# symmetric instability with moisture (PSI/MSI/CSI)

```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
1.
2.
3.
4.
5.
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 (%)
relative humidity (%)
Jet
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)
Condition for moist or potential SI (MSI):
e lines steeper than M lines
or: de/dz < 0 along M lines
or: dM/dx <0 along e lines
PV (EPV)
or: equivalent PV (EPV) < 0
But: MSI only occurs if the atmosphere is
potentially and inertially stable
Rimoist Emanuel (1983)

Pe  (  f kˆ )    e
 w v   e  u w   e  v u
  e

 



 

 f 

x  y
 z
 y z  x
 x y
 z
 
v  e
z x

u  e
 v u
  e
 

 f 
z y
 x y
 z
Example:
note: the condition for conditional instability:
de*/dz <0
MSI: an intuitive explanation
M = absolute zonal momentum
30
40
M = fy-ug
dM/dy>0
60
70
Potential Symmetric INstability
Potential
Potential Symmetric Stability
-
Dash: e
Solid: Mg
-
-
-
-
-
-
Where does MSI occur?
EPVg
Also important for the effective
release of the instability: moisture
 Overlay RH
EPVg
And frontogenesis … why?
F 
D  p
Dt
Mapping PI, PSI, frontogenesis,
and RH
900-700 mb
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
Frontal boundary
•
•
Initial EPV anomaly larger:
 Multiple bands develop
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
```