1. PRECIPITATION PROCESSES AT FRONTS

2. POSSIBLE CONDITIONS PRESENT AT FRONT 1.Air ahead of the front is stable to all forms of instability Forcing mechanism for vertical motion: ageostrophic circulation associated with frontogenesis 2.Air is potentially or conditionally unstable Lifting of air to saturation by ageostrophic circulation triggers convection 3.Air is stable to potentially or conditionally unstable to upright displacement but unstable to slantwise displacement Lifting of air to saturation by ageostrophic circulation triggers slantwise convection

3. Frontogenesis As we have learned from the previous analysis of the SE equation: Frontogenesis leads to a direct circulation Warm (moist) air rises on the warm side of the front, leading to widespread clouds and precipitation HOW DO INSTABILITES MODULATE THIS PRECIPITATION?

4. Instabilites: Convective instability: Body force is gravity, buoyancy acts opposite gravity and parcels accelerate vertically vertical momentum equation Assume base state density is a function of height and and perturbation is given by Assume base state pressure is a function of height and and perturbation is given by Base state is in hydrostatic balance (1) (2) (3) (4) Put (2), (3), (4) into (1), approximate, approximate do some algebra and get: Vertical accelerations result from imbalances between the vertical perturbation pressure gradient force and buoyancy

5. Assume for for rising parcel, environmental pressure instantly adjusts to parcel movement (atmosphere is everywhere hydrostatic (p = 0) H L real atmosphere A parcel’s stability can be determined by displacing it vertically a small distance  z, assuming that the environmental virtual potential temperature at  z is, and realizing that the parcel virtual potential temperature will be conserved From this equation, we obtain the criteria for gravitational stability in an unsaturated environment: stableneutralunstable  v = virtual potential temperature

6. Condensation makes the stability problem considerably more complicated. In the interest of time, I will state the stability criteria for moist adiabatic vertical ascent (see Holton p.333, Bluestein’s books or other books for details): Absolute instability Conditional Instability (CI) (parcel) Potential Instability (PI) (layer) Definitions: Saturation equivalent potential temperature Equivalent potential temperature

7. Example of Potential Instability Stable sounding to parcel ascent Lift layer between 1 and 1.25 km one km in altitude AIR DESTABILIZES

8. Synoptic environment conducive to the development of potential instability

9. Inertial instability: Body force is centrifugal acceleration due to Coriolis effect, parcels accelerate horizontally Assume a base state flow that is geostrophic horizontal momentum equations Assume a parcel moving at geostrophic base state velocity is displaced across stream Parcel conserves its absolute angular momentum Geostrophic wind at location y +  y (1) (2) (3) (4) Put (3) and (4) into (1) Equation governing inertial instability

10. = absolute geostrophic vorticity If the absolute vorticity is negative, a parcel of air when displaced in a geostrophically balanced flow will accelerate away from its initial position To understand inertial instability Consider this simple example  +8    300 mb height field in the vicinity of a jetstream For a parcel displaced north of jet axis, f is positive while is negative. Therefore is negative and parcel will return to its original position. For a parcel displaced south of jet axis, f is positive while is positive. If f exceeds the geostrophic shear, is negative and parcel will accelerate away from its original position. COR= PGF COR > PGF Inertially stable Inertially unstable

11. Instability summary In an atmosphere characterized by a hydrostatic and geostrophic base state: Conditional Instability Inertial Instability Vertical displacement Horizontal displacement Or if we define the absolute geostrophic momentum as so that Conditional Instability Inertial Instability Vertical displacement Horizontal displacement What happens if a parcel of air is displaced slantwise in an atmosphere that is inertially and convectively stable? Momentum equations

12. Let’s assume: 1)We have an east-west oriented front with cold air to the north. 2)The base state flow in the vicinity of the front is in hydrostatic and geostrophic balance 3)No variations occur along the front in the x (east-west) direction 4)We consider the stability of a tube of air located parallel to the x axis (east-west oriented tube) Starting point

13. 11 22 33 44 55 y m1m1 m2m2 m3m3 m4m4 m5m5 x p Barotropic Atmosphere (no temperature gradient) m surfaces and  surfaces in a barotropic and baroclinic environment 11 22 33 44 55 y m1m1 m2m2 m3m3 m4m4 m5m5 x p Baroclinic Atmosphere (temperature gradient) Because of temperature gradient geostrophic wind increases with height And m surfaces tilt since m = u g + fy m only a function of f along y direction

14. y N S z Strong shear Weak shear This surface represents a surface where a parcel of air Rising slantwise would be in equilibrium shape of surface depends on moisture distribution in environment Absolute geostrophic momentum surface Consider a tube at X that is displaced to A X At A, the tube’s  v is less that its environment At A, the tube’s m is greater than its environment Tube will accelerate downward and southward…. Return to its original position STABLE TO SLANTWISE DISPLACEMENT

15. y N S z Strong shear Weak shear This surface represents a surface where a parcel of air Rising slantwise would be in equilibrium shape of surface depends on moisture distribution in environment Absolute geostrophic momentum surface Consider a tube at B that is displaced to C X At C, the tube’s  v is greater that its environment At A, the tube’s m is less than its environment Tube will accelerate upward and northward…. Accelerate to D UNSTABLE TO SLANTWISE DISPLACEMENT

16. Requirements for convection (slantwise or vertical) Instability LiftMoisture

17. Evaluating Moist Symmetric Instability Three different methods 1. Cross sectional analysis 1. Flow must be quasi-two dimensional on a scale of u 0 /f where u 0 is the speed of the upper level jet (e.g. 50 m s -1 /10 -4 s -1 = 500 km) 2. Cross section must be normal to geostrophic shear vector (parallel to mean isotherms) in the layer where the instability is suspected to be present 3. Air either must be saturated, or a lifting mechanism (e.g. ageostrophic circulation associated with frontogenesis) must be present to bring the layer to saturation. 4. Air must not be conditionally (or potentially) unstable, or inertially unstable. If either condition is true, the vertical or horizontal instability will dominate.

18. RH = 100% Two approaches depending on the nature of the lifting: is it expected that a layer will be lifted to saturation or a parcel? LAYER : Potential Symmetric Instability PARCEL : Conditional Symmetric Instability On cross section plot (superimpose on RH w or RH i to determine saturation) On cross section (superimpose on RH w or RH i to determine saturation) y z z z yy Stable NeutralUnstable Slantwise instability evaluation RH = 100%

19. Evaluating Moist Symmetric Instability 2. Evaluation of (saturation) equivalent geostrophic potential vorticity Determining if CSI possible is equivalent to determining if the saturation equivalent geostrophic potential vorticity is negative Note that using the MPV g criteria does not differentiate between regions of CI/PI and CSI/PSI An independent assessment of CI must be done to isolate regions of CSI/PSI Determining if PSI possible is equivalent to determining if the equivalent geostrophic potential vorticity is negative

20. Evaluating Moist Symmetric Instability 3. Evaluation of slantwise convective available potential energy (SCAPE) using single soundings Governing equations for displaced tube Potential energy for reversible lifting of tube Emanuel (1983, MWR, p.2018-19) shows that the maximum potential energy available to a parcel ascending slantwise in an environment characterized by CSI occurs when the parcel ascends along an M g surface. SCAPE for this ascent is The susceptibility of the atmosphere to slantwise convection can be assessed by reversibly lifting a (2-D) parcel along a surface of constant Mg and comparing its virtual temperature (or  v ) to that of its environment

21. 3 Dec 82 00 UTC Surface 3 Dec 82 12 UTC Surface 3 Dec 82 00 UTC 500 mb 3 Dec 82 12 UTC 500 mb Meteorological conditions at the surface and 500 mb on 3 Dec 1982

22. Satellite images showing storm system – winter frontal squall line with trailing stratiform region

23. Cross section approximately normal to geostrophic shear showing 00Z during strong upright convection 12Z during more “stratiform” period Neutral to slantwise convection : implies that slantwise convective adjustment may have occurred Conditionally unstable: dominant mode will be upright convection

24. T TdTd Moist Adiabat for parcel lifted from 690 mb Sounding along M = 40 M = 70 Sounding along M = 70 Stable to upright convection Neutral to slantwise convection Neutral to slantwise convection Dots take into account centrifugal potential energy To compare to M surface

25. Nature of banding Frontogenetic forcing in the presence of small positive EPV g Frontogenetic forcing in the presence of large negative EPV g Vertical velocity in model simulation: solid = upward, dashed = downward As EPV g is reduced from positive values toward 0, the single updraft becomes narrow and more intense. For more widespread and larger negative EPV g the preferred mode becomes multiple bands