Lackmann, Chapter 1:

Basics of atmospheric motion

time scales of atmospheric variability

Lovejoy 2013, EOS

Lovejoy 2013, EOS

time scales of atmospheric variability

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

35

kSD

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

From Ludlam (1973)

Energy cascade

synoptic scale

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

Markowski & Richardson 2010, Fig. 1.1

Scales of atmospheric motion

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. 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

• smaller features, whose relative vort adv > planetary vort adv• 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 (100-500 km) – stratiform & convective clouds

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

– microscale: cumuli, thermals, K-H billows, turbulence: static instability (1-5 km) – convective clouds

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

b gg vv

2p/N ~ 2p/10-2 ~ 10 minutes2p/f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°

1.4 thermal wind balance

yT

pp

fRu

yT

fpR

ygp

RT

fg

pu

gpRT

pZ

yZ

fgu

g

g

g

)2(

)1( geostrophic wind

hypsometric eqn

plug (2) into (1)

finite difference expression:

this is the thermal wind: an increase in wind with height due to a temperature gradient

greater thickness

lower thickness

y

ug

ug

The thermal wind blows ccw around cold pools in the same way as the geostrophic wind blows ccw around lows. The thermal wind is proportional to the T gradient, while the geostrophic wind is proportional to the pressure (or height) gradient.

ug=0

Let’s verify qualitatively that climatological temperature and wind fields are roughly in thermal wind balance.

For instance, look at the meridional variation of temperature with height (in Jan)

Around 30-45 ºN, temperature drops northward, therefore westerly winds increase in strength with height.

The meridional temperature gradient is large between 30-50ºN and 1000-300

hPa

thermal wind

Therefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa.

Question:

Why, if it is colder at higher latitude, doesn’t the wind continue to get stronger with altitude ?

There is definitively a jet ...

Answer: above 300 hPa, it is no longer colder at higher latitudes...

tropopause

Tp

Tp

Tp

Tp

Z500500500 ˆ Zk

fgv g

Z500-Z1000

ZkfgZZk

fgvvv

TkfpR

fpR

xT

yT

fpR

pv

pu

pv

ggT

ggg

ˆˆ

ˆ,,

100050010005001000,500

baroclinicity• The atmosphere is baroclinic if a horizontal temperature gradient is

present• The atmosphere is barotropic if NO horizontal temperature gradient

exists– the mid-latitude belt typically is baroclinic, the tropical belt barotropic

• The atmosphere is equivalent barotropic if the temperature gradient is aligned with the pressure (height Z) gradient– in this case, the wind increases in strength with height, but it does not

change direction equivalent barotropic

Z Theight

gradienttemperature gradient

warmcold

baroclinic

warm

cold

geostrophic wind at various levels

1gv

1gv

12 ggT vvv

1.4.2 Geostrophic T advection:cold air advection (CAA) & warm air advection

(WAA)

highlight areas of cold air advection (CAA) & warm air advection (WAA)

CAA

WAA

WAA & CAA

geostrophic temperature advection: the solenoid method

lower

heigh

t Z

greate

r Z

geostrophic wind: Z

fgv

xZ

yZ

fgZk

fgv

g

g

,ˆ

warm

cold

warm

cold

lower

Z

greate

r Z

fatter arrow: larger T gradient T

TZfgTv

Tv

g

g

geo. temperature advection is:

the magnitude is:

the smaller the box, the stronger the temp advection

Let us use the natural coordinate and choose the s direction along the thermal wind (along the isotherms) and n towards the cold air. Rotating the x-axis to the s direction, the advection equation is:

)0∂T∂ that (note ,

∂T∂

∂T∂

sn

Vt n

Thermal wind and geostrophic temperature advection

V nwhere is the average wind speed perpendicular to the thermal wind.

local T change T advection

The sign of     

+ -

V n

VT VT

V n V n

12 ggT vvv

warm

coldwarm

cold

If the wind veers with height,      is positive and there is warm advection. If the wind is back with height,      is negative and there is cold advection.

V n V n

+ -

VTVT

V n V n

WARM

WARM

COLD

COLD

)0∂T∂ that (note ,

∂T∂

∂T∂

sn

Vt n

0>∂T∂t

WAA

0<∂T∂tCAA

Thermal wind and temperature advection

Procedure to estimate the temperature advection in a layer:

1. On the hodograph showing the upper- and low-level wind, draw the thermal wind vector.

2. Apply the rule that the thermal wind blows ccw around cold pools, to determine the temperature gradient, and the unit vector n (points to cold air)

3. Plot the mean wind      , perpendicular to the thermal wind. Note that      is positive if it points in the same direction as n. Then the wind veers with height, and you have warm air advection.

If there is warm advection in the lower layer, or cold advection in

the upper layer, or both, the environment will become less stable.

V n

V n

thermal wind and temperature advection

example

x

y

1000gv

850gv

1000850 ggT vvv

WARM

COLD

0>∂T∂t

n

V n

0 nV

veering wind warm air advectionbetween 1000-850 hPa

10°C

5°C

s

friction-inducednear-surfaceconvergence into lows/trofs

1.5 vorticity

shear and curvature vorticity

fa

? ora

a

av

Hovmoller diagrams (Fig. 1.20)