Revie view w for Exam m 1. Electromagnetic radiation exhibits the - PowerPoint PPT Presentation

Lecture 14. Revie view w for Exam m 1.

Electromagnetic radiation exhibits the dual nature: wave properties and particulate properties Wave nature of radiation: Electromagnetic waves are characterized by wavelength l (or frequency ,or ~ n wavenumber n ) and speed n ~ ~ Relation between l, and : n = / c = 1/ l n n Particulate nature of radiation: can be described in terms of particles of energy, called photons. ~ n E photon = h = h c /l = h c n h is Plank’s constant ( h = 6.6256x10 -34 J s).

Flux (or irradiance) is defined as radiant energy in a given direction per unit time per unit wavelength (or frequency) range per unit area perpendicular to the given direction: dE dF  l l l dtdAd UNITS : (J sec -1 m -2 m m -1 ) = (W m -2 m m -1 ) The radiative flux is the integration of normal component of monochromatic intensity over some solid angle.          F I ( ) n d  cos(   F I ) d l l l l   2

Net radiative flux Monochromatic net flux is the integration of normal component of monochromatic intensity over the all solid angles (over 4  ):  2 1        m  m m  F net F F I ( , ) d d l l l l ,  0 1 What is the net flux of the isotropic radiative field?

Extinction (scattering +absorption) and emission. Extinction is a process that decreases the radiant intensity , while emission increases it. Extinction (or attenuation) is due to absorption and scattering . Absorption is a process that removes the radiant energy from an electromagnetic field and transfers it to other forms of energy. Scattering is a process that does not remove energy from the radiation field, but may redirect it.

Lecture 3 The fundamental law of extinction is the Beer-Bouguer-Lambert law: the extinction process is linear in the intensity of radiation and amount of matter, provided that the physical state (i.e., T, P, composition) is held constant.   ,    , dI J ds dI I ds Extinction: Emission: l l l l l e l e where  e ,l is the volume extinction coefficient (LENGTH -1 ); J l is the source function.      l l l e , a , s ,      dI I ds J ds l l l l l e , e ,

Lecture 3 The differential form of radiative transfer equation      dI I ds J ds l l l l l e , e , dI    l I J l l  ds l e , dI     Using     l d ( s ) ds We have I J l , l l l e  d l dI   l I J l l  Elementary solution: d l s 1 See         I ( s ) I ( 0 ) exp( ( s ; 0 )) exp( ( s ; s )) J ds l l l l l l p.12 1 1 1 e , 0

Lecture 3 Solution of the radiative transfer equation in the plane-parallel atmosphere (called the integral form)       m    m   * I ( ; ; ) I ( ; ; ) exp( ) l l m *      * 1        m   exp( ) J ( ; ; ) d l m m       m    m   I ( ; ; ) I ( 0 ; ; ) exp( ) l l m      1         m   exp( ) J ( ; ; ) d l m m 0

Lecture 4 Blackbody emission Planck function, B l (T), gives the intensity (or radiance) emitted by a blackbody having a given temperature. 2 2 hc  B ( T ) l l l  5 (exp( / ) 1 ) hc k T B Stefan-Boltzmann law: F = s b T 4 =  B(T) Wien displacement law: l m = 2898 / T Kirchhoff law: e l = A l

Molecular Absorption/Emission Spectra

Lorentz profile of a spectral line is used to characterize the pressure broadening and is defined as:   / n  n  f ( ) n  n   L 0 2 2 ( ) 0  is the half-width of a line at the half maximum (in cm -1 ), (often called the line width ) n   P T      0 ( P , T ) 0   P T 0 Doppler profile is defined in the absence of collision effects (i.e., no pressure broadening) as:   2   n  n 1     n  n   0 f ( ) exp    D 0         D D  D is the Doppler line width n   1 / 2 0 ( 2 k T / m ) D B c

Comparison of the Doppler and Lorentz profiles for equivalent line strengths and widths.

Absorption coefficient is defined by the position, strength, and shape of a spectral line: k a, n = S f ( n – n 0 )   n  n n   n f ( ) d 1 S k n d 0 a , Dependencies : S depends on T; f ( n – n 0 ,  ) depends on the line halfwidth  (p, T), which depends on pressure and temperature.

Path length (or path ) is defined as the amount of an absorber along the path If the amount of an absorber is given in terms of mass density, path length is s 2    u ( s ) ds s 1 Homogeneous absorption path: when k a, n does not vary along the path => optical depth is  = k a, n u Inhomogeneous absorption path: k a, n varies along the path u 2    k du , n a u 1

Absorbing gas Absorption Line intensity (path length u ) coefficient (S) cm -1 cm -2 cm g cm -2 cm 2 g -1 cm g -1 molecule cm -2 cm 2 /molecule cm/molecule (cm atm) -1 cm -2 atm -1 cm atm

Monochromatic transmittance and absorbance    T exp( ) n n       A 1 T 1 exp( ) n n n

Spectral intensity = intensity averaged over a very narrow interval that B n is almost constant but the interval is large enough to consist of several absorption lines. Narrow-band intensity = intensity averaged over a narrow band which includes a lot of lines; Broad-band intensity= intensity averaged over a broad band (e.g., over a whole longwave region) 1 1 1      n    n   n T ( u ) T ( ) d exp( ) d exp( k u ) d n n n n  n  n  n  n  n  n 1 1         n    n A 1 T ( u ) ( 1 exp( )) d ( 1 exp( k u )) d n n n n  n  n  n  n

The solutions of the radiative transfer equation for the monochromatic upward and downward intensities in the IR for a plane-parallel atmosphere consisting of absorbing gases (no scattering):    *   m       * I ( ; ) B ( ) exp( )   m    m  n n * I ( ; ) I ( ; ) exp( ) m n n m *       1 *    *         1  exp( ) B ( T ( )) d       n m m exp( ) B ( ) d n m m        m   m  I ( ; ) I ( 0 ; ) exp( )      n n m 1       m     I ( ; ) exp( ) B ( ) d n n      m m 1        exp( ) B ( T ( )) d 0 n m m 0

For isothermal atmosphere and black body surface   * *  m       * I ( 0 ; ) B ( ) exp( ) B ( T )[ 1 exp( )] n n n m m eff For fluxes – see 4.6.2 pp.154-157

M onochromatic net flux (net power per area) at a given height     F ( z ) F ( z ) F ( z ) n n n and total net flux     F ( z ) F ( z ) F ( z ) Introducing the net flux F (z+  z) at the level z+  z , the net flux divergence for the layer  z is      F F ( z z ) F ( z )

F (z+  z) < F (z) (hence  F < 0 ) => a layer gains radiative energy => heating F (z+  z) > F (z) (hence  F > 0 ) => a layer losses radiative energy => cooling The IR radiative heating (or cooling) rate is defined as the rate of temperature change of the layer dz due to IR radiative energy gain (or loss):   dT 1 dF g dF      net net    dt c dz c dp IR p p where c p is the specific heat at the constant pressure ( c p = 1004.67 J/kg/K) and  is the air density in a given layer.

Effect of the varying amount of a gas on IR radiation under the same atmospheric condition Consider the standard tropical atmosphere and “dry” tropical atmosphere: same atmospheric characteristics, except the amount of H 2 O 10 9 8 7 Altitude, km 6 5 4 3 2 1 0 0 5 10 15 20 H2O (g/kg)

IR fluxes for tropical (dotted lines) and dry tropical atmospheres (solid lines) 10 9 8 7 Fup Altitude, km 6 Fdw 5 Fup, dry 4 Fdw, dry 3 2 1 0 60 160 260 360 460 Flux, W/m2  • H2O increases in a layer => increases because more IR radiation emitted in a layer => F F  ( surface ) increases  • H2O increases in a layer => decreases because more IR radiation absorbed but F F  reemitted at the lower temperature => decreases ( TOA ) • Increase of an IR absorbing gas contributes to the greenhouse effect.

IR net fluxes for tropical (dotted lines) and dry tropical atmospheres (solid lines) 10 9 8 Altitude, km 7 6 Fnet 5 Fnet, dry 4 3 2 1 0 60 110 160 210 260 Flux, W/m2