Welcome to Mesoscale Meteorology

- the scales of fronts and cyclones studied first byNorwegian 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 ofkilometers and time scales of a few days are generallyaccepted to be “synoptic scale” phenomena.

Scale definitions - historical

Synoptic scale:

- derived from Greek “synoptikos” meaning generalview of the whole. In meteorology has been acceptedto imply “simultaneous”, since the “view of the whole” isobtained by mapping observations made simultaneously ata number of locations.

-the scale of individual thunderstorms and cumulus cells.

This scale became the second important scale of meteorological research when radars first began observingweather systems after World War II.

-Spatial scale of about 1-50 km and time scale of a few minutes toseveral hours.

Scale definitions - historical

Cumulus scale:

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 meteorologicallyinsignificant or “meteorological noise”, but rather are vital to local forecasts.

Tepper, M., 1959: Mesometeorology – the link between macro-scale atmosphericMotions 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 mesoscalemeteorology. Chapter 1, Mesoscale Meteorology andForecasting. 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 onthe characteristic time and size of atmospheric phenomena

This scale remains the most widely used terminology in meteorologybecause of its simplicity

Fujita (1981) and (1986) proposed a scale that was based on order-of-magnitude categories starting at the circumference of the earth

40000-4000 km Maso- 4000-400 km Maso- 400-40 km Meso-

40-4 km Meso- 4-0.4 km Miso- 400-40 m Miso-

40-4 m Moso- 4-0.4 m Moso- 40-4 cm Musu-4-0.4 cm Musu-

Fujita’s scale never caught on with the meteorological community

Scales have traditionally been assigned based on:

observationsobservation networkstheory

Mesoscale meteorology involves:

specific processes of energy transferspecial events associated with instability or local forcing

Emanuel (1986) viewpoint

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 Hurricane is an example of an air-sea interaction instability, but on what scale?

The Mesoscale Convective System is an example of convective instability, but on what scale?

Consider the simplified frictionless equations of motion:

s

p

Dt

DV

1

fuy

p

Dt

Dv

1

gz

p

Dt

Dw

1

We can write these in natural coordinates (see Holton, p. 57) as

Force balance parallel to flow direction “s”

fVR

V

n

p

21

Force balance normal (n) to flow direction “s”

gz

p

Dt

Dw

1

Force balance in vertical

fvx

p

Dt

Du

1

PHYSICAL SIGNIFICANCE OF MESOSCALE

Two major categories of force balances result:

Hydrostatic gz

p

1 gravity vs. vertical PGF

Inertial

s

p

1

0fVn

p

1

fVR

V

2

R

V

n

p 21

(geostrophic) Coriolis vs. Horizontal PGF

Coriolis vs. Centrifugal force

H. PGF vs. Centrifugal force

(inertial)

(cyclostrophic)

s

p

1

0

s

p

1

0

s

p

1

0(gradient) H. PGF vs. Centrifugal And Coriolis force

fVR

V

n

p

21

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

z

gL

k

Nc z

g

2

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

2x

R

fL

k

fc

Perturbations from unstable balance leads to disturbances (e.g. baroclinic instability and cyclones)

In nature, both hydrostatic and inertial, stable and unstablebalances 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

fL

NL

c

cR

x

z

R

go 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:

1oR

f

HN

f

NLL z

R

In the middle latitudes: f ~ 10-4 s –1

H ~ 10 km (depth of disturbance) N ~ 1 10 –2 s –1

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- Scale

Disturbances characterized by gravity (buoyancy) waves in stableconditions and convection in unstable conditions

Coriolis effect generally negligible, although local inertial effectscan arise to change the character of the disturbance

2 – 20 km (<< Rossby radius)

Tornadoes Supercells

Valley flows Lake-effect convection

Meso- Scale

Gravity (buoyancy) waves govern system evolutionOrganized convection in unstable conditions

Inertial oscillations important to wave dynamics (gravity-inertia waves)Inertial effects modify the organization of convection

20 – 200 km (Approaching Rossby radius)

Sea Breeze convection Mesoscale convective system

Hurricane eyewall

Meso- Scale

Smaller circulations characterized by gravity-inertia response

Larger circulations characterized by near geostrophic/gradient wind balance

Ageostrophic circulations driven by disturbances in balanced flow

200 – 2000 km (> Rossby radius)

Hurricane Mesoscale convective vortex

Fronts Jetstreaks

Meso 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°NTropical squall line vs Mid-latitude squall lineCoriolis is 0 at equator – equatorial disturbances

are governed by gravity waves even atthe global scale!

Changes in the depth of a system alters the governing dynamics

Sea breeze with convection vs. withoutConvective vs Stratiform region of MCS

Rotation induced by the system can shrink the Rossby radiusaltering the governing dynamics

Mesocyclone with its gust frontsContracting eyewall of a hurricane

Problems for mesoscale research:

• Synoptic observation systems have horizontalresolutions of 50 km (or worse) and 1 hour at the surfaceand 400 km and 12 hours aloft and are clearlyinadequate to capture all but the upper end of themeso

• The dynamics of mesoscale disturbances containimportant non-balanced or transient features thatpropagate rapidly.

• The systems are highly three-dimensional so thatthe vertical structure is equally important to thehorizontal structure.

• 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

Problems for mesoscale research:

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 thedynamics of mesoscale phenomena requires a temporally and spatially complete, dynamically consistent data set, allof which a model provides.

High resolution: Models can now simulate many mesoscalephenomena 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 layerforcing, 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 togoverning 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 completeobservations, high resolution revealing model simulations, andbasic theory for mesoscale phenomena.