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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