MesoscaleM. D. Eastin Deep Convection: Physical Processes

Mesoscale M. D. Eastin

Deep Convection: Physical Processes


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


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…

Why Buoyancy and Shear?

We will cover the application of these forecast parameters in future lectures…


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?

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!

Buoyancy

zFgz

p

Dt

Dw

1

VerticalAcceleration

VerticalPGF

Gravity Friction

0Dt

Dw0zF

gz

p

gz

p

1

0


• 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

mixingBz

p

Dt

Dw

1


Buoyancy

zFgz

p

Dt

Dw

1

rc qqgqgT

TgB

61.0

What does each termphysically represent?

tenvironmenparcel TTTTT

tenvironmenparcel ppppp

tenvironmenparcel qqqqq


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

rc qqgqgT

TgB

61.0


Buoyancy and CAPE

dzT

TTgCAPE

EL

LFC env

envpar

CAPE has units of J/kg

envpar TTTTT

CAPE has units of J/kg

LFC

EL

TparTenv


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

rc qqgqgT

TgB

61.0


Buoyancy and CIN

CIN has units of J/kg

Methods to overcome CIN:

1. Mesoscale Lifting 2. Near-surface Heating 3. Near-surface Moistening

dzT

TTgCIN

LFC

SFC env

envpar

LFC

SFC


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

rc qqgqgT

TgB

61.0


Buoyancy and Moisture Effects

qTTv 61.01

dzT

TTgCAPE

EL

LFC envv

envvparv

Remember:

rc qqgqgT

TgB

61.0



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

Buoyancy and Water Loading


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: →

Updraft Velocity

CAPEw 2max

1

1

22

22max

6.31

2.63

4000

20002

sm

sm

sm

smwkgJCAPE /2000

Accounting for thesimplifications


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

Limiting Factors

H H

L L

H H

L L

H H

L L


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

Limiting Factors

H H

L L


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?

Limiting Factors




• 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

Limiting Factors




• 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?

Limiting Factors




• 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

Limiting Factors


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

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

Downdrafts

θw

ColdestPossible

SFC Temp

Downdraftoriginatingat 700 mb

Evaporationbrings parcelto saturation

Tw

DCAPEw 2max

DCAPE

dzT

TTgDCAPE

origZ

SFC env

envpar


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

Downdrafts


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

Buoyancy Summary


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?

Vertical Shear


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

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”

Hodograph Basics


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 magnitudethrough a deep layer

Measure the length of

all the vectorsaligned

along an axis

Vertical Shear



• 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 magnitudethrough a deep layer

Find the total shear,then divide by the layer depth

Vertical Shear



• 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

Vertical Shear

Bulk ShearVector



• The distribution of vertical shear through the depth of the hodograph can also have important implications for convective storm type

Total shear = 30 ktsMean shear = 23 kts

Most shear (~23 kts)

is confined to thelowest 3 km

Supercells / Tornadoesare more likely

Total shear = 30 ktsMean shear = 15 kts

Shear evenly

distributed throughthe depth

Multicells / Squall Linesare more likely

Vertical Shear Distribution


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

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

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

Hodograph Shape


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

Storm Motion & Storm Relative Flow

Ground Relative Winds Storm Relative Winds


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.

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

Storm Motion

Example component separation for 3–km wind Example Mean Wind Calculation


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.

Storm-Relative Winds


Difference between the Mean Wind and the Bulk Shear:

Mean Wind vs. Bulk Shear

Mean Wind

• Relative to the stationary ground• Used to estimate storm motion

Bulk Shear

• Relative to the surface wind• Used to estimate storm evolution

(more on this aspect later)

Stationaryground

Mean WindVector

Mean ShearVector


Vertical Shear and Storm Type

Supercells

Single Cells

From Chisholm and Renick (1972)

Multicells

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


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



From Weisman and Klemp (1986)

Weak Deep ShearSemicircular

Weak Multicell

Moderate Deep ShearSemicircular

Strong MulticellWeak Supercell

The cold pool gust frontout ran the convection

Convectionalong

gust front



Weak Shallow Shear

Curved

Weak Multicell

Moderate Shallow Shear

Curved

Strong Multicell

Convectionalong

gust front




Moderate Deep Shear

Curved-Straight

Two Multicells

(Split)

Moderate Deep Shear

Straight

Two Supercells

(Split)

Convectionalong

gust front

Convectionalong

gust front



Strong Deep Shear

Curved-Straight

Strong SupercellWeak Multicell

(Split)Convection

along gust front



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

Vertical Shear Summary


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…

Effects of Buoyancy and Shear


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

Cold Pool and Shear Interactions

ghc 2


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):


x

B

t

x

z


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



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

u

x

z

Shear Vector

“Upshear” “Downshear”Shear Vector


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 DownshearShear Vector


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 circulationdominates

Shear circulation

Shear circulationdominates

Cold Pool circulation


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



ReferencesBrooks, 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.

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MesoscaleM. D. Eastin Deep Convection: Physical Processes