Cumulus Clouds

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Cumulus Clouds
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Instabilities Resulting in Vertical Overturning

• Thermal Instability (Assuming uniform vertical
  pressure gradient)
• a) Static (Parcel buoyancy)
• b) Conditional (Parcel buoyancy)
• c) Rayleigh Benard (Parcel buoyancy, surface
  friction)
• Dynamic Instabilities
• a) Shear (or inflection point) (Vorticity or
  shear gradient)
• (analogous to barotropic instability)
• 3. Dynamic-Thermal Instabilities
• a) Vertical Shear vs Static Stability
• i. Kelvin-Helmholtz
• iii Gravity wave convection (growing) ,
  evanecent (decaying)
• b) Inertial production (Horizontal Shear) vs
  Static Stability
• i. Symmetric Instability
• ii. Conditional Symmetric Instability (CSI)
• ii Convective - Symmetric Instability(C-SI)

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General Classification of Moist
Convection

• Shallow Cumulus (cumulus, scatted cumulus,
  strato-cumulus)
• Depth small compared to scale height of
  troposphere, i.e.
• Usually confined to Planetary Boundary Layer
  (PBL)
• Typically non-precipitating
• Surface friction plays critical role to
  organization
• Deep Cumulus (congestus, cumulonimbi)
• Depth comparable to scale height of troposphere
• Precipitating
• Friction plays secondary role to organization

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What goes on inside a cumulus cloud?
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Evolution of a thermal from a Numerical Model
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Conceptual Model

• Series of convective plumes rising to form
  individual turrets comprising cloud
• Each rising pulse a toroidal circulation
• Successive toroids give rise to mean upward
  current called updraft
• Sustained downward current between toroids, if
  existing, would be downdraft

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Liquid Water Content
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What causes liquid water content to be below
adiabatic LWC?

• Lateral entrainment
• Neutral mixing
• Dynamic entrainment
• Cloud Top Entrainment

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Bubble and JetModels of Convection
lt mixing lateral entrainment
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Dynamic Lateral Entrainment
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Dynamic Entrainment
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Effects of Dynamic Lateral Entrainment
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Effects of Dynamic Lateral Entrainment
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Cloud Top entrainment
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Deep Cumulus

• Must consider impact of precipitation on cumulus
  circulation
• Must consider pressure effects because of cloud
  depth
• Thermodynamic pressure, ie hydrostatic pressure
• Dynamic pressure due to inertia of air motions
• Friction layer small compared to cloud and we
  generally ignore friction

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Vertical Acceleration(using Pressure)
Inertia
Pressure
Buoyancy
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Vertical Acceleration(Using Total Pressure)
Inertia
Pressure
Buoyancy
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Vertical Acceleration(using Exner function)
Inertia
Pressure
Buoyancy
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Traditional Buoyancy




Vapor less dense than dry air
Warm/Cold air rises/sinks
Liquid water loading
Ice water loading
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Anelastic Approximation

• Neglect frequencies higher than those associated
  with meteorological phenomena such as sound wave
  frequencies
• Similar to incompressible assumption, but for a
  compressible system

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Continuity Equation
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Multiply momentum equation (momentum form) by
density
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Multiply momentum equation (vorticity form) by
density
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Decomposition of Pressure into Dynamic and
Buoyancy Pressure
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Dynamics (or inertia) Terms
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Buoyancy Terms
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Take divergence of density multiplied by three
momentum equations and then result set to zero
and solve for pressure
or
Where pressure is divided into dynamic and
buoyancy pressure contributions
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Buoyancy vs. Dynamic Pressure

• Dynamic pressure, , is zero if flow is at
  rest.
• Buoyancy pressure, , is hydrostatic
  pressure for flow at rest.
• Dynamic pressure results from inertia such as
• Rotation (cyclostrophic pressure)
• Straight line accelerations
• Coordinate system accelerations (coriolis)
• Buoyancy pressure results from
• Moisture anomalies
• Thermal anomalies
• Condensate (precipitation drag)

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Real Buoyancy Acceleration

• True buoyancy acceleration is
• Where we see the acceleration is caused by
  thermal, moisture or precipitation drag anomalies

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Dynamic Pressure Acceleratrion

• True dynamic pressure gradient acceleration is
• Where we see the acceleration is caused by
  inertial effects of rotation, straight line
  movement and coordinate system movement

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Conditional Instability of the First Kind

• Occurs when a parcel is statically unstable when
  saturated but stable when dry
• Results in the formation of moist convective
  thermal plumes, ie cumulus clouds
• Instability favors horizontal scales vertical
  scale of overturning, i.e. meso-gamma scale for
  deep convection

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Three Stages of a Deep Convective Thermal

• Simplest Case
• Conditionally unstable for deep convection
• No environmental wind
• Dry middle layers
• Moist unstable boundary layer

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Stage 1 Cumulus Stage

• Updraft only
• Cloud droplets only (no precipitation)
• Level of Non-divergence (LND) near top of moist
  Planetary Boundary Layer (PBL)
• Cloud positively buoyant throughout
• Environment neutrally buoyant
• Low pressure under updraft
• High pressure throughout cloud

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Stage 2 Mature Stage

• Updraft and downdraft
• Precipitation and cloud droplets throughout cloud
• Level of Non-divergence (LND) at middle levels
• Cloud positively buoyant at middle levels,
  negatively buoyant in lower part
• Cold air dome (density current) at surface
• Environment neutrally buoyant but warming
• Low pressure at middle levels
• High pressure at surface and top of cloud

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Stage 3 Dissipating Stage

• Downdraft only
• Precipitation only throughout cloud
• Level of Non-divergence (LND) at upper levels
• Cloud negatively buoyant throughout
• Environment positively buoyant
• Low pressure at middle levels and above in cloud
• High pressure at surface
• Low pressure at surface of environment

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Reasons for Breakdown

• Water loading of updraft from precipitation drag
• Cooling due to dynamic entrainment of mid level
  dry air

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Introduce Environmental Wind Shear to Prevent
Breakdown

• Assume
• two-dimensions, i.e. infinitely long convective
  line
• Straight-line shear with height, I.e. wind speed
  change with without direction change

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Three-Dimensional Effect of Wind Shear

• As before but now assume convective plume is
  initially circular rather than infinitely long
• Also start by assuming a straight line shear
  profile again
• Assume westerly shear and veering winds in lowest
  6 km

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View from South
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View from East
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Helicity
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Convective Richardson Number
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CAPE
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Wind Shear