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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

Symmetric instability



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
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)


What causes this precip?


N. Dakota

S. Dakota


Example 2

E. Nebraska







relative humidity (%)


PV min


pvor (thte,wnd)

banded precipitation
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


Emanuel (1983)



  • note: the condition for conditional instability:
  • dqe*/dz <0
msi an intuitive explanation
MSI: an intuitive explanation

M = absolute zonal momentum



M = fy-ug




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



Potential Symmetric INstability

Potential Symmetric Stability


Dash: qe

Solid: Mg











Also important for the effective release of the instability: moisture

 Overlay RH

And frontogenesis … why?


Mapping PI, PSI, frontogenesis, and RH

900-700 mb


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
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
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
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