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ENAC-SSIE Laboratoire de Pollution de l'Air
The Atmospheric Layers
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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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
Incoming and Emitted Radiation
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
The Greenhouse Gas
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
Night
The Earth Surface Energy Balance
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
ENAC-SSIE Laboratoire de Pollution de l'Air
The Earth Surface Energy Balance
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
Global Atmospheric Circulation
High pressure
High pressure
High pressure
High pressure
Polar front
Polar front
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
Sea breeze
ENAC-SSIE Laboratoire de Pollution de l'Air
Slope WindsDay Night
ENAC-SSIE Laboratoire de Pollution de l'Air
Distance en miles nautiques
Pre
ssio
n em
mb
Mountain Waves
ENAC-SSIE Laboratoire de Pollution de l'Air
The Transport
Con
cent
rati
ons
Distance
Analytical solutionInitial Condition
ENAC-SSIE Laboratoire de Pollution de l'Air
The Diffusion
Con
cent
rati
ons
Distance
Analytical solutionInitial Condition
ENAC-SSIE Laboratoire de Pollution de l'Air
The Chemistry
Con
cent
rati
ons
Distance
A + C B
ENAC-SSIE Laboratoire de Pollution de l'Air
The Turbulence
Wind Speed
Eddies
Space or Time
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
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
ENAC-SSIE Laboratoire de Pollution de l'Air
Laminar profile Turbulent profile
Shear Stress
ENAC-SSIE Laboratoire de Pollution de l'Air
Shear Stress
Mean Wind Speed Turbulent Viscosity Size of the biggest Eddies
Ground
Obstacles
ENAC-SSIE Laboratoire de Pollution de l'Air
Heating
Ground Cloud Formation
ENAC-SSIE Laboratoire de Pollution de l'Air
Tropospheric Layers
Mean Wind Speed Turbulent Viscosity
Free Troposhere
Mixing Layer
Surface Layer
ENAC-SSIE Laboratoire de Pollution de l'Air
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)