Introduction to Mesoscale Meteorology

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Introduction to Mesoscale Meteorology
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Overview

• Scale Definitions
• Synoptic
• Synoptic derived from Greek synoptikos meaning
  general view of the whole. Also has grown to
  imply at the same sime or simultaneous.
• Synoptic Scale
• The scales of fronts and cyclones studied by the
  early Norwegian scientists. The classic synoptic
  scale are the time and space scales resolved by
  observations taken at major European cities
  having a mean spacing of about 100 km. Hence
  weather systems having scales of a few hundred
  kilometers or more and time scales of a few days
  are generally what is accepted to be synoptic
  scale phenomena.

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Overview

• Scale Definitions
• Cumulus
• Defined by the rise of RADAR meteorology in the
  late 1940s to be the scale of individual
  thunderstorm and cumulus cell echos, this became
  the second important scale of meteorology
  research. This scale is on the order of a couple
  of kilometers to about 50 km and time scales of a
  few minutes to several hours.

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Overview

• Scale Definitions
• Mesoscale (original definition)
• Coined by Lidga (1951), mesoscales are the
  Middle Scales between synoptic scale and
  cumulus scale. This original definition hence
  refered to weather phenomena of scales between
  what were thought to be the two primary energy
  containing scales of cumulus and synoptic scale.
  The Modern Definition is much more robust.

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Overview

• Scale Definitions
• Mesoscale (modern definition)
• Orlanski (1975) proposed a new set of scales
  (ignoring synoptic and cumulus) that include the
  micro-, meso- and macro- scales. Figure 1
  depicts these three definitions. All three
  definitions have gained wide acceptance, despite
  an even newer proposal by Fugita (1981). His
  definition of the mesoscale was scales between
  2 km and 2000 km. Scales larger than 2000 km are
  macroscale and scales smaller than 2 km are
  microscale

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Mesoscale Over The Years
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Overview

• Scale Definitions
• Mesoscale (modern definition, continued)
• Orlanski divides the mesoscale into three
  sub-mesoscales
• Meso- 2-20 km
• Meso- 20-200 km
• Meso- 200-200 km
• We will attach a physical significance to these
  three mesoscales.

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Equations of Motion
Momentum form
Vorticity Form
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Gravity (Buoyancy)
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Pressure Gradient
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Inertial
Coriolis Effect
Rotation Inertial
Irrotational Inertial
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Force Balance
Inertial Balance
_________________________




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Rotation
Hydrostatic Balances
Irrotational
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Physical Significance of Mesoscale

• Two Major Categories of Dynamic Force Balances
  Result
• Hydrostatic Gravity versus Pressure Gradient
• Inertial Inertial Force Versus Gravity
• Geostrophic (Horizontal Pressure Gradient versus
  vertical Coriolis effect)
• Cyclostrophic (Pressure Gradient versus
  rotational and irrotational inertial)
• Gradient (Horizontal Pressure gradient versus all
  inertial)

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Perturbations from Balance

• For stable balance, i.e. stability restores
  balance, perturbations initiate oscillations that
  result in waves
• For unstable balance, perturbations produce a
  growing disturbance

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Perturbations from Hydrostatic Balance

• Perturbations from stable balance lead to
• Gravity or Buoyancy waves
• Horizontal phase speed is
• Perturbations from unstable balance lead to
• Convection

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Perturbations from Geostrophic Balance

• Stable Balance Produces
• Oscillation frequency is f
• Wave speed is on order of
• Unstable Balance produces
• Inertial Instability

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If both hydrostatic and inertial balances occur
and the flow is perturbed,what is the result?

• Depends on which adjustment dominates.
• Determine dominant adjustment from ratio of
  gravity wave phase speed to inertial wave phase
  speed

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The Rossby Radius of Deformation

• Scale at Which There is Equal Inertial and
  Gravity Wave Response
• The definition of Rossby Radius is

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Rossby Radius for axi-symmetric vortex having
tangential wind V and Radius R
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Scale Based on Physical Mechanism

• Small Scales
• Frequency of gravity waves, ie Brunt-Visalia
  Frequency, larger than frequency of inertial
  waves
• Tendency toward hydrostatic balance with g
  dominate
• Large Scales
• Frequency of inertial wave involving Coriolis
  larger than gravity wave
• Balance against inertial acceleration dominates

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Back to Mesoscale Definitions

• At middle latitudes (40 N)
• For a disturbance depth of 7 km
• Hence Rossby radius is typically

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• Scales from 2-20 km
• Disturbances characterized by Gravity (Buoyancy)
  Waves (stable) or Deep Convection (unstable).
• Coriolis effect generally negligible, although
  local inertial effects can arise to change
  character of disturbances (i.e. rotating
  thunderstorms, tornadoes, dust devils, etc)

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Actinae
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Bounadry Layer Convection
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Thunderstorm
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Thunderstorms
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Thunderstorms
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Supercells
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Tornado
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• Scales of 20-200 km
• Less than but near to Rossby Radius
• Gravity (Buoyancy) Waves govern system evolution
  and propagate relative to the wind
• Inertial oscillation important to wave dynamics,
  i.e. Gravity-Inertia Waves

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Sea Breeze Convection
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Meso-beta squall lines
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• Scales of 200-2000 km
• Scales greater than but near to Rossby Radius of
  deformation
• Characterized by Geostrophic Balance
• Geostrophic disturbance determines evolution of
  the system
• Vertical ageostrophic motions driven by
  geostrophic disturbance, ie quasi-geostrophic
  dynamics

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Squall Line
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MCC
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MCC
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ITCZ Cluster
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Tropical Cyclone
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Exceptions to these rules

• These above rules are an approximate description
  of how the three mesoscales divide typical
  disturbances.
• Changes in latitude mean changers in attitude!
  As we move to lower latitudes Coriolis effect
  decreases and the Rossby Radius scale increases,
  going to infinity at the equator! Hence relative
  to the Earths inertial effect, all disturbances
  around the equator are dynamically small, and are
  governed by gravity (buoyancy) waves. Hence, the
  Kelvin wave, a gravity type wave, is a global
  scale equatorial disturbance.

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• Deeper disturbances lead to larger gravity wave
  phase speeds and so larger Rossby Radius and vise
  versa for shallow disturbances. Hence depth of
  the disturbance will affect its governing
  dynamics, the deeper disturbance less likely to
  be inertially balanced and the shallower
  disturbances more likely. Some examples
• Sea Breeze without deep convection shallow,
  likely to achieve significant geostrophic balance
• Sea Breeze with Deep convection Deep, not likely
  to achieve inertial balance
• Mesoscale Convective Complex Deep convection
  parts of the system clearly less than Rossby
  Radius. Stratiform anvil has large horizontal
  scale shallow melting layer that may excite
  inertially balanced disturbance, ie an MCV
  (mesoscale convective vortex).

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• Rotation induced in the system may locally shrink
  the Rossby Radius, making the system dynamically
  large even on meso-beta scales. For example
• Mesocyclone or rotating thunderstorm with its
  forward flanking gust front and rear flanking
  gust fronts actually become quasi balanced and
  evolve very similar to a developing
  quasi-geostrophic baroclinic cyclone with warm
  and cold fronts respectively. This makes the
  supercell thunderstorm long lived.
• The tropical cyclone eye wall becomes inertially
  stable from the strong storm rotation giving rise
  to Rossby wave disturbances (relative to cyclone
  rotation instead of Coriolis) that move around
  the eye, and play significant roles in horizontal
  momenum transport through their tilt!
• Tornadoes survive relatively long periods for
  their size because of their inertial balance and
  locally vey small Rossby Radius of Deformation.

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Special Observation and Analysis Problems of the
Mesoscale

• Synoptic observation systems have horizontal
  resolutions of 100 km and 1 hour at the surface
  and 400 km and 12 hours aloft and are clearly
  inadequate to capture all but the upper end of
  the meso- .
• The dynamics of mesoscale disturbances contain
  important non-balanced or transient features that
  propagate rapidly.
• The systems are highly three-dimensional where
  the vertical structure is equally important to
  the horizontal structure.

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• Mesoscale disturbances are more likely to be a
  hybrid of several dynamic entities interacting
  together to maintain the system.
• Process Interaction is especially significant
  such as microphysical and radiative transfer
  interactions.
• Scale Interactions are basic to the mesoscale
  problem and particularly interactions across the
  Rossby Radius of Deformation

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How Can we Deal with This?

• Use observations as clues to the analysis, and
  do not expect the data to ever be sufficient to
  reveal the process behind the observations.
• Attach a strong dynamical model to the
  observations to fill in the gaps. To the extent
  that the model reproduces the observations at
  points where it is coincident with the
  observations, it gains credibility.
• Study the model to understand the dynamics. If
  the model is consistent with the few
  observations, then the model can be used (always
  with caution) to reveal the dynamics of the
  system.

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What is a Model?

• Models range from simple to complex.
• Simple model Quasi-Geostrophic model positive
  vorticity advection results in upward vertical
  motion. Its so simple we can do it in our heads!
  But it has many approximations and is likely to
  miss features that can be represented in more
  complex models.

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• Primitive Equation Forecast Model Such as the
  Eta model, or AVN model or ECMWF model. Must be
  solved on the computer but much more precise than
  the simple PVA model. Why would anyone look at a
  500mb map predicted by the Eta model and then
  disagree with its vertical motion pattern because
  it doesnt obey the mentally tractable PVA model?
  Some people do!

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• Research Models More precise physics, too big to
  execute in real time but able to provide a deeper
  understanding of specific processes causing an
  observed event.
• These models, used in case study or idealized
  mode provide our basic understanding that we use
  to construct truncated models that can run in
  real time.