Chapter 1: What is the Mesoscale?

Mesoscale energy sources

Gage and Nastrom (1985)

[shifted x10 to right]Note two spectral extremes:

(a) A maximum at about 2000 km(b) A minimum at about 500 km

1100 101000wavelength [km]

(1) Scales of atmospheric motion

inertial subrange(Kolmogorov 1941)

35

kSD

power spectrumunits: m2 s-2 per wavenumber (m-1) bin

k = 1/l

FA=free atmos.BL=bound. layerL = long wavesWC = wave cyclonesTC=tropical cyclonescb=cumulonimbuscu=cumulusCAT=clear air turbulence

From Ludlam (prior to Gage/Nastrom)

energy cascade

mes

osca

le

Big whirls have little whirlsthat feed on their velocity;and little whirls have lesser whirls,and so on to viscosity.                  -Lewis Fry Richardson

Scales of atmospheric motion

• Air motions at all scales from planetary-scale to microscale explain weather:– planetary scale: low-frequency (10 days – intraseasonal) e.g. MJO, blocking highs

(~10,000 km) – explains low-frequency anomalies• size such that planetary vort adv > relative vort adv• hydrostatic balance applies

– synoptic scale: cyclonic storms and planetary-wave features: baroclinic instability (~3000 km) – deep stratiform clouds

• size controlled by b=df/dy• hydrostatic balance applies

– mesoscale: waves, fronts, thermal circulations, terrain interactions, mesoscale instabilities, upright convection & its mesoscale organization: various instabilities – synergies (10-500 km) – stratiform & convective clouds

• time scale between 2p/N and 2p/f• hydrostatic balance usually applies

– microscale: buoyant eddies (cumuli, thermals), turbulence: static and shear instability (1-5 km) – convective clouds

• Size controlled by entrainment and perturbation pressures• no hydrostatic balance

gg vv

buoyancy: 2p/N ~ 2p/10-2 ~ 10 minutesinertial: 2p/f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°

gg vv

1fL

URo

1fL

URo

Fig. 1.1

Eulerian vs Lagrangian

• Eulerian time scale te: time for system to pass, assuming no evolution– te=L/U , where L is size, U is basic wind speed

• Lagrangian time scale tl : time for particle to travel through system

– for tropical cyclone or tornado,

– for sea breezes,

– for internal gravity waves,

• Lagrangian Rossby number: intrinsic frequency / Coriolis parameter

– Rol = 1 for inertial oscillations, but Rol >>1 for buoyancy oscillations

• Rossby radius of deformation:

– see COMET module “the balancing act of geostrophic adjustment”

fftRo

ll

2

Nt

ft

V

Rt

l

l

tl

2

2

2

𝐿𝑅=𝑐𝑔𝑟𝑎𝑣𝑖𝑡𝑦𝑤𝑎𝑣𝑒

𝑓≅ 𝑁𝐻𝜋√ 𝑓 𝜁

geostrophic adjustment: principle

𝐿𝑅=𝑐𝑔𝑟𝑎𝑣𝑖𝑡𝑦𝑤𝑎𝑣𝑒

𝑓≪𝐿

L

Will a feature last or dissipate? Estimate its LR

1.2 Mesoscale vs. synoptic scale

Fig. 1.2(Fujita 1992)

1.2 Mesoscale vs. synoptic scaleStorm Predictions Center

Meso-analysis page

Fig. 1.3

24 hr radar loop

1.2 Mesoscale vs. synoptic scale1.2.1 gradient wind balance

1.2.2 hydrostatic balance

on chalkboard key results:

Fig. 1.4

Ro≥1 for mesoscale flow

The aspect ratio (D/L) determines whether hydrostatic balance applies