditional instability:

• dqe*/dz <0

### MSI: an intuitive explanation

M = absolute zonal momentum

30

40

M = fy-ug

dM/dy>0

60

70

Potential

Potential Symmetric INstability

Potential Symmetric Stability

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Dash: qe

Solid: Mg

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-

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Where does MSI occur?

EPVg

Also important for the effective release of the instability: moisture

 Overlay RH

And frontogenesis … why?

EPVg

Mapping PI, PSI, frontogenesis, and RH

900-700 mb

EPVg

Characteristics of bands due to the release of MSI

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

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

• 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 qe to be close to qe*, or RH close to 100%.

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

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

• 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

### Conclusion: some words of caution about CI

• 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