enac-ssie laboratoire de pollution de l'air the atmospheric layers

ENAC-SSIE Laboratoire de Pollution de l'Air

The Atmospheric Layers

10

20

30

40

50

60

70

80

90

100

0

265

55

12

2.9

0.8

0.22

0.052

0.011

0.0018

0.00032

1013

Pressure (m

b)A

ltit

ude

(km

)

Temperature (K)180 200 220 240 260 280 300

Mesopause

Stratopause

Tropopause

Thermosphere

Mesosphere

Troposphere

StratosphereOzone layer


The Gas Energy Exchanges

Radiation

Sensible Heat

Tin > T

out

Tin < T

out

Latent Heat

Evaporation

Condensation

WATERVAPOR

Work

Pressure and volume

variation

LSRv dQdQdQVdm

PdTC

LSR dQdQdQdWdE


Incoming and Emitted Radiation


The Atmospheric Energy BalanceIncoming Solar Radiation

100% - 343 Wm -2

Absorbed by the earth 46%

Reflected by the atmosphere 25%

(gas, aerosols, clouds)

Absorbed by the atmosphere 23%

(gas, aerosols, clouds)

Absorbed by the atmosphere 106%

(greenhouse gases, clouds)

Re-emitted by the atmosphere (greenhouse gases, clouds) and absorbed by the earth 100%

Emitted by the earth 115%

Latent and Sensible Heat

31%

Re-emitted by the atmosphere 60%

(greenhouse gases, clouds)

Emitted by the earth 9%

Reflected by the

earth 6%

Long Wave

Long Wave

Long Wave

ShortWave


O2 + h → O + O1D < 175 nm

O2 + h → O + O 175 < < 245 nm

O3 + h → O2 + O1D < 310 nm

O3 + h → O2 + O > 310 nm

O1D + M → O + M

O + O2 + M → O3 + M

The Absorption in the Stratosphere


The Greenhouse Gas


The Earth Surface Energy Balance

Short Wave Radiation

Long Wave Radiation

Sensible Heat

Latent Heat

Tsurf > Tatm

Tsurf > TsoilGround

Evaporation

Day

fe

gg**

4lS

gg

g ELdz

dTκθu)σT -ε(Rα)R-(1

dzρC

1

dt

dT


Night


Tsurf < Tatm

Tsurf < Tsoil

Condensation

Long Wave Radiation

Sensible Heat

Latent Heat

Ground

fe

gg**

4lS

gg

g ELdz

dTκθu)σT -ε(Rα)R-(1

dzρC

1

dt

dT


The Effect of the Earth Rotation

ra UUU

RΩrU

RΩΩUΩ2dt

Ud

with

Coriolis Centripetal

ac1 = - f V + 2 W cos in X-direction

ac2 = f U in Y-direction

ac3 = 2 U cos in Z-direction

f = 2 sin

ac1

R

ac3ac2 Acceleration


dz

dy

dx

Sx = dy dzV = dx dy dz

m

-ac

P(x)P(x+dx) =P(x) + dP

The Effect of the Earth Rotation

In X direction: Sx.dPG = m f VG

In Y direction: Sy.dPG = - m f UG

dx

dP

f

1V G

G

dy

dP

f

1U G

G


Global Atmospheric Circulation

High pressure

High pressure

High pressure

High pressure

Polar front

Polar front


The Effects of the Surface Friction

Alt

itud

e

Geostrophic wind

dz

dy

dx

zx

zyzz

zx+dzx

zy+dzy

zz+dzz

dz

dU

dz

d1

dz

dV

dz

d1

Friction forces

z)cos(z -2G

2G e-1V-UU

z)sin(z -2G

2G eV-UV

2

f

dz

dUμ

dz

d

ρ

1fV

dx

dP

ρ

1 G

dz

dVμ

dz

d

ρ

1fU

dy

dP

ρ

1 G

Ekman Layer


The Effects of the Gravity

dz

dy

dx

S = dx dy

V = dx dy dz

m

-g

P(z)

P(z+dz) =P(z) + dP

gdz

dP

ρ

1

Hydrostatic Pressure

RTP dT

dz

g

Cp

Vertical Temperature Gradient

v Vdm

PdTC


0dt

dm

Mass conservation

sss SD

dt

dm

m

1

Substance

Air

0x

Uρ

dt

dρ

i

i

rii

Sx

rK

xρ

1

dt

dr

0x

ρU

t

ρ

i

i


dt

dQ

dt

dW

dt

dE

Energy conservation

pC

R

0P

P

T

θ

Eiii

i Sx

Tκ

xρ

1

x

U

ρ

P

dt

dE

Eii

p Sx

Tκ

xρ

1

dt

dP

ρ

1

dt

dTC

The potential temperature is the

temperature an unsaturated air parcel

attains if it brought adiabatically from

its altitude down to a pressure of

P0=1000 mb (approximately the sea

level).

θiip

Sx

Tκ

xθ

T

ρC

1

dt

dθ


Motion conservation

H

H

H

H

θ

θθ

ρ

ρρ

Buoyancy

jij3i3ijji

i UfεgδμSxρ

1

x

P

ρ

1

dt

dU

where i

j

j

i

x

U

x

U

ijS

Gjjij3H

i3ijji

i UU fεgρ

ρρδμS

xρ

1

x

p

ρ

1

dt

dU

GH PPpP

Gjjij3H

HHi3ij

ji

i UU fεgθ

θθ

ρ

ρδμS

xρ

1

x

p

ρ

1

dt

dU


Atmospheric Stability

50 m

1000 m

Altitude

Température Vitesse du vent

COUCHE LIMITE INSTABLE

1000 m

AltitudeTempérature Vitesse du vent

50 m

COUCHE LIMITE STABLE

Temperature Wind Speed

Unstable Boundary Layer

Temperature Wind Speed

Stable Boundary Layer

PC

g

dz

dT

T

θ

dz

dθ

PC

g

dz

dT

PC

g

dz

dT

Stable Atmosphere

Unstable Atmosphere

0dz

dθ

0dz

dθ

or

or


Conservation form of the equations

Sx

NU

t

N

ii

z

Nw

y

Nv

x

Nu

t

N

dt

dN

ρSx

ρNU

t

ρN

i

i

riii

i ρSx

rK

xx

ρrU

t

ρr

θiipi

i ρSx

Tκ

xθ

T

C

1

x

ρθU

t

ρθ

Gjjij3HH

Hi3ij

jij

iji UU ρfεgθθθ

ρδμS

xx

p

x

ρUU

t

ρU

0x

ρU

t

ρ

i

i


Sea breeze


Slope WindsDay Night


Distance en miles nautiques

Pre

ssio

n em

mb

Mountain Waves


The Transport

Con

cent

rati

ons

Distance

Analytical solutionInitial Condition


The Diffusion

Con

cent

rati

ons

Distance

Analytical solutionInitial Condition


The Chemistry

Con

cent

rati

ons

Distance

A + C B


The Turbulence

Wind Speed

Eddies

Space or Time


The turbulence averaging

cCC r'rr iuUU ii

iii x

rK

xx

CU

t

C i

iiii x

rK

xx

cu

x

CU

t

C ii

iti x

rKcu

it

ii

i

x

rK

xx

CU

t

C


The turbulence averaging

ri

tii

i ρSx

rK

xx

ρrU

t

ρr

θi

tii

i ρSx

θκ

xx

ρθU

t

ρθ

Gjjij3HH

Hi3ijt

jij

iji UU ρfεgθθθ

ρδSμ

xx

p

x

ρUU

t

ρU


Turbulent kinetic energy

.U.lCK Kt .U.lCt .U.lCμ μt

kEU 222wvu

2

1uu

2

1E iik

i

kt

ikk

i

kik

x

Eλ

xεGP

x

ρEU

t

ρE

j

ijik x

UuρuP

ρθ'uθ

gδG ii3k

l

Eε

3/2k

.lE.Cλ kλt


Laminar profile Turbulent profile

Shear Stress


Shear Stress

Mean Wind Speed Turbulent Viscosity Size of the biggest Eddies

Ground

Obstacles


Heating

Ground Cloud Formation


Tropospheric Layers

Mean Wind Speed Turbulent Viscosity

Free Troposhere

Mixing Layer

Surface Layer


Prandtl (surface) boundary layer

0z

uμ

z τ

z

uμu τ

2*

zu.kμ *τ k z

u

z

u *

0

*

z

zlog

k

uU(z)

enac-ssie laboratoire de pollution de l'air the atmospheric layers

Documents

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lair night

emitted radiation slide

stratosphere slide

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