Lackmann - PowerPoint Presentation

Slide1

Lackmann, Chapter 1:

Basics of atmospheric motionSlide2

time scales of atmospheric variability

Lovejoy 2013, EOS Slide3

Lovejoy 2013, EOS

time scales of atmospheric variabilitySlide4

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

1

100

10

1000

wavelength [km]

(1) Scales of atmospheric motion

inertial subrangeSlide5

FA=free atmos.

BL=bound. layer

L = long waves

WC = wave cyclones

TC=tropical cyclones

cb

=cumulonimbus

cu=cumulus

CAT=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 Slide6

Markowski

& Richardson 2010, Fig

. 1.1

Scales of atmospheric motionSlide7

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

smaller features, whose relative vort adv > planetary vort advsize 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 cloudstime scale between 2p/N and 2p/fhydrostatic balance

usually appliesmicroscale: cumuli, thermals, K-H billows, turbulence: static instability (1-5 km) – convective cloudsSize controlled by entrainment and perturbation pressuresno hydrostatic balance

2p/N ~ 2p/10-2 ~ 10 minutes2p/f

= 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°Slide8

1.4 thermal wind balance

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

u

g

u

g

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

.

u

g

=0Slide9

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)Slide10

Around 30-45 º

N, temperature drops northward, therefore westerly winds increase in strength with height.Slide11

The meridional temperature gradient is large between 30-50º

N and 1000-300 hPa

thermal wind

Therefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa.Slide12

Question:

Why, if it is colder at higher latitude, doesn’t the wind continue to get stronger with altitude ?Slide13

There is definitively a jet ...Slide14

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

tropopauseSlide15
Slide16

Z

500Slide17

Z

500

-Z

1000Slide18
Slide19

baroclinicity

The atmosphere is

baroclinic

if a horizontal temperature gradient is presentThe atmosphere is barotropic if NO horizontal temperature gradient existsthe mid-latitude belt typically is baroclinic, the tropical belt barotropicThe atmosphere is equivalent barotropic if the temperature gradient is aligned with the pressure (height Z) gradientin this case, the wind increases in strength with height, but it does not change direction

equivalent barotropic

height gradient

temperature gradient

warm

cold

baroclinic

warm

cold

geostrophic wind at various levelsSlide20

1.4.2 Geostrophic T advection:cold air advection (CAA) & warm air advection (WAA)Slide21

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

CAA

WAASlide22

WAA & CAASlide23

geostrophic temperature advection: the

solenoid method

lower height Z

greater Z

geostrophic wind:

warm

cold

warm

cold

lower Z

greater Z

fatter arrow: larger T gradient

geo. temperature

advection is:

the magnitude is:

the smaller the box, the stronger the temp advectionSlide24

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:

T

hermal

wind and

geostrophic temperature

advection

where is the average wind speed perpendicular to the thermal wind.

local T change

T advection

The sign of     

+

-

V

T

V

T

warm

cold

warm

coldSlide25

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

T

V

T

WARM

WARM

COLD

COLD

WAA

CAA

T

hermal

wind and temperature advectionSlide26

Procedure to estimate the temperature advection in a layer:

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

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.

thermal wind and temperature advectionSlide27

example

x

y

WARM

COLD

n

veering wind

 warm air advection

between 1000-850 hPa

10°C

5°C

sSlide28

friction-induced

near-surface

convergence into lows/

trofsSlide29

1.5 vorticity

shear and curvature

vorticitySlide30
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Slide35
Slide36

Hovmoller diagrams (Fig. 1.20)Slide37