Thermosphere Part-3. EUV absorption Thermal Conductivity Mesopause Thermospheric Structure Temperature Structure on other planets
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1 Thermosphere Part-3 EUV absorption Thermal Conductivity Mesopause Thermospheric Structure Temperature Structure on other planets
2 Thermosphere Absorbs EUV Absorption: Solar Spectrum µm EUV--very little heat flux But also very little atmosphere But it is the region for escape And diffusive separation
3 Thermosphere (heating at short wavelengths) 1. EUV Heats (also : soft x - rays, charged particles) O 2 + h" # O + O J 2 [= $ abs F EUV (z)] from before N 2 + h" # N + N smaller O + h" # O + + e also creates ionosphere X + h" # X + + e 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 2 O, O 3 etc. Mesopause (Roughly) Z 130km 80km EUV heating Thermal conduction R cooling mesopause rough picture
4 Thermosphere (cont) Heating F s (z) Δz Heat Source : Absorption of EUV Photons " c p dt dt = µ df s dz : reduction in the energy flux assumes unit efficiency of photon energy to heat dt " c p = µ df s = # abs n abs F s dt dz
5 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) Write : (1D) Thermosphere (cont) Heat conduction " T = $ K dt dz or (3D) "T = $ K &T 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 : Δz Φ T + ΔΦ Φ T Heating/ Cooling rate = ' c p dt dt = $ d dz " T
6 Thermosphere Continued Heat Flux : What is K " T = # K dt/dz K $ const ( % c v ) L d vd L d is a diffusion length (molecular or eddy) vd is a mean diffusion speed (molecules or parcels of air) Heat Eq. with thermal conduction (diffusion) % c p dt dt = # d dz dt (#K ) + S(z) # L(z) dz (Source - Loss) This is a region where diffusive separation dominates Here conduction is by gas - phase collisions
7 Thermosphere Continued Heat Eq. with thermal conduction (diffusion) " c p dt dt = # d dz dt (#K ) + S(z) # L(z) dz (Source - Loss) Thermosphere : Heating by absorption of sunlight (EUV) : S(z) = µ[df s /dz] ( in 1D ) Assume : " c dt p = 0; steady state dt Assume L(z) = Radiative Loss = 0 except at the bottom 'boundary' Treat as a boundary value problem Below mesopause : we will do radiative transfer soon
8 Thermosphere T Structure Heat equation for the thermosphere 0 = d dz [K dt dz ] + S(z) [S(z) : Chapman Layer] Solve : First Integrate from z to infinity 0 = K (dt/dz) z " + S(z')dz' # " z No Heat Loss to Space (dt/dz = 0 at top of atmosphere) K dt dz # " = S(z')dz' z A realistic K : K(T) $ K o T 4/3 Integrate again : from Mesopause (z m ) to z gives T(z) T 7/4 (z) $ T m 7/4 + 7 z " # dz' # S(z'')dz' ' 4K z m z' o T m is the boundary: where heat conducted downward is radiated to space Relationship to our old T e?
9 Thermosphere Structure (Cont) HEAT FLUX DOWN = HEAT DEPOSITED ABOVE K dt dz = # " S(z' )dz' z $ # " [µ df s /dz'] dz' z $ # " µ df z s $ F s o 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
10 Thermosphere Structure (Cont) K dt " F o s µ [1- exp(- # /µ)] dz For simplicity let K = K o a constant; µ =1. T (z) " T m + F o s K o $ z z m dz' [1 - exp(- #')] If absorption maximum is high (z max > ~ 130km) then, below maximum- - variation is nearly linear T (z) " T m + F s o K o [z - z m ] for z m < z < z max
11 Thermosphere Structure (Cont) For K = K o ; µ =1. T (z) " T m + F o s K o $ z z m dz' [1 - exp(- #')] Change variable : Optical depth - - # = T(z) " T m + & d#/dz " - # /H $ % abs n abs (z') dz' " % abs H n abs (z) z F s o H K o $ # # m [d#' /#'] [1 - exp(-#')]
12 Integral for thermosphere model X m = 100 X m = 10 X m = 5 τ(z ) τ=0 z--> x τ(z ) ; [ T(z) -T m ] = [F o /K o ][H y] y(x) = x xm { [1-exp(-x )]/x } dx Over how many scale hieght does heat have to be conducted
13 z Z m =80km Mesopause 220 K T 1000 K Thermospheric Temperature
14 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
15 Earth s Thermal Structure Thermosphere T depends on Solar Activity
16 Photo-chemistry Venus + Mars Simpler CO 2 + hν CO + O (1) CO+O+M CO 2 + M (2) On Venus CO --> CO 2 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 H 2 O H 2 O + hν OH + H (3) CO + OH CO 2 + H (4) Recycles CO 2 but Can lose the H--hence loss the H 2 O
17 Venus Atmosphere Clouds Cloud Tops --> T e CO 2 even at high altitudes --> cooling Slow Rotation 1 year = 2 days (retrograde due to thickatmosphere and tidal forces?)
18 Mars Atmosphere T e at Surface Dust absorbs hν and changes the lapse rate Thermosphere strongly dependent on solar activity
19 Titan s Atmosphere Stratosphere/ mesosphere due to absorption in hydrocarbon haze CH 4 + hν -> CH 3 +H (CH f +H 2 ) React to form C n H m and H 2 escapes. Thermosphere subject to particles from Saturn s magnetosphere
20 Giant Planets Internal heat sources Adiabatic lapse rate down to liquid metal hydrogen Jupiter has evidence of a stratosphere and a mesosphere
21 Atmosphere Thermal Structure: Summary Typically troposphere (Lower, Convective) Mesosphere [ Stratosphere ] (Middle, Radiative) Thermosphere (Upper, Conductive) Exosphere (Escape) Venus Temperature Lapse, γ Γ d Tropopause at cloud layer (~ 70 km) T e ~ Top of cloud layer Thermosphere (Cryosphere) T d ~ 300 km (CO 2 at high altitudes) T n ~ 100 km (Slow rotation 1yr 2 days) Mars Temperature Lapse γ Γ d (Strong Day / Night Variations: Dust γ << Γ d Mesosphere T < Te (CO 2 cooling) Thermosphere like Mesosphere (Strongly affect by solar activity) Titan Temperature Lapse γ Γ d 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 ~ Γ d, Temperature + pressure increase to about 2M bar so phase change to a liquid (metallic) state (4x10 4 km) and a metallic core (3x10 4 K) (1x10 4 km) (Jupiter) Mesosphere (stratosphere) bar Hydrocarbon coolants Thermosphere (Solar EUV)
22 #3 Summary Things you should know EUV asborption Mesopause Thermosphere Thermal conductivity Heat flux General picture of the vertical structure
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