1. Symmetric instability Sources: Texts: – Martin p. 224-228 – Holton p. 277-281 – Lackmann does not cover this topic Meted modules: – an operational approach to slantwise convection : highly recommended (by Kent Johnson), 28 min an operational approach to slantwise convection Try the case exercise (location: BC)Try the case exercise – listen to in class: heavy banded snow (by J. Moore), 34 min heavy banded snow 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 minCSI pitfalls: the use and misuse of CSI Required reading material Real-time charts (PV and SI): – Canadian maps (chart description)  he’s dead JimCanadian mapschart description – SPC meso-analysis, click on winter weatherSPC meso-analysis

2. Symmetric instability outline 1.examples 2.static and inertial instability 3.SI as inertial instability on isentropic surfaces 4.basic state energy release in an SI exchange 5.a computational method to determine SI (PV)

3. Example 1 What causes this precip?

4. N. Dakota S. Dakota

6. Example 2 E. Nebraska

7. Jet PSI? M

8. relative humidity (%)

9. PV min Jet 0 0 relative humidity (%) pvor (thte,wnd)

10. Example 3 (Schumacher et al. 2015) 700 mb, 21 UTC on 16 Feb

11. Simulated composite radar reflectivity (dBZ, color shading), 700-hPa potential temperature (red contours every 2 K), 700-hPa frontogenesis [thick black contours in K (100 km) −1 h −1, 700-hPa PV (negative values shaded in gray where the environment is statically stable), 700-hPa wind barbs 21 UTC on 16 Feb SWNE potential temperature (thin solid contours every 4 K), potential vorticity (negative values shaded in PVU), frontogenesis [thick dashed lines every 5 K (100 km) −1 h −1 above 5], and simulated reflectivity (the 0- and 5-dBZ contours are shown in blue) Example 3 (Schumacher et al. 2015)

13. 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)

14. From dry to moist SI Static instability –Absolute: d  /dz <0 –Conditional: d  e  /dz <0 –Potential: d  e /dz <0 Inertial instability: –  g  f 0 with M = u g -fy –It is rare, it most commonly occurs on the anticyclonic shear side of jets and in upper- level outflows from thunderstorms and hurricanes. –Here M = fx+v g  –unstable if dM/dx <0

15. PV is preferred to the M g -  relationship for assessing dry SI: –Flow is not assumed to be 2D –Not dependent on cross-section orientation –PV quantifies amount of instability –Horizontal maps of PV can be examined Condition for dry SI:  lines steeper than M lines or: d  /dz < 0 along M lines or: dM/dx < 0 along  lines or: PV g < 0 (Martin p. 227) But: SI only occurs if the atmosphere is absolutely and inertially stable isentropic inertial instability or:

16. 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 or: equivalent PV (EPV) < 0 But: MSI only occurs if the atmosphere is potentially and inertially stable Example: Ri moist Emanuel (1983) PV (EPV) note: the condition for conditional instability: d  e  /dz <0

17. MSI: an intuitive explanation M = fy-u g 70 60 40 30 dM/dy>0 M = absolute zonal momentum see also: Jim Moore’s meted module on frontogenetic circulations & stability)frontogenetic circulations & stability d  e /dz>0

18. - - - - - - - - - - dash:  e solid: M g Potential Symmetric Stability Potential Potential Symmetric INstability solid:  e dash: M g

19. MSI EPV Slope method EPV method dashed:  e solid: M

20. Where does MSI occur? EPV g YBR (Brandon, Manitoba) ATY (Waterton South Dakota) Jet cross section

21. Also important for the effective release of the instability: moisture  Overlay RH And frontogenesis … why? Mapping PI, PSI, frontogenesis, and RH 900-700 mb EPV g

22. 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.

23. 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

24. Secondary circulations near jet streak develop narrow updraft and broad downdraft due to SI jet exit region NW SE frontogenetic circulation with weak symmetric stability (Emanuel 1987)

25. 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

26. The existence of SI alone is not sufficient to initiate convection (need moisture) SI is not a forcing mechanism for slantwise ascent over a front (frontogenesis is … SI leads to slantwise convection within the frontogenetic circulation) The terms slantwise convection and SI are not interchangeable Upright convection always prevails over slantwise convection Conclusion: some words of caution about CI