Introduction to Mesoscale Meteorology

Overview

Scale Definitions Synoptic

Synoptic derived from Greek “synoptikos” meaning general view of the whole. Also has grown to imply “at the same time” or “simultaneous”.

Overview

Scale Definitions 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.

Overview

Scale Definitions Cumulus

Defined by the rise of RADAR meteorology in the late 1940’s to be the scale of individual thunderstorm and cumulus cell echoes, 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.

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 referred 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.

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 Fujita (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”

Mesoscale Over The Years

Overview

Scale Definitions Mesoscale (modern definition,

continued) Orlanski divides the “mesoscale” into

three “sub-mesoscales”:1. Meso-α : 200-2000 km2. Meso-β : 20-200 km3. Meso-γ : 2-20 km

We will attach a physical significance to these three mesoscales.

Equations of Motion

' '

, , 3i i

j i j k j k ij i o

u uu f u g

t x x

' '

, , 3( )ii j k j j k i

i i o

u kf u g

t x x

Momentum form:

Vorticity Form

21

2 ik u , ,j

i i j kk

u

x

, ,i j k j kA B A B

, ,

0 i=j, or j=k, or i=k

1 i,j,k are 1,2,3 or 2,3,1 or 3,1,2

1 i,j,k are 3,2,1 or 2,1,3 or 1,3,2i j k

if

if

if

1000

p

R

c

p

pc

mb

Gravity (Buoyancy)

'

o

g

Pressure Gradient

'

ix

Inertial

i

k

x

, ,i j k j ku

, ,i j k j kf u Coriolis Effect

Rotation Inertial

Irrotational Inertial

Force Balance

iu

t

Inertial Balance

' '

, , 3( )i j k j j k ii i o

kf u g

x x

RotationIrrotational

Hydrostatic Balances

________________

|_________________________

|

| |

Physical Significance of Mesoscale

Two Major Categories of Dynamic Force Balances Result

1. Hydrostatic: Gravity versus Vertical Pressure Gradient

2. Inertial: Inertial Force versus Horizontal Pressure Gradienta) Geostrophic (Horizontal Pressure Gradient

versus Coriolis Force)b) Cyclostrophic (Horizontal Pressure Gradient

versus Rotational Inertial)c) Gradient (Horizontal Pressure Gradient versus

all Inertial)

Perturbations from Balance

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

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

2z

go

N L gc

k z

Perturbations from Geostrophic Balance

Stable Balance Produces Oscillation frequency is f Wave speed is on order of :

Unstable Balance produces: Inertial Instability

2x

i

fLfc

k

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:

g zo

i h

c L NR

c L f

The Rossby Radius of Deformation

Scale at Which There is Equal Inertial and Gravity Wave ResponseThe definition of Rossby Radius is:

g ZR

c L N HNL

f f f

Rossby Radius for axi-symmetric vortex having tangential wind “V” and Radius “R”

1

1 22

2

gR

cL

Vf f

R

Scale Based on Physical Mechanism

Small Scales Frequency of gravity waves, i.e. Brunt-

Vaisala Frequency, larger than frequency of inertial waves

Tendency toward hydrostatic balance with gravity dominate

Large Scales Frequency of inertial wave involving

Coriolis larger than gravity wave Balance against inertial acceleration

dominates

Back to Mesoscale Definitions

At middle latitudes (40 N) :

For a disturbance depth of 7 km:

Hence Rossby radius is typically:

4 110f s

120gc ms

200RL km

Meso-γ

Scales from 2-20 kmDisturbances 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)

Actinae

Boundary Layer Convection

Thunderstorms

Thunderstorms

Thunderstorms

Supercells

Tornado

Meso-β

Scales of 20-200 kmLess than but near to Rossby RadiusGravity (Buoyancy) Waves govern system evolution and propagate relative to the windInertial oscillation important to wave dynamics, i.e. Gravity-Inertia Waves

Sea Breeze Convection

Meso-beta squall lines

Meso-beta squall lines

Meso-α

Scales of 200-2000 km Scales greater than but near to Rossby Radius of deformationCharacterized by Geostrophic Balance Geostrophic disturbance determines evolution of the systemVertical ageostrophic motions driven by geostrophic disturbance, i.e. quasi-geostrophic dynamics

Squall Line

MCC

MCC

ITCZ Cluster

Tropical Cyclone

Exceptions to these rulesThese 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 Earth’s 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.

Exceptions (Cont’d.)

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, i.e. an MCV (mesoscale convective vortex).

Exceptions (Cont’d.)

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.

Examples (Cont’d.)

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 momentum transport through their tilt!Tornadoes survive relatively long periods for their size because of their inertial balance and locally very small Rossby Radius of Deformation.

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-α.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.

Observation and Analysis (Cont’d.)

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

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.

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.

Models (cont’d.)

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 doesn’t obey the mentally tractable PVA model? Some people do!

Models (cont’d.)

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.