Chapter 1: What is the Mesoscale? Mesoscale energy sources
Mar 28, 2015
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