Download Thermosphere EUV absorption Thermal Conductivity Mesopause

Thermosphere
Part-3
EUV absorption
Thermal Conductivity
Mesopause
Thermospheric Structure
Temperature Structure on
other planets
Thermosphere Absorbs EUV
Absorption: Solar Spectrum
0.2
0.6
1.0
1.4
1.8
2.2
2.6
3.0µm
EUV--very little heat flux
But also very little atmosphere
But it is the region for escape
And diffusive separation
Thermosphere
(heating at short wavelengths)
1. EUV Heats
(also : soft x - rays, charged particles)
O 2 + h" # O + O
N 2 + h" # N + N
O
+ h" # O + + e
X
+ h" # X + + e
J 2 [= $ absFEUV (z)] from before
smaller
also creates ionosphere
2. At Lower Altitudes : Cooling
(Recombine O, N etc.)
% N 2 , O 2 and O Cannot Radiate IR
Homonuclear Diatomics and Atoms
Discuss briefly will return :
% no CO 2 ( diffusive separation )
# Must Conduct Deposited Heat to a Region Containing
CO 2 , H 2O , O 3 etc.
Mesopause (Roughly)
!
Z
rough
picture
EUV
heating
130km
I R cooling
80km
Thermal
conduction
mesopause
!
Thermosphere (cont)
Heating
Fs(z)
Δz
Heat Source : Absorption of EUV Photons
dT
dFs
" cp
= µ
: reduction in the energy flux
dt
dz
assumes unit efficiency of photon energy to heat
dT
dFs
" cp
= µ
= # absn abs Fs
dt
dz
________________________________________
!
Thermosphere (cont)
Heat conduction
Heat loss : Conduction
Considered the thermal heat flux : "T
Conductive flux is opposite to temperature difference
"T # $%T
Negative sign - -flow of heat is from high T to low T
(you may have called it Newton cooling law)
dT
Write : (1D) "T = $ K
or (3D) "T = $ K &T
dz
K is the thermal conductivity
Energy left in the volume gives the heating rate
- d"T /dz > heating - -leaves heat in dz :
- d"T /dz < cooling - -removes heat from, dz :
ΦT + ΔΦ
Δz
ΦT
Heating/ Cooling rate = ' c p
dT
d
= $
"T
dt
dz
!
Thermosphere Continued
Heat Flux : What is K
"T = # K dT/dz
K $ const ( % c v ) L d v d
L d is a diffusion length
(molecular or eddy)
v d is a mean diffusion speed
(molecules or parcels of air)
Heat Eq. with thermal conduction (diffusion)
% cp
dT
d
dT
= #
(#K ) + S(z) # L(z)
dt
dz
dz
(Source - Loss)
This is a region where diffusive separation dominates
Here conduction is by gas - phase collisions
Thermosphere Continued
Heat Eq. with thermal conduction (diffusion)
dT
d
dT
" cp
= #
(#K ) + S(z) # L(z)
dt
dz
dz
(Source - Loss)
Thermosphere :
Heating by absorption of sunlight (EUV) :
S(z) = µ[dFs/dz] ( in 1D )
Assume :
Assume
dT
" cp
= 0; steady state
dt
L(z) = Radiative Loss = 0
except at the bottom 'boundary'
Treat as a boundary value problem
Below mesopause : we will do
radiative transfer soon
Thermosphere T Structure
Heat equation for the thermosphere
0 =
d
dT
[K ] + S(z)
dz dz
[S(z) : Chapman Layer]
Solve : First - - - Integrate from z to infinity
"
z
0 = K (dT/dz)
+
#
"
z
S(z')dz'
No Heat Loss to Space (dT/dz = 0 at top of atmosphere)
K
dT
=
dz
A realistic K : K(T)
#
"
z
S(z')dz'
$ K o T 4/3
Integrate again : from Mesopause (z m ) to z gives T(z)
z
"
7
T 7/4 (z) $ Tm7/4 +
dz'
S(z'')dz''
#
#
z
z'
4K o m
Tm is the boundary:
where heat conducted
downward is radiated to space
Relationship to our old Te?
Thermosphere Structure (Cont)
HEAT FLUX DOWN = HEAT DEPOSITED ABOVE
dT
K
=
dz
#
#
$#
$
"
z
"
z
"
z
S(z' )dz'
[µ dFs /dz'] dz'
µ dFs
$ Fso µ [1- exp(- % / µ)]
This says that the downward heat flux at any altitude
must be equal to all the energy deposited above
by the absorption of EUV photons
Thermosphere Structure (Cont)
dT
K
" Fso µ [1- exp(- # / µ)]
dz
For simplicity let K = K o a constant; µ =1.
o
s
F
T (z) " Tm +
Ko
$
z
zm
dz' [1 - exp(- # ')]
If absorption maximum is high (zmax > ~ 130km)
then, below maximum - - variation is nearly linear
Fso
T (z) " Tm +
[z - z m ] for z m < z < z max
Ko
Thermosphere Structure (Cont)
For K = K o; µ =1.
Fso
T (z) " Tm +
Ko
$
z
zm
dz' [1 - exp(- # ')]
Change variable :
&
Optical depth - - # = $ % abs n abs (z') dz' " % absH n abs (z)
z
d#/dz " - # /H
Fso H
T(z) " Tm +
Ko
$
#m
#
[d# ' /# '] [1 - exp(-# ')]
Integral for thermosphere model
Xm = 100
Xm = 10
Xm = 5
τ(z ) ∝
τ=0
z-->∞
x ∝ τ(z ) ;
[ T(z) -Tm ] = [Fo/Ko][H y]
y(x) = ∫xxm { [1-exp(-x’)]/x’} dx’
Over how many scale hieght does heat
have to be conducted
z
Mesopause
Zm=80km
220 K
T
1000 K
Thermospheric
Temperature
Temperature vs. Altitude
Earth’s Atmosphere
Rise in T in Thermosphere
due to EUV Absorption
and Thermal Conduction
to Mesopause
These are averages
Tropopause is higher and hotter
Near equator ~16-18km and ~ 10km near poles
Drives high altitude horizontal flow
Jets planes ~10km:e close to stratosphere
to avoid turbulence
Earth’s Thermal Structure
Thermosphere T depends on Solar Activity
Photo-chemistry Venus + Mars
Simpler
CO2 + hν → CO + O
CO+O+M → CO2 + M
(1)
(2)
On Venus CO --> CO2
may be aided by sulfur + chlorine species
On Mars: (2) is very slow
(density Is very small):
Expect considerable CO, especially so
as free O oxidize surface (iron oxide)
BUT there is a small amount of H2O
H2O + hν → OH + H
CO + OH → CO2 + H
(3)
(4)
Recycles CO2 but
Can lose the H--hence loss the H2O
Venus Atmosphere
Clouds
Cloud Tops --> Te
CO2 even at high altitudes --> cooling
Slow Rotation
1 year = 2 days
(retrograde due to thickatmosphere and tidal forces?)
Mars Atmosphere
Te at Surface
Dust absorbs hν and changes the
lapse rate
Thermosphere strongly dependent
on solar activity
Titan’s Atmosphere
Stratosphere/ mesosphere due to
absorption in hydrocarbon haze
CH4 + hν -> CH3 +H (CHf +H2)
React to form CnHmand H2 escapes.
Thermosphere subject to particles
from Saturn’s magnetosphere
Giant Planets
Internal heat sources
Adiabatic lapse rate down
to liquid metal hydrogen
Jupiter has evidence of a
stratosphere and a
mesosphere
Atmosphere Thermal Structure: Summary
Typically
troposphere (Lower, Convective)
Mesosphere [ Stratosphere ] (Middle, Radiative)
Thermosphere (Upper, Conductive)
Exosphere (Escape)
Venus
Temperature Lapse, γ ≤ Γd
Tropopause at cloud layer (~ 70 km)
Te ~ Top of cloud layer
Thermosphere (Cryosphere)
Td ~ 300 km (CO2 at high altitudes)
Tn ~ 100 km (Slow rotation 1yr ≈ 2 days)
Mars
Temperature Lapse γ ≤ Γd
(Strong Day / Night Variations: Dust γ << Γd
Mesosphere T < Te (CO2 cooling)
Thermosphere like Mesosphere
(Strongly affect by solar activity)
Titan
Temperature Lapse γ ∼ Γd
Stratosphere (Haze Layer)
Mesosphere (Cooler to space)
Thermosphere (Solar UV + Energetic Particles
from Magnetosphere Cooled by
HCN, Slow Rotations)
Grant Planets
Internal heat source comparable to solar
Tropopause ~ 0.1 bar, γ ~ Γd,
Temperature + pressure increase to about 2M bar so phase
change to a liquid (metallic) state (4x104 km) and a metallic
core (3x104 K) (1x104 km) (Jupiter)
Mesosphere (stratosphere) ≤ 0.001 bar Hydrocarbon coolants
Thermosphere (Solar EUV)
#3 Summary
Things you should know
EUV asborption
Mesopause
Thermosphere
Thermal conductivity
Heat flux
General picture of the
vertical structure