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Deep Convection: Physical Processes

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Deep Convection: Physical Processes

M. D. Eastin

Deep Convection: Physical Processes

- Buoyancy:
- Definition, CAPE, and CIN
- Maximum Vertical Motion
- Effects of Updraft Diameter
- Effects of Entrainment
- Downdrafts

- Vertical Shear:
- Hodograph Basics
- Estimating Vertical Shear from Hodographs
- Hodograph Shape
- Estimating Storm Motion from Hodographs
- Hodographs and Convective Storm Type

- Effects of both Buoyancy and Shear:
- Cold Pool – Shear Interactions

M. D. Eastin

Why Buoyancy and Shear?

- Useful Forecast Parameters:
- Forecasters must use synoptic observations to anticipate mesoscale weather:
- Forecast the likelihood of deep convection
- Forecast convective type (single cell, multicell, or supercell)
- Forecast convective storm evolution
- Forecast the likelihood of severe weather

- These mesoscale events can be forecast using common, simple forecast parameters
- that incorporate the concepts of buoyancy and shear using observations obtained
- from soundings
- CAPE and CIN
- Lifted Index (LI)
- Bulk Richardson Number (BRN)
- Storm-Relative Environmental Helicity (SREH)
- Energy Helicity Index (EHI)
- Supercell Composite Parameter (SCP)
- Significant Tornado Parameter (STP)
- CAPE/Shear and BRN Phase Spaces

- First, let’s examine the basic shear and buoyancy processes, and tools to estimate each…

We will cover the

application of these

forecast parameters

in future lectures…

M. D. Eastin

Buoyancy

- Definition of Buoyancy
- Force that acts on a parcel of air due to a density difference between the parcel
- and the surrounding “environmental” air
- The force causes the air parcel to accelerate upward or downward
- Buoyancy is a basic process in the generation of all convective updrafts and downdrafts
- What physical factors determine a parcel’s buoyancy?
- How can we estimate buoyancy from standard observations?
- What are limiting factors for those buoyancy estimates?

M. D. Eastin

Buoyancy

- What physical factors determine a parcel’s buoyancy?
- Let’s return to basic dynamics and the vertical equation of motion:
- For synoptic-scale motions in the free atmosphere the vertical accelerations are small
- and friction is negligible
- Thus, the equation reduces to hydrostatic equation
- Or
- Synoptic-scale systems are largely in hydrostatic balance!

Vertical

Acceleration

Vertical

PGF

Gravity

Friction

M. D. Eastin

Buoyancy

- What physical factors determine a parcel’s buoyancy?
- On the mesoscale, vertical accelerations can be very large, and thus not in hydrostatic
- balance. Also, friction (or turbulent mixing) is no longer negligible, so we now have:
- This equation can be re-written as (see Sections 2.3.3 and 3.1 of you book):
- where:
- Total Buoyancy Force

What does each term

physically represent?

M. D. Eastin

Buoyancy and CAPE

- What physical factors determine a parcel’s buoyancy?
- Thermal Buoyancy:
- Temperature difference between an air parcel
- and its environment
- We estimate the total buoyancy force available to
- accelerate an updraft air parcel by computing the
- Convective Available Potential Energy (CAPE)
- CAPE is the sum of the energy in the positive area

CAPE has units of J/kg

EL

Tenv

Tpar

LFC

CAPE has units of J/kg

M. D. Eastin

Buoyancy and CIN

- What physical factors determine a parcel’s buoyancy?
- Thermal Buoyancy:
- We can also estimate the total buoyancy force
- available to decelerate an updraft air parcel by
- computing the Convective Inhibition (CIN)
- CIN is the sum of the energy in the negative area
- CIN is the result of a capping inversion located
- above the boundary layer
- Remember: The CIN must be overcome before
- deep convection can develop

LFC

CIN has units of J/kg

SFC

Methods to overcome CIN:

1. Mesoscale Lifting

2. Near-surface Heating

3. Near-surface Moistening

M. D. Eastin

Buoyancy and Moisture Effects

- What physical factors determine a parcel’s buoyancy?
- Moisture Buoyancy:
- Specific humidity difference between an air
- parcel (often saturated) and its environment
- Smaller in magnitude, but not negligible
- Can be incorporated into CAPE (and CIN)
- by using virtual temperatures (Tv)
- This incorporation is NOT always done
- When neglected → small underestimation of CAPE
- → small overestimation of CIN

Remember:

M. D. Eastin

Buoyancy and Water Loading

- What physical factors determine a parcel’s buoyancy?
- Water Loading:
- Total liquid (and ice) cloud water content (qc) and
- rain water content (qr)
- Effectively adds weight to the air parcel
- Always slows down (decelerate) updrafts
- Can be large
- Can initiate downdrafts
- Difficult to observe → Can be estimated from
- radar reflectivity once
- storms develop
- Always neglected in the CAPE and CIN calculations

M. D. Eastin

Updraft Velocity

- What is a parcel’s maximum updraft velocity?
- One reason CAPE is a useful parameter to forecasters is that CAPE is directly related
- to the maximum updraft velocity (wmax) an air parcel can attain:
- This equation is obtained from a simplified version of the vertical momentum equation
- that neglect the effects of water loading, entrainment (mixing), and the vertical
- perturbation pressure gradient force (see Section 3.1.1 of your text)
- Due to these simplifications, the above equation often over estimates the maximum
- vertical motion by a factor of two (2):
- Example: →

Accounting for the

simplifications

M. D. Eastin

Limiting Factors

- Effects of Updraft Diameter:
- Any warm parcel produces local
- pressure perturbations on the
- near environment
- A simple mesoscale application
- of the hypsometric equation
- The positive pressure perturbation
- (a relative high pressure) above
- the parcel combined with the
- negative pressure perturbation
- (a relative low pressure) below
- the parcel produce a symmetric
- overturning circulation that allows
- air to move out of the parcel’s path
- and then fill in behind the parcel
- to maintain mass continuity

H

H

L

L

H

H

L

L

H

H

L

L

M. D. Eastin

Limiting Factors

- Effects of Updraft Diameter:
- These pressure perturbations
- produce a downward-directed
- pressure gradient that opposes
- the upward-directed buoyancy
- force – slows down the updraft
- Wide updrafts (bubbles)
- Larger pressure gradients
- Slower updrafts
- Narrow updrafts (bubbles)
- Smaller pressure gradients
- Faster updrafts

H

H

L

L

M. D. Eastin

Limiting Factors

- Effects of Entrainment:
- Entrainment mixing of environmental air into the updraft parcel always decreases
- the net buoyancy force acting on the updraft parcel (which reduces wmax)
- The vertical distributionof CAPE can have a significant effect on how entrainment
- mixing limits updraft strength
- Consider two soundings (A and B)
- with identical CAPE
- Which sounding will produce the
- strongest updraft? Why?

M. D. Eastin

Limiting Factors

- Effects of Entrainment:
- Entrainment mixing of environmental air into the updraft parcel always decreases
- the net buoyancy force acting on the updraft parcel (which reduces wmax)
- The vertical distribution of CAPE can have a significant effect on how entrainment
- mixing limits updraft strength
- Sounding A:
- CAPE confined to the lower levels
- Updraft will accelerate more quickly,
- allowing less time for entrainment
- mixing to reduce its net buoyancy
- Stronger updraft
- Sounding B:
- CAPE spread throughout the depth
- Slow updraft acceleration allows
- more time for entrainment to reduce
- the net buoyancy
- Weaker updraft

M. D. Eastin

Limiting Factors

- Effects of Entrainment:
- Entrainment mixing of environmental air into the updraft parcel always decreases
- the net buoyancy force acting on the updraft parcel (which reduces wmax)
- The amount of environmental moisture can have a significant effect on how
- entrainment mixing limits updraft strength
- Consider two soundings (A and B)
- with identical distributions of CAPE,
- but different environmental moisture
- at mid-levels
- Which sounding will produce the
- strongest updraft? Why?

M. D. Eastin

Limiting Factors

- Effects of Entrainment:
- Entrainment mixing of environmental air into the updraft parcel always decreases
- the net buoyancy force acting on the updraft parcel (which reduces wmax)
- The amount of environmental moisture can have a significant effect on how
- entrainment mixing limits updraft strength
- Sounding A:
- The entrainment of environmental
- air will produce some evaporational
- cooling, reducing the net thermal
- buoyancy
- Updraft will weaken some
- Sounding B:
- Entrainment of environmental air
- will produce lots of evaporational
- cooling, significantly reducing the
- net thermal buoyancy
- Updraft will weaken considerably
- Downdraft may develop

M. D. Eastin

Downdrafts

- What Processes Produce Downdrafts?
- The two primary buoyancy forcing processes
that generate downdrafts are water loading

and evaporational cooling

Water Loading:

- Effectively “drags” air parcels down
- Forcing magnitude depends on the amount
- of water and the initial updraft strength
- (strong updrafts can suspend more water)
- Difficult to determine or forecast
- Evaporational Cooling:
- Results from entrainment mixing
- Cools air parcels → negative thermal buoyancy
- Forcing magnitude depends on the amount of
- water available for evaporation and the dryness
- of the air into which the water would evaporate
- Can determine the maximum cooling a parcel
- might experience → wet-bulb temperature

M. D. Eastin

Downdrafts

- Estimating Downdraft Strength:
- Air parcels experiencing evaporation will
- cool to their wet-bulb temperature (Tw)
- (remember sling psychrometers?)
- Downdrafts experiencing evaporation will
- descend from their wet-bulb temperature
- along a moist adiabat, or at a constant
- wet-bulb potential temperature (θw)
- Represents the coldest temperature
- a downdraft parcel could achieve
- Similar to updrafts, we estimate the total
- buoyancy force available to accelerate a
- descending air parcel by computing the
- Downdraft Convective Available Potential
- Energy (DCAPE)
- The maximum downdraft velocity can also
- be estimated in a similar manner

Evaporation

brings parcel

to saturation

Downdraft

originating

at 700 mb

Tw

DCAPE

Coldest

Possible

SFC Temp

θw

M. D. Eastin

Downdrafts

- Cold Pool Development:
- Besides contributing to downdraft strength,
- evaporative processes also contribute to
- the development, strength, and speed of
- the surface cold pool (and gust front)
- Since the cold pool and gust front help
- initiate further convection, evaporation
- and convective downdrafts are almost
- required for long-lived storms
- Storms in a very moist environment will
- experience minimal evaporation cooling,
- weak downdrafts, small cold pools, and
- often short lifetimes
- Storms in a drier environment experience
- moderate evaporational cooling, ample
- downdrafts, moderate cold pools, and
- often experience long lifetimes
- “Catch 22”: A very dry environment is BAD

M. D. Eastin

Buoyancy Summary

- Summary of Buoyancy Processes:
- Buoyancy is a fundamental process in the generation and maintenance of all convective
- updrafts and downdrafts
- Positive contributions to buoyant energy and updraft strength come from potential
- temperature and water vapor differences from the large-scale environment
- CAPE provides a quantitative estimate of buoyant energy available for updrafts to
- accelerate, especially when calculated using an appropriate low-level average of
- both moisture and temperature (e.g., the lowest 100mb layer)
- • CAPE can be used to estimate updraft strength (wmax)
- CIN can either prevent convective storm development entirely or delay initiation until
- maximum heating is reached
- • Thermodynamic diagrams are the essential tool for estimating the effects of vertical
- buoyancy distribution and entrainment on both updraft and downdraft strength
- • Downdraft strength depends on both water loading and evaporation processes
- • In general, drier mid-levels are associated with stronger downdrafts
- DCAPE provides a quantitative estimate of buoyant energy available for downdrafts to
- accelerate, and can be used to estimate downdraft strength

M. D. Eastin

Vertical Shear

- Definition of Vertical Shear
- The vector difference between the horizontal winds at two levels
- The resulting vector is called the “vertical wind shear”
- A description of how the horizontal winds change with height
- Vertical shear is present in all environments where convective updrafts and downdrafts
- occur (ranging from minimal shear to very large shear)
- How can we estimate vertical shear
- from standard observations?
- How does vertical shear modulate
- storm structure and evolution?

M. D. Eastin

Hodograph Basics

- A Method to Show Vertical Wind Shear: The Hodograph
- A means to convey the vertical profile of winds observed by a sounding (rawindsonde)
- Based on observed winds displayed as vectors
- Shows structure of vertical shear throughout the troposphere

M. D. Eastin

Hodograph Basics

- How a Hodograph is Constructed
- Start with wind observations from a sounding
- Use the polar coordinate system (or a polar stereographic grid)
- Starting at the origin, plot each wind vector as a function of direction and magnitude
- Connect the endpoints of each vector to “form the hodograph”

M. D. Eastin

Vertical Shear

- Estimating Vertical Shear from a Hodograph
- The hodograph is actually composed of the vertical wind shear vectors between each layer
- The shear magnitude and direction for an individual layer is shown by each yellow arrow
- The total shear over a deep layer can be found by summing the length of all shear vectors
through the layer (can be done on hodograph – easier with software → Excel)

Estimating the shear magnitude

for any individual layer

Estimating the total shear magnitude

through a deep layer

Measure the

length of

all the vectors

aligned

along an axis

Measure the

length of any

individual shear

along an axis

M. D. Eastin

Vertical Shear

- Estimating Vertical Shear from a Hodograph
- The hodograph is actually composed of the vertical wind shear vectors between each layer
- The shear magnitude and direction for an individual layer is shown by each yellow arrow
- The mean shear over some layer can be found by first computing the total shear over that
- layer and then dividing by the depth of the layer (more easily done with software → Excel)

Estimating the mean shear magnitude

through a deep layer

Find the total shear,

then divide by

the layer depth

M. D. Eastin

Vertical Shear

- Estimating Vertical Shear from a Hodograph
- The bulk shear through a deep layer can estimated by the following process:
- (experienced forecasters can visually estimate – others use software → Excel):
- Determine the shear vector for each level
- relative to the surface wind (light blue vectors)
- Separate these surface-relative shear vectors
- into their “u” and “v” components
- Compute the mean “u” and “v” through the layer
- Combine the mean components back into vector
- form to get the bulk shear vector
- This four-step process is valid for all hodograph
- shapes and sizes
- The bulk shear magnitude has been found
- to be a good predictor of convective storm type

Bulk Shear

Vector

M. D. Eastin

Vertical Shear Distribution

- Estimating Vertical Shear from a Hodograph
- The distribution of vertical shear through the depth of the hodograph can also have
- important implications for convective storm type

Total shear = 30 kts

Mean shear = 15 kts

Shear evenly

distributed through

the depth

Multicells / Squall Lines

are more likely

Total shear = 30 kts

Mean shear = 23 kts

Most shear (~23 kts)

is confined to the

lowest 3 km

Supercells / Tornadoes

are more likely

M. D. Eastin

Hodograph Shape

- Vertical Shear and Hodograph Shape
- The shape of the vertical shear through the hodograph depth can also have important
- implications for convective storm type as well as structure and evolution …more on
- this later
- Important questions:
- What is the general hodograph shape?
- 1. curved
- 2. straight
- When does it curve?
- 1. throughout the depth
- 2. near the surface
- 3. only aloft
- Through what levels does it curve?
- 1. shallow curve
- 2. deep curve
- What direction does it curve?
- 1. clockwise
- 2. counter-clockwise

M. D. Eastin

Hodograph Shape

- Vertical Shear and Hodograph Shape
- The shape of the vertical shear is influenced by whether speed shear (due to
- wind magnitude differences), directional shear (due to directional differences),
- or some combination of both speed and directional shear are present

Speed Shear

Directional Shear

M. D. Eastin

Hodograph Shape

- Vertical Shear and Hodograph Shape
- The shape of the vertical shear is influenced by whether speed shear (due to
- wind magnitude differences), directional shear (due to directional differences),
- or some combination of both speed and directional shear are present

Examples of Combined Speed and Directional Shear

M. D. Eastin

Storm Motion & Storm Relative Flow

- Significance of Storm-Relative Flow:
- In forecasting storm structure and evolution, a crucial factor is the nature of the storm’s
- inflowing air… Will the inflow be warm and moist or cold and dry?
- Since most storms move through their environment, one must consider a storm’s inflow
- relative to its motion through the environment (i.e. look at the storm-relative flow)
- Thus, we first need estimate the expected storm motion from a hodograph so we can
- subtract it from the ground-relative winds to obtain the storm-relative winds

Ground Relative Winds

Storm Relative Winds

M. D. Eastin

Storm Motion

- Estimating Storm Motion from a Hodograph
- If storms have already developed → Use radar animations to get storm motion
- If storms have not developed → Use hodograph to estimate
- Which levels do we use?
- Observations and numerical models suggest that most convective storms move with a
- velocity close to the 0-6 km AGL mean wind.

M. D. Eastin

Storm Motion

- Estimating Storm Motion from a Hodograph:
- Separate the ground-relative winds at each level in to their “u” and “v” components
- Compute a mean “u” and a mean “v”
- Combine the mean values back into vector form to get the storm motion
- This three-step process is applicable to all hodograph shapes and sizes

Example component separation for 3–km wind

Example Mean Wind Calculation

M. D. Eastin

Storm-Relative Winds

- Estimating Storm-Relative Motions from a Hodograph:
- Re-orient the polar grid origin to the computed storm motion
- Storm-relative winds are determined by drawing vectors from this new origin to the
- shifted hodograph at each level (blue vectors below).
- This two-step process is valid for all hodograph shapes and sizes.

M. D. Eastin

Mean Wind vs. Bulk Shear

Difference between the Mean Wind and the Bulk Shear:

- Bulk Shear
- Relative to the surface wind
- Used to estimate storm evolution
- (more on this aspect later)

- Mean Wind
- Relative to the stationary ground
- Used to estimate storm motion

Mean Shear

Vector

Mean Wind

Vector

Stationary

ground

M. D. Eastin

Vertical Shear and Storm Type

- Composite Observed Hodographs:
- The magnitude and shape of the vertical
- shear profile has a strong influence on
- convective storm type:
- Observed hodographs near deep convection:
- Single cells→ Weak shear
- Multicells→ Moderate shear
- Supercells→ Strong shear

Single Cells

Multicells

Supercells

From Chisholm and Renick (1972)

M. D. Eastin

Vertical Shear and Storm Type

- Spectrum of Hodographs and Storm Types:
- With the help of a numerical model, Joe Klemp and Morris Weisman (NCAR), documented
- how changing only the hodograph shape and shear magnitude can have profound effects
- on storm structure:
- Klemp and Wilhelmson numerical model
- Each simulation has identical initial conditions EXCEPT for the environmental winds
- Environmental CAPE = ~2200 J/kg in each simulation
- A total of seven (7) simulations
- For each simulation the follow information is shown
- Hodograph
- Rainfall structure (contours) at 1.8 km AGL
- Updraft locations (shaded) at 4.6 km AGL
- Surface gust front location (cold front)

Shown for 40, 80,

and 120 min

M. D. Eastin

Vertical Shear and Storm Type

Weak

Deep Shear

Semicircular

Weak Multicell

The cold pool gust front

“out ran” the convection

Convection

along

gust front

Moderate

Deep Shear

Semicircular

Strong Multicell

Weak Supercell

From Weisman

and Klemp (1986)

M. D. Eastin

Vertical Shear and Storm Type

The cold pool gust front

out ran the convection

Weak

Shallow Shear

Curved

Weak Multicell

Convection

along

gust front

Moderate

Shallow Shear

Curved

Strong Multicell

M. D. Eastin

Vertical Shear and Storm Type

Moderate

Deep Shear

Curved-Straight

Two Multicells

(Split)

Convection

along

gust front

Convection

along

gust front

Moderate

Deep Shear

Straight

Two Supercells

(Split)

M. D. Eastin

Vertical Shear and Storm Type

The cold pool gust front

out ran the convection

Strong

Deep Shear

Curved-Straight

Strong Supercell

Weak Multicell

(Split)

Convection

along

gust front

M. D. Eastin

Vertical Shear Summary

- Summary of Shear Processes:
- Vertical shear is a fundamental process in modulating convective storms
- Hodographs are the essential tool for determining the magnitude, direction, and
- shape of the environmental and storm-relative vertical wind shear
- Storm motion can be estimated from a hodograph as the 0-6 km mean wind
- The magnitude and shape of the vertical wind shear has a strong influence on
- convective storm type:
- Weak shear → Single cells and multicells
- Moderate shear → Multicells and supercells
- Strong shear → Supercells
- Shear over a greater depth increases the likelihood of supercells
- Greater curvature increases the likelihood of sueprcells

M. D. Eastin

Effects of Buoyancy and Shear

- Interactions between the Cold Pool and the Vertical Shear :
- The numerical simulation results indicated that the stronger and longer-lived
- multicell and supercell storms where those that continued to develop deep
- convection along the gust front
- Storm type, intensity, and longevity are linked to how the cold pool interacts with
- the low-level vertical shear to continuously lift parcels to their level of free convection
- Let’s examine this process…

M. D. Eastin

Cold Pool and Shear Interactions

- Cold Pool Motion:
- The majority of a cold pool’s “forward”
- speed (c) is a function of it depth and
- its temperature difference from the
- environmental air
- where: h = cold pool depth
- Colder and deeper cold pools move faster
- than “warmer” and shallower cold pools
- A small portion of a cold pool’s forward
motion results from local high pressure

produced hydrostatically within the cold air

and its down gradient flow

M. D. Eastin

Cold Pool and Shear Interactions

- Cold Pool Circulations:
- The spreading cold pool can also be
- described in terms of the circulation
- found at its leading edge
- Vorticity is created at the leading edge
- Vorticity can be created by either:
- Shear
- Tilting
- Density (buoyancy) gradients

- Horizontal vorticity (η) is generated
- when ever there are horizontal
- gradients of buoyancy (B):

z

x

M. D. Eastin

Cold Pool and Shear Interactions

- Cold Pool Circulations:
- By itself, the cold pool can only
- generate deep convection if the
- upward motion on its leading edge
- can lift the warm air to its LFC
- Because the cold pool circulation
- also pulls the warm air back down,
- by itself it may not be efficient at
- retriggering new cells unless the
- LFC is very close to the ground
- Now, let’s add vertical wind shear
- to the picture

M. D. Eastin

Cold Pool and Shear Interactions

- Shear Circulations:
- Vertical shear creates horizontal
- vorticity within the ambient
- (or environmental) flow
- Given westerly vertical wind shear:
- What sign will the ambient
- horizontal vorticity be?
- On which side of the cold
- pool will there be deeper
- lifting as it interacts with
- the vertical wind shear?

z

x

“Upshear”

“Downshear”

Shear Vector

Shear Vector

M. D. Eastin

Cold Pool and Shear Interactions

- Cold Pool – Shear Circulations:
- In this example, new cells will be
triggered on the east side of the

cold pool where the lifting is deeper

- The deeper lifting is created by the
balance between the cold pool and

shear horizontal vorticity

- Thus, assessing the low- to mid-level
- shear vector is crucial for determining
- how a multicell system will propagate

Upshear

Downshear

Shear Vector

M. D. Eastin

Cold Pool and Shear Interactions

- Optimal Interactions:
- Optimal vertical lifting will
- occur when the cold pool
- circulation is of the same
- strength as the shear
- circulation
- (i.e. balanced circulations)
- If either the cold pool
- or shear circulation is
- dominant, then the
- warm inflowing air will
- be “pulled back” by the
- dominant circulation
- creating tilted convection
- Will be discussed more
- when squall lines are
- covered in detail
- (Section 9.3 in your text)

Cool Pool circulation

dominates

Shear circulation

Balanced Cool Pool

and Shear Circulations

Shear circulation

dominates

Cold Pool circulation

M. D. Eastin

Cold Pool and Shear Interactions

- Summary of Cold Pool – Shear Interactions:
- Buoyancy and vertical wind shear are necessary in the creation of long-lived convection
- The propagation speed of a cold pool depends on its magnitude and depth
- • Buoyancy gradients generate horizontal vorticity
- • The lifting created by cold pool circulation alone may be insufficient to allow a surface
- parcel to reach the LFC (unless the LFC is quite low)
- • When low-level wind shear is weak, environmental inhomogeneities determine where
- new cells will be triggered along a spreading cold pool
- • When low-level wind shear is moderate to strong, new cell development is favored
- downshear of the low-level shear vector
- The deepest lifting occurs when the horizontal vorticity generated along the cold pool's
- leading edge is nearly equal in magnitude to and has the opposite sense rotation as
- the horizontal vorticity associated with the low-level vertical wind shear
- In the mid-latitudes, 0 to 2.5 km AGL shear values of 10-20 m/s are generally sufficient
- to promote lifting deep enough to favor new cell development along the downshear
- portion of a gust front (5 m/s can be sufficient in tropical environments). Additional
- shear above this layer can also enhance lifting

M. D. Eastin

References

Brooks, H. E., and R. B. Wilhelmson, 1993: Hodograph curvature and updraft intensity in numerically modeled supercells.

J. Atmos. Sci., 50, 1824-1833.

Chisholm, A. J. and J. H. Renick, 1972: The kinematics of multicell and supercell Alberta hailstorms. Alberta Hail Study, Research Council of Alberta hail Studies, Rep. 72-2, Edmonton, Canada, 24-31.

Doswell C. A., and E. N. Rasmussen, 1994: The effect of neglecting the virtual temperature correction on CAPE calculations. Wea. Forecasting, 9, 625-629.

Gilmore, M. S., and Louis J. Wicker, 1998: The influence of mid-tropospheric dryness on supercell morphology and evolution. Mon. Wea. Rev., 126, 943-958.

Houze, R. A. Jr., 1993: Cloud Dynamics, Academic Press, New York, 573 pp.

Klemp, J. B., 1987: Dynamics of tornadic thunderstorms. Ann. Rev. Fluid Mech., 19, 369-402

Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong long-lived squall lines. J. Atmos. Sci., 45, 463- 485.

Weisman, M. L., and J. B. Klemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Wea. Rev., 110, 504-520.

Weisman, M. L., and J. B. Klemp, 1984: The structure and classification of numerically simulated convective storms in directionally varying wind shears. Mon. Wea. Rev., 112, 2479-2498.

Weisman, M. L. , and J. B. Klemp, 1986: Characteristics of Isolated Convective Storms. Mesoscale Meteorology and Forecasting, Ed: Peter S. Ray, American Meteorological Society, Boston, 331-358.

M. D. Eastin