Absorption/emission by atmospheric gases. Solar, IR and microwave spectra of main atmospheric gases.

Transcription

1 Lecture 7 Aborption/emiion by atmopheric gae. Solar, IR and microwave pectra of main atmopheric gae. Objective:. Concept of a pectral line.. Baic principle of molecular emiion/aborption. 3. Spectral line hape: Lorentz profile Doppler profile Voigt profile 4. Beer-Bouguer-Lambert law. Ga aborption coefficient. 5. Aborption pectra of radiatively active atmopheric gae. Required reading: G Advanced reading: McCartney E.J. Aborption and emiion by atmopheric gae. John Wiley&Son, Concept of a pectral line. Atomic Aborption (Emiion) Spectrum. Radiation emiion (aborption) occur only when an atom make a tranition from one tate with energy E k to a tate with lower (higher) energy E j : for emiion: E k - E j = hc Aborption Emiion

2 Molecular Aborption/Emiion Spectra Molecular aborption pectrum i ubtantially more complicated than that of an atom becaue molecule have everal form of internal energy. Thi i the ubject of pectrocopy and quantum theory. Three type of aborption/emiion pectra: i) Sharp line of finite width ii) Aggregation (erie) of line called band; iii) Spectral continuum extending over a broad range of wavelength Figure 7. Concept of a line, band, and continuou pectra

3 . Baic principle of molecular emiion/aborption. NOTE: The tructure of molecule i important for an undertanding of their energy form (ee Lecture 6): Linear molecule (CO, N O; C H, all diatomic molecule): Symmetric top molecule (NH 3, CH 3 CL): Spherical ymmetric top molecule (CH 4 ): Aymmetric top molecule (H O, O 3 ): Review of main underlying phyical principle of molecular aborption/emiion: ) The origin of aborption/emiion lie in exchange of energy between ga molecule and electromagnetic field. ) In general, total energy of a molecule can be given a: E = E rot + E vib + E el + E tr E rot i the kinetic energy of rotation (energy of the rotation of a molecule a a unit body): about -5 cm - (far-infrared to microwave region) E vib i the kinetic energy of vibration: energy of vibrating atom about their equilibrium poition; about 5 to 4 cm - (near- to far-ir) E el i the electronic energy: potential energy of electron arrangement; about 4-5 cm - (UV and viible) E tr i tranlation energy: exchange of kinetic energy between the molecule during colliion; about 4 cm - for T =3 K From E rot < E tr < E vib < E el follow that: i) Rotational energy change will accompany a vibrational tranition. Therefore, vibrationrotation band are often formed. ii) Kinetic colliion, by changing the tranlation energy, influence rotational level trongly, vibrational level lightly, and electronic level carcely at all. Energy E rot, E vib, and E el are quantized and have only dicrete value pecified by one or more quantum number. Not all tranition between quantized energy level are allowed - they are ubject to election rule. 3

4 3) Radiative tranition of purely rotational energy require that a molecule poe a permanent electrical or magnetic dipole moment. (recall Table 6.) If charge are ditributed ymmetrically => no permanent dipole moment => no radiative activity in the far-infrared (i.e., no tranition in rotational energy) Example: homonuclear diatomic molecule (N, O ); O ha a weak permanent magnetic dipole and thu ha a rotational tranition in microwave. CO, N O, H O and O 3 exhibit pure rotational pectra becaue they all have the permanent dipole. CO and CH 4 don t have permanent dipole moment => no pure rotational tranition. But they can acquire the ocillating dipole moment in their vibrational mode => have vibration-rotation band 4) Radiative tranition of vibrational energy require a change in the dipole moment (i.e., ocillating moment) Figure 7. Vibrational mode of diatomic and triatomic atmopheric molecule (ee alo Figure 6.3) N O CO no vibrational tranition (ymmetric tretching mode) ingle vibrational mode CO (ymmetric tretching mode => radiatively inactive) a b two bending mode have ame energy (degenerated mode) 3 (aymmetric tretching mode => radiatively active) 4

5 NOTE: Homonuclear diatomic molecule N and O don t have neither rotational nor vibrational tranition (becaue of their ymmetrical tructure) => no radiative activity in the infrared. But thee molecule become radiatively active in UV. NOTE: The number of independent vibrational mode of a molecule with N> atom are 3N-6 for non-linear molecule and 3N-5 for a linear molecule. Both H O and O 3 have three normal band, and 3 : all are optically active. CH 4 ha nine normal mode but only 3 and 4 are active in IR. 5) Electronic tranition Electron on inner orbit (cloe to the atomic nucleu) can be diturbed or dilodged only by photon having the large energie (hort-wave UV and X-ray); Electron on the outermot orbit can be diturbed by the photon having the energie of UV and viible radiation => thee electron are involved in aborption/emiion in the UV and viible. Both an atom and a molecule can have the electronic tranition. Electronic tranition of a molecule are alway accompanied by vibrational and rotational tranition and are governed by numerou election rule.. Spectral line hape: Lorentz profile, Doppler profile, and Voigt profile. Three main propertie that define an aborption line: central poition of the line (e.g., the central frequency ~ or wavenumber ), trength of the line (or intenity, S), and hape factor (or profile, f) of the line. Each aborption line ha a width (referred to a natural broadening of a pectral line). 5

6 In the atmophere, everal procee may reult in an additional broadening of a pectral line of the molecule: ) colliion between molecule (referred to a the preure broadening); ) due to the difference in the molecule thermal velocitie (referred to a the Doppler broadening); and 3) the combination of the above procee. Lorentz profile of a pectral line i ued to characterize the preure broadening and i defined a: α / π f L ( ) = [7.] ( ) + α where f(- ) i the hape factor of a pectral line; i the wavenumber of a central poition of a line; α i the half-width of a line at the half maximum (in cm - ), (often referred a a line width) The half-width of the Lorentz line hape i a function of preure P and temperature T and can be expreed a n P T α ( P, T ) = α [7.] P T where α i the reference half-width for STP: T = 73K; P=3 mb. α i in the range from about. to. cm - for mot atmopheric radiatively active gae. For mot gae n=/. NOTE: The above dependence on preure i very important becaue atmopheric preure varie by an order of 3 from the urface to about 4 km. The Lorentz profile i fundamental in the radiative tranfer in the lower atmophere where the preure i high. The colliion between like molecule (elf-broadening) produce the large linewidth than do colliion between unlike molecule (foreign broadening). Becaue radiatively active gae have low concentration, the foreign broadening often dominate in infrared radiative tranfer. 6

7 7 Doppler profile i defined in the abence of colliion effect (i.e., preure broadening) a: = exp ) ( D D f D α π α [7.3] α D i the Doppler line width ) / / ( m T k c B D α = [7.4] where c i the peed of light; k B i the Boltzmann contant, m i the ma of the molecule (for air m = 4.8x -3 ). The Doppler broadening i important at the altitude from about to 5 km. Voigt profile i the combination of the Lorentz and Doppler profile to characterize broadening under the low-preure condition (above about 4 km in the atmophere). (i.e., it i required becaue the colliion (preure broadening) and Doppler effect can not be treated a completely independent procee: α α π α α + = = d d f f f D D D L Voigt 3 / ' exp ) ' ' ( ) ( ) ( ) ( [7.5] NOTE: The Voigt profile require numerical calculation. Nature of the Voigt profile: At high preure: the Doppler profile i narrow compare to the Lorentz profile o under thee condition the Voigt profile i the ame a Lorentz profile. At low preure: the behavior i more complicated a kind of hybrid line with a Doppler center but with Lorentz wing.

8 3. Beer-Bouguer-Lambert law. Ga aborption coefficient. The fundamental law of extinction i the Beer-Bouguer-Lambert law, which tate that the extinction proce i linear in the intenity of radiation and amount of matter, provided that the phyical tate (i.e., T, P, compoition) i held contant. Conider a mall volume V of infiniteimal length d and unit area A containing optically active matter (gae, aerool, and/or cloud drop). Thu, the change of intenity along a path d i proportional to the amount of matter (number concentration) in the path. For extinction For emiion: di ke Iλd λ,λ d = [7.6] I λ I λ + d I λ diλ = ke,λjλd where κ e,λ i the volume extinction coefficient (LENGTH - ) and J λ i the ource,λ function. NOTE: In general, the ource function i due to emiion and cattering, where a extinction i due to aborption and cattering (ee Lecture 3). Integrating Eq.[7.6], we have I, = I, λ exp( k e, λ ( ) d) = I, λ exp( τ λ ) [7.7] λ where I,λ and I,λ are the incident and tranmitted intenitie, repectively. Optical depth along the path i defined a τ λ = k e, λ ( ) d [7.8] UNITS: optical depth i unitle. NOTE: ame name : optical depth = optical thickne = optical path 8

9 Tranmiion function i defined a UNITS: tranmiion function i unitle (between and ) T = exp( τ ) λ [7.9] λ In general, the extinction coefficient i a um of the aborption coefficient and cattering coefficient of gae and particulate. NOTE: cattering by gae and cattering and aborption by particulate will be dicued in Lecture 9. Aborption coefficient of a ga i defined by the poition, trength, and hape of a pectral line: where S in the line intenity and f i the line profile: k a, = S f( ) [7.] S = ka, and f ( ) d = d Dependencie: S depend on T; f(, α) depend on the line halfwidth α (p, T), which depend on preure and temperature. Becaue the amount of an aborbing ga may be expreed in a number of poible way ( e.g., molecule per unit volume, ma of molecule per unit volume, etc.), different kind of aborption coefficient may be introduced i uch a way that the optical depth remain unitle. Introducing a path length (or amount of ga), u, we have τ = ka du u u, [7.] 9

10 Mot commonly ued aborption coefficient: k a, Volume aborption coefficient (in LENGTH - ) k m,a, Ma aborption coefficient (in LENGTH /MASS) k c,a, Aborption cro ection (in LENGTH ) Ma aborption coefficient = volume aborption coefficient/denity Aborption cro ection = volume aborption coefficient/number concentration Thu, optical depth can be expreed in everal way k a, d = ρk m, a, d = τ (, ) = Nk c, a, d [7.] Table 7. Unit ued for path length, aborption coefficient, and line intenity (for Eq.[7.] - [7.]) Aborbing ga (path length u) Aborption coefficient Line intenity (S) cm cm - cm - g cm - cm g - cm g - cm - cm cm cm atm (cm atm) - cm - atm - Unit of the line profile, f: LENGTH (often cm) 4. Aborption pectra of main atmopheric gae (H O, CO, O 3, CH 4, N O, CFC). Each atmopheric ga ha a pecific aborption/emiion pectrum it own radiative ignature. HITRAN i a main pectrocopic data bae that contain information (e.g., intenity and half-width) for a total of about,8, pectral line for 36 different molecule.

11 Microwave region Molecule Aborption line (Frequency, GHz) H O 35; 83.3 O about 6; 8.75 (ee Figure 3.4) Thermal IR region Figure 7.3 Low-reolution IR aborption pectra of the major atmopheric gae.

12 Table 7. The mot important vibrational and rotational tranition for H, CO, O 3, CH 4, N O, and CFC. Ga Center (cm - ) (λ(µm)) H O (6.3) continuum* CO 667 (5) 96 (.4) 63.8 (9.4) 349 (4.3) O 3 (9.) 43 (9.59) 75 (4.) Tranition pure rotational ; P, R far wing of the trong line; water vapor dimmer (H O) ; P, R, Q overtone and combination 3 ; P, R overtone and combination ; P, R 3 ; P, R ; P, R Band interval (cm - ) CH (7.6) N O 85.6 (7.9) (7.) 3.5 (4.5) CFC 7-3 * Continuum aborption by water vapor in the region from 8- cm - remain unexplained. It ha been uggeted that it reult from the accumulated aborption of the ditant wing of line in the far infrared. Thi aborption i caued by colliion broadening between H O molecule (called elf-broadening) and between H O and non-aborbing molecule (N) (called foreign broadening).

13 Near-IR and viible region Aborption of viible and near-ir radiation in the gaeou atmophere i primarily due to H O, O 3, and CO. NOTE: Atmopheric gae aborb only a mall fraction of viible radiation. Figure 7.4 Solar pectral irradiance (flux) at the top of the atmophere and at the urface. Table 7.3 Wavelength of aborption in the olar pectrum (UV + viible) by everal atmopheric gae Ga Aborption wavelength (µm) N <. O <.45 O H O < H O hydrogen peroxide <.35 NO nitrogen oxide <.6* N O <.4 NO 3 nitrate radical HONO nitrou acid <.4 HNO 3 nitric acid <.33 CH 3 Br methyl bromide <.6 CFCl 3 (CFC) <.3 HCHO formaldehyde * NO aborb at λ<.6 µm, but photodiociate at λ <.4 µm 3

14 UV region Aborption of UV radiation in the gaeou atmophere i primarily due molecular oxygen O and ozone O 3. Thermophere /Meophere Stratophere Tropophere Figure 7.5 Spectral aborption cro-ection of O and O 3 NOTE: a) Band of O and O 3 at wavelength < µm are electronic tranition. b) Thee aborption band are relatively uncomplicated continua becaue practically all aborption reult in diociation of the molecule (o the upper tate i not quantized); c) Depite the mall amount of O 3, no olar radiation penetrate to the lower atmophere at wavelength < 3 nm (becaue of large aborption cro-ection of O 3 ); To avoid very complicated calculation of electronic tranition, numerou meaurement of the aborption cro-ection of the atmopheric atom and molecule aborbing in the UV and viible have been performed in laboratory experiment. In general, the aborption cro ection varie with temperature. 4