Convection Initiation (Some Theory & Fundamentals)

Stan Trier

NCAR (MMM Division)

Outline

1. Assessment of vertical stability

a. Review of parcel theory and conditional instability

i. CAPE, CIN and Skew-T (sounding) diagrams

b. Potential instability and layer lifting

2. Thermodynamic destabilization processes

a. Equations for moisture and lapse rate change

b. Physical processes

i. Turbulent heat and moisture fluxes

ii. Horizontal advections

iii. Vertical motions

3. Broad categories of vertical motion mechanisms

Parcel Theory (Assumptions)

• Vertically displaced air exchanges no mass or heat with surroundings

• Instantaneous adjustment to the ambient pressure

• Subsaturated air parcels change temperature at dry adiabatic lapse rate

• Saturated air parcels change temperature at moist adiabatic lapse rate which ranges from ~ 4 K / km (warm lower troposphere) to ~ 10 K / km

• Vertical accelerations governed only by the buoyancy force

pz ~ 10 K/kmd pdT d g c

s

(z) (z) (z)vp v vB

Parcel Theory Cont. (Definitions)

• Conditional Instability: Vertical displacement must be sufficient to saturate the air parcel, whereby the reduced rate of cooling upon subsequent ascent would allow the parcel to eventually become positively buoyant

• Lifting Condensation Level (LCL): An air parcel (which conserves ) becomes saturated at this level (owing to adiabatic cooling) if given a sufficient upward displacement

• Level of Free Convection (LFC): Level at which vertically displaced air parcel becomes warmer than ambient atmosphere and subsequently accelerates vertically due to positive buoyancy

• Level of Neutral Buoyancy (LNB): Level at which ascending air parcel becomes colder than ambient atmosphere and decelerates vertically due to negative buoyancy

/ zs dT

, vq

Parcel Theory Cont. (Definitions)

Parcel theory assumes complete conversion of potential to kinetic energy

Strength of vertical motion required to raise air parcel to its LFC

p

zvp v

vz z

[ (z) (z)]CIN dz

(z)

LFC

g

zvp v

vz

[ (z) (z)]CAPE dz

(z)

LNB

LFC

g

max p (z ) 2CAPEw w LNB

2CINw

Example Skew-T Diagrams

Central U.S. Warm-Season Oceanic Tropical

Characteristics (CAPE=2750 J/kg, CIN=110 J/Kg):• Moderate PBL RH• Stable layer above PBL• Steep midtropospheric lapse rate (very unstable)

Characteristics (CAPE=1000 J/kg, CIN=10 J/Kg):• High PBL RH• No stable layer above PBL• Nearly moist-neutral lapse rate (slightly unstable)

Deep lifting required LIttle lifting required

Some Other Examples

Western U.S. Warm Season Central U.S. “Elevated” Instability

• Deep, dry PBL with moist midlevels• Strong downdraft, wind potential, little rain

• Most unstable air with little CIN located above PBL• Common at night and north of warm/stationary fronts

Boundary Layer Temperature / Moisture Effects on CAPE and Vertical Velocity

• Positive buoyancies occur under saturated conditions

Moist static energy (h = gz + cpT + Lq) conserved

Since L / cp ~ 2.5

Parcel theory predicts complete conversion of buoyancy to kinetic energy with wmax = (2 CAPE)1/2

r = 0.9

Rough equivalence of boundary layer Tempand moisture effects on storm strengthin well-developed convection cases

From Crook (1996), Mon. Wea. Rev.

(1 g/kg) ~ 2.5 (1 C)vq T

Boundary Layer Temperature / Moisture Effects on Convection Inhibition (CIN)

When LCL is above boundary layer, CIN does not depend uniquely on moist static energy

More Boundary Layer Temperature / Moisture Effects on Convection Inhibition (CIN)

Quantification from Crook (1996):

For temperature and moisture increases of equal moist static energy

Some limiting cases:

Some Limitations of Parcel Theory

• Tends to overestimate convective strength (vertical velocities) or triggering

- no consideration of dry entrainment, water loading, adverse VPGFs

• Cases with limited CAPE can produce very strong convection

- strong forcing features (e.g., sharp fronts) and strong environmental vertical shear can produce favorable VPGFs

• Most applicable to conditionally unstable air parcels in localized regions

- convection may also occur in rapidly evolving environments with potential instability when deep layer lifting occurs

z 0e

Case of a Severe Frontal Rainband with Negligible CAPE

From Carbone (1982, J. Atmos. Sci.)

Some Limitations of Parcel Theory

• Tends to overestimate convective strength (vertical velocities) or triggering

- no consideration of dry entrainment, water loading, adverse VPGFs

• Cases with limited CAPE can produce very strong convection

- strong forcing features (e.g., sharp fronts) and strong environmental vertical shear can produce favorable VPGFs

• Most applicable to conditionally unstable air parcels in localized regions

- convection may also occur in rapidly evolving environments with potential instability when deep layer lifting occurs

z 0e

Effects of Layer Lifting on Potentially Unstable Sounding

From Bryan and Fritsch (2000, BAMS)

Initial Sounding:• No CAPE for any parcels

Layer Lifting Final Sounding:• Deep Moist Absolutely Unstable Layer (MAUL)• Positive CAPE w/ no CIN

-1

100 mb~ 6 h

5 b s

pt

Thermodynamic Destabilization

• Forecasting of CI is hampered by limited availability of sounding information in space and time

• Knowledge of physical processes must generally be used to anticipate local evolution of thermodynamic stability

• Both CAPE and CIN are sensitive to the lapse rate and the lower-tropospheric moisture

Moisture Tendency Equation

mean advection eddy fluxconvergence

diabaticsources

Lapse Rate Tendency Equation

differentialhorizontaladvection

differentialverticalmotion

differentialdiabaticforcing

Turbulent Heat and Moisture Fluxes

Daytime heating results in increaseof PBL depth and potential temperature

PBL growth depends on severalfactors including:

• vigor of turbulent eddies

• stability of air above PBL

Turbulent Heat and Moisture Fluxes (Cont.)

• In quiescent conditions the vertical moisture flux convergence < 0 term can be critical

• Unlike , qv decreases above PBL

• When not balanced by surface evaporation or moisture advection, as PBL grows qv can decrease significantly due to vertical flux term

• Large temporal decreases most common when dry air exists above PBL and inversion is not too strong

In this example vertical heat flux convergence > 0 in PBL helps eliminate

CIN but the strong drying from vertical moisture flux reduces PBL CAPE

Turbulent Heat and Moisture Fluxes (Cont.)

• Different Example (Day Before, Same Location and Quiescent Synoptic Condition)

• Stronger initial inversion and moister conditions above the PBL than previous example

• No temporal drop in PBL qv

In this example, the heating/vertical mixing process also reduces CIN but this time

results in increased PBL CAPE

Heating Gradients and Induced Circulations

Cloud Streets

DeepConvective

Initiation

Numerical Simulation

From Trier, Chen and Manning (2004, Mon. Wea. Rev.)

• Simulation indicates convective initiation within 100-200 km zone of PBL rolls near surface moisture gradient (dryline)

Heating Gradients and Induced Circulations

1000-1400 CST Time-Averaged Sfc Heat Flux

Legend: Color Shading (updrafts 2 cm/s intervals) Green Lines (downdrafts 2 cm/s intervals) Labeled Black Lines (Winds in cross-section)

From Trier, Chen and Manning (2004, Mon. Wea. Rev.)

Heating Gradients and Induced Circulations

Legend: Color Shading (updrafts 2 cm/s intervals) Green Lines (downdrafts 2 cm/s intervals) Labeled Black Lines (Winds in cross-section)

From Trier, Chen, and Manning (2004, Mon. Wea. Rev.)

Terrain Influence on Timing of Convection Initiation

AC – Dry adiabat from sfc convective temperature to CCLEG – Dry adiabat from mtn convective temperature to CCLHatched Areas – Energy Input required to reach convective temperature at different elevations

From Bluestein (1993) Synoptic-Dynamic Meteorology in Midlatitudes Vol. II

• Daytime convection over “lowlands” typically begins later than over adjacent terrain due to greater surface heating required

• Mountain high-level heat source may help initiate solenoidal circulation in which ascent and moisture transport occur over slope

• Convection over “lowlands” more intense due to greater CAPE Mtn. Top

Plains

Influence of Vertical Motions

22 LST Surface Winds / Reflectivity

Sounding location

• Afternoon sounding conditionally unstable but with stable layer above PBL

• Lifting above frontal surface contributes to 100-deep unstable “saturated” layer that allows development of E-W oriented nocturnal convective band

• Here, the lifting both 1) transports moisture in the vertical, raising the RH as ascending air adiabatically cools, and 2) steepens the midtropospheric lapse rate, which together allow organized convection to proceed

Lifting and Horizontal Advection of Moisture

Sounding location

• Another case of nocturnal convection along and north of a quasi-stationary surface front

• Unlike previous case, lifting alone cannot explain local evolution of the sounding

• Here, the MAUL has mixing ratio values much greater than at any level in the 6-h old sounding indicating importance of horizontal advection

02 LST Surface Winds/ Reflectivity

• Environmental lower-tropospheric ascent (at some horizontal scale) generally required to initiate organized convection

• In many cases mesoscale vertical motion is important in allowing organized convection to persist beyond several cycles of convective cells (caveat, self-sustaining convection in strong shear)

Forced (Isentropic) Mesoscale Ascent

• Occurs with horizontal warm temperature advection

- Can saturate conditionally or potentially unstable lower-tropospheric layers (direct initiation)

- Can reduce CIN defining where fine-scale mechanisms can more easily initiate convection (indirect initiation)

- May be orographically forced or associated with overrunning of statically stable air masses

• Examples:

- Relative flow up frontal surfaces (e.g., Low-level jets)

- Mesoscale convective vortices (MCVs)

Raymond and Jiang (JAS 1990) Conceptual Model of Isentropic Lifting within a Steady Balanced Vortex (e.g., MCV)

Solenoidal Circulations

• Thermally-direct atmospheric flows forced by baroclinity

- under hydrostatic conditions strength is governed by horizontal temperature gradient and depth through which it extends

- often associated with differential surface heating

• Sources:

- sloped or irregular terrain (e.g., mountain-valley circulation)

- land-water contrasts (e.g., sea-breezes)

- land-surface contrasts (e.g., vegetative differences, soil moisture gradients)

- spatial variations in cloudiness

- antecedent convection (e.g., gust fronts)

Sea-Breeze Circulation

Gravity Waves and Related Phenomena

• Unbalanced circulations resulting from convection and

other sources

• Examples related to convective sources

- Deep (full tropospheric)

- Shallow (trapped)

Deep (Full-Tropospheric) Gravity Waves

From Mapes (1993) J. Atmos. Sci.

Vertical Motion Associated with MCS-like Vertical Heating Profile

L

Lower-tropospheric ascentnear MCS

Deep subsidencefarther away

• L=1 mode associated with convective part of heating profile has rapid phase speed

• L=2 mode associated with stratiform component of MCS heating profile has slower phase speed (~ 20 m/s) and may cause vertical displacements sufficient to destabilize initially small CIN environments

Shallow (Trapped) Wave-Like Disturbances

Density Current Internal Bore ofWavelength

• Gravity-wave related phenomena can be excited by antecedent convection

• Statically stable nocturnal PBL provides an environment where such disturbances can maintain coherence

From Simpson (1997), An Introduction to Atmospheric Density Currents

Turbulent PBL-Based Circulations

• In situations with little or no CIN, PBL-based circulations can determine where deep convection first initiates

• Horizontal convective roll circulations (for example) have differences in potential temperature and moisture between ascending and subsiding branches

• Can define sites where deep convective clouds form on mesoscale boundaries

HCRs Intersecting Sea-Breeze Front

From Atkins et al. (1995) Mon. Wea. Rev.

Thank You!

• Stay tuned for Howie and 6 o’clock magic!