Mesoscale Processes

James T. Moore

Cooperative Institute for Precipitation Systems

Saint Louis University

Dept. of Earth & Atmospheric Sciences

moore@eas.slu.edu

COMET-RFC/HPC Hydrometeorology Course

27 November - 4 December 2001

Mesoscale Processes Which Can Result in Enhanced Precipitation

• Conditional Instability• Convective Instability• Inertial Instability• Potential Symmetric Instability• Conditional Symmetric Instability• Weak Symmetric Stability• Convective-Symmetric Instability• Frontogenesis

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) des/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.

Conditionally Unstable Lapse Rate on Skew-T log P Diagram

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.

es es+1 es+2

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)

Understanding Convective Instability

Elevated Convective Instability

• Typically develops north of quasi-stationary or warm fronts

• Associated with moderate southerly low-level jets ( > 15 m s-1) oriented nearly normal to the frontal boundary

• Usually there is a strong north-south gradient of e

• In many cases the CAPE based on the lowest 100 mb is nearly zero while the max e CAPE is over 100 J kg-1

(winter) or 1000 J kg-1 (summer)• Usually associated with strong vertical wind shear;

especially veering with height

Elevated Convective Instability (cont.)

• Thunderstorms may form directly north of boundary or several hundred km north of boundary

• Where thunderstorms form depends upon:– Relative humidity of incoming air stream– Slope of isentropes in vicinity of frontal zone– Strength of the low-level jet (LLJ)– Magnitude of the moisture convergence

Elevated Convective Instability

Trier and Parsons, 1993; MWR, vol. 121, 1078-1098

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)

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

Inertial Instability (cont.)

Typical Regions Where MCS Tend to Form with Respect to the Upper-Level Flow

Blanchard, Cotton, and Brown, 1998 (MWR)

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/ es and 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)

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

Diagnosing PSI/CSI (cont.)

• For PSI we use e and Mg surfaces.• 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.

Understanding Conditional Symmetric Instability: Cross section of es and Mg taken normal to the 850-300 mb thickness contours

es

Mg +1

es+ 1es-1

Mg

Mg -1

s

Note: isentropes of es

are sloped more verticalthan lines of absolutegeostropic momentum,Mg.

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!

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

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

Wiesmueller and Zubrick, 1998 (WAF)

Rawinsonde observations for IAD for 1200 UTC 26 February 1993:

Region of CSI is above 600 mb in this case

Typical CSI Sounding

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)

Conditional Symmetric Instability: Physical Characteristics

• Width of the bands is approximately 100 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

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

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.

Note: 2-D Form of EPV; Mg must use vg; which is the geostrophic wind component normal to the cross section

Equivalent Potential Vorticity (EPV)

• When EPV < 0 potential symmetric instability (PSI) is present.

• However, EPV is also < 0 when there is convective instability – you need to see if the lines of e are “folded” , I.e., where e decreases with height to separate areas of CI from areas of CSI. CI will dominate.

• Schultz and Schumacher (1999, MWR) suggest using es (saturated e instead of regular e) to assess CSI.

E P V gx

v

p y

u

p

v

x

u

yf

p

e g e g g g e

Three-Dimensional Form of EPV Equation

McCann (1995, WAF) derived a 3-D form of the EPV equation which can be computed from gridded data:

Note that in this form EPV is a function of the:

1) Horizontal gradient of e,

2) Vertical shear of the geostrophic wind (a.k.a. the thermal wind,

3) Absolute geostrophic vorticity, and

4) Convective stability

Nicosia and Grumm (1999, WAF) Conceptual Model for CSI

• Differential moisture advection northeast of the surface low (in the previous diag.) leads to a steepening of the e/es surfaces.

• Mid-level frontogenesis increases the north-south thermal gradient, thereby increasing the vertical wind shear. In this case the easterlies increase below while the westerlies increase above – which increases the differential moisture advection, increasing the e/ es surfaces’ slope.

EPV Tendency Equation from Nicosia and Grumm (1999, WAF)

d(EPV)/dt k e x

Figure from Nicosia and Grumm (1999,WAF). Zone of EPV reduction occurs where the mid-level dry tongue jet overlays the low-level easterly jet (or cold conveyor belt), north of the surface low. In this area dry air at mid-levels overruns moisture-laden low-level easterly flow, thereby steepening the slope of the e surfaces.

Nicosia and Grumm (1999, WAF) Conceptual Model for CSI

• Also….since the vertical wind shear is increasing with time the Mg surfaces become more horizontal (become flatter). Thus, a region of PSI/CSI develops where the e/es

surfaces are more vertical than the Mg surfaces.

• In this way frontogenesis and the develop- ment of PSICSI are linked.

Problems in Diagnosing CSI Operationally

• Temporal Resolution: CSI is resolved in 3-5 h while current data collection is every 12 h.

• Spatial Resolution: Precipitation bands are meso- scale with lengths of 100-200 km and widths of 50-100 km.

• Geostrophic assumption is not always valid (e.g., in regions of cyclonic curvature or within ULJ exit/entrance regions).

• When the shear vector turns with height, the inertial stability criteria is no longer valid for some portions of the cross section; Mg is not strictly conserved.

Convective-Symmetric Instability

• In certain mesoscale environments, typically in the spring, with large CAPE and strong vertical wind shear (associated with an upper-level jet streak), the atmosphere may be convectively and symmetrically unstable

• Under these conditions, parcel descent is along sloped isentropic surfaces in the symmetrically unstable region, and is directed back toward the generating convection

• There is upright convection in the region of large CAPE with associated vertical subsidence and warming. This circulation is coupled with the sloped descent.

• Convective-SI has been discussed by Blanchard, et al. (1998, MWR) and Jascourt et al. (1988, MWR).

Schematic of Convective-Symmetric Instability Circulation

Blanchard, Cotton, and Brown, 1998 (MWR)

Convective-Symmetric Instability

Multiple Erect Towers with Slantwise Descent

Conditional Symmetric Instability in the Presence of Synoptic Scale Lift – Slantwise Ascent and Descent

Multiple Bands with Slantwise Ascent

Frontogenesis: Shear Term

Shearing Advection changes orientation of isotherms and contracts them

Carlson, 1991 Mid-Latitude Weather Systems

Frontogenesis: Confluence Term

Cold advection to the north

Warm advection to the south

Carlson, 1991 Mid-Latitude Weather Systems

Frontogenesis: Tilting Term

Adiabatic cooling to north and warming to south increases horizontal thermal gradient

Carlson, 1991 Mid-Latitude Weather Systems

Frontogenesis: Diabatic Heating/Cooling Term

frontogenesis

frontolysis

T constant T increases

T increases T constant

Carlson, 1991 Mid-Latitude Weather Systems

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.

West East

West East

Ageostrophic Adjustments in Response to Frontogenetical Forcing

North South

Thermally Direct Circulation

Strength and Depth of the vertical circulation is modulated by static stability

Note: The slope and magnitude of the vertical circulation is modulated by the static stability

Frontogenetical Circulation

Q vectors

Direct Thermal Circulation

Confluent Flow

Holton, 1992

Frontogenetical Circulation

• Frontogenetical circulations typically result in one band of precipitation which is parallel to the frontal zone.

• The strength of this circulation is modulated by the ambient static stability.

• Grumm and Nicosia (1997, NWD) found in their studies that a weakly stable environment in the presence of frontogenesis lead to one transient band of heavy precipitation.

• However, they also found that frontogenesis in the presence of greater stability resulted in classic CSI bands of precipitation.

Frontogenesis and Weak Symmetric Stability

• Emanuel (1985, JAS) has shown that in the presence of weak symmetric stability the frontogenetical circulation is changed.

• The upward branch of the vertical circulation becomes contracts and becomes stronger. The strong updraft is located ahead of the region of maximum geostrophic frontogenetical forcing.

• The distance between the front and the updraft is typically on the order of 50-200 km

• On the cold side of the frontogenetical forcing EPV >>0 and the downward motion is broader and weaker than the updraft.

Frontogenetical Circulation

Frontogenetical Circulation + WSS

Emmanuel (1985, JAS)

Sanders and Bosart, 1985: Mesoscale Structure in the Megalopolitan Snowstorm of 11-12 February 1983. J. Atmos. Sci., 42, 1050-1061.

Nolan-Moore Conceptual Model

• Many heavy precipitation events display different types of mesoscale instabilities including:– Convective Instability (CI; e decreasing with

height)– Conditional Symmetric Instability (CSI; lines

of es are more vertical than lines of constant absolute geostrophic momentum or Mg)

– Weak Symmetric Stability (WSS; lines of es

are nearly parallel to lines of constant absolute geostrophic momentum or Mg)

Nolan-Moore Conceptual Model for CI-CSI-WSS

Nolan-Moore Conceptual Model

• These mesoscale instabilities tend to develop from north to south in the presence of strong uni-directional wind shear (typically from the SW)

• CI tends to be in the warmer air to the south of the cyclone while CSI and WSS tend to develop further north in the presence of a cold, stable boundary layer.

• It is not unusual to see CI move north and become elevated, producing thundersnow.

Nolan-Moore Conceptual Model

• CSI may be a precursor to elevated CI, as the vertical circulation associated with CSI may overturn e surfaces with time creating convectively unstable zones aloft.

• We believe that most thundersnow events are associated with elevated convective instability (as opposed to CSI).

• CSI can generate vertical motions on the order of 1-3 m s-1 while elevated CI can generate vertical motions on the order of 10 m s-1 which are more likely to create charge separation and lightning.

Emanuel’s Conceptual Model of CSI-associated Vertical Circulation

Emanuel (1985, JAS)

Parting Thoughts on Banded Precipitation

• Numerical experiments suggest that weak positive symmetric stability (WSS) in the warm air in the presence of frontogenesis leads to a single band of ascent that narrows as the symmetric stability approaches neutrality.

• Also, if the forcing becomes horizontally widespread and EPV < 0, multiple bands become embedded within the large scale circulation; as the EPV decreases the multiple bands become more intense and more widely spaced.

• However, more research needs to be done to better understand how bands form in the presence of frontogenesis and CSI.