The Effect of Stability on Frontogenetical Circulations

1. The Effect of Stability on Frontogenetical Circulations James T. Moore Saint Louis University Cooperative Institute for Precipitation Systems COMET-MSC Winter Weather Course 29 Nov. - 10 Dec. 2004

2. Frontogenetical Circulations:The Influence of Stability • Conditional Instability • Convective Instability • Inertial Instability • Potential/Conditional Symmetric Instability • So…first we will discuss these instability types • Then…we will see how they influence frontogenetical circulations

3. Conditional Instability Conditional Instability is diagnosed through an examination of lapse rates of temperature or saturated equivalent potential temperature (es): (a) m < e < d ; where e = -dT/dz OR (b) des/dz < 0; where es = saturated equivalent potential temperature In (a) one can simply look for environmental lapse rates which are between the dry and moist adiabatic lapse rate. In (b) one can compute es at each level and look for layers where it decreases with height.

4. Conditionally Unstable Lapse Rate on Skew-T log P Diagram es es+1 es+2 Note how the lapse rate is between the dry and moist adiabatic lapse rates. Also, note that the temperature curve cuts across lines of es. As long as the parcel is unsaturated it is stable, after saturation it will become unstable.

5. Understanding Convective Instability Dry over Moist Moist over Dry Very Dry over Moist e/z = 0 e/z > 0 e/z < 0 Convectively Neutral Convectively Stable Convectively Unstable Results of lifting an initially stable, unsaturated layer to saturation given various gradients of moisture. Initial lapse rate is isothermal and 50 mb deep. Dry adiabats are thin solid lines, saturation adiabats are dash-dot lines. Adapted from Hess (1959)

6. Inertial Instability Inertial instability is the horizontal analog to gravitational instability; i.e., if a parcel is displaced horizontally from its geostrophically balanced base state, will it return to its original position or will it accelerate further from that position? Inertially unstable regions are diagnosed where: g + f < 0 ; absolute geostrophic vorticity < 0 OR if we define Mg = vg + fx = absolute geostrophic momentum, then inertially unstable regions are diagnosed where: Mg/ x = vg/ x + f < 0 ; since g = vg/ x (NOTE: vg = geostrophic wind normal to the thermal gradient)

7. Inertial Instability (cont.) • Inertial stability is weak or unstable typically in two regions (Blanchard et al. 1998, MWR): • g + f = (V/Rs - V/ n) + f ; in natural coordinates • Where V/Rs = curvature term and V/ n = shear term • Equatorward of a westerly wind maximum where the anticyclonic relative geostrophic vorticity is large (to offset the Coriolis parameter which is always > 0 in the NH) • In sub-synoptic scale ridges where the anticyclonic curvature is large

8. Typical Regions Where MCS Tend to Form with Respect to the Upper-Level Flow Blanchard, Cotton, and Brown (1998, MWR)

9. Diagnosing Potential Symmetric Instability (PSI) and Conditional Symmetric Instability (CSI) • Construct a cross section taken normal to the 850-300 mb thickness isopleths with the x axis directed towards the warm air. • In the cross-sectional plane display isentropes of e/ esand isopleths of absolute angular momentum (Mg), defined as: Mg = vg + fx , where vg is the geostrophic wind component normal to the cross section, f is the Coriolis parameter, and x is the distance along the x axis. • Note that e/es tends to increase both upward (in convectively/conditionally stable air) and along the x axis (towards the warmer air); Mg tends to increases both upward (as the normal wind component increases with height) and along the x axis (as x increases)

10. Diagnosing PSI/CSI (cont.) • It can be shown that: du/dt = f ( M(parcel) – Mg) and dw/dt = g/e ( e(parcel) - e (env) ) • Where the first expression evaluates the inertial stability and the second expression evaluates the convective stability of the parcel. • If M(parcel) > Mg , the parcel accelerates to the east ( + x) • If M(parcel) < Mg , the parcel accelerates to the west (- x) • If e(parcel) > e (env) , the parcel accelerates upward • If e(parcel) <e (env) , the parcel accelerates downward

11. Diagnosing PSI/CSI (cont.) • For PSI we use e and Mgsurfaces. • For CSI we use es and Mg surfaces. • You should display relative humidity on the cross section since CSI requires near- saturated conditions (i.e., RH > 80%) • There should also be large scale vertical motion in order to “realize” the CSI. • Note: when the e surfaces “fold” underneath themselves there is convective instability.

12. Understanding Conditional Symmetric Instability: Cross section of esand Mg taken normal to the 850-300 mb thickness contours s es-1 es es+ 1 Mg +1 Note: isentropes of es are sloped more vertical than lines of absolute geostropic momentum, Mg. Mg Mg -1

13. Conditional Symmetric Instability (CSI): Theory Parcel A es (parcel) > es (environ) ;  dw/dt > 0 (accel. up) M g (parcel) > M g (environ);  du/dt > 0 (accel. to southeast) Parcel B es (parcel) < es (environ) ;  dw/dt < 0 (accel. down) M g (parcel) < M g (environ);  du/dt < 0 (accel. to northwest) Parcel C es (parcel) > es (environ) ;  dw/dt > 0 (accel. up) M g (parcel) < M g (environ);  du/dt < 0 (accel. to northwest)  Parcel C will accelerate along a slantwise path away from its initial position….it is unstable to slantwise motions!

14. Conditional Symmetric Instability: Synoptic Characteristics • Typically a cool season phenomena • Wind profile: speed increasing with height and weak directional veering with height; indicative of strong baroclinicity • Thermodynamic profile: nearly saturated and close to the moist-adiabatic lapse rate. Parcel motion will be neutral to moist ascent. Lapse rate is NOT conditionally unstable • Often found in the vicinity of a extratropical cyclone warm front, ahead of long-wave troughs in regions of strong, moist, mid-tropospheric southwesterly flow • Large scale forcing for upward vertical motion is usually present

15. Conditional Symmetric Instability: Synoptic Characteristics (cont.) • Soundings reveal a deep, moist layer that is convectively stable with a moist-adiabatic lapse rate • On satellite or radar imagery CSI is exhibited by multiple bands of clouds/precipitation oriented parallel to the mid-tropospheric thermal wind (or thickness lines); sometimes the bands have a component of motion toward the warm air • These heavier precipitation bands may be embedded (obscured) by other lighter precipitation • Warm frontal rain/snow bands are often good candidates for being associated with CSI

16. Typical CSI Sounding Rawinsonde observations for IAD for 1200 UTC 26 February 1993: Region of CSI is above 600 mb in this case Wiesmueller and Zubrick, 1998 (WAF)

17. VWP from WSR-88D KLWX (Sterling, VA) for 1134-1233 UTC 26 February 1993: Note speed shear dominates above 7000 feet Wiesmueller and Zubrick, 1998 (WAF)

18. Conditional Symmetric Instability: Physical Characteristics • Width of the bands is approximately 10-50 km; length of the bands is approximately 100-400 km; time scale of the bands is approximately 3-4 h • Typical CSI vertical motions are on the order of tens of cm s-1 to a few m s-1 and thus, usually DO NOT produce lightning/thunder (need > 5 m s-1 to produce lightning) • However, these mesoscale bands of precipitation can be intense and result in significantly higher rain/snow fall totals than the surrounding area • CSI is characterized by inertial stability and convective stability but, when realized, results in slanted or tilted mesoscale circulations which convert inertial energy into buoyant energy

19. Conditional Symmetric Instability: Physical Characteristics (cont.) • The atmosphere can contain regions of CSI and convective instability (CI), but since CI has a faster growth rate (tens of minutes) relative to CSI (a few hours), it will dominate. • CSI is favored to occur in regions of: • High vertical wind shear • Weak absolute vorticity (values near zero) • Weak convective stability • High mean relative humidity • Large scale ascent • Often these conditions are found in the entrance region of an upper-level jet streak during the cool season

20. Schematic illustration of moist slantwise convective updrafts and downdrafts; slanted updrafts are narrow, saturated and intense, while downdrafts are diffuse, unsaturated and weak. From Emanuel (1984) Dynamics of Mesoscale Weather Systems, NCAR Summer Colloquium Lecture Notes, 11 June – 6 July 1984, p. 159.

21. Three-Dimensional Frontogenesis Equation 1 2 4 3 5 6 7 8 9 10 11 12 Terms 1, 5, 9: Diabatic Terms Terms 2, 3, 6, 7: Horizontal Deformation Terms Terms 10 and 11: Vertical Deformation Terms Terms 4 and 8: Tilting Terms Term 12: Vertical Divergence Terms Bluestein (Synoptic-Dynamic Met. In Mid-Latitudes, vol. II, 1993)

22. Assumptions to Simplify the Three-Dimensional Frontogenesis Equation y’   + 1 x’  + 2 • y’ axis is set normal to the frontal zone, with y’ increasing towards the cold air (note: y’ might not always be normal to the isentropes) • x’ axis is parallel to the frontal zone • Neglect vertical and horizontal diffusion effects

23. Simplified Form of the Frontogenesis Equation A B C D Term A: Shear term Term B: Confluence term Term C: Tilting term Term D: Diabatic Heating/Cooling term

24. Frontogenesis: Shear Term Shearing Advection changes orientation of isotherms Carlson, 1991 Mid-Latitude Weather Systems

25. Frontogenesis: Confluence Term Cold advection to the north Warm advection to the south Carlson, 1991 Mid-Latitude Weather Systems

26. Shear and Confluence Terms near Cold and Warm Fronts Shear and confluence terms oppose one another near warm fronts Shear and confluence terms tend to work together near cold fronts Carlson (Mid-latitude Weather Systems, 1991)

27. Frontogenesis: Tilting Term Adiabatic cooling to north and warming to south increases horizontal thermal gradient Carlson, 1991 Mid-Latitude Weather Systems

28. Frontogenesis: Diabatic Heating/CoolingTerm frontogenesis T constant T increases frontolysis T increases T constant Carlson, 1991 Mid-Latitude Weather Systems

29. Frontogenesis/Frontolysis with Deformation with No Diabatic Effects or Tilting Effects where: and = angle between the isentropes and the axis of dilatation Petterssen (1968)

30. Kinematic Components of the Wind Vorticity Translation Divergence Deformation

31. Stretching and Shearing Deformation Patterns Stretching Deformation Shearing Deformation

32. Stretching Deformation Patterns Stretching along the flow Translational component of wind removed Stretching normal to the flow Translational component of wind removed Bluestein (1992, Synoptic-Dynamic Met)

33. Shearing Deformation Patterns Stretching in a direction 45° to the left of the flow Translational component of wind removed Stretching in a direction 45° to the right of the flow Translational component of wind removed Bluestein (1992, Synoptic-Dynamic Met)

34.  < 45° Frontogenesis Axis of dilatation  > 45° Frontolysis Axis of dilatation Petterssen (Weather Analysis and Forecasting, vol. 1, 1956)

35. Pure Deformation Wind Field Acting on a Thermal Gradient Isotherms are rotated and brought closer together Keyser et al. (MWR, 1988)

36. Deficiencies of Kinematic Frontogenesis • Fronts can double their intensity in a matter of several hours; kinematic frontogenesis suggests that it takes on the order of a day. • Kinematic frontogenesis does not account for changes in the divergence of momentum fields; values of divergence and vorticity in frontal zones are on scales <= 100 km, suggesting highly ageostrophic flow. • Kinematic frontogenesis fails since temperature is treated as a passive scalar. As the thermal gradient changes the thermal wind balance is upset, therefore there is a continual readjustment of the winds in the vertical in an attempt to re-establish geostrophic balance. Carlson (Mid-Latitude Weather Systems, 1991)

37. Frontogenetical Circulation • As the thermal gradient strengthens the geostrophic wind aloft and below must respond to maintain balance with the thermal wind. • Winds aloft increase and “cut” to the north while winds below decrease and “cut” to the south, thereby creating regions of div/con. • By mass continuity upward motion develops to the south and downward motion to the north – a direct thermal circulation. • This direct thermal circulation acts to weaken the frontal zone with time and works against the original geostrophic frontogenesis.

38. Ageostrophic Adjustments in Response to Frontogenetical Forcing West East West East

39. Frontogenetical Circulation North South COLD WARM Thermally Direct Circulation Carlson (Mid-latitude Weather Systems, 1991) Strength and Depth of the vertical circulation is modulated by static stability

40. Sawyer-Eliassen Description of the Frontogenetic Circulation • Includes advections by the ageostrophic component of the wind normal to the frontal zone or jet streak. • The ageostrophic and vertical components of the wind are viewed as nearly instantaneous responses to the geostrophic advection of temperature and geostrophic deformation near the frontal zone. • The cross-frontal (transverse) ageostrophic component of the tranverse/vertical circulations is significant and can become as large in magnitude as the geostrophic wind velocity. • Thus, divergence/convergence and vorticity production in the vicinity of the front take place more rapidly than predicted by purely kinematic frontogenesis. Carlson (Mid-latitude Weather Systems,1991)

41. Frontogenetical Circulation Factors • According to the Sawyer-Eliassen equations (see Carlson, Mid-Latitude Weather Systems, 1991): • The major and minor axes of the elliptical circulation are determined by the relative magnitudes of the static stability and the absolute geostrophic vorticity; the vertical slope is a function of the baroclinicity. • High static stability compresses and weakens the circulation cells. • If the absolute geostrophic vorticity is small (weak inertial stability) in the presence of high static stability the circulation ellipses are oriented horizontally. • If the absolute geostrophic vorticity is large (strong inertial stability) in the presence of small static stability the circulation cells are oriented vertically.

42. High static stability and low inertial stability Result is a shallow but broad circulation. With high static stability, a little vertical motion results in large change in temperature. With low inertial stability, takes longer for Coriolis force to balance the pressure gradient force. Greg Mann, 2004

43. Low static stability and high inertial stability With low static stability, need large vertical motion to change the temperature. With high inertial stability, Coriolis force quickly balances the pressure gradient force. Greg Mann, 2004

44. Role of symmetric stability • Symmetric stability plays a large role in determining the strength and width of the ageostrophic frontal circulation • Small symmetric stability • Intense and narrow updraft • Large symmetric stability • Broad and weak updraft. Greg Mann, 2004

45. Defining Fs and Fn Vectors from the Frontogenesis Function Keyser et al. (1988, MWR)

46. Defining Fs and Fn Vectors from the Frontogenesis Function Keyser et al. (1988, MWR) and Augustine and Caracena (1994, WAF)

47. Interpreting F Vectors • The component of F normal to the isentropes (Fn) is the frontogenetic component; it is equivalent but opposite in sign to the Petterssen frontogenesis function. When F is directed from cold to warm (Fn < 0), the local forcing is frontogenetic, i.e., the large scale is acting to fortify the frontal boundary by strengthening the horizontal potential temperature gradient and increasing the slope of the isentropes. • Conversely, when F is directed from warm to cold (Fn > 0), the forcing is acting in a frontolytic fashion. • The component of F parallel to the isentropes (Fs) quantifies how the forcing acts to rotate the potential temperature gradient. • The F vector is equivalent to the Q vector only when the horizontal wind is geostrophic; thus F is less restrictive. The divergence of F is a only a good approximation of the Q-G forcing for vertical motion when the wind is in approximate geostrophic balance. • However, F vector convergence does NOT necessarily imply upward vertical motion.

48. Application of Frontogenetical Vectors for MCS Formation Synoptic setting favorable for large MCS development. Dashed lines are isentropes and arrows are F vectors, at 850 hPa. Red arrow indicates the low-level jet. ) Augustine and Caracena (1994, WAF)