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  s ~ 4 K / km (warm lower troposphere) to ~ 10 K / km
•
Vertical accelerations governed only by the buoyancy force
 d  dTp dz  g cp ~ 10 K/km
B   vp (z)   v (z)   v (z)
Parcel Theory Cont. (Definitions)
• Conditional Instability:  s    T / z   d
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  , qv )
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
Parcel Theory Cont. (Definitions)
z  LNB
CAPE 

g
z  LFC
[ vp (z)   v (z)]
 v (z)
dz
Parcel theory assumes complete conversion of potential to kinetic energy
wmax  wp (z  LNB)  2CAPE
z  LFC
CIN  

z  zp
g
[ vp (z)   v (z)]
 v (z)
dz
Strength of vertical motion required to raise air parcel to its LFC
w  2CIN
Example Skew-T Diagrams
Central U.S. Warm-Season
Characteristics (CAPE=2750 J/kg, CIN=110 J/Kg):
• Moderate PBL RH
Deep lifting required
• Stable layer above PBL
• Steep midtropospheric lapse rate (very unstable)
Oceanic Tropical
Characteristics (CAPE=1000 J/kg, CIN=10 J/Kg):
• High PBL RH
LIttle lifting required
• No stable layer above PBL
• Nearly moist-neutral lapse rate (slightly unstable)
Some Other Examples
Western U.S. Warm Season
• Deep, dry PBL with moist midlevels
• Strong downdraft, wind potential, little rain
Central U.S. “Elevated” Instability
• 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
Parcel theory predicts complete conversion of
buoyancy to kinetic energy with wmax = (2 CAPE)1/2
• Positive buoyancies occur under saturated conditions
Moist static energy (h = gz + cpT + Lq) conserved
Since L / cp ~ 2.5
qv (1 g/kg) ~ 2.5T (1 C)
r = 0.9
Rough equivalence of boundary layer Temp
and moisture effects on storm strength
in well-developed convection cases
From Crook (1996), Mon. Wea. Rev.
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  e z  0 when deep layer lifting occurs
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  e z  0 when deep layer lifting occurs
Effects of Layer Lifting on Potentially Unstable Sounding
Initial Sounding:
• No CAPE for any parcels
Layer Lifting
t 
p


100 mb
~6h
5  b s -1
Final Sounding:
• Deep Moist Absolutely
Unstable Layer (MAUL)
• Positive CAPE w/ no CIN
From Bryan and Fritsch (2000, BAMS)
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 flux
convergence
diabatic
sources
Lapse Rate Tendency Equation
differential
horizontal
advection
differential
vertical
motion
differential
diabatic
forcing
Turbulent Heat and Moisture Fluxes
PBL growth depends on several
factors including:
• vigor of turbulent eddies
• stability of air above PBL
Daytime heating results in increase
of PBL depth and potential temperature
Turbulent Heat and Moisture Fluxes (Cont.)
• In quiescent conditions the vertical moisture flux convergence
term can be critical
<0
• Unlike q, 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
Numerical Simulation
Cloud Streets
• Simulation indicates convective initiation
within 100-200 km zone of PBL rolls
near surface moisture gradient (dryline)
Deep
Convective
Initiation
From Trier, Chen and Manning (2004, Mon. Wea. Rev.)
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
• 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
Mtn. Top to greater CAPE
Plains
AC – Dry adiabat from sfc convective temperature to CCL
EG – Dry adiabat from mtn convective temperature to CCL
Hatched Areas – Energy Input required to reach convective
temperature at different elevations
From Bluestein (1993) Synoptic-Dynamic Meteorology in Midlatitudes Vol. II
Influence of Vertical Motions
22 LST Surface q
/
Winds / Reflectivity
• Afternoon sounding conditionally unstable
but with stable layer above PBL
Sounding location
• 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
02 LST Surface q
/
Winds/ Reflectivity
• Another case of nocturnal convection along
and north of a quasi-stationary surface front
Sounding location
• 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
• 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
Vertical Motion Associated with MCS-like Vertical Heating Profile
Lower-tropospheric ascent
near
MCS
L
Deep subsidence
farther 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
From Mapes (1993) J. Atmos. Sci.
Shallow (Trapped) Wave-Like Disturbances
Density Current
Internal Bore of
Wavelength 
• 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!