1. Deep Convection: Physical Processes
Mesoscale
M. D. Eastin

2. 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
Mesoscale
M. D. Eastin

3. 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…
Mesoscale
M. D. Eastin

4. 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?
Mesoscale
M. D. Eastin

5. 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
Mesoscale
M. D. Eastin

6. 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 and 3.1 of you book):
where:
Total Buoyancy Force
What does each term
physically represent?
Mesoscale
M. D. Eastin

7. 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
Mesoscale
M. D. Eastin

8. 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
Mesoscale
M. D. Eastin

9. 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:
Mesoscale
M. D. Eastin

10. 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
Mesoscale
M. D. Eastin

11. 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 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
Mesoscale
M. D. Eastin

12. 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
Mesoscale
M. D. Eastin

13. 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
Mesoscale
M. D. Eastin

14. 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
Consider two soundings (A and B)
with identical CAPE
Which sounding will produce the
strongest updraft? Why?
Mesoscale
M. D. Eastin

15. 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
Mesoscale
M. D. Eastin

16. 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?
Mesoscale
M. D. Eastin

17. 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
Mesoscale
M. D. Eastin

18. 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
Mesoscale
M. D. Eastin

19. 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 θw
Coldest
Possible
SFC Temp
Downdraft
originating
at 700 mb
Evaporation
brings parcel
to saturation Tw
DCAPE
Mesoscale
M. D. Eastin

20. 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
Mesoscale
M. D. Eastin

21. 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
Mesoscale
M. D. Eastin

22. 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?
Mesoscale
M. D. Eastin

23. 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
Mesoscale
M. D. Eastin

24. 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”
Mesoscale
M. D. Eastin

25. 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
Measure the
length of any
individual shear
along an axis
Estimating the total shear magnitude
through a deep layer
Measure the
length of
all the vectors
aligned
along an axis
Mesoscale
M. D. Eastin

26. Estimating the mean shear magnitude
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
Mesoscale
M. D. Eastin

27. 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
Mesoscale
M. D. Eastin

28. Multicells / Squall Lines Supercells / Tornadoes
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
Mesoscale
M. D. Eastin

29. 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
Mesoscale
M. D. Eastin

30. 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
Mesoscale
M. D. Eastin

31. Examples of Combined Speed and Directional Shear
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
Mesoscale
M. D. Eastin

32. 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
Mesoscale
M. D. Eastin

33. 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.
Mesoscale
M. D. Eastin

34. 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
Mesoscale
M. D. Eastin

35. 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.
Mesoscale
M. D. Eastin

36. 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
Mesoscale
M. D. Eastin

37. From Chisholm and Renick (1972)
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)
Mesoscale
M. D. Eastin

38. 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
Mesoscale
M. D. Eastin

39. The cold pool gust front “out ran” the convection
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)
Mesoscale
M. D. Eastin

40. The cold pool gust front
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
Mesoscale
M. D. Eastin

41. 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)
Mesoscale
M. D. Eastin

42. The cold pool gust front
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
Mesoscale
M. D. Eastin

43. 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
Mesoscale
M. D. Eastin

44. 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…
Mesoscale
M. D. Eastin

45. 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
Mesoscale
M. D. Eastin

46. 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
Mesoscale
M. D. Eastin

47. 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
Mesoscale
M. D. Eastin

48. 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? x z
Shear Vector
“Upshear”
Shear Vector
“Downshear”
Mesoscale
M. D. Eastin

49. 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
Shear Vector
Downshear
Mesoscale
M. D. Eastin

50. 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)
Balanced Cool Pool
and Shear Circulations
Cool Pool circulation
dominates
Shear circulation
Cold Pool circulation
Mesoscale
M. D. Eastin

51. 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 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
Mesoscale
M. D. Eastin

52. References Mesoscale M. D. Eastin
Brooks, H. E., and R. B. Wilhelmson, 1993: Hodograph curvature and updraft intensity in numerically modeled supercells.
J. Atmos. Sci., 50,
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,
Doswell C. A., and E. N. Rasmussen, 1994: The effect of neglecting the virtual temperature correction on CAPE calculations. Wea. Forecasting, 9,
Gilmore, M. S., and Louis J. Wicker, 1998: The influence of mid-tropospheric dryness on supercell morphology and evolution. Mon. Wea. Rev., 126,
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,
Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong long-lived squall lines. J. Atmos. Sci., 45,
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,
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,
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,
Mesoscale
M. D. Eastin