MID-IR Nadir/Limb Retrieval

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1 MID-IR Nadir/Limb Retrieval Karlruhe Intitute of echnolog IMK-AS

2 hank to: André Butz rank Hae homa v Clarmann

3 Inverion of remote ening obervation orward: ˆ ˆ ˆ 8 Signal eg nadir pectrum Altitude [km] 6 4 polar ummer polar winter emperature [K] L Radiative tranfer τ, µ, ϕ L τ, Boden, µ, ϕ e τ, Boden µ τ τ τ τ, Boden µ J,, e d τ µ ϕ τ µ τ Invere: ˆ ˆ ˆ???

4 ˆ ˆ ˆ ˆ ˆ ˆ

5 dl / d - β a, L - β, L β a, B β, 4π - PΩ,Ω L diff Ω dω β, 4π- PΩ,Ω ol ol

6 Emiion and Aborption - Onl emiion and aborption of radiation, no cattering mot important for radiative tranfer in MW and IR - Local thermodnamic equilibrium Planckfunction a ource function Kirchhoff law: emiion aborption dl L dl β L d β a, d L, ab Schwarzchild-equation: a, dl, emi B d dl β a, d Aborption coefficient: Aborption cro-ection: Number denit: Planck function: B L β a, σ a, N σ a, N B

7 , τ, τ L L,,, a d e B e L L τ τ β Solution of Schwarzchild equation,, a d τ β Optical depth:

8 Emiion of a laer with contant B cont B L τ, B e τ, dτ, L ranmiion of the laer, τ, dτ, B e B t, τ, τ B e Emiivit of the laer or three laer: L B, B, t, t t,3, t t, t t,,,3 t,3 B 3, B t, t,,3 t t,3, t,3 B,3 B t,3,3 t,3

9 hermal contrat in nadir ounding: the lowet laer L B urfacet, B, t,, B, urface B, L B, B urface B,, t, B L,, urface B, No information about tranmiion of lowet laer B B, t, B,urface

10 Schwarzchild equation a function of tranmiion and weighting function, d W B t L L d dt W, Weighting function:,,, a d e B e L L τ τ β [ ], ep, t τ ranmiion:

11 dt z dz t z

12 Nadir ounding weighting function Smith et al, 9

13 Looking up or down? Pett6

14 Looking up: where? Pett6

15 IASI and monochromatic pectrum 5

16 6

17 7

18 8

19 Geometric cro-ection Aborption coefficient: Aborption cro-ection: Number denit: β a, σ a, σ a, N N

20 Radiative effective cro-ection at tronl aborbing wavelength

21 Radiative effective cro-ection at weakl aborbing wavelength

Quantum mechanic: a bound microcopic tem can onl be in ditinct

tate can occur through emiion/aborption of electromagnetic radiation

vibration of a molecule; changing dipole moment UV-VIS: electronic

22 Quantum mechanic: a bound microcopic tem can onl be in ditinct rotational/vibrational/electronic tate ranfer from one to the other tate can occur through emiion/aborption of electromagnetic radiation photon Microwave: rotation of a molecule with tatic dipole moment IR: vibration of a molecule; changing dipole moment UV-VIS: electronic tranition Ε h f P W Atkin, Phikaliche Chemie, 996

23 Beipiel: Schwingung und Rotation de H O-Molekül 74 µm 67 µm 66 µm

24 Ro-vibrational tranition in the mid-ir, ranmiion,8,6,4, HBr mbar cm Zelle C 3,7 3,8 3,9 4, 4, Wellenlänge [µm]

25 5

26 he finite width of pectral line Doppler-broadening: hermal movement of molecule along the line-of-ight Gauian hape ~ cm cm - Proportional to the frequenc,,8,6,4,, Gau Lorentz Voigt Preure-broadening: Colliion with other molecule diturb their ocillation ranition frequenc become blurred Lorentz hape ~5 cm hpa Proportional to the colliion rate preure Radianz [W / m r cm - ] ditance from line center ClNO O 3 olar CO Wellenzahl [cm - ] Höpfner / riedl-vallon - Meverfahren: IR-Spektrokopie

28 Dicretiation and meaurement error ˆ ˆ ˆ ε Error pectral noie Meaurement vector pectral channel Vector with altitude profile n point Radiative tranfer model

29 Lineariation ε ε ε K irt gue Jacobi-Matri ~weighting function n m m n K

30 K ε Cae : m n df f d ε Newton-Iteration: df d i i i i f Error etimation: σ df d σ

31 ε ε d d d d K K i vector and cannot be inverted Wa : Calculate error for each i a in eample, σ σ 3 Calculate the reult a weighted mean σ σ σ σ 4 And the error of a: σ σ σ Calculate eparatel for each a in eample Cae : m n

32 Wa: Leat-quare inverion Minimie the weighted quadratic difference: [ ] [ ] [ ] [ ] S S K K Covariance matri of obervation: σ σ S Reult of minimiation σ σ σ σ Same reult a in wa Cae : m n

33 or non-linear problem thi can be written a iteration: i i i S K K S K K S K σ Variance σ σ σ σ Cae : m n

34 i i i S K K S K K S K S General cae for m,n

35 Regularization More unknown than obervation n > m m > n but linear dependent Introduction of contraint Regularization

36 ikhonov-phillip regularization he altitude profile hould be mooth [ ] [ ] S Intead of: [ ] [ ] S L L γ L Solution: [ ] i a i i i L L S K L L K S K γ γ Minimize:

37 Linear tatitical regularization optimal etimation Ue tatitical knowledge about atmopheric parameter [ ] [ ] S Solution: [ ] [ ] a a a S S a-priori covariance matri [ ] i a a i a i i S S K S K S K

38 Averaging kernel matri ikhonov-phillip Optimal etimation A A K S K L L γ K S K K S K S K S K a MIPAS ClONO ikhonov Regul Column k: anwer of the retrieval to a delta-function at altitude k Row j: contribution of diffenent altitude to the reult in altitude j Smoothing decribed b inv A true

39 O 3 O 3 Ozone inverion from ground-baed IR K ij / Iterative inverion of linearized problem: Minimize: K [ ] [ ] S γ L L i K S K γ L L [ K S γl ] i i i L j a i Radianz [W / m r cm - ] Höhe [km] Wellenzahl [cm - ] Invertierte O 3 -Profil O 3 -Startprofil 4 6 Michungverhältni [ppmv]

40 Averaging kernel and vertical reolution Ozone from ground-baed IR ClONO from MIPAS 5 4 Höhe [km] Höhe [km] 5 Höhe [km] 4 3 km 4 km km 3 km 4 km Antwort

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