Course Summary&Review for Exam II Upward/downward intensity in - PowerPoint PPT Presentation

Lecture 16. Course Summary&Review for Exam II

Upward/downward intensity in the plane-parallel atmosphere with scattering/absorption (Lecture 5):     *                      * I ( , , ) I ( , , ) exp( ) I ( , , ) I ( 0 , , ) exp( )         *         1 1                      exp( ) J ( , , ) d exp( ) J ( , , ) d        0   2 1                 0 J ( , , ) I ( , ' , ' ) P ( , , ' , ' ) d ' d '  4  0 1          0 F P ( , , , ) exp( / )  0 0 0 0 4 Upward/downward intensity in the plane-parallel atmosphere with emission/absorption (Lecture 9): 2

Clouds: Cloud amount/coverage (cloud mask) Visible+ IR => Lecture 12 and Lab 10 Principles: based on a combination of thresholds for solar reflectivity and brightness temperature (in the IR) Active (CALIPSO, CloudSat) => Lectures 13-14 Cloud liquid water content (column integrated) Microwave => Lecture 9 Cloud type ISCCP classification => Lecture 12 Cloud particle size distribution (effective size) and optical depth MODIS retrieval technique => Lecture 12 and Lab 10 Cloud thermodynamic phase MODIS retrieval technique => Lecture 12 Cloud – top pressure O2 absorption technique” and “CO2 slicing technique = > (see textbook) Cloud height and cloud detection Lidars/Radars => Lectures 13-14 and Lab 12

Problem solving example You analyze a satellite image of two clouds with one appearing brighter at the visible wavelengths. In general, would you expect more, less, or unknown infrared radiance emitted by the brighter-looking cloud? ---------------------------------------------------- Correct answer: unknown

For optically thin atmosphere (R atm <<1 and T atm ~ 1):

Approximate eqs: SOLAR SPECTRUM Cloud reflectivity (conservative scattering:  0 =1):   ( 1 g )  R cld    1 ( 1 g ) THERMAL SPECTRUM Atmospheric features (cloud) with emission/absorption      cld      μ) I ( 0 ; = B T 1 B T src    cld cld

Problem solving example Consider a cloud with temperature of 220 K overlying a surface with T=285 K. Assume that the atmosphere above and below the cloud is transparent to the radiation at 11  m. If the cloud emissivity is 1, what is the brightness temperature that will be measured by a nadir looking satellite radiometer at 11  m? ------------------------------------------------------------------------------------ Solution: Use the following Eq., and then find BT from I by inverting the Planck function : cloud

Brightness temperature (Lecture 2) Brightness temperature, T b , is defined as the temperature of a blackbody that emits the same intensity as measured. Brightness temperature is found by inverting the Planck function. C 2  2 hc 2 T b  B ( T ) C     5   (exp( hc / k T ) 1 ) 1 ln[ 1 ] B  5 I  where C 1 = 2hc 2 =1.1911x10 8 W m -2 sr -1  m 4 C 2 = hc/k B =1.4388x10 4 K  m

Aerosols: Aerosol optical depth / particle size distribution/Angstrom exponent Sunphotometers (AERONET ) => Lecture 5 and Lab 4 Principles: based on measurements of direct solar radiation that permit to retrieve the aerosol optical depth Visible-near IR satellite remote sensing (MODIS, MISR, AVHRR, SeaWiFS) => Lecture 5 Principles: based on measurements of reflected solar radiation and look-up tables for pre- defined aerosol models (size distribution and refractive index) Vertical profile of backscattering, extinction and optical depth (lidars) => Lecture 14 and Lab 12

Assuming no surface reflection (dark surface), the upwelling intensity at the level Z (or  ) is  *                    I ( , , ) J ( , , ) exp[ ( ) / ] d /  Substituting in the source function   *                     0 I ( , , ) F P ( ) exp[ ( ) / / ] d /  0 0 4  Satellite sensor measures   1 1          0 0 I ( 0 , , ) F P ( ) [ 1 exp( ( ) *)]       0 4 0 o In the single scattering approximation when  * <1 :   *      0 I ( 0 , , ) F P ( )   0 4

Lidar equations R k C h  MIE lidar:     b P ( R ) exp( 2 k ( r ) d r )  r e 2 R 2 4 o RAMAN lidar:   R C h k ( R , , )            b L R P ( R , , ) exp( [ k ( r , ) k ( r , )] d r )  r L R e L e R 2 2 4 R o

Scattering domains: Rayleigh scattering regime: 2  r/  <<1, and the refractive index m is arbitrary (applies to scattering by molecules and small aerosol particles) Rayleigh-Gans scattering : ( m – 1) <<1 (not useful for atmospheric application) Mie-Debye scattering: 2  r/  and m are both arbitrary but for spheres only (applies to scattering by aerosol and cloud particles) Geometrical optics: 2  r/  is very large and m is real ( applies to scattering by large cloud droplets). The size parameter x = 2  r/  is a key factor determining how a particle interacts with EM radiation

MIE theory: Efficiencies (or efficiency factors) for extinction, scattering and absorption are defined as       a s e Q Q Q   a s 2  e 2 2 r r r     Q Q Q b Q  b a e s 2 r      0 P ( 180 ) b s (Lecture 13) From Mie theory:  2     Q ( 2 n 1 ) Re[ a b ] e n n 2 x  n 1  2    2  2 Q ( 2 n 1 )[ a b ] s n n 2 x  n 1

In Rayleigh scattering regime:    2 m 1     4 Im Q a x    2   m 2 2  2 2  m 1 2 8 m 1  4  Q b 4 x 4 Q s x  2  m 2 2 3 m 2

Integration over the size distribution: For a given type of particles characterized by the size distribution N(r)dr, the extinction, scattering and absorption coefficients (in units LENGTH -1 ) are determined as r r 2 r 2  2         k ( r ) N ( r ) dr k ( r ) N ( r ) dr k ( r ) N ( r ) dr e e a a s s r r r 1 1 1 Backscattering coefficient (Lecture 14)

Gases: Absorption (emission): • depends on molecular structure (dipole!) • wavelength-selective Scattering: • a point dipole approach – Rayleigh scattering • ~ wavelength -4 => important in UV-vis negligible in IR&microwave

Ozone and trace gases (NO 2 , SO 2 , BrO, OClO): Ozone profile Sounding => Lecture 10 Other gases => see Table 15.1 in Lecture 15 Lidars (profile) => Lecture 14 Water vapor : Integrated column (total precipitable water) from microwave => Lecture 9 Profile from IR sounding => Lecture 10 Profile from microwave sounding => Lecture 10 Profile from Raman lidar, DIAL => Lecture 14

u 2    k du   u 1   z z     1         k d z T ( z , z , ) exp( k d z )   gas    gas  z  z    z k dT ( z , z , ) 1          gas exp( k d z )     gas d z  z   z ( , , ) dT z z            I ( z , ) I ( 0 , ) T ( z , 0 , ) B ( T ( z )) d z      d z 0     z z z 1 1 1                       I ( z , ) I ( 0 , ) exp k d z exp k d z B ( T ( z )) k d z          gas gas gas      0 0 z

Weighting functions for near-nadir sounding: For a satellite sensor looking down:     dT ( , z , )              I ( , ) I ( 0 , ) T ( , 0 , ) B ( T ( z )) d z      d z 0     k ( , , ) T z 1          gas W ( , z , ) exp( k dz )     gas dz z

Microwave 30   ( in cm ) ~  ( in GHz )

Precipitation Visible/IR techniques => Lecture 12 Principles: indirect method that relates properties of clouds to precipitation Microwave techniques => Lecture 12 Principles: direct method that relates the optical depth associated with the emitting rain drops and brightness temperature measured by a passive microwave radiometer. Radar => Lecture 13 and Lab 11 Principles: measured backscattering from rain drops is related to the Z factor (size distribution) and then to precipitation via the Z-R relationship