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Welcome to Mesoscale Meteorology
Scale definitions - historical
Synoptic scale:
- derived from Greek “synoptikos” meaning general
view of the whole. In meteorology has been accepted
to imply “simultaneous”, since the “view of the whole” is
obtained by mapping observations made simultaneously at
a number of locations.
- the scales of fronts and cyclones studied first by
Norwegian scientists. The “classic” definition of the synoptic
scale was based on the space scales resolved by observations
taken at European cities, which have a mean spacing of about
100 km. Weather systems having scales of hundreds of
kilometers and time scales of a few days are generally
accepted to be “synoptic scale” phenomena.
Scale definitions - historical
Cumulus scale:
-the scale of individual thunderstorms and cumulus cells.
This scale became the second important scale of
meteorological research when radars first began observing
weather systems after World War II.
-Spatial scale of about 1-50 km and time scale of a few minutes to
several hours.
Scale definitions - historical
Mesoscale:
First coined by M. Lidga* (MIT radar meteorologist) in 1951
“It is anticipated that radar will provide useful information concerning the
structure and behavior of that portion of the atmosphere which is not covered
by either micro- or synoptic meteorological studies. We have already observed
on with radar that precipitation formations which are undoubtedly of
significance occur on a scale too gross to be observed from a single station,
yet too small to appear even on sectional synoptic charts. Phenomena of this
size might well be designated meso-meteorological.”
*Ligda, M. G. H., 1951: Radar storm observations. In Compendium
of Meteorology, AMS, Boston, 1265-1282
Scale definitions - historical
Mesoscale:
Concept expanded in paper by Tepper (1959)
“…the emphasis on the larger scale motion and the deliberate disregard of
the smaller scale motions has become well engrained among meteorologists.”
He argued that motions smaller than macro-scale are not meteorologically
insignificant or “meteorological noise”, but rather are vital to local forecasts.
Tepper, M., 1959: Mesometeorology – the link between macro-scale atmospheric
Motions and local weather. Bull. Amer. Meteor. Soc., 40, 56-72.
Scale definitions - modern
There have been several papers that attempt to “define” mesoscale
Orlanski, I, 1975: A rational subdivision of scales for atmospheric
processes. BAMS, 56, 527-530
Fujita, T. T., 1981: Tornadoes and downbursts in the context of
generalized planetary scales. J. Atmos. Sci., 38, 1512-1534.
Fujita, T. T., 1986: Mesoscale classifications: their history and their
application to forecasting. Chapter 2, Mesoscale Meteorology and
Forecasting, pp. 18-35
Emanuel, K.A., 1986: Overview and definition of mesoscale
meteorology. Chapter 1, Mesoscale Meteorology and
Forecasting. pp 1-17.
Thunis, P., and R. Bornstein, 1996: Hierarchy of Mesoscale Flow
Assumptions and Equations. J. Atmos. Sci., 53, 380–397.
Orlanski (1975) proposed a scale definition based on
the characteristic time and size of atmospheric phenomena
This scale remains the most widely used terminology in meteorology
because of its simplicity
Fujita (1981) and (1986) proposed a scale that was based on orderof-magnitude categories starting at the circumference of the earth
40000-4000 km
4000-400 km
400-40 km
40-4 km
4-0.4 km
400-40 m
40-4 m
4-0.4 m
40-4 cm
4-0.4 cm
Maso-
Maso-
Meso-
Meso-
Miso-
Miso-
Moso-
Moso-
Musu-
Musu-
Fujita’s scale never caught on with the meteorological community
Emanuel (1986) viewpoint
Scales have traditionally been assigned based on:
observations
observation networks
theory
Mesoscale meteorology involves:
specific processes of energy transfer
special events associated with instability or local forcing
Physical significance of scales of motion:
Definition of system: Emanuel proposes defining a “system” as a
rapidly evolving perturbation in a more slowly evolving larger
circulation (e.g. below). (Can you think of other examples?)
Scales associated with atmospheric systems:
Some scales are naturally defined by radiational processes
(troposphere depth, diurnal cycle, N-S temperature gradient).
Some scales may be related to the normal mode oscillations
inherent in the atmosphere (gravity waves, Rossby waves)
Some scales may be related to instabilities in the atmosphere
(convective cells, jetstream circulations associated with interial
instability)
Some scales may be related to external forcing of flows
(sea breeze, lake effect storms, mountain waves, valley flows)
Emanuel proposes a natural breakdown of phenomena into
free (associated with instabilities)
forced (circulations driven by boundaries).
Factors that control convective instabilities operate below the mesoscale,
although the resulting circulations, such as MCSs, are considered mesoscale.
The Mesoscale Convective System is an
example of convective instability, but on what
scale?
The Hurricane is an example of an air-sea
interaction instability, but on what scale?
Consider the simplified frictionless equations of motion:
Du
1 p

 fv
Dt
 x
Dv
1 p

 fu
Dt
 y
Dw
1 p

g
Dt
 z
We can write these in natural coordinates (see Holton, p. 57) as
DV
1 p

Dt
 s
Force balance parallel to flow direction “s”
1 p V 2


 fV
 n R
Force balance normal (n) to flow direction “s”
Dw
1 p

g
Dt
 z
Force balance in vertical
PHYSICAL SIGNIFICANCE OF MESOSCALE
Two major categories of force balances result:
Hydrostatic 
1 p
g
 z
gravity vs. vertical PGF
Inertial
(geostrophic)  1 p  fV
 n
V2
  fV
(inertial)
R
1 p V 2

(cyclostrophic) 
 n R
(gradient)
1 p V 2


 fV
 n R
0
1 p
 s
Coriolis vs. Horizontal PGF
0
1 p
 s
Coriolis vs. Centrifugal force
0
1 p
 s
0
1 p
 s
H. PGF vs. Centrifugal force
H. PGF vs. Centrifugal
And Coriolis force
Perturbations from balance
For stable balance:
Stability restores balance: perturbations initiate oscillations
that result in waves
For unstable balance:
A growing disturbance results
Perturbations from Hydrostatic Balance
Perturbations from stable balance lead to gravity (buoyancy) waves
Horizontal phase speed
N Lz
cg  
k 2
g 
 z
Perturbations from unstable balance leads to convection
Perturbations from Inertial Balance
Perturbations from stable balance lead to inertial (e.g. Rossby) waves
Horizontal phase speed
fLx
f
cR  
k 2
Perturbations from unstable balance leads to disturbances
(e.g. baroclinic instability and cyclones)
In nature, both hydrostatic and inertial, stable and unstable
balances exist and the flow is perturbed in numerous ways
So what is the result??
Depends on which adjustment dominates….
We can estimate what the dominant adjustment will be from
the ratio of the gravity wave speed to the inertial wave speed
cg
Lz N
Ro 

cR Lx f
Rossby Radius of Deformation
What is the Rossby Radius of Deformation?
Scale at which there is an equal inertial and gravity wave response
The Rossby Radius is given by:
Ro  1
Lz N HN
LR 

f
f
-4
–1
In the middle latitudes: f ~ 10 s
H ~ 10 km (depth of disturbance)
–2
–1
N ~ 1 10 s
Rossby radius of deformation is about 1000 km
MESOSCALE METEOROLOGY
Scale based on Physical Mechanisms
Small scales (Lx << LR)
- Tendency toward hydrostatic balance with gravity
the dominant restoring force for perturbations.
Large scales (Lx >> LR)
- Tend toward geostrophic balance with the Coriolis
force the dominant restoring force for perturbations.
Meso-g Scale
2 – 20 km (<< Rossby radius)
Disturbances characterized by gravity (buoyancy) waves in stable
conditions and convection in unstable conditions
Coriolis effect generally negligible, although local inertial effects
can arise to change the character of the disturbance
Tornadoes
Supercells
Valley flows
Lake-effect convection
Meso- Scale
20 – 200 km (Approaching Rossby radius)
Gravity (buoyancy) waves govern system evolution
Organized convection in unstable conditions
Inertial oscillations important to wave dynamics (gravity-inertia waves)
Inertial effects modify the organization of convection
Sea Breeze convection
Mesoscale convective system
Hurricane eyewall
Meso- Scale
200 – 2000 km (> Rossby radius)
Smaller circulations characterized by gravity-inertia response
Larger circulations characterized by near geostrophic/gradient
wind balance
Ageostrophic circulations driven by disturbances in balanced flow
Hurricane
Fronts
Mesoscale convective vortex
Jetstreaks
Meso ,,g designations a convenience, but are neither firm
boundaries nor clear discriminators of underlying dynamics
Consider for example that:
Changes in latitude alter the Coriolis effect
Hurricane at 10°N vs 40°N
Tropical squall line vs Mid-latitude squall line
Coriolis is 0 at equator – equatorial disturbances
are governed by gravity waves even at
the global scale!
Changes in the depth of a system alters the governing dynamics
Sea breeze with convection vs. without
Convective vs Stratiform region of MCS
Rotation induced by the system can shrink the Rossby radius
altering the governing dynamics
Contracting eyewall of a hurricane
Mesocyclone with its gust fronts
Problems for mesoscale research:
• Synoptic observation systems have horizontal
resolutions of 50 km (or worse) 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 so that
the vertical structure is equally important to the
horizontal structure.
Problems for mesoscale research:
• 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
processes include microphysical and radiative
transfer interactions.
• Scale Interactions and particularly interactions
across the Rossby Radius of Deformation are
basic to the mesoscale problem
Approaches to understanding mesoscale processes
1. Observations (advantages)
Discovery: Mesoscale phenomena are discovered
through observation (Models rarely if
ever predict the existence of a phenomena
until it is observed).
Structure: The basic physical structure of phenomena
can be described through analysis of observations
Hypothesis: Hypotheses concerning the dynamic forcing
thermodynamic processes, and microphysical
processes are posed on the basis of observations.
Validation: Observations serve as the benchmark for
validating the quality of numerical model
simulations of the phenomena.
Approaches to understanding mesoscale processes
1. Observations (disadvantages)
Incomplete: Mesoscale phenomena are never observed
adequately to determine their complete structure
or underlying dynamics
Dynamically inconsistent: Observations have errors that
are large enough that the dynamics of mesoscale
systems are difficult to retrieve.
Rare: Focused field campaigns that cost millions of dollars
are required to collect special data sets. These often
yield a few high quality case studies.
Approaches to understanding mesoscale processes
2. Modeling (advantages)
Comprehensive dataset: Understanding the
dynamics of mesoscale phenomena requires a temporally
and spatially complete, dynamically consistent data set, all
of which a model provides.
High resolution: Models can now simulate many mesoscale
phenomena at high resolution.
Dynamically consistent: If the model is consistent with the
observations, then the model can be used (always with caution)
to reveal the dynamics of the system.
Approach in understanding mesoscale processes
2. Models (disadvantage)
Modeled processes inconsistent with true atmospheric behavior:
Parameterizations within model (e.g. radiation, boundary layer
forcing, diffusion, microphysical processes, convection)
Can produce misleading, yet good looking solutions
(worst case: right answer for wrong reason).
Boundaries and initial conditions inconsistent with atmosphere
structure and forcing: Poorly posed boundary conditions and
initial conditions can render model solutions inadequate.
Approach in understanding mesoscale processes
3. Theory
Explain basic phenomena in terms of analytical solution to
governing equations.
Advantage: Explanation is grounding in basic physical
arguments. Provides foundation for understanding.
Disadvantage: Can be wrong or misleading.
Example: The Conditional Instability of the Second Kind (CISK)
theory for tropical cyclone formation, taught
for almost 40 years, did not incorporate air-sea interaction
processes related to sea surface temperature and
near surface wind speed.
OUR APPROACH IN THIS COURSE
We will be reviewing key papers that present the most complete
observations, high resolution revealing model simulations, and
basic theory for mesoscale phenomena.

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