Convection Initiation Some Theory

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Convection Initiation (Some Theory Fundamentals)

• Stan Trier
• NCAR (MMM Division)

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Outline

• 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
• 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

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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

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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

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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
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Example Skew-T Diagrams
Central U.S. Warm-Season
Oceanic Tropical

• Characteristics (CAPE2750 J/kg, CIN110 J/Kg)
• Moderate PBL RH
• Stable layer above PBL
• Steep midtropospheric lapse rate (very unstable)

• Characteristics (CAPE1000 J/kg, CIN10 J/Kg)
• High PBL RH
• No stable layer above PBL
• Nearly moist-neutral lapse rate (slightly
  unstable)

Deep lifting required
LIttle lifting required
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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

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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
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.
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Boundary Layer Temperature / Moisture Effects on
Convection Inhibition (CIN)
When LCL is above boundary layer, CIN does not
depend uniquely on moist static energy
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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
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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

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Case of a Severe Frontal Rainband with Negligible
CAPE
From Carbone (1982, J. Atmos. Sci.)
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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

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Effects of Layer Lifting on Potentially Unstable
Sounding

• Initial Sounding
• No CAPE for any parcels

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

Layer Lifting
From Bryan and Fritsch (2000, BAMS)
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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

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Moisture Tendency Equation
mean advection
eddy flux convergence
diabatic sources
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Lapse Rate Tendency Equation
differential horizontal advection
differential vertical motion
differential diabatic forcing
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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
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Turbulent Heat and Moisture Fluxes (Cont.)

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

• 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
gt 0 in PBL helps eliminate CIN but the
strong drying from vertical moisture flux reduces
PBL CAPE
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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
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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.)
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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.)
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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.)
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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
• to greater CAPE

Mtn. Top
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
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Influence of Vertical Motions
22 LST Surface q / Winds / Reflectivity

• 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

Sounding location
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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
• 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

Sounding location
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• 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)

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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)

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

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Sea-Breeze Circulation
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Gravity Waves and Related Phenomena

• Unbalanced circulations resulting from convection
  and
• other sources
• Examples related to convective sources
• - Deep (full tropospheric)
• - Shallow (trapped)

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Deep (Full-Tropospheric) Gravity Waves
Vertical Motion Associated with MCS-like Vertical
Heating Profile
Lower-tropospheric ascent near MCS
Deep subsidence farther away
L

• L1 mode associated with convective part of
  heating profile has rapid phase speed
• L2 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.
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Shallow (Trapped) Wave-Like Disturbances
Internal Bore of Wavelength
Density Current

• 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
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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

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HCRs Intersecting Sea-Breeze Front
From Atkins et al. (1995) Mon. Wea. Rev.
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Thank You!

• Stay tuned for Howie and 6 oclock magic!