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# Remote Sens Atmos&Oceans EAS 6145

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Lecture 6 W2 Scattering and absorption by aerosol and cloud particles Obiectives 1 Properties of atmospheric aerosols 2 Properties of clouds and precipitation 3 Refractive indices of water ice and aerosol species 4 Principles of scattering 5 Rayleigh scattering 6 Scattering and absorption by aerosol and cloud particles Required reading S 16 41 43 5154 56 57 Additional reading S 42 55 Advanced reading Bohren C F and D R Huffman Absorption and scattering of light by small particles John WileyampSons New York pp 531 1983 1 Pronelties of 39 in aerosols Atmospheric aerosols are solid or liquid particles or both suspended in air with diameters between about 0002 pm to about 100 pm 0 Interaction of the particulate matter aerosols and clouds particles with electromagnetic radiation is controlled by particle size composition and shape 0 Atmospheric particles vary greatly in sources production mechanisms sizes shapes chemical composition amount distribution in space and time and how long they survive in the atmosphere ie lifetime Primary and secondary aerosols Primary atmospheric aerosols are particulates that emitted directly into the atmosphere for instance seasalt mineral aerosols or dust volcanic dust smoke and soot some organics Secondary atmospheric aerosols are particulates that formed in the atmosphere by gas toparticles conversion processes for instance sulfates nitrates some organics Location in the atmosahere Geograghical location marine continental rural industrial polar desert aerosols etc 39 39 manmade and natural aerosols Anthropogenic sources various biomass burning gas to particle conversion39 industrial processes agriculture s activities Natural sources various seasalt dust storm biomass burning volcanic debris gas to particle conversion Chemical composition Individual chemical species sulfate SO42 nitrate N 0339 soot elemental carbon seasalt N aCl minerals e g quartz SiO4 Multicomponent MC aerosols complex makeup of many chemical species called internally mixed particles Shgge Spheres all aqueous aerosol particles eg sulfates nitrates etc Complex shapes dust soot ie solid particles Scanning electron microscope image of a dust particle Classical re resentation of article size s ectrum Chemical Conversion of Gases to Low Volatility Vapors Condensation Low Volatility Primary Vapor Particles Homogeneous coagmauon Nucleation Condensation Growth of Nuclei lWind Blown Dust l Emissions Droplets Sea Spray Volcanoes Coagulation Plant Particles Washout I I 0001 001 01 1 10 100 Particle Diameter um Transient Nuclei or Accumulation Mechanically Generated Aitken Nuclei Range Range Aerosol Range Fine Particles Coarse Particles Figure 61 ldealized schematic of the distribution of particle surface area of atmospheric aerosol particle from Whitby and Cantrell 1976 NOTE fine mode d lt 25 pm and coarse mode d gt 25 pm fine mode is divided on the nuclei mode about 0005 pm lt d lt 01 pm and accumulation mode 01um lt d lt 25 pm o The particle size distribution of aerosols are often approximated by a sun of three lognormal functions as Z NI 1nrr072 exp 61 V271quot 1no r 21110392 where Nr is the particle number concentration Ni is the total particle number Nr concentration of ith size mode with its median radius 1 0 and geometric standard deviation oi kmoment of a lognormal distribution can be found as J rkNrdr Norok 6Xpk2ll 103922 62 NOTE A common approach in the satellite retrieval algorithms is to use a lookup table of aerosol candidate models Table 61 Aerosol components used in the MISR Multiangle ImagingSpectro Radiometer retrieval algorithm 1 0 rmin rmax 039 RH Vary Hb H1 H5 type with km km km yes no no Oblate spheroids Here Hb is the base height of the aerosol layer H1 is the top height of the aerosol layer and HS is the scale height of the aerosol layer p is the density of an aerosol particle 2 Pronelties of clouds and A Major characteristics are cloud type cloud coverage liquid water content of cloud cloud droplet concentration and cloud droplet size Important properties of clouds 0 Cloud droplet sizes vary from a few micrometers to 100 micrometers with average diameter in 10 to 20 um range 0 Cloud droplet concentration varies from about 10 cm393 to 1000 cm393 with average droplet concentration of a few hundred cm393 o The liguid water content of typical clouds often abbreviated LWC varies from approximately 005 to 3 gwater m393 with most of the observed values in the 01 to 03 gwater m393 region NOTE Clouds cover approximately 60 of the Earth s surface Average global coverage over the oceans is about 65 and over the land is about 52 Table 63 szes and properties of clouds Height of Freq over Coverage Freq over Coverage base km oceans over lan over land Type oceans Low level StratocumulusSc 02 45 18 Stratus St 02 ScSt ScSt ScSt ScSt Nimbostratus Ns 04 6 6 6 5 Mid level Altocumulus Ac 27 46 22 35 21 Altostratus As 27 AcAs AcAs AcAs AcAs High level Cirrus Ci 718 37 13 47 23 Cirrostratus Cs 718 CiCsCc CiCsCc CiCsCc CiCsCc Cirrocumulus Cc 7 18 Clouds with vertical development Cumulus Cu 03 14 5 Cumulonimbus Cb 03 10 6 7 4 0 Cloud droplets size distribution is often approximated by a modi ed gamma distribution N0 1 Nr CXP VVn 63 Where No is the total number of droplets cm393 rn in the radius that characterizes the distribution a in the variance of the distribution and 1quot is the gamma function Table 64 Characteristics of representative size distributions of some clouds for a 2 Cloud type N0 rm rmax re LWC m Stratus over ocean 50 10 15 17 0105 over land 300400 6 15 10 0105 o For many practical applications the optical properties of water clouds are parameterized as a function of the effective radius and liquid water content LWC The effective radius is defined as J In 3 N r dr r2 2 64 J In N r dr where Nr is the droplet size distribution e g in units m393ym391 NOTE Mean radius rm a 1 rn Effective radius re a 3 rn The liquid water content LWC is defined as 4 3 LWC pWV g pwjm Nrdr 65 gt Raindrop Srmw ake Runer Drum N5 mm 2 mm map quota 5 mm Nonsphencal perheles shape depends ofshze ofa ram drop Rahde stze desthbutmh 15 otteh represented by the Marshelh Palmer distributinn Nr NO exp72Ar 6 5 where N 8x103m393mmquot but m general No depends on ram type A15 related to the hethfen rate R m mmhour as A 4 1Rr mmquot ems clouds once crystalwater droplet mixtures mm m tt H Y r t haveb nrn dD tnt t t Agmnm Needles w39dntwtdknmhAt W bk mm mm mm Innu Fm Hallaw column at Wequot 3 Refractive indioes d39vmter ice and aerosol sneaks Iquot n n ml L r mfracdve index gives the phase velocity ofpropaga on w he smallest acmosth39c aerosol particles H i We I i Ice Imaginary Pm 5 M 05 10 15 20 25 m 13 40 Wavelenmh mm Figure 63 The refractive index ofwater and ice in due visible and nearIR um drops in due visible Imaglnzry Pan A 0 sun mm 150 mm 2300 mun 15m 4 Vawuumlm cm F39gum m The rehchve mdex ufwater and me m the IR 4km I I I I I QUARTZ 4 ql I I l I AMSULF x I I 1 ID I I o l g I I g 2 i3 390 M NaCI 7 E 39 LL AEROSOL I In Ii39 I 3 I I A 0 K K 1 r I I E I I a I I E 396 39 39 g I U l E 3960 I6a lt WATER gt1 H oumrz gt1 k lt 0 HAM sum H K NuCl I I I I l Ii I I I l l l l i I I l DJ 0 IO IOO Figure 65 The imaginary part of the refractive indices of some aerosol species 0 Aerosol particles often consist of several chemical species called the internal mixture There are several approaches called mixing rules to calculate the effective refractive index me of the internally mixed particles using the refractive indices of the individual species Volume weighted mixing mlZmeJ 67 Where mj is the refractive index of jspecies and is its volume fraction NOTE Other commonly used mixing rules are the Bruggeman and MaxwellGamett 4 Principles of scattering Incident radiation I gt Scattered radiation gt Particle Consider a single arbitrary particle consisted of many individual dipoles The incident electromagnetic eld induces dipole oscillations The dipoles oscillate at the frequency of the incident eld and therefore scatter radiation in all directions In a given direction of observation the total scattered eld is a superposition of the scattered wavelets of these dipoles accounting for their phase difference scattering by the dipoles is coherent ie there is a de nite relation between phases Scattering phase function Pcos is defined as a nondimensional parameter to describe the angular distribution of the scattered radiation as l jPcos dQ 1 68 47239 Q where D is called the scattering angle between the direction of incidence and observation NOTE Another form of 68 1 27 If I E Pcos sm d d 1 69 NOTE The phase function is often expressed as Pcos P939qp399qp39 where 639 p39 and 6 p are the spherical coordinates of incident beam and direction of observation Using the spherical geometry it can be shown see S Appendix 1 that c0s c0s639c0s9 sin639sin9 c0sltp39 qgt The asymmetry factor g is de ned as l g JPcos cos dcos 610 71 g0 for isotropic scattering Forward scattering refers to the observations directions for which 9 lt n2 ggt0 scattering in the forward direction Backward scattering refers to the observations directions for which 9 gt n2 glt0 scattering in the backward direction Scattering domains Rayleigh scattering anl ltlt1 and the refractive index m is arbitrary applies to scattering by molecules and small aerosol particles Rayleigh Cans scattering m 1 ltlt1 not useful for atmospheric application Mie Debye scattering 21cr7u and m are both arbitrary but for spheres only applies to scattering by aerosol and cloud particles Geometrical optics 21tr7u gtgt1 and m is real applies to scattering by large cloud droplets and ice crystals 5 Rayleigh scattering 0 Because the sizes of atmospheric molecules are much smaller than the wavelengths of solar and IR radiation the scattering by atmospheric gases is the Rayleigh scattering o In the Rayleigh scattering approximation a molecule or a small particle is considered as an individual dipole Consider a small homogeneous spherical particle e g a molecule with size smaller than the wavelength of incident radiation E0 Let Z70 be the induced dipole moment then from the classical electromagnetic theory we have 130 an 611 where on is the polarizability of the particle NOTE Do not confuse the polarization of the medium with polarization associated with the EM wave The scattered electric eld at the large distance r called far eld scattering from the dipole is given in cgs units by a 1 1 015 E C Z7 mn 7 612 where y is the angle between the scattered dipole moment if and the direction of observation In oscillating periodic eld the dipole moment is given in terms of induced dipole moment by j e eXp ikr ct 613 and thus the electrical eld is a ex ik r ct E E0 Mkzoz s1n 7 614 r Decomposing the electrical vector on two 01thogonal components perpendicular and parallel to the plane of scattering a plane containing the incident and scattering beams We have E E0r WHO M m 615 r E1 E01wkla Sin yz 616 r EOr Direction of incident radiation En2 yzn2 Using that 1 Li E2 617 A9 47239 the perpendicular and parallel intensities or linear polarized intensities are I 10rk4062 r2 618 II OIC4612 cos2 r2 619 Using that the natural light incident beam in not polarized Io IolIo2 and that k277 we have 4 2 1 r 11Iga22 M 620 r it 2 Eq 620 gives the intensity scattered by molecules Rayleigh scattering for unpolarized incident light Rayleigh scattering phase function for incident unpolarized radiation is 3 Pcos Zl cos 2 G 621 Eq 620 may be rewritten in the form I 128 7239 5 P 1 cos 6 a2 622 r 2 314 M Eq 622 may be rewritten in the terms of the scattering cross section I P G Icos G ax Q 623 r 4 7239 Here the scattering cross section in units of area by a single molecule is U 0 212872395 624 J 3 24 I The polarizability is given by the LorentzLorenz formula 3 m2 l 0 W m 625 where NS in the number of molecules per unit volume and mn ik in the refractive index For air molecules in solar spectrum n is about 1 but depends on 7 and k 0 Thus the polarizability can be approximated as l a m W012 1 626 Therefore the scattering cross section of an air molecule becomes 8 7239 3 n 2 l2 a J MW f 5 627 wheref6 is the correction factor for the anisotropic properties of air molecules defined as f6 6386 76 and 50035 Using this scattering cross section one can calculate the optical depth of the entire atmosphere due to molecular scattering as 11 0520 NZd2 628 NOTE The Rayleigh scattering cross section Eq 624 and hence optical depth are inversely proportional to the fourth power of the wavelength gt blue color of the sky App 39 39 of Rayleigh optical depth ie optical depth due to molecular scattering down to pressure level p in the Earth s atmosphere 11 z 00088 L 4 1M 629 1013 mb o Rayleigh scattering results in the sky polarization The degree of linear polarization is Q 11 cos2 l sin2 LPG I 11 cos2 l cos2 l 630 6 Scattering and absorption by aerosol and cloud particles Mie Debye theory NOTE MieDebye theory is often called Mie theory or Lorentz Mie theory Mie th ear outline Assumptions i Particle is a sphere ii Particle is homogeneous therefore it is characterized by a single refractive index mn ik at a given wavelength NOTE Mie theory requires the relative refractive index refractive index of a particlerefractive index of a medium But for air In is about 1 so one needs to know the refractive index of the particle ie refractive index of the material of which the particle is composed NOTE If a particle has complex chemical composition the effective refractive index must be calculated at a given wavelength 0 Mie theory calculates the scattered electromagnetic field at all points in the particle called internal field and at all points of the homogeneous medium in which the particle is embedded For all practical applications in the atmosphere light scattering observations are carried out in the far eld zone ie at the large distances from a particle In the farfield zone ie at the large distances r from a sphere the solution of the vector wave equation can be obtained as exp ikrikz52 631 LEM ikr S4 S1 here k 2n7t E and E are the parallel and perpendicular components of incident electrical eld and E f and E j are the parallel and perpendicular components of scattered electrical eld 526 536 546 516 is the amplitude scattering matrix unitless For spheres S3 S4 0 and thus Eq 631 gives E13 7 exp7ikr ikz52 0 HE E f 39 632 zkr 0 519 E Eq632 is a fundamental equation of scattered radiation by a sphere including polarization Mie theory scattering amplitudes 2n 1 516 man7rncos bnrncos 633 Sz i b7r cos ar cos 634 n1nn1 n n nn where an and In are Mie angular functions 1 1 635 7r cos Sin 9 P cos 9 139 cos 8 LP1cos o 6 36 V1 H I 1 where Pr are the associated Legendre polynomials Mie theory also gives the scattering phase matrix P that relates the Stokes parameters 10 Q0 U0 and V0 of incident radiation eld and the Stokes parameters 1 Q U and Vof scattered radiation Q as P Q 637 U 47272 U0 V V where Pu Pu 0 0 P P Pzz 0 0 0 1333 1334 638 0 0 B4 P44 For spheres P22 P11 and P 44 P33 NOTE In general for a particle of any shape the scattering phase matrix consists of 16 independent elements but for a sphere this number reduces to four Thus for spheres Eq637 reduces to 1 P11 P12 0 0 a Q 03 P12 P11 0 0 Q 639 U 47er 0 0 P33 7 P34 U0 V 0 0 P34 P33 Va where each element of the scattering phase matrix is expressed Via the scattering amplitudes S1 and S2 P11 P is the scattering phase function of a particle From Mie theory it follows that the extinction cross section of a particle is 47139 0 0e FR6S0 640 But for the forward direction ie 00 from Eqs633634 we have S1lt0 gtSzlt00gt ilt2n1gtltan12 Efficiencies or efficiency factors for extinction scattering and absorption are de ned a o 0 a as Q 2 Q 2 Q 2 6411 IN IN 7r r Where in is the particle area projected onto the plane perpendicular to the incident beam Mie ef ciency factors are derivedfrom the Mie scattering amplitude Q if lt2n1gtRe a m 6421 x nl Qxizi2nlanz bnz 643 x n and the absorption ef ciency can be calculated as Q Q2 Q 644 Extinction ef ciency vs size parameter x assuming NO ABSORPTION 1 small in Rayleigh limit Q2 02 x 4 2 largest Qe when particles and wavelength have similar size 3 Q8 gt 2 in geometric limit x a co 40 3 5 7 m133 000i 39 7 m1330li 30 m133003i 7 ml33010i 25 C521 15 10 00 quot39y 0 10 20 30 40 50 60 70 80 Size parameter x Figure 66 Examples of Q8 calculated with Mie theory for several refractive indexes END of Mie theory outline For a single spherical particle Mie theory gives the extinction scattering and absorption cross sections efficiency factors the scattering amplitudes and phase matrix Strate to com ute 0 tics 0 an ensembleo s herical articles Particle size r Refractive index m0 Vie theory Scattering cross section 039s Absorption cross section ca Extinction cross section O39e Phase function P11 as a function of a particle size and wavelength Integration over size distribution Nr Scattering coefficient Ks Absorption coefficient Ka Extinction coefficient Ke Phase function P11 as a function of the wavelength Integration over the size distribution For a given type of particles characterized by the size distribution Nr the volume extinction scattering and absorption coefficients in units LENGTH39I are determined as kg jag rNrdr jm2Q2Nrdr 645 k5 To rNrdr 1 szSNrdr 646 k JaarNrdr j szaNrdr 647 u Mquot u M m a M a mu wuuumu Similarto Eq 5tl3 the optical depth of an aerosol layer is given as sZ sZ 11s1s2JkeyldsJMdes s1 s1 mi Us i plight m n im single scattered event and it is defined as k me k l ilfl NOTE No absorption conservative scattering on No scattering on 0 Scattering phase function of particles characterized by the size distribution N r z momma P quot 6 49 IGJNUW w MUHMJH Cloud Drop 77 Aerosol mi Malecule Phase Funchan Fla 60 12 Scattering Auge 6 Figure 67 Examples of scattering phase functions at a wavelength of 05 pin gt Optical properties of the external mixture ie the mixture of several types of particles kg k kg 650 where k k and k are calculated for each particle type characterized by its particle size distribution Nir and a refractive index or effective refractive index mi NOTE Do not sum the single scattering albedo and scattering phase functions H o In general an atmospheric layer has molecules aerosols andor cloud particles Thus one needs to calculate the effective optical properties of this layer as an external mixture of the optical properties of these constituents gt How to calculate the effective optical properties of an atmospheric layer of gas and aerosols or clouds Effective also called total optical depth M M A A 2391239a1239x1239a1239xI 651 M M where 7amp1 and 75 are opt1ca1 depth due to absorptron by gases and molecular Rayleigh scattering respectively 71 and 71 are optical depth due to absorption and scattering by aerosol particles respectively Effective single scattering albedo 1M TA 6004 M 652 11 Effective scattering phase function TMPM 139A PA 6 1316 51 A M 1 A 653 751 751 Effective asymmetry parameter A A ragga M A 751 751 g1 654 gt Optics of cloud particles In contrast to atmospheric aerosols the cloud droplets consist of a single species 7 water Thus to calculate the absorption and scattering cross sections of cloud droplets one needs to know the size of droplets and the refractive index of water versus wavelength NOTE Cloud droplet sizes vary from a few micrometers to 100 micrometers with average diameter in 10 to 20 um range Extinction coef cient of cloud droplets Using the effective radius I 7273Nrdr r I 7272Nrdr and the liquid water content LWC 4 3 LWC pWV pwj7zr Nrdr the extinction coef cient of cloud droplets is k creamnah ermzer and that Q m 2 for water droplets at solar wavelengths we have NELWC k N 2 cm 655 Lecture 7 Principles of passive remote sensing using extinction and scattering Scattering as a source of radiation Multiple scattering Obiectives 1 BeerBouguerLambert law 2 Direct and diffuse radiation Scattering as a source of radiation 3 Radiative transfer equation with multiple scattering 4 Examples of aerosol passive remote sensing using extinction and scattering in the solar spectral region Required Reading S 61 63 64 661 1 BeerBouguerLambert law The fundamental law of extinction is the Beer Bouguer Lambert law which states that the extinction process is linear in the intensity of radiation and amount of matter provided that the physical state ie T P composition is held constant Consider a small volume AV of infinitesimal length ds and unit area AA containing optically active matter gases aerosols and or cloud drops Thus the change of intensity along a path ds is proportional to the amount of matter in the path 0 15 SI For extinction dI t ke 112015 71a I 11 d 1 For emission A keJtJ tds 7 lb where KM is the volume extinction coef cient LENGTH39I and J 1 is the source function Integrating Eq 7 l we have 51 yr1 104 m J ke1Sds 104 eXPT1 72 o where 1M and 15 are the incident and transmitted intensities respectively Optical depth along the path s is de ned as 51 71 IkMGMS 73 0 UNITS optical depth is unitless NOTE same name optical depth optical thickness optical path Transmission function is de ned as T2 2 511 101 eKIM Q 74 UNITS transmission function is unitless between 0 and l 2 Direct and diffuse radiation Scattering as a source of radiation 0 The solar radiation eld is traditionally considered as a sum of two distinctly different components direct and diffuse I 101 Idif Direct radiation is a part of the radiation eld that has survived the extinction passing a layer with optical depth 1 and it obeys the BeerBouguerLambert law or Extinction law i Idir IOCXM Tu0 75 where Io is the incident intensity at a given wavelength at the top of a layer and go is a cosine of the incident zenith angle 00 p0 c0s60 A l in the Extinction law to direct solar radiation Io is the solar intensity at a given wavelengths at the top of the atmosphere surface Thus direct solar radiation reaching the surface is i Idir 10 eXpT 0 76 where 39c is the optical depth on the entire atmosphere NOTE For radiative transfer in the atmosphere optical depth is defined along vertical coordinate ie altitude Diffuse radiation Diffuse radiation arises from the light that undergoes one scattering event single scattering or many multiple scattering Incident light Third order scattering Second order scattering First order scattering a lt1 Scattering is a source of light at a given direction because light is scattered into this beam from other directions For single scattering 1152 6 2 77 6145 Cs1515114999 47239 where 55239 is the incident intensity in the direction de ned by a solid angle Q Ut 0 For multiple scattering integrating over all directions MIAQ MQ 78 47239 d nds39 47 NOTE The above equation shows that the phase lnction redirects the incident intensity in the direction 201 7 to the direction 520 a and the integral accounts for all possible scattering events within the 411 solid angle According to the BeerBouguerLambert law scattering radiance from path ds is 6111 keJJlds see Eq7lb thus from Eq78 the scattering source function is 0 56 41111 P1 d9 79 Q where 00 x5 Key is the single scattering albedo The scattering source function 1 has units of intensity 2 plays the role of the Planck function in thermal radiative transfer but the scattering source function is more complex 3 depends on the radiation intensity in the incident direction 1 152 fraction of radiation Pam m 47139 which is scattered we 1 fraction scattered into the new direction The monochromatic radiative transfer eg uation for a plane parallel atmosphere expresses the net change in intensity due to extinction and scattering along path dz d1 d extinction d scattering A planeparallel atmosphere Ztop 10 Z 1 Z0 1 Using ds dzc0s the radiative transfer equation can be written as d 26 mow Ilz6 new 710 key1612 Introducing the optical depth measured from the outer boundary downward as T4Z0 Ike4zdz 711 0 and using d1 Mzdz and p c0s0 we have a r ur Mama 712 NOTE Eq712 is called the Schwarzchild s equation This is a basic equation for the radiative transfer in a planeparallel atmosphere T Upward or upwelling intensity I is for l 2 u 2 0 or 0 S 9 S 7239 2 Downward or downwelling intensity I is for l S u S 0 or 7239 2 S 9 S 7239 The radiative transfer equation 712 can be written for upward and downward intensities d1T r zz mm JT 713a dIl r 2 ILg JT u 713b d r Solution of Eq713a gives the upward intensity in the plane parallel atmosphere T T T T 11T 111 CXP T 1 rquot T T T 714a jexplt gt J1 13941de 1 Solution of Eq713b gives the downward intensity in the plane parallel atmosphere L L T 11 r 110 6Xp 714b 17 7 7 Jexplt gt Jim 1de 0 First order scattering Observer Sun 3 i Gowuawu Ztop x 39I0 Direct solar radiation reaching the altitude z is i F Z F0 eXpkgZz Z39l0 Fa eXpTIu0 where F o is the solar constant at the top of the atmosphere Scattering of the direct beam is the source of diffuse radiation see Eq 7 9 0 Hum Fo eXp T0P2 20 0 715 Assuming no surface re ection dark surface the upwelling intensity at the level Z or 395 can be found from Eq7 14a as WWW JT expT TdT 716 Substituting in the source function Ilr EP T eXpT TT 0dT 717 An observer ie a satellite detector at Ztop or r 0 measures ow ame 0 1 exp iir 718 47239 u 0 0 ll If 1 lt1 called the single scattering approximation Eq 718 simpli es t0 r a 7 I 0 F0P 719 47239 u NOTE Eq7 19 provides the basic for the retrieval of aerosol optical depth from a satellite sensor For instance the AVHRR aerosol retrieval algorithm is based on the singlescattering approximation see S 642 3 Radiative transfer eguation with multiple scattering In the general case of multiple scattering 27 1 a l l l l l l Ame jjxw p PP ra d dra 0 1 720 a FoPa 70 0eXpTzuo Using the source function for scattering we can write the radiative transfer equation for diffuse radiation as an integrodifferential equation 71627139 gain E j 1r 2P 2 zdg F 0135 gape T 0 721 T 4774 47239 NOTE To solve Eq721 one needs to know the scattering coefficient k5 absorption coefficient km and scattering phase function Pp q u ltp as a function of wavelength in each atmospheric layer To nd a solution of the radiative transfer equation for diffuse radiation ie to solve Eq721 various approximate and exac techniques have been developed Approximate methods i Single scattering approximation see above Eq 7 19 ii Twostream approximations for instance Eddington and Delta Eddington approximations Exact methods i Discreteordinate technique ii Addingdoubling technique iii MonteCarlo technique 4 Examples of aerosol passive remote sensing using extinction and scattering in the solar spectral region Retrieval of the optical depth particle size distribution and Angstrom parameter of aerosols see below Retrieval of stratospheric aerosols based on limb viewing remote sensing see S 622 Retrieval of ocean color Lecture 8 and lab Retrieval of cloud properties Lectures and lab Retrieval of surface properties eg surface albedo NDVI Normalized Differential Vegetation Index after the atmospheric correction is applied see S 641 gt Retrieval of aerosol ogtical dgth from groundbased sunghotometer measurements A sunphotometer narrowfield of view radiometer that tracks the sun measures the direct solar radiation attenuated by the atmosphere a Fain1 F01 eXpT1u0 722 where T is the optical depth of the entire atmospheric column ie 77 77Zzop20 Ike7zdz 723 0 For cloudless atmospheric conditions T 1 is due to attenuation by aerosols Rayleigh scattering and gaseous absorption 03 and N02 depending on 7 Thus I If 73 I 724 From Eq722 we have 1nFdi7 1nFo7 1 U10 725 and r u0lnFM maninn 726 Thus 7 u0lnFM 1nFldM 73 753 727 NOTE To retrieve the aerosol optical depth one needs to correct for Rayleigh scattering and gaseous absorption NOTE If the aerosol optical depth is known or negligibly small Eq727 gives the optical depth due to absorption of gases used in the retrievals of 03 and H20 column amount NOTE If the aerosol optical depth remains constant during the day Eq7 27 enables to measure solar constant F071 by plotting measured F 0er A vs 0 called Langley plot ln FM i In Fdirj L r 2 4 6 m1 yo Figure 71 Illustration of the Langley plot method for determining the solar constant gt Retrieval of aerosol optical depth from a satellite sensor that measures the solar re ected radiation Retrievals of aerosol optical depth is often done in the single scattering approximation see Eq1015 0 239 I 0 F0P 47239 u Thus T 47271 T I 0 728 A A mo1Fo1P1 NOTE Example of aerosol retrievals from AVHRR see S 642 NOTE Satellite sensors channels are selected to avoid the absorption of atmospheric gases At shorter solar wavelengths one needs to correct for the Rayleigh scattering where as at the longer solar wavelength about 7 gt 700 nm the Rayleigh scattering is negligible NOTE To retrieve the aerosol optical depth from Eq728 one must provide the aerosol single scattering albedo no and scattering phase function P These properties are precalculated called lookup tables for the range of aerosol size distribution and refractive indices e g MODIS aerosol retrieval algorithm or using candidate aerosol models eg MISR aerosol retrieval algorithm see Table 61 0 Spectral aerosol optical depth are used to retrieve the Angstrom exponent and particle size distribution Angstrom Exponent describes the dependence of aerosol optical properties on the wavelength and hence on particle size De nition using scatterin 39 measured by a nephelometer l k k 2 a q12 0g All 2 729 IOgar 392 Definition using spectral optical depth 10gf qTl2 041112 730 kqu 392 For r ltlt 2 gt 1 4 for instance Rayleigh scattering For r gtgt 2 gt 11 0 for instance cloud drops or coarse aerosol particles dust in the visible gt Retrieval of aerosol particle size distribution from spectral aerosol optical dgth Aerosol optical depth is measured at several wavelength ztap t Ik67zdz 0 The volume extinction coefficient at the altitude z is Lecture 3 The nature of electromagnetic radiation Obiectives 1 Basic introduction to the electromagnetic field gt De nitions gt Dual nature of electromagnetic radiation gt Electromagnetic spectrum 2 Main radiometric quantities energy ux and intensity 3 Concepts of extinction scattering absorption and emission 4 Polarization Stokes parameters Required reading S 21 221 222 23 24 41 Appendix 1 Recommended reading Petty chapters 23 1 Basic introduction to electromagnetic eld Electromagnetic radiation is a form of transmitted energy Electromagnetic radiation is sonamed because it has electric and magnetic fields that simultaneously oscillate in planes mutually perpendicular to each other and to the direction of propagation through space Electromagnetic radiation has the dual nature its exhibits wave properties and particulate properties gt Wave nature of radiation Radiation can be thought of as a traveling transverse wave Electric Field LE Figure 1 A schzmahc new af an electmmaguzuc Wm pxwpagnhng almgthe 2 axxs m 2mm Emmy H ddsascnummexrypm mummm dun W m yuynmvm Wm mm mm angi mm mm WNW 5 m u cg mm mm 5 5 1 Equot x z 21 herecxsmzypeedaflxgmmwcmxn 29979xl xm ZUUXIUXmsjmd 5n 5 vacuum permittivity a elecmc mustard S 5 m nts af mg per mum per umt area 2 g w NOTE Ex means avectnrpmducl mm mm i 15 u en called inshntznzuus ran vectnr E amuse n ascdlates stupid mg a 6mm measuresxts mung mu ltsgt We same mm mural um 15 chmamm af the datum Wzvts are huacunzedbyfmuzncywzveknglh quad undying Fmguzncx xs de md as the number uf waves mm per secmd um pass a gvm mm m gym symbahzedby v Wavelength is the distance between two consecutive peaks or troughs in a wave symbolized by the 2 Wavelength Relation between 2 and 7 32 0 Since all types of electromagnetic radiation travel at the speed of light short wavelength radiation must have a high frequency 0 Unlike speed of light and wavelength which change as electromagnetic energy is propagated through media of different densities frequency remains constant and is therefore a more fundamental property Wavenumber is defined as a count of the number of wave crests or troughs in a given unit of length symbolized by v 33 UNITS Wavelength units length Angstrom A 1A lxlO3910 m Nanometer nm 1 nm1x10399 m Micrometer pm 1 pm lxlO39 m Wavenumber units inverse length often in cmquot NOTE Conversion from the wavelength to wavenumber 71 Vcml 100000m um 3 4 lm Frequency units unit cycles per second Us or s is called hertz abbreviated Hz Frequency gt Particulate nature of radiation Radiation can be also described in terms of particles of energy called photons The energy of a photon is given as Ephoton h V h ck hcv 35 where h is Plank s constant h 6625621103934 J s 0 Eq 35 relates energy of each photon of the radiation to the electromagnetic wave characteristics 17 and 7t 0 Photon has energy but it has no mass and no charge NOTE The quantized nature of light is most important when considering absorption and emission of electromagnetic radiation PROBLEM A light bulb of 100 W emits at 05 pm How many photons are emitted per second Solution Energy of one photon is Sphmon hch thus using that 100 W 100 Js the number of photons per second N is 100Js 1 1m7 100 x 05 x1076 7 2517 1020 hm Cmsil 66256 x10734 x 29979 x108 X Ns 1 NOTE Large number of photons is required because Plank s constant h is very small gt Spectrum of electromameljc radiation to energy or eqmvalenuy according to me Wavelength or frequency ENERGY mcxms ES 1cr5 1n 3 wavelength cm WAVELENGTH INCREASES Figure 32 The elemomagneuc specm THE ELECTROMAGNETIC SPECTRUM ankngllv m m m x m m w m I HT HTquot 107 W W In InH mquot m manH y r km a i 39 39 va W q 1 m Cry a s We W W Ennunnn mm nu We W173 satMY Mquot I0 W WV m N W N W H7 1 NYquot m 0 n7 Vnngyn W WW WWW war an m w w w vr w w m m39 1 m ultraviolel rays microwaves Vislble xrays gamma rays J i 400 nm 500 nm 600 nm 700nm Figure 33 Visible region omie electromagnetic spectrum NOTE 39 euui quot quot calledbytheir color eg blue green and read channels NF 39 quot quot 4 quot39 Lecture 5 V i 5 INWRED mmm quot1 i i c l IHANSMISSJDM w II inquot minimum mu W mamas m mow 5quot W m low Id Mn Mm 10m lDzM Mam mm mm Fimlro A quot 4 439 39 39 39 quot 39 m u r 39 39 39 uni uiii radiaiion A 39 39 39 39 doesn39t L interact much with air molecules and hence isn39t absorbed o In this course we study UV Visible infrared and microwave radiation Name of Wavelength Spectral equivalence spectral region pm Longwave Far Table 3 3 Frequency Example Lband is used onboard American SEASAT and Japanese JERSl satellites 2 Basic radiometric uantities intensit and ux Solid angle is the angle subtended at the center of a sphere by an area on its surface numerically equal to the square of the radius Q 12 36 UNITS of a solid angle steradian sr r A differential solid angle can be expressed as 9 d9 2 sin 6d6d Iquot using that a differential area is ds r 619 r sin9 de Examgle Solid angle of a unit sphere 411 PROBLEM What is the solid angle of the Sun from the Earth if the distance from the Sun to the Earth is d15XlO8 km Sun s radius is RS 696XlO5 km 71R d2 SOLUTION Q 676 x10 sr Intensity 0139 radiance is defined as radiative energy in a given direction per unit time per unit wavelength or frequency range per unit solid angle per unit area perpendicular to the given direction I L 37 ds cos 6detdl IA is referred to as the monochromatic intensity 0 Monochromatic does not mean at a single wavelengths 7 but in a very narrow infinitesimal range of wavelength A centered at 7 NOTE same name intensity specific intensity radiance UNITS from Eq37 J sec391 sr391 m392 um39l W sr391 m392 um39l ZetlliI Nari1 plq cleo sw 39zce 0 cos 6 Ears Figure 35 Intensity is the ow of radiative energy carried by a beam within the solid angle dQ a In general intensity is a function of the coordinates 17 direction 52 wavelength or frequency and time Thus it depends on seven independent variables three in space two in angle one in wavelength or frequency and one in time b In a transparent medium the intensity is constant along a ray 0 If intensity does not depend on the direction the electromagnetic field is said to be isotropic o If intensity does not depend on position the field is said to be homogeneous el UNITS from Eq38 J sec391 m392 um39l W m392 um39l From Eqs 3738 the ux is integral of normal component of radiance over some solid angle F j I cos6dQ 39 Q NOTE Many satellite sensors have a narrow viewing angle and hence measure the intensity not ux To measure the ux a sensor needs to have a wide viewing angle 0 Depending on its spectral resolution a detector measures electromagnetic radiation in a particular wavelength range M The intensity 1M and ux F M in this range are determined by integrating over the wavelength the monochromatic intensity and ux respectively 3 q 1M JIAdl39 FM IF1d 310 41 41 NOTE Lecture 2 gives classi cation of the sensors with respect to their spectral resolution broadband narrowband spectral and hyperspectral Examgles Broadband sensor CERES Clouds and the Earth39s Radiant Energy System Three bands channels Solar region 03 50 pm IR window 8 12 um and total 03 to gt 100 um Narrowband sensor MODIS Moderate Resolution Imaging Spectroradiometer NHJDIS bands 620 670 841 876 459 479 545 565 1230 1250 1628 1652 2105 2155 405420 438 448 483 493 526 536 546 556 662 672 673 683 M3n3 862 877 890 920 931941 915 965 045 300K 238 335K 0167 300K 079 300K 017 250K 25 4482 059 4549 275K Cirrus Clouds 26 1360 600 Water Vapor 1390 27 6535 116 6895 240K 28 7175 218 7475 250K Cloud Properties 29 8400 958 8700 300K Ozone 30 9580 369 9880 250K SurfaceCloud 31 10780 955 Temperature 11280 300K 32 11770 894 12270 300K cloud Top 33 13185 452 Altitude 13485 260K 34 13485 376 13785 250K 35 13785 311 14085 240K 36 14085 208 14385 220K Footnotes 1 Bands 1 to 19 are in nm Bands 2 to 36 are in pm 2 Spectral Radiance values are Wm2 Jm sr 3 SNR Signal to noise ratio 4 NEdetaT I Jvigc 1 39 39 r L lu Note Performance goal is 30 40 better than required 025 150SNR 025 3 The concepts of extinction gscattering absorption and emission Electromagnetic radiation in the atmosphere interacts with gases aerosol particles and cloud particles 0 Extinction and emission are two main types of the interactions between an electromagnetic radiation eld and a medium eg the atmosphere General de nition Extinction is a process that decreases the radiative intensity while emission increases it NOTE same name extinction attenuation Radiation is emitted by all bodies that have a temperature above absolute zero 0 K often referred to as thermal emission o Extinction is due to absorption and scattering Absorption is a process that removes the radiative energy from an electromagnetic eld and transfers it to other forms of energy Scattering is a process that does not remove energy from the radiation eld but may redirect it NOTE Scattering can be thought of as absorption of radiative energy followed by re emission back to the 39 quot field with quot quot 39 39 of energy Thus scattering can remove radiative energy of a light beam traveling in one direction but can be a source of radiative energy for the light beams traveling in other directions 0 Elastic scattering is the case when the scattered radiation has the same frequency as that of the incident field Inelastic Raman scattering results in scattered light with a frequency different from that of the incident light 4 Polanzanon Stokes naramelers Pnlarilztinn is a phenomenon peeuhar to transverse waves te a duecuon perpendmularto then oneehon ofpropaganon WOTF through medJa by altemauvely forcing the molecules of the medmm closer together then spreadmg thenn apart dArecuon Horizontal and vemcal polanzauons are an example oflinear pnlarilztinn Mathematical representation of a plane wave propagating in the direction Z is EEocoskz at 0 311 where E0 is the amplitude k is the propagation or wave constant k 210 m is the circular frequency a kc Zircl p 0 is the constant or initial phase a kz at 00 is the phase ofthe wave Introducing complex variables Eq311 can be expressed as E E0exp z39qp 312 NOTE we use expiiqp cosqp iisin The electric vector E may be decomposed into the parallel E l and perpendicular Er components as We can express E1 and E in the form E1 E0 cos k2 wt p10 E E0 cos k2 wt pro Then we have El El0 cos cos 110 sin sin lo E Eo 0054 005P0 Sin 5in0o where g kz at Performing simple mathematical manipulation we obtain E1 E102 E Eo2 2E1E10EEocosAqo sin 2Aqo 313 where A p p 0 p 0 called the phase shift Eq3 13 de nes an ellipse gt elliptically polarized wave Ifthe phase shift A w n 1 n0 1 2 then sin Aw 0 andcos Aw i1 and Eq 313 becomes E E 2 E 1 0 or Eir WEI 314 E10 E70 Eq314 de nes straight lines gt linearly polarized wave Ifthe phase shift A w 11 1 2 n 1 3 and E10 Era Eg then sin Aw i1 and cos Aw 0 and Eq313 becomes Ef E E02 315 Eq315 de nes a circle gt circular polarized wave NOTE The sign of the phase shift gives handedness righthanded and lefthanded polarization Unpolarized radiation or randomly polarized is an electromagnetic wave in which the orientation of the electrical vector changes randomly If there is a de nite relation of phases between different scatterers gt radiation is called coherent If there is no relations in phase shift gt light is called incoherent 0 Natural light is incoherent 0 Natural light is unpolarized o The state of polarization is completely de ned by the four parameters two amplitudes the magnitude and the sign of the phase shift see Eq313 Because the phase difference is hard to measure the alternative description called a Stokes vector is often used Stokes Vector consists of four parameters called Stokes parameters intensity I the degree of polarization Q the plane of polarization U the ellipticity V Notation 103 or IQUV V o Stokes parameters are de ned Via the intensities which can be measured I total intensity Q 10190 differences in intensities between horizontal and vertical linearly polarized components U L45 7145 differences in intensities between linearly polarized components oriented at 450 and 450 V Ircl 711 differences in intensities between right and left circular polarized components 0 Stokes parameters can be expressed Via the amplitudes and the phase shift of the parallel and perpendicular components of the electric field vector I E 30 E I Q E2 EZ 316 U ZEMEIO cosA V 2EroElo Lecture 11 Remote sensing of precipitation and clouds Obiectives 1 Classi cation of remote sensing techniques to measure precipitation 2 Visible and infrared remote sensing techniques to measure precipitation 3 Sensing precipitation in the microwave region 4 Cloud detection methods MODIS cloud mask 5 Retrievals of cloud properties from passive remote sensing Required reading S 74 66 76 AdditionaVadvanced reading Microwave Surface and Precipitation Products System http wwworbitnesdisnoaa govcorpscsbmsppsmainhtml ATBD MODIS cloud products httpmodisatmosgsfcnasagovidocsatbdimodOSpdf Baum B A and S Platnick 2006 Introduction to MODIS cloud products httpmodisatmosgsfcnasagovreferencedocsBaum7and7Platnick72006pdf A A 1 Classi cation of remote sensing 39 39 to measure m Only a small fraction of clouds produces rain gt need to separate raining from nonraining clouds Classification of remote sensing techniques 0 Passive remote sensing i Visible and infrared techniques ii Microwave techniques 0 Active remote sensing Radar e g TRMM radar 0th er techniques Meteorological Weather Stations rain gauges 2 Visible and infrared remote sensing 39 39 to measure Basic Qrincigles Clouds are not transparent in the IR and visible ie rain drops can not be sensed directly thus one needs to relate the independent measurements of rainfall to the properties of a cloud measured by IR and visible remote sensing called indirect measurements of precipitation Main problem a lack of ground truth data to establish a reliable correlation between satellite data and rainfall Technigues gt Cloud Indexing developed by Barrett 1970 Principle assign a rate rain to each cloud type RV 27 f 111 where Rr is the rainfall rate ri is the rain rate assigned to cloud type i is the fraction of time or fraction of area covered by cloud type i gt Cloud Visible Re ection developed by Kilonsky and Ramage 1970 Principle tropical oceanic rainfall dominates by deep clouds which are highly re ective in the visible Highly re ective clouds are more likely to precipitate that dark clouds because re ection is related to optical depth and hence to cloud thickness gt relate the frequency of highly re ective clouds to precipitation Parameterization by Garcia 1981 for tropical oceanic rainfall Rr626374ND 112 Rr is the monthly rainfall in mm Nd is the number of days during the month that the location was covered by highly re ective clouds eg analysis of GOES visible channel gt OLR outgoing longwave radiation developed by Arkin 1979 to estimate precipitation for climatological studies Principle clouds that are cold in the IR are more likely to precipitate than warm clouds because cold clouds have higher tops exception cirrus clouds GOES Precipitation Index GPI for the tropical Atlantic GP 3Acl where GPI is the mean rainfall in mm Ac is the fractional area unitless from 0 to l of cloud colder that 235 K in 250x250 box and t is the time period hours for which Ac was determined gt Bispectral techniques Principle clouds that have the high probability to produce rain are both cold IR brightness temperature and bright high re ection in visible gt Cloud model techniques Principle use cloud models to relate satellite visible and IR observations to precipitation A A 3 Sensing in the microwave region Advantages 39239 microwave radiation penetrates clouds because cloud droplets only weakly interact with microwave radiation 39239 rainsize drops interact strongly with microwave radiation Disadvantages 39239 microwave radiometers have poor spatial resolution 39239 contamination from ice crystal scattering Main principles Ice crystals scatter but do not absorb microwave radiation Rain liquid drops both scatter and absorb but absorption dominates gt relate the optical depth associated with the emitting rain drops and brightness temperature measured by a passive microwave 139 Recall the MarshallPalmer precipitation size distribution N r N 0 eXp 2A r Where No 8X103m393mm391 but in general N0 depends on rain type A 41 Rr 03921 mm39l Rr is the rainfall rate mmhour Thus the volume extinction coefficient is k NOJ WZQE eXp 2Ardr 113 27am 1 Volume Absurptlan E E 9 a U C 9 E L Cl I 4 1 Volume Scans ring Scattering Inef cient Ran I Hate Ifr39nrns39h l Figure 111 Volume absorption top and scattering coefficients bottom calculated with Mie theory for the MarshallPalmer precipitation size distribution of water and ice spheres at three frequencies 1935 37 855 GHz Recall the radiative transfer equation in the microwave region Lecture 10 TM 851 s exp 7r u Tm r39exp ir39udr39u 0 vaexp7139uj Tmr39exp7r 7 r39udr39u 0 Let s assume that T m is constant in the rain layer and that the volume absorption coefficient is nearly zero except the rain layer In r exp r dr39 T 1 exp rquot W 0 We can rewrite the above equation for the microwave brightness temperature observed by a nadir looking microwave radiometer in the following form T1747 S gTsur eXpT Tatm1 eXpT t 1 14 1 SVP 6XpT Tam eXPT where 1 is the optical depth associated with the emittingabsorbing rain drops 7 k arain z rain z min is the depth of the rain layer Rearranging the terms in the above equation we have Tm 72 7nm18 16XPT 18 6XPT Dz 115 aim Eql 15 helps to understand the brightness temperaturerain rate relationships 39239 No rain 1 0 gt Tb 85711 sis small for water surfaces and 809 for dry land 39239 Rain increases 1 increases gt Tb gt Tam Therefore for water surfaces the brightness temperature strongly increases with the increases of rain rate gt raining areas are easily detected over the oceans gt over the dry land the changes in brightness temperature are small with increasing rain rate not useful for rainfall estimations Lam I new Lam 3 E p m m 439 E 9 i n m Absorption pmmm dominate warm masses duminam asxa GHz Adapted f UlTl Spanner Bid 1939 K 20 5D 30 4 Rain Rate mml39hh Figure 112 Brightness temperature vs rain rate for three frequencies MSPPS Microwave Surface and Precipitation Products System project http www0rbitnesdisn0aa govcorpscsbmsppsmainhtml Uses NOAA 39 wave J39 A d d quot Sounding Unit AMSU AMSUA and AMSUB launched on NOAA 15 1998 AMSUA 15channel cross track scanning microwave radiometer mixed polarization AMSUB 5channel cross track scanning microwave radiometer Table 111 Microwave sensing of precipitation AMSU vs SSMl AMSU SSMl Microwave processes Retrieved product Frequency Frequency Controlled by absorptionemission by cloud water 31 GHz 9 GHz large dropshigh water cloud water and content rainfall over oceans 50 GHz 37 GHz medium dropsmoderate cloud water and water content rainfall over oceans 89 GHz 85 GHz small dropslow water nonraining clouds content over oceans 89 GHz 85 GHz Controlled by icecloud rainfall over the land scattering an ocean 4 Cloud detection methods MODIS cloud mask Effects of clouds on solar re ectance MODIS Atmosphere Bands 10 I I Spherical Albedo 16015 pm16 Wavelength um Figure 113 Cloud spherical albedo as a function of wavelength for selected values of the effective radius of cloud droplet Computations were done for a water cloud having a modified gamma size distribution with an effective variance 0111 cloud optical depth rc075 pm16 and water vapor content 045 g Cm2 King et al Cloud retrieval algorithm for MODIS NOTE spherical albedo is defined as F 0 M0170 Effects of clouds on IR brightness temperature Wavelength pm 16 12 1O 8 6 5 4 l I l I l I l I l I l l I 340 39 39 Clear Sky overhead sun i4 320 Thermalre161m E Thermal re 8 pm g Solar amp Thermal re 16 pm 3 300 Solar amp Thermal r8 8 pm 602 280 39 m I E 9 CE 260 240 I I I I I 1000 1500 2000 2500 3000 Wavenumber cm39l Figure 114 39 39 r function of wavelength 39 39 adir f0 observations and selected values of the effective radius of cloud droplets cloud optical depth 19075 um5 for all cases Computations were done for awater cloud having a modi ed gamma size distribution for quot4 mi I J aurio pime with clou p Tct14 C cloud base temperature ch17 C and blackbody surface temperature Tsur21 C CLOUD DETECTIONMETHODS 1 Maximum Temperature all observations of a small surface area over a relatively short period of time are compared The highest temperature is retained as the best estimate of temperature in that area This method is based on a ocean surface features are more persistent than clouds b clouds are colder than the surface NOTE T his method workr poory for persistent thin cloudr 5x T W0 Wavelength Infrared compare temperatures from 37 pm and 105 pm or any pair of wavelengths in the window If the temperatures are the same then one can assume the measured signal came from a the sea surface OR b uniform clouds which will probably be detected in a Visual image of the area of interest LA 4 If the temperatures at the two wavelengths are different then there are scattered undetected clouds in the scene Infrared Variability temperatures of clouds tend to be much more variable in space than temperature of the sea surface Therefore all areas having a small deviation from a mean brightness temperature close to that expected of the sea in the region are accepted as good values Two Wavelength VisibleInfrared uses re ected sunlight to detect clouds on the assumption that the sea is much darker in visible wavelengths than clouds MODIS Cloud Mask Ackerman et al JGR 103 1998 MODIS cloud mask uses multispectral imagery to indicate whether the scene is clear cloudy or affected by shadows Cloud mask is input to rest of atmosphere land and ocean algorithms Mask is generated at 250 m and 1 km resolutions dayampnight Mask uses 17 spectral bands ranging from 0551393 um including new 138 pm band 11 different spectral tests are performed with different tests being conducted over each of 5 different domains land ocean coast snow and desert temporal consistency test is run over the ocean and at night over the desert Algorithm based on radiance thresholds in the infrared and re ectance and re ectance ratio thresholds in the visible and nearinfrared Cloud mask consists of 48 bits of information for each pixel including results of individual tests and the processing path used bits 1 amp 2 give combined results confident clear probably clear probably cloudy cloudy TROPICAL CYCLONE RITA Example of MODIS products King at 711 Apnl 19 2000 0220 UTC MOD021KMA20001100220002200011307113 Probably c1 ear Probably Cloudy 5 Removal cloud Emyer es from wire I emale seggl39gg Sensmsusedfm cluudremme sensmg mm and IanaIEdImageIs mem Immems Saunders Am sensms radars andhdars Clnud charactensncs Iemevedfrmn gasswe mm sermgg data a Clnuddetechmc17udpresence mum clnudfmmnn nslectme b Claudre ecmcemnble mm c Cluud emsme IR Imagery a CluudquuIdwateIcmtem a C1wduphcaldep1hthslemne I C19udphasewatemme mum g Claudpamde me dIslnbuhunuIaneffemveIadIus museum h Claudtupmusure suundIrgtechmques may wm39m 11 cloud M 13m clasn catmn If clnudy FIX 21 usedm mm sermrg If cluuds NOTE ISSCP stands fur the Imermumal satellmz claudchmamlngypmgam I I I In DEE A cwwus mnmms WWW W m g m m m 3 m m m m a 5 aau mncumus Aunsmms mmansmms mums a 3 E U m cuMuLus swAmcuMuw swAms Law I I 13 a 94 an CLOUD OPTICAL THICKNESS MODIS cloud products gmtical thickness and particle size effective radius MODIS 1 km spatial resolution daytime only liquid Water and ice clouds using individual cloud mask tests Solar re ectance technique VIS through NearIR 7Water nonabsorbing bands 065 086 124 pm 7Water absorbing bands 16 21 37 pm iLand surface 065 pm Ocean surface 086 pm isnoWice surfaces 124 pm Solar re ectance technique Principle s Land ocean and snowsea ice surfaces The re ection function of a nonabsorbing band is primarily a mction of optical depth The re ection function of a nearIR absorbing band is primarily a function of effective mdius Water cloud over the ocean 0 8 08 u 556 E e 50 l 067 41445 a2 06 I in i 0 V o 8 H 04 o 4 E E lt E 02 r 02 00 r r r I J or 04 05 08 1o 12O39OOD DA He39lemame O as W Re ectance 1086 pm ASC 6 NOTE here re ectance is de ned as RU y u 7a 7 111 0 uuFu Cloud Opllcal Thickness Ice only 19 Apnl 2000 0220 UTC n2 us 120 24 123 132 260 gt Cloud thermodynamics phase Effects of Water and ice clouds on solar re ectance and IR brightness temperature 056 pm R161 pmR066 um 1 A E 206 t 7 8 few 9 9 M 1 04 4 7 E E 4 1 4 a 21 5 339 02 1 7 n 11 39230 240 250 260 2 70 39230 240 250 26 2 V0 11 um Brightness Temperature K 11 um Brightness Temperature K Figure 115 The upper le hand panel shows the 066 image from MAS MODIS airborne simulator of a convective cumulonimbus cloud surrounded by loWerlevel Water clouds Subsequent panels show the plots of the re ection function ratio as a function of the corresponding brightness temperature at 1102 pm Nadir observations The MAS 188 umband is the analog for the MODIS 138 pm channel King et al Cloud retrieval algorithm for MODIS Ice cloud loW re ectance at 161 and 213 pm and high re ectance at 188 pm MODIS algonthm for cloudthermodynamicr phare BrpectralIRtertBT8SBT11BT11threrholdr Urer waterrce emrrnvrty drfferencer m 8 5 pm band BT8 5BT11 pouuve and large forrce cloudr rmall andnegatrve forwater cloudr 5 km reroluuon currently Solartert egR1 6RU 86rat1otertm deve opment Decruon tree approach ecoryrtemdependent arrerrment ofrndrvrdual cloud mark text rerultr current techmgue 1n productron Bnghtnerr temperature techmgue 1 8 mm 1397 mrcrun EHer K 1 mos t2mret on BTDtF Kl MAS mrxed c oud scene 50mreroluuon Vlnble rmage Boxer reprerent drfferent cloud regrme colorcodedm thebnghtnerr temperature drfference dragram Lecture 5 WM Absorptionemission by atmospheric gases Obiectives 1 Structure of the Earth s atmosphere 2 Properties of atmospheric gases 3 Basic principles of molecular emissionabsorption 4 Spectral line shapes Lorentz Doppler and Voigt pro le 5 Absorption spectra of main atmospheric gases Required reading S 1315 3135 Advanced reading McCartney EJ Absorption and emission by atmospheric gases John WileyampSons 1983 1 Structure of the Earth s 39 Propagation of the electromagnetic radiation in the atmosphere is governed by its state temperature pressure air density and composition ie gases and particulates Except cases with temperature inversion temperature always decreases in the lower troposphere Temperature lapse rate is the rate at which temperature decreases with increasing altitude 1quot T2 T1zz z1 ATAz 51 where T is temperature and the height 2 Adiabatic process is of special signi cance in the atmosphere because many of the temperature changes that take place in the atmosphere can be approximated as adiabatic For a parcel of dry air under adiabatic conditions it can be shown that dTdz gcp 52 where 0 is the heat capacity at constant pressure per unit mass of air and Cl cV Rma and ma is the molecular weight of dry air The quantities gcp is a constant for dry air equal to 976 C per km This constant is called dry adiabatic lapse rate The law of hydrostatic balance states that the pressure at any height in the atmosphere is equal to the total weight of the gas above that level The hydrostatic equation dPz dz pz g 53 where pz is the mass density of air at height 2 and g 981 ms is the acceleration of gravity 0 Integrating the hydrostatic equation at constant temperature as a function of 2 gives P P0 eXp zH 54 where H is the scale height H k3 T mg and m is the average mass of air molecule m 4 8096XlO3926 kgair molecule Examgle T290KH8500m T210 KH6000m Variations of temperature pressure and density are much larger in vertical directions than in horizontal This strong vertical variations result in the atmosphere being stratified in layers that have small horizontal variability compare to the variations in the vertical Therefore a planeparallel model of the atmosphere is used in radiation transfer simulations a 4 4 v 39 39 39 mmin quot 39 madelingeachmodelinCludeS pro les of T P and concentration of main gases 70 y l l y I y l x 60 n Mesosphere 5O i I 7 V r 739 Stratosphere E 40 x v E 39 39g 30 std1976 I gt V 7 V V 7 i me K I subtropsum 39 7 subtropwin 20 lt l V V subarcsum quot V subarcwin 10 r V t r i V 4 r V V V r t 39 Z 0 l l l l l l i l Pk l90 200 210 220 230 240 250 260 270 280 290 300 Temperature K Figure 51 Temperature pro les of the standard atmospheric models Which are o en used in radiative transfer calculations Standard US 1976 atmosphere is representative of the global mean atmospheric conditions Tropical atmosphere is for latitudes lt 300 Subtropical atmosphere is for latitudes between 300 and 45 Subarctic atmosphere is for latitudes between 450 and 60 and Arctic atmosphere is for latitudes gt 600 2 Propelties of atmospheric gases Table 51 Three most abundant gases in each planetary atmosphere Yung and DeMore 1999 Mixing ratios are given in parentheses All compositions refer to the surface or I barfor the giant planets Jupiter H2 093 He 007 CH430X10393 Saturn H2 096 He 003 CH445X10393 Uranus H2 082 He 015 CH41 72 x102 Neptune H2 080 He 019 CH4 20x10393 Titan N2 095 097 CH4 30x10392 H2 20x10393 Triton N2 099 CH4 20x10392 CO lt001 Pluto N2 7 CH4 7 CO 7 10 so2 098 so 005 0 001 Mars CO2 095 N2 27x10392 Ar 16X10392 Venus CO2 096 N2 3 5x102 so2 15x10394 Earth N2 078 02 021 Ar 93x10 3 Atmospheric gases are highly selective in their ability to absorb and emit radiation Each radiatively active gas has a speci c absorption spectrum 7 its own signature atmosphere controls the overall spectral absorption time An atmosphere is the mixture of gases and thus the abundance of gases in the Radiatively active gases in the Earth s atmosphere are highly variable in space and Table 52 The gaseous composition of the atmosphere Gases by volume I Comments Constant ga ses Nitrogen N2 7808 Photochemical dissociation high in the ionosphere mixed at lower levels Oxygen 02 2095 Photochemical dissociation above 95 km mixed at lower levels Argon Ar 093 Mixed up to 110 km Neon Ne 00018 Helium He 00005 Mixed in most of the middle Krypton Kr 00001 1 atmosphere Xenon Xe 0000009 Variable gases Water vapor H2O 40 maximum Highly variable photodissociates in the tropics above 80 km dissociation 000001minimum at the South Pole Carbon dioxide CO2 00365 increasing 04 per ear Slightly variable mixed up to 100 km photodissociates above Methane CH4 000018 increases due to agriculture Mixed in troposphere dissociates in mesos Ehere Hydrogen H2 000006 Variable photochemical product decreases slightly with height in the middle atmosphere Nitrous oxide N2O 000003 Slightly variable at surface dissociates in stratosphere and mesos Ehere Carbon monoxide CO 0000009 Variable Ozone 03 0000001 00004 Highly variable photochemical origin Fluorocarbon 12 CF2C12 000000005 Mixed in troposphere dissociates in stratosphere altitude km 5 8 N o l J l 105 10 10 mixing ratio 0 10 Figure 52 Representative vertical pro les of mixing ratios of some gases in the Eartyh s atmosphere Some imnortant quot 39 39 gases Obey ideal gas laws Boyle s law V N lP at constant T and the number of gas moles u Charles s law V N T at constant P and u Avogadro s law V N the number of gas molecules at constant P and T The egua on of state says that the pressure exerted by a gas is proportional to its temperature and inversely proportional to its volume P V p R T 55 Where R is the universal gas constant If pressure P is in atmospheres atm volume V in liters L and temperature T in degrees Kelvin K thus R has value R 008206 L atm K l mor1 The amount of the gas mav be expressed in several wavs i Molecular number density molecular number concentration molecules per unit volume of air ii Density molecular mass concentration mass of gas molecules per unit volume of air iii Mixing ratios Volume mixing ratio is the number of gas molecules in a given volume to the total number of all gases in that volume when multiplied by 106 in ppmv parts per million by volume Mass mixing ratio is the mass of gas molecules in a given volume to the total mass of all gases in that volume when multiplied by 106 in ppmm parts per million by mass NOTE Commonly used mixing fraction one part per million 1 ppm 1x10396 one part per billion 1 ppb 1x10399 one part per trillion 1 ppt 1x103912 iv Mole fraction is the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture NOTE mole fraction is equivalent to the volume fraction NOTE The equation of state can be written in several forms using molar concentration of a gas c pv P c T R using number concentration of a gas N c NA P N T RNA or P N T k3 using mass concentration ofa gas q c mg P q T R mg Avogadro s number NA 602212xlO23 moleculesmole gt Structure of molecules is important for understanding energy forms and the ability of a molecule to absorbemit radiation Based on their geometric structure molecules can be divided into four types 0 Linear molecules C02 N20 Csz all diatomic molecules eg 02 N2 etc o Symmetric top molecules NH3 CH3CL o Spherical symmetric top molecules CH4 0 Asymmetric top molecules H20 03 W212 Rmzu39unzl and vimeiunzl mminns uf Lhe mulecules Molecules M 11 rigid q39umm39zzd mmmr l l o I LINEAR DIATDMIC LINEAR TRIATDMIC N2 02 co ND N02 N20 l 0 K gt lt ASYMMETRIC TOP H20 03 o M alecules as a quantized vibrator DIATOMIC MOLECULES N2 02 co 4 4 TRIATOMIC MOLECULES symmetric bending antisymmetric N20 coz O MONO 97 Figure 54 Vibrational modes of diatomic and triatomic atmospheric molecules NOTE The number of independent vibrational modes called normal modes of a molecule with Ngt2 atoms are 3N6 for nonlinear molecules and 3N5 for a linear molecule 0 The geometrical structure of a molecule determines its dipole NOTE A dipole is represented by centers of positive and negative charges Q separated by a distance d the dipole moment Q 1 Example water molecule The unique way in which the hydrogen atoms are attached to the oxygen atom causes one side of the molecule to have a negative charge and the area in the opposite direction to have a positive charge The resulting polarity of charge causes molecules of water to be attracted to each other forming strong molecular bonds Table 53 Atmospheric molecule structure and dipole moment status Molecule Structure Permanent May acquire dipole moment dipole moment N2 N H N No No 02 O 0 O No No CO C 0 Yes Yes C02 0 m0 No Yes in two vibrational modes N20 N NO Yes Yes H20 A Yes Yes H 03 A Yes Yes 0 H O H O O H H No Yes V in two vibrational C modes H NOTE The structure of a molecule determines whether the molecule has a permanent dipole or may acquire the dipole The presence of the dipole is required for absorptionemission processes by the molecules I I II 3 Basic nrincinles 0f ptiuu Review of main derlvin phvsicaly 39 ciples 0f 39 39 39 1 The origins of absorptionemission lie in exchanges of energy between gas molecules and electromagnetic eld 2 In general total energy of a molecule can be given as E Erm Evib Eel Etr Em is the kinetic energy of rotation energy of the rotation of a molecule as a unit body about 1500 cm391 farinfrared to microwave region Evil is the kinetic energy of vibration energy of vibrating atom about their equilibrium positions about 500 to 104 cm391 near to farIR Eel is the electronic energy potential energy of electron arrangement about 104105 cm391 UV and visible Eu is translation energy exchange of kinetic energy between the molecules during collisions about 400 cm391 for T 300 K 0 From Ermlt E lt Eviblt Eel follows that i Rotational energy change will accompany a vibrational transition Therefore vibration rotation bands are often formed ii Kinetic collisions by changing the translation energy in uence rotational levels strongly vibrational levels slightly and electronic levels scarcely at all 0 Energy Em Evib and Eel are quantized and have only discrete values speci ed by one or more quantum numbers Not all transitions between quantized energy level are allowed they are subject to selection rules 3 Radiative transitions of purely rotational energy require that a molecule possess a permanent electrical or magnetic dipole moment 0 If charges are distributed symmetrically gt no permanent dipole moment gt no radiative activity in the farinfrared ie no transitions in rotational energy Example homonuclear diatomic molecules N2 02 o 02 has a weak permanent magnetic dipole and thus has a rotational transition in microwave 0 C0 N20 H20 and 03 exhibit pure rotational spectra because they all have the permanent dipoles C02 and CH4 don t have permanent dipole moment gt no pure rotational transitions But they can acquire the oscillating dipole moments in their Vibrational modes gt have Vibrationrotation bands 4 Radiative transitions of vibrational energy require a change in the dipole moment ie oscillating moment N N 2 no vibrational transition 02 symmetric stretching mode Hgt C0 single vibrational mode gt C 02 V1 symmetric stretching mode gt adiatively inactive 9 6 9 V2a two bending modes have same energy l l Vzb degenerated modes V3 asymmetric stretching mode gt radiatively active Figure 55 Vibrational modes of diatomic and triatomic atmospheric molecules see also Figure 54 NOTE Homonuclear diatomic molecules N2 and 02 don t have neither rotational nor Vibrational transitions because of their symmetrical structures gt no radiative activity in the infrared But these molecules become radiatively active in UV NOTE The number of independent vibrational modes of a molecule with Ngt2 atoms are 3N 6 for nonlinear molecules and 3N 5 for a linear molecule Both H20 and 03 have three normal band v1 v and V3 all are optically active CH4 has nine normal modes but only V3 and v4 are active in IR 5 Electronic transitions 0 Electrons on inner orbits close to the atomic nucleus can be disturbed or dislodged only by photons having the large energies shortwave UV and X rays 0 Electrons on the outermost orbits can be disturbed by the photons having the energies of UV and visible radiation gt these electrons are involved in absorptionemission in the UV and visible 0 Both an atom and a molecule can have the electronic transitions Electronic transitions of a molecule are always accompanied by vibrational and rotational transitions and are governed by numerous selection rules 4 Spectral line shapes Lorentza Doppler and Voigt pro le Atomic Absorption Emission Spectrum 0 Radiation emission absorption occurs only when an atom makes a transition from one state with energy Ek to a state with lower higher energy or emission E E hCV k J Absorption Emission Molecular AbsorptionEmission Spectra Molecular absorption spectrum is substantially more complicated than that of an atom because molecules have several forms of internal energy This is the subject of spectroscopy and quantum theory Three types of absorptionemission spectra i Sharp lines of nite Widths ii Aggregations series of lines called bands iii Spectral continuum extending over a broad range of wavelengths Fiw v Line WWW Band Continuous spectra wavelength gt Figure 56 Concept of a line band and continuous spectra Three main properties that de ne an absorption line central position of the line eg the central frequency 170 or wavenumber v0 strength of the line or intensity S and shape factor or profile f of the line 0 Each absorption line has a width referred to as natural broadening of a spectral line 0 In the atmosphere several processes may result in an additional broadening of a spectral line of the molecules 1 collisions between molecules referred to as the pressure broadening 2 due to the differences in the molecule thermal velocities referred to as the Doppler broadening and 3 the combination of the above processes Lorentz pro le of a spectral line is used to characterize the pressure broadening and is defined as a 7239 fLV V0 56 v v0 2 a 2 wherefv Va is the shape factor of a spectral line vo is the wavenumber of a central position of a line a is the halfwidth of a line at the half maximum in cm39l often referred as a line width 0 The half width of the Lorentz line shape is a function of pressure P and temperature T and can be expressed as aPTa0P 0 57 0 where 10 is the reference halfwidth for STP To 273K P1013 mb 10 is in the range from about 001 to 01 cm391 for most atmospheric radiatively active gases For most gases n12 NOTE The above dependence on pressure is very important because atmospheric pressure varies by an order of 3 from the surface to about 40 km o The Lorentz pro le is fundamental in the radiative transfer in the lower atmosphere where the pressure is high 0 The collisions between like molecules self broadening produces the large line widths than do collisions between unlike molecules foreign broadening Because radiatively active gases have low concentrations the foreign broadening often dominates in infrared radiative transfer Doppler pro le is defined in the absence of collision effects ie pressure broadening as 2 1 V V fDV V0 O D exp j 58 OLD is the Doppler line width V0 12 05D 2kBTm 59 c where c is the speed of light k1 is the Boltzmann s constant In is the mass of the molecule for air m 4 8XlO3923 g o The Doppler broadening is important at the altitudes from about 20 to 50 km Voigt pro le is the combination of the Lorentz and Doppler profiles to characterize broadening under the lowpressure conditions above about 40 km in the atmosphere ie it is required because the collisions pressure broadening and Doppler effect can not be treated as completely independent processes fVoigtVV0 IfLVV0fDVVdl a w 1 VV 2 510 ex dv 0D7Z3932 JV v0 2 052 p 05D foo NOTE The Voigt profile requires numerical calculations Nature of the Voigt profile 0 At high pressure the Doppler pro le is narrow compare to the Lorentz pro le so under these conditions the Voigt pro le is the same as Lorentz pro le 0 At low pressure the behavior is more complicated 7 a kind of hybrid line with a Doppler center but with Lorentz wings Absorption coef cient of a gas is de ned by the position strength and shape of a spectral line kwvSfv vo 511 where S in the line intensity and f is the line pro le Szjkavdv and IfV V0dvl Dependencies S depends on T fv v0 1 depends on the line halfwidth 0 p T which depends on pressure and temperature Optical depth due to gaseous absorption is de ned as a product of the absorption coef cient and the path length Because the amount of an absorbing gas may be expressed in a number of possible ways eg molecules per unit volume mass of molecules per unit volume etc different kinds of absorption coef cient may be introduced is such a way that the optical depth remains unitless Introducing a path length or amount of gas 14 we have TV J kayd 512 1 Most 39 used absorption coef cients km Volume absorption coef cient in LENGTH39I km Mass absorption coef cient in LENGTHZ MASS keg Absorption cross section in LENGTHZ Mass absorption coef cient volume absorption coef cientdensity Absorption cross section volume absorption coef cientnumber concentration Thus optical depth can be expressed in several ways Tv51sz 2 Thde 2 Tpkmmds TNkmavdS 513 51 51 Table 54 Units used for path length absorption coef cient and line intensity for Eqs5ll 513 Absorbing gas Absorption coefficient Line intensity Units of the line pro le f LENGTH often cm Monochromatic transmittance Tv and absorbance Av of radiance along the path are defined as TV eXp 1V AV l TV l eXp Tv 514 NOTE same name Transmission function Transmittance 5 Absor tion ectra of main atmos heric ases H O CO 0 CH4 N O CFCs 0 Each atmospheric gas has a speci c absorptionemission spectrum 7 its own radiative signature HITRAN is a main spectroscopic data base that contains information eg intensity and halfWidth for a total of about 1080000 spectral lines for 36 different molecules httpWWWhitrancom gt Microwave region see Figure 34 Molecule Absorption 1ine Frequency GHZ HZO 22235 1833 02 about 60 11875 gt Thermal IR region Aasonmau x Figure 57 Lowresolution IR absorption spectra of the major atmospheric gases Table 55 The most important vibrational and rotational transitions for H20 CO2 03 CH4 N20 and CFCs Gas Center Transition Band interval v m Mum cm l H2O pure rotational 01000 15948 63 v2 P R 6402800 continuum far Wings of the strong 2001200 lines water vapor dimmers H2O2 C02 667 15 v2 P R Q 540800 961 o rtone and combination 8501250 10638 94 V3 P R overtone and 2349 43 combination 21002400 03 1110 901 v1 P R 9501200 1043 959 V3 P R 600800 705 142 V2 P R 600800 CH4 13062 76 V4 9501650 N20 12856 79 v1 12001350 5888 170 V2 520660 22235 45 V3 21202270 CFCS 7001300 NOTE Continuum absorption by water vapor in the region from 8001200 cm391 remains unexplained It has been suggested that it results from the accumulated absorption of the distant wings of lines in the far infrared This absorption is caused by collision broadening between H2O molecules called self broadening and between H20 and non absorbing molecules N2 called foreign broadening gt Neapm and visible regions r H20 03 and co Engrgy Curve m Blzickbouy m 6000 K Snlilr lrrad nce Cum Oumde Alnmsphere Solar lmidmncc Curve a Sea Level E Pf 15 E 3 H Li Ui UV I m 0 12 16 20 3 Wuvelcngth um rigmc a a TableS a nosphenc gases Gas N1 lt 01 01 lt 024s 0 017035 045075 H10 lt 021 05072 H101 hydrngen permdrle lt 035 N01 39a lt 05 nitrngen 0x1 2 N o 1 N02 nitrate radical HDNO nimm s acid HCHO fm39maldeh de NOTI NO absoxb at Alt o 6 0m butphotodissocmte at Alt o 4 0m gt UV region Absorption of UV radiation in the gaseous atmosphere is primarily due molecular oxygen 02 and ozone 03 Thermosnhere Mesosnhere Strato snhere LT ronosnhere 1039 I I shumag Runga V 3 1017 continuum I 3 Ionization I 1 continuum H rquot a e oi 10 8 bandsy 1 039 g Huggms bands 39 Shuman Runge 8 1 can L bands 2 Lyman on f 2I 2 1 0 Chappuis o hands 2 Q 1 0 Herzberg 8 1 022 continuum D lt 24 1 039 1 025 v v o 1000 2000 3000 4000 3000 Wavelength A Figure 59 Spectral absorption crosssections of Oz and 03 NOTE a Bands of Oz and 03 at wavelengths lt 1 mm are electronic transitions b These absorption bands are relatively uncomplicated continua because practically all absorption results in dissociation of the molecule so the upper state is not quantized c Despite the small amount of 03 no solar radiation penetrates to the lower atmosphere at wavelengths lt 310 nm because of large absorption crosssections of 03 To avoid very complicated calculations of electronic transitions numerous measurements of the absorption cross sec ons of the atmospheric atoms and molecules absorbing in the UV and visible have been performed in laboratory experiments In general the absorption cross section varies with temperature Lecture 2 Basics of remote sensing Introductory survey Obiectives 1 Types of platforms used for remote sensing 2 Passive and active remote sensing 3 General characteristics of satellite platforms orbits resolutions types of sensors Required reading S 11 17 pp395398 426427 CCRS online tutorial Chapter 2 Satellites and Sensors httpccrs nrcan gc caresourcetutorfundamchapter2017e php Additional reading NASA online tutorial Sections Overview The Concept of Remote Sensing and History of Remote Sensing Remote Sensing Systems http rst gsfcnasa govFrontoverviewhtml 1 Types of platforms used for remote sensing Ground based platforms ground vehicles andor towers gt up to 50 m Exalees DOE ARM Atmospheric radiation Program httpwwwarmgov NASA AERONET AErosol Robotic NETwork httpaeronetgsfcnasagov Airborne platforms airplanes helicopters highaltitude aircrafts balloons gt up to 50 km Examples NCAR NOAA and NASA research aircrafts httpwwweolucareduraf Spaceborne rockets satellites shuttle gt from about 100 km to 36000 km Space shuttle 250300 km Space station 300400 km Lowlevel satellites 7001500 km Highlevel satellites about 36000 km NASA current and planned Earth s observing satellite missions httpsciencehqnasagovmissionsea1thhtml NOAA weather satellites httpwwwnoaagovsatelliteshtml NPOESS National Polarorbiting Operational Environmental Satellite System httpwwwiponoaagov 2 Passive and active remote sensing Passive sensors measure natural radiation emitted by the target material or and radiation energy from other sources re ected from the target Examples Passive microwave radiometer that detects naturally emitted microwave energy Radiometers that measure re ected or backscattered sun light from the atmosphere and ocean Active sensors transmit their own signal and measure the energy that is re ected or scattered back from the target material Examples Lidar LIght Detection And Ranging Radar RAdio Detection And Ranging NashMm Radar transmits a pulse and measures re ected echo backseatter 3 Satellite platforms orbits resolutions sensor thes gt Satellites orbits lowilevel and higl171evel Lowilevel 7001500 km Earth observation satellites called LEO fall into three broad groups i Equatorial orbiting satellites ii Polar orbiting satellite iii Oblique orbiting or nearpolar satellites o LEO satellites are often on sunisynchronous orbits Sunisynchronous means that the satellite remains xed with respect to the Sun with the Earth rotating under the satellite ie satellite passes over its target on the Earth at roughly the same local time Equatorial orbiting satellites whose orbits are within the plane of the Equator Example TRMM Polar orbiting satellites whose orbits are in the plane ofthe Eanh s polar axis 3 hours 2 orbits later 6 hours 9 hours 6 orbits later Earth s rotation Figure 21 Oblique orbiting nearpolar orbiting satellites Sunsynchronous orbits each 3 hours 0 Ascending pass is when the satellite travels from south to north and descending when the satellite travels from north to south 0 Oblique orbiting satellites can be launched eastwards into direct called prograde orbit so called because the movement of such satellites is in the same direction as the rotation of the Earth or westwards into retrograde orbit o The inclination of an orbit is speci ed in terms of the angle between its ascending track and the Equator o Prograde orbits w while retrograde orbits wwith respect to the planes of their initial orbits because the Earth is not a perfect sphere and it causes a gyroscopic in uence on satellites in oblique orbits Examples of nearpolar orbiting satellites Terra inclination9820 TOPEXPoseidon Topography Experiment for Ocean Circulation inclination660 glre 22 Example of the ground track of a polar orbiting satellite Exam es of neargolar orbiting satellites Terra inclination9 82O Iopogmpn L mm o Swath is the width ofthe track covered by a sensing system on the surface ofthe Earth In general swaths for spacebome sensors vary between tens and hundreds of kilometers wide H39 Jewel ahnlll mun satellites Censtau39nnary 213111135 u En eaneu Wtha39 5212111135 are xed abuve a gvm pmnl un me Eanh sun39aee because the eueular urblls shame the equalur have mtauun penuu equals m me anh39s mtauun penuu GOESEast Figuxeuu s geustauunary 5212111135 GOES Polar orbiting vs geostation satellites Example at NPOESS ul r u while geostationary satellites are limited to approximately 60quot of latitude at a xed point over the aboard a polar orbiting satellite at a higher spatial resolution than from a geostationary satellite The N39POESS satellites are inserted into a sunsynchronous polar orbit An early morning satellite Will make its ascending pass over the e uator in the earl momin independent 0 Earth39s West to east rotation For example ifa moming s a 39ngton DC at 600 am Eastern time then roughly three hours later it Will y over Califom39a at 600 am Paci c time And later that day itWill y over Tokyo at 600 am Japan time The label applied to a polarorbiting satellite is determined by the local time as it crosses the equator The crossing from north to south is labeled as its descending node time from south to north is labeled as its ascending node time The N39POESS satellite Will be ying ascending node times of 1330 1730 and 2130 ie they Will cross the equator from south to north at 130 pm 530 pm and 930 pm respectively gt Resolutions spatial spectral radiometric and temporal Spatial resolution is often defined as the ability to distinguish between two closely spaced objects on an image No single definition for spatial resolution exists 0 Spatial resolution depends on the eld of view FOV altitude and viewing angle of a sensor 5 K Satellite Pixel Foolprinl NOTE small pixel gt large spatial resolution The srze ofthe purel sets alowerhmrt on the spatra1 resoluuon A measure ofthe srze othe purel rs gryen by the rnstantaneous eld ofvxew sensmve to radAauon bands m the e1eetromagnetre speetrum to whreh the sensor rs sensrtrye broadrband nanowrband speetral and hyperspeetra1 sensors Trunsmtsston g WaveengIh 7712 nmmwer the bandwidjh the be er the xpecmnl mxabltian Radinmetric resolutron rs a measure of the sensrtryrty of a sensor to dAfferences m the rntensrty ofthe radAanon measured the sensor The frner the radmmetn resolutron of a sensor the more sensruye rt rs to deteeung small dAfferences m re eeted or emrtted energy Technical dz n on black and pure whrte The radwmem resoluuon rs measured m brts Hut system 2 e 2 measures onlytwo radAauon 1eye1s zebrt system measures 22m fourlevels ete n me ante med n e how often an area can be rev 1s1ted The temp oral resolutton vanes from hours for some systems to about 20 days to others Htgh temporal resolution datly or twtce datly gt Types of sensors Classt catson based on energy source or generated product Energy source Passwe owns no energy source or actwe owns energy source 1n restrtcted spectral bands ltke radar systems Product 0 Notmagtng Generates no 1mages of the observed surface used to collect prectse spectral stgaature of objects 0 Imagtng Generates 1mages of the observed surface Imagtng systems are classtfted by 0 Framtng systems acqutsttson of awhole 1mage at the same ttme o Scanntng systems Scans ltnes to generate 1mage mn MHan scanntng or ob ltque scanners e g radar mm MW my numth mg emm39 mm m A CROSSJRACK SCAN NEH CV ALONG TRACK SCANNER Lecture 4 Blackbody radiation Main Laws Brightness temperature Obiectives 1 Concepts of a blackbody thermodynamical equilibrium and local thermodynamical equilibrium 2 Main laws gt Blackbody emission Planck function gt StefanBoltzmann law gt Wien s displacement law gt Kirchhoff 5 law 3 Brightness temperature 4 Emission from the ocean and land surfaces Required reading S 25 44 ppl77183 1 Concepts of a blackbody and thermodynamical eguilibrium Blackbody is a body whose absorbs all radiation incident upon it Thermodynamical equilibrium describes the state of matter and radiation inside an isolated constanttemperature enclosure Blackbody radiation is the radiative field inside a caVity in thermodynamic equilibrium Blackbody cavity NOTE A blackbody cavity is an important element in the design of radiometers Cavities are used to provide a welldefined source for calibration of radiometers Another use of a cavity is to measure the radiation that ows into the cavity eg to measure the radiation of sun Properties 0tblackb0d13 radiation 0 Radiation emitted by a blackbody is isotropic homogeneous and unpolarized Blackbody radiation at a given wavelength depends only on the temperature Any two blackbodies at the same temperature emit precisely the same radiation A blackbody emits more radiation than any other type of an object at the same temperature NOTE The atmosphere is not strictly in the thermodynamic equilibrium because its temperature and pressure are functions of position Therefore it is usually subdivided into small subsystems each of which is effectively isothermal and isobaric referred to as Local Thermodynamical Equilibrium LTE gt A concept of LTE plays a fundamental role in atmospheric studies e g the main radiation laws discussed below which are strictly speaking valid in thermodynamical equilibrium can be applied to an atmospheric air parcel in LTE 2 Main radiation laws gt Blackbody Emission Planck function Planck function BT gives the intensity or radiance emitted by a blackbody having a given temperature o Plank function can be expressed in wavelength frequency or wavenumber domains as 2hc2 B T 25exphckBM 1 4391 2h173 BvT2N 42 c 6XphVkBT l 2h 3 2 Ra 43 eXph vckBT l where A is the wavelength 17 is the frequency v is the wavenumber h is the Plank s constant k1 is the Boltzmann s constant kB 138XlO3923 J K39l c is the velocity of light and T is the absolute temperature in K of a blackbody NOTE The relations between B T 3 T and BA T are derived using that VdVZIVdV Zl dd andthat lc17lv D BVTBAT and BVT2ZBT 39 behavior of Planck function 0 If 7 gt 00 or 17 gt 0 known as Rayleigh Jeans distributions 2k 0 BAT 4 T 44a 2k N2 BVT ff T 44b NOTE Rayleigh Jeans distributions has a direct application to passive microwave remote sensing For large wavelengths the emission is directly proportional to T o Ifk gt0or 17 gtoo 2hc 2 BAT 15 6XP 410 MkBT 45a 2hN3 N B C eXp hv kBT 45b Io w 1 1 sift Puma MEIMICE w mquot u a H I I m mpquot W VE L39BIGTH Figure 41 Planck function on loglog plot for several temperatures gt StefanBoltzmann law The Stefan Boltzmann law states that the radiative ux emitted by a blackbody per unit surface area of the blackbody varies as the fourth power of the temperature F n BT 039 T4 46 where 039 is the Stefan Boltzmann constant O39b 567le 0398 W m392 K394 F is energy ux W m39z and T is blackbody temperature in degrees Kelvin K and BT TBJTd gt Wien s displacement law The Wien s displacement law states that the wavelength at which the blackbody emission spectrum is most intense varies inversely with the blackbody s temperature The constant of proportionality is Wien s constant 2897 K um km 2897 T 47 where km is the wavelength in micrometers pm at which the peak emission intensity occurs and T is the temperature of the blackbody in degrees Kelvin K NOTE This law is simply derived from dBAdk 0 NOTE Easy to remember statement of the Wien s displacement law the hotter the object the shorter the wavelengths of the maximum intensity emitted gt Kirchhoff s law The Kirchhoft s law states that the emissivity 8quot of a medium is equal to the absorptivity AA of this medium under thermodynamic equilibrium 8 A 48 where 87quot is de ned as the ratio of the emitting intensity to the Planck function AxL is de ned as the ratio of the absorbed intensity to the Planck function For a blackbody 8x Ah 1 For a gray body ie no dependency on the wavelength 8 A lt 1 For a non blackbody 8quot AAlt 1 NOTE Kirchhoft s law applies to gases liquids and solids if they in TE or LTE NOTE In remote sensing applications one needs to distinguish between the emissivity 0f the surface e g various types of lands ice ocean etc and the emissivity of an atmospheric volume consisting of gases aerosols andor clouds 3 Brightness temperature Brightness temperature Tb is de ned as the temperature of a blackbody that emits the same intensity as measured at a given wavelength or frequency or wavenumber Brightness temperature is found by inverting the Planck function For instance from Eq4 l T C2 b 11n1 f1 11 49 where I is the measured intensity and C111911gtlt108Wm392sr391um4 Cz14388x104Kum I For a blackbody brightness temperature kinetic temperature Tb T 39 For natural materials T134 S T4 S is the broadband emissivity NOTE In the microwave region the Rayleigh iJeans distributions gives Tb S T However a is a complex function of several parameters see below 4 Emission from the ocean and land surfaces The ocean and land surfaces can modify the atmospheric radiation eld by a re ecting a portion of the incident radiation back into the atmosphere b transmitting some incident radiation c absorbing a portion of incident radiation Kirchhoff 5 law d emitting the thermal radiation Kirchhoff s law INCIDENT RADIATION REFLECTED RADIATION EMITTED RADIATION 3 ABSORBED RADIATION 3 TRANSMITTED RADIATION Conservation of energy requires that monochromatic radiation incident upon any surface L is either re ected lr absorbed la or transmitted It Thus IiIrIa It 410 1IrIiIaIiItIiRAT 411 where T is the transmission A is the absorption and R is the re ection of the surface In general T A and R are functions of wavelength RAAA TA 1 412 Blackbody surfaces no re ection and surfaces in LTE from Kirchhoff s law AA 8L 413 Opaque surfaces no transmission RxAx1 414 Thus for the opaque surfaces 8M 1 RA 415 Emission from the ocean and land surfaces 0 In general emissivity depends on the direction of emission surface temperature wavelength and some physical properties of the surface In the thermal IR 4ymlt7tlt 100 um nearly all surfaces are efficient emitters with the emissivity gt 08 and their emissivity does not depend on the direction Therefore the intensity emitted from a unit surface area at a given wavelength is In 8 BATS In the shortwave region 01 pm ltlt 4 pm emissivity is negligibly small In microwave 01 cmlt7tlt 100 cm emissivity depends on the type and state of the surface NOTE Differences in the emissivity of ice vs water provide the basis for microwave remote sensing of seaice see Lab 1 Table 41 Emissivity of some surfaces in the IR region from 10 t012 um Surface Emissivit Water 0993 0998 Ice 098 Green grass 0975 0986 Sand 0949 0962 Snow 0969 0997 Granite 0898 Lecture 13 WW precipitation Obiectives 1 Radar basics Main types ofradars 2 Basic antenna parameters 3 Particle backscattering and radar equation 4 Sensing of precipitation and clouds with radars weather radars space radars TRMM and CloudSat Required reading S 81 p401402 57 821 822 823 83 Tutorial and Quiz httpwww met tzmn edn classATMO 51 39 39 39 html AdditionaVadvanced reading Online tutorial Chapter 3 mm Wwwrrr nrr an r 39 1 ehtml CloudSat web site httpcloudsatatmoscolostateedu TRMM web site httpwwweorcnasdagojpTRMMindeX7ehtm http trmm gsfcnasa gov 1 Radar basics Main thes of radars 0 Radar is an active remote sensing system operating at the microwave wavelength 0 Radar is a ranging instrument RAdio Detection And Ranging Basic principles The sensor transmits a microwave radio signal towards a target and detects the backscattered radiation The strength of the backscattered signal is measured to discriminate between di erent targets and the time delay between the transmitted and re ected signals determines the distance or range to the target Two primary advantages of radars all weather and day night imaging Radar modes at aggration o Constant wave CW mode continuous beam of electromagnetic radiation is transmitted and received gt provides information about the path integrated backscattering radiation 0 Pulsed mode transmits short pulses typically 1039610398 s and measures backscattering radiation or echoes as a function of the range Radar range resolution Consider a radar with pulse duration tp dV ttp2 gt R2 c ttp22 t gt R ct 2 ttp2 gt R1c ttp22 Thus radar range resolution is RlRz ctpZ h2 131 where c is the speed of light Problem A police pulsed speedmeasuring radar must be able to resolve the returns from two cars separated by 10 In Find the maximum pulse duration that can be used to prevent overlapping of the returns from the two vehicles Ignore the Doppler effect Solution RlRz 10 m thus tp 210m3108 ms 66710397 s Polarizing Radar has four possible combinations of both transmit and receive polarizations as follows HH for horizontal transmit and horizontal receive VV for vertical transmit and vertical receive HV for horizontal transmit and vertical receive and VH for vertical transmit and horizontal receive Microwave bands used in radar remote sensing see table 33 Ka K and Ku bands very short wavelengths used in early airborne radar systems but uncommon today Xband used extensively on airborne systems for military terrain mapping Cband common on many airborne research systems CCRS Convair580 and NASA AirSAR and spacebome systems including ERSl and 2 and RADARSAT Sband used on board the Russian ALMAZ satellite Lband used onboard American SEASAT and Japanese JERSl satellites and NASA airborne system Pband longest radar wavelengths used on NASA experimental airborne research system T Eyes of radars gt Non imaging galtimeters and scatterometers Altimeters often nadirlooking Operation principle transmit short microwave pulses and measure the round trip time delay to targets to determine their distance from the sensor Applications used on aircraft for altitude determination and on aircraft and satellites for topographic mapping sea surface height measurements from which wind speed can be estimated Example ERS altimeter Figure 131 Re ection of an altimeter pulse from a at surface As the pulse advances the illuminated area grows rapidly from a point to a disk as does the returned power Eventually an annulus is formed and the geometry is such that the annulus area remains constant as the diameter increases The returned signal strength which depends on the re ecting area grows rapidly until the annulus is formed remains constant until the growing annulus reaches the edge of the radar beam where it starts to diminish t02Hc tpgt tp tp is the duration of the pulse Example TOPEXPoseidon and Jason 1 radar altimeter sea surface height deviation from the mean in cm Scatterometers Operation principle transmit microwave signal and measures the strength of the backscattering radiation re ection Applications measurements of wind speed and wind direction over the oceans Ground based scatterometers are used extensively to accurately measure the backscatter from various targets in order to characterize different materials and surface types Example NASA Quick Scatterometer QuikSCAT 0 Radar 134 gigahertz llOwatt pulse at l89hertz pulse repetition frequency PRF o Antenna lmeterdiameter rotating dish that produces two spot beams sweeping in a circular pattern QaikSCAT measurement eagabili o 1800kilometer swath during each orbit provides approximately 90percent coverage of Earth s oceans every day 0 Windspeed measurements of 3 to 20 ms with an accuracy of 2 ms direction with an accuracy of 20 degrees Wind vector resolution of 25 km 002 08011999 gt Imaging radars see many examples below dlrnenslon dlmenslonal representataon oflmaglng sensors Sidebaking viewing geametiy afimaging mdar system the alongrtrack dlmenslon parallel to the rght dlrecuon 2 Basic antenna Earameters spaee and the uetuanng voltages m the erreurt to whlch rtrs eonneeteol Kari antenna Emumeters m free spaee 1 Frelolpattern 37D quantataes lnvolvlng the vanataon ofEMfleld or EM power as a functlon of the spheneal coordlnates e and p powerpattern 116 p m w s quot and normallzed power pattern 136 zp me go Pme w by apartaele Figure 132 Anlenna power pattern in polar coordinates and in rectangular coordinates Major lobe First null beamwxd h FNRW Halfpower beamwidlh HPBWJ Minor lobes Radiation intensin Half power hcamwidlmlIPBW First null beamwidlMFNBW Majnr lobe Minor lobes Side lobe Back lube A 1r 112 0 112 1r NOTE same name Major lobeMain lobe Main beam Since the difference between the power transmitted by an antenna Pt in W and the power received from backscattering is typically several orders of magnitude the received signal is expressed in Decibels dB Pz39n dB1010g 132 I 2 Antenna gain is de ned as the ratio of the intensity at the peak of the transmission pattern 11 to an isotropic intensity that is derived assuming that the total power Pt in W is distributed equally in all direction I pz 133 Pt 47239R R is the range L V Beam area or beam solid angle in sr is de ned as QA I Pn6pdQ 134 4 The beam area is a solid angle through which all of the power radiated by the antenna would stream if P9 p maintained its maximum value over Q A and was zero elsewhere gt Power radiated in W Pmax9 p Q A The beam area can be approximated by the product of the halfpower beamwidths HPBW see Fig 132 in two principal planes QA z HP HP 135 where 6H is A9 of the HPBW and pH is the Aq of the HPBW 4 Effective aperture A6 in m2 is de ned as 2 AeQA 136 where 7 is the wavelength in m 5 Directivity D Z l dimensionless is de ned as the ratio of the maximum power to its average value D Pmax9 p PMS p Other expressions for the directivity 47239 D Q d1rect1v1ty from pattern 137 A A3 D 47239 7 d1rect1v1ty from aperture 138 gt Friis transmission formula Consider a transmitting antenna of effective aperture Act and receiving antenna with effective aperture Aer The distance between the antennas is R If transmitted power P1 is radiated by an isotropic source the power received per unit area at the receiving antenna if Pt 13 9 47239R2 I and the power available to the receiver is P FAB 1310 But the transmitting antenna has an effective aperture Act and hence a directivity D from Eq138 A D 47239 2122 Thus the power available to the receiver is D times greater 4 7239Aet P FAWD FAB 12 1311 Substituting Eq139 into Eq1311 gives P BABY 472Aet MR2 12 1312 or Pr Aer Aer F R 2 22 1313 t 3 Particle L 39 luv and radar emmtinn Recall Lecture 6 in which we introduced the ef ciencies 0r ef ciency factors cross sections and volume coef cients for extinction scattering and absorption Let s introduce backscattering characteristics needed in active remote sensing radar and lidars Differential scattering cross section Cd is de ned as the amount of incident radiation scattered into the direction Q per unit of solid angle 75 P 1314 0 d 4 where P0 is the scattering phase function Bistatic scattering cross section 6 is de ned as 0391 47F0d 1315 Backscattering cross section 6 is de ned as ab47rad 180 1316 Using Eql3l4 Eql3 16 can be rewritten as 0 03P 180 1317 Recall that the incident intensity I and scattered intensity IS by a particle relates as 15 11 1318 where R is the distance from the particle For the backscattering case we can write Fbs 180 FZ 1800 1319 or 11556 180 47rR2 Flob 1320 Thus the physical meaning of the backscattering crosssection is the area that when multiplied by the incident ux gives the total power radiated by an isotropic source such that it radiates the same power in the backward direction as the scatterer For the particle number size distribution Nr the backseattering volume coef cient Kb is kb IabrNrdr 1321 and thus kb kJP 180 1322 where P is the scattering phase function averaged over the size distribution Small size parameter limit Rayleigh limit it can be shown from Mie theory see S 571 that 72395 2 6 ab 7K D 1323 where IK I m z 1 m if the refractive index of the particle andD is the particle m Z 2 diameter gt Radar eguation Consider a transmitting radar with an antenna of effective aperture Act and pulse duration tp or length hctp The radar illuminates an object e g a cloud at the distance R Suppose that the object has the backscattering crosssection called radar crosssection 6r Using the Friis transmission formula we can nd the power intercepted by the object PM as 2 13115 object 13 O39r 1324 Using that the scattering object can be considered as an isotropic source such that it radiates the same power in the backward direction it has directivity D1 and effective aperture Ae 73411 see Eq138 And using the Friis transmission formula we can find the power received by the antenna P Pm by object M i r R212 4 1325 Substituting Eq1324 into Eq1325 we obtain Pr A2 039 FZWF t called the radar equation 1326 where A Aet Aer is the effective aperture of antenna same for transmitting and receiving If the object is a cloud with size distribution Nr and the volume backscattering coefficient kb The power backscattered by the volume IV and received by lidar can be expressed as P A2 Icde F 47ZR4 7 1327 From lidar beam geometry the illuminated volume can be approximated as W m RZGHquHPhZ 1328 and using Eq1321 for kb we have h QHS DHP abrNrdr 1329 Assuming that particle are in the Rayleigh limit and using Eq1323 we have P 7239412 hQHPquP 2 6 K D N D dD 1330 P 416 R2 I l J the above equation can be rewritten as 133 1 where factor C depends on the antenna characteristics and Z J D 6NDdD is called the radar re ectivity factor NOTE Eq1331 is often called the radar equation We can relate the backscattering coefficient and radar reflectivity as 7139s 2 7139s 2 7139s 2 k 0bDNDdD 7m D6NDdD 71lt J39 D6NDdD 71lt Z 1332 0 If particle are not in the Rayleigh limit andor nonspherical eg ice crystals the effective radar re ectivity factor Ze is introduced 0 In the more general case Eq 1331 must be corrected to account for the attenuation along the path to and from the scattered volume a cloud ie attenuation may arise from absorption by atmospheric gases absorption by cloud drops and precipitation R r r P C Zexp 2 krdr 1333 7 R2 where kg is the extinction coefficient along the path 4 Sensing of 39 quot quot and clouds with radars Principle use a relationship between the radar re ectivity factor Z or Z6 and the rainfall rate Rr mmhour in the form called ZR relationships Z A Rr 1334 where A and b are constants depending on the type of rains Einrical ZR relationshigs Rr in mmh and Z in mm6m393 Stratiform rain Z 200RVL6 1335 Orographic rain Z 31 R7171 1336 Snow Z 2000Rr2 1337 The power returned to a radar see Eql331 can be normalized using Eql32 Pin dBZ1010g P 1338 Pref where Prefis the reference power which is often taken to be that power which would be returned if each m3 of the atmosphere contained one drop with D 1 mm Z 1 mm6m393 gt National Weather Service radars httpradarweather20v The National Weather Service NWS Weather Surveillance Radars WSR are of three types WSR57S WSR74C and WSR88D D stands a Doppler radar Wavelength Dish Diameter cm feet Radar WSR57 103 12 05 or 4 WSR74C 54 8 3 WSRSSD 111 28 157 or 45 Kimball snuey Cheyenne Stating we r cmquot w Lamar La Junta Em Example oflhe WSR radar Image for Colorado for Aprll Z 2002 36 025 mm gt Space radars TRMM radar and CloudSat radar TRMM radar rst radar m space aurlched m 1997 13 8 GHz 4 3kmfootpr1rlL ZSOm vemcal resolutlorl l 67 HS pulse duratlorl crossLrack scarlrurlg Zl 5km swath Tropical Rainfall Measuring Mission February 10 1998 a Houston TX pmipnunmmdd 91 mm precipilmion vodur vernmi mm mm 1 anquot mensily gt CloudSat radar Cloud Pro ling Radar CPR o 94GHz nadirlooking radar which measures the power backscattered by clouds as a function of distance from the radar CPR System Characteristics Nominal Frequency 94 GHz Pulse Width 33 psec PRF 43 00 HZ Minimum Detectable 2 26 dBZ Data Window 025 km Antenna Size 195 m Dynamic Range 70 dB Integration Time 03 sec Vertical Resolution 500 m Crosstrack Resolution 14 km Alongtrack Resolution 25 km Lecture 12 WW pro le trace gases and air pollution Obiectives 1 Concept of weighting functions weighting functions for nadir and limb soundings 2 Concept of an inverse problem 3 Sounding of the atmospheric temperature NOAA sounders 4 Sounding of atmospheric gases Required reading S75 12 754 77 Additional reading COMET tutorial httpcimssssecwiscedugoescometl7html Advanced reading C D Rodgers Inverse methods for atmospheric sounding Theory and practice 2000 1 Concept of weighting functions Recall Eq10 10 that gives the upward intensity in the plane parallel atmosphere with emission neglecting scattering T L39 1Jrlfrexp T 1Bvr dr u iifexp Let s introduce the transmittance along the path from the optical depth 139 to the optical depth 1 as r39 r TVT TueXp 121 where is the cosine of zenith angle of observation Thus miexpT39 T dr ll ll 122 Eq1010 can be rewritten as I LIT 39 IfltamIVltr Tvr Hm I Bvr dr 123 r Eq123 can be expressed in different vertical coordinates such as z P or lnP Let s denote an arbitrary vertical coordinate by E so Eq123 becomes Mam IVETVEE j BVE39gtW239Egtd239 124 where the weighting function is de ned as N N dTV E 3 WV zany 125 d Physical meaning of the weighting function Radiances emitted from a layer 2 I is determined by a blackbody emission Bv 3 ofthe layer weighted by the factor WV 73 00539 Let s rewrite the solutions of the radiative transfer equation for upward and downward radiances in the altitude coordinate 2 Recall see Lecture 5 that the optical depth of a layer due to absorption by a gas in this layer is TV 2 Tkydu 1 Let s express the optical depth in terms of a mass absorption coefficient of the absorbing gas and its density 1 Ikvpgasdz 126 Thus transmission between 2 and 2 along the path at u is mum W ij kvpgasdz 127 Zr and Mbw dz39 u 1 z N eXp J kvpgmdz 128 Therefore for the upward intensity and downward intensities at the altitude z we have Z J I IJ 211 If 0Tvz0m 1 Bv Tz dz39 129 0 1114 11 j UW39DWdZ 1210 and thus 12111 IJ0uexp ijkvpgmdz 1 0 z 2 1211 LJ 6XP LJ k p dz39 B Tz39k p dz39 I 0 I z v gar v v gar 1 w 1 z I I I 13z Z expl ijvpgmdz Tz kvpgmdz 12121 NOTE Eq12 l l is fundamental to remote sensing of the atmosphere It shows that the upwelling intensity in the IR is a product of the Planck function spectral transmittance and weighting function The information on temperature is included in the Planck function while the density profile of relevant absorbing gases is involved in the weighting function u Thus one can retrieve the profile of temperature if the profiles of relevant absorbing gases are known Example sounding of the atmospheric temperature profile by utilizing the 15 um and 43 pm of C02 bands done operationally on the NOAA weather satellites Weighting 39 for nearnadir 139 From Eq 129 upwelling radiance detected by a satellite sensor at Z0C is since 239 y dz39 1000 If awn 00011 j BVTz dz39 1213 0 01 now If WM 000 1 Bv TzWvoozmdz 1214 0 where Wvooz dTVZ Z thus from Eq128 we have Tvwz km a 1 Wv0022 g PF J kvpgmdz 1215 dz 2 decreases with altitude increases with altitude Transmission Weighting function Transmission Weighting function 0 50 50 50 45 45 45 45 40 40 40 40 E 35 E 35 2 15 T 35 g 30 g 30 g 30 g 30 E 25 g 25 g 25 g 25 on n as as g 20 3 20 L3 30 20 H L 15 I L i L 15 10 10 10 10 i 5 5 i 0 0 u 0 00 02 04 06 00 0 00 0025 005 00 02 04 06 08 10 00 0023 005 lrannmsnon welghukm lransnnssmn welglmkm Figure 121 Schematic of weighting functions for optically thick and optically thin media We39 39 unt unx nr Mb mun 39 The intmsity measured by a satellite far limb Viewing geometry is the integral ofthe enission along a lineof sign 1 dT o IVhI vad1 12m h is the tangmt altitude m 1a levels of the atrnosphae at s no Figure 122 viewing geometry oflimb sounding We canrelate sandz as RhzvzRz2 1217 whae R is the radius of the Earth Using that Rgtgth we have 11s2Rzeh 1218 Thus Eq1216 becomes as 1 1111 31239d239 12191 and 1111 I B z39gtWlthzoogtdz39 1220 h where WV hz000 forzlth Jr W hzw R2z h forzgth 1221 enhancement of the tangent path relative to a vertical path limb sounding has higher sensitivity to emission from trace gases CO NO N20 C10 Advantages of limb sounding 0 Can measure emission from gases of low concentrations 0 Surface emission does not effect limb sounding 0 Good vertical distribution since it senses outgoing radiation from just a few kilometers above the tangent height gt weighting functions have spikes see Sf1g7 18 Disadvantages of limb sounding 0 Can not be used below the troposphere o Requires precise information of the viewing geometry 2 Concept of an inverse problem Recall Eq12 13 which gives the solution of the radiative transfer equation with emission for the outgoing intensity at the top of the atmosphere Z OC T T w IV ow IV 0yTvooom j Bv TzWvoozmdz 0 where Wvoo 2 la is the weighting function Forward problem is to calculate outgoing radiances for given temperature and gas concentration pro les Inverse problem in remote sounding is to determine what temperature and gas concentration pro les could have produced a set of radiances observed at closely spaced wavenumbers Let s assume that TV 000 u is negligible small The for nadir sounding we have Rook BTzWVoozdz 1222 0 where vi i l 2 N is the wavenumbers ie centers of the nite spectral bands of a spectrometer We can ignore the frequency dependence of the Planck function if vi are closely spaced Eq1222 becomes 1200 2 J 30712th oozdz 1223 0 Consider that measurements are done in the CO2 absorbing band so the weighting function are known and B17TZ is unknown Thus we want to solve Eq1223 to nd BVTZ and henceTz Eq1222 is a socalled Fredholm integral equation of the rst kind which has long been known for many associated dif culties The general form of the Fredholm integral equation because the limits of the integral are xed not variable of the rst kind because fx appears only in the integral is 17 gyj fxKyxdx 1224 where fx is unknown in our case BVTz K02 x is called the kernel or kernel function in our case WV ooz g is known in our case I 00 Problems in solving the inverse problem ie problems in solving Eq12 23 I The inverse problem is ill posed ie underconstrained because there are only a nite number of measurements and the unknown is a continuous function I This inverse problem is ill conditioned ie any experimental error in the measurements of radiances can be greatly ampli ed so that the solution becomes meaningless 3 139 0fthe 39 EL temnerature Let s nd the simplest solution of Eq1223 assuming that transmittance and hence weighting functions does not depend on temperature Thus Eq 1223 is linear in B 17 T Z A standard approach is to express B17 Tz as a linear function of N variables bj N BVTz 2 13ij2 1225 1 where L j Z is a set of representation functions such as polynomials or sines and cosines Eq1223 becomes N w N If Z bl LZWVZ6k 2 be 1226 11 0 1 where the square matrix C whose elements CV J L zWV zdz can be easily 0 calculated Thus for the N unknown bj there are N equations which can be solved The solution of Eq1226 is called an exact solution to the linear problem Problems Eq1226 is illconditioned ie any experimental error in the measurements can be greatly amplified and the solution can be physically meaningless though it satisfies Eq1226 Strategy instead of an exact solution nd the solution that lies within the experimental error of the measurements gt it gives us more freedom in a choice of a solution but a new problem is how to make this choice Thus the problem of retrieval can be re stated as Given the measured radiances the statistical experimental error the weighting functions and any other relative information what solutions for B 17 T 2 are physically meaningful A priori information is often used to provide other relative information A priori information for the retrievals of temperature I Radiosonde data I Forecast atmospheric dynamical models Example GOES soundings are generated every hour using an ETA model forecast as a first guess NOAA sounders N 0AAseries polar orbiting satellites HIRSZ High Resolution Infrared Radiation Sounder 2 20 channels resolution 19 km nadir MSU Microwave sounding Unit 4 channels resolution 111 km nadir SSU Stratospheric Sounding Unit 3 channels in the lSum CO band resolution 111 km nadir HIRSMSUSSU is called T OVS TIROS N Operational Vertical Sounder NOTE MSU SSU were replaced by AMSUA and AMSUB Advanced Microwave Sounding Units on NOAA K L M series Retrieval meth ads 0 Physical retrievals 0 Statistical retrievals 0 Hybrid retrievals Physical retrievals use the forward modeling to do the iterative retrieval of the temperature profile Steps Selection of a rst guess initial temperature pro le 2 Calculation of the weighting functions 3 Forward modeling of the radiance in each channel of a sensor 4 If the calculated radiance agrees with the measured radiance within the noise level of the sensor the current pro le gives the solution UI V If convergence has not been achieved the current pro le is adjusted and steps 2 through 5 are repeated until a solution is found Advantages 0 Relevant physical processes are taken into account at each step 0 No data is necessary Disadvantages o Computationally intensive o Requires accurate predictions of the transmittance Statistical retrievals Do not solve the radiative transfer ie n0 forward modeling Instead a training data set 7 a set of J39 J 139 that are quot J in time and space with satellite soundings 7 is used to establish a statistical relationship between the measured radiances and temperature pro les These relationships are then applied to other measurements of the radiances to retrieve the temperature Advantages o Computationally easy and fast does not require to solve the radiative transfer equation Disadvantages o A large training data set covering different region seasons land types etc is required 0 Physical processes are hidden in the statistics Hybrid retrievals also called inverse matrix methods Use the weighing functions but do not solve the radiative transfer equation and available data but do not require a large data set One at man linear methods lVIinimum variance method is used for routine soundings from the TOVS TIROS N Operational Vertical Sounder Strategy to seek the solution which minimizes the meansquare differences between the retrieved profile and true profiles Start with a matrix equation I At e where l is the column vector of radiance deviations from the true profile t is the vector of temperature deviations from the true profile e is the column vector of measurement errors A is the matrix containing the weighting functions the Planck sensitivity factors dBdT and it can be calculated with a knowledge of the transmittances Let s assume at the moment that we have a set of collocated radiosonde and satellite observations L AT E 1227 here upper cases means that matrices are N columns for N sounding pairs We seek a matrix C that T CL It can be shown that the matrix C which in a least squares sense minimizes errors in T CL is C TLT LLT1 1228 where the superscript T indicates matrix transpose and 1 indicates the matrix inverse Substituting Eq 1227 in Eq1228 we have C TAT ET ATEAT ET391 1229 Expanding and using that ABTBTAT it becomes C T TAT ET AT TTAT ATET ETTAT EE 1230 Assuming that the measurement errors are uncorrelated with temperature deviations TET and ETT are negligible small and therefore C STATASTAT SE1 1231 ST the temperature covariance matrix SE the radiance error covariance matrix Eq123 l is called minimum variance method 4 Sounding of atmospheric gases Strategy make satellite measurements at frequencies in absorption bands of atmospheric gases The principles of the methods for gas retrievals are generally the same as for temperature retrievals but gas inversion is more difficult o The inverse problem is more nonlinear for constituents because they enter the radiative transfer equation through the mixing ratio profile in the exponent It is not possible to separate the radiative transfer equation into the product of a simple constituent function and one which is constituentindependent The second main problem is that in some cases the radiances are insensitive to changes in the mixing ratio For instance for an isothermal atmosphere at temperature T any mixing ratio profile will result in the same radiances ie BVT In practice we find this problem in the retrieval of lowlevel water vapor because the temperature of the water vapor is close to that of the surface infrared radiances are relatively insensitive to changes in lowlevel water vapor Examgles of sonnders and 0th er sensors or remote sensing of gaseous sQecies GOME Global Ozone Monitoring Experiment ESAERS retrievals of 03 N02 H20 Br0 S02 HCHO 0CLO httpwwwiupphysikunibremendegome SCIAMAT CH Y Scanning Imaging Absorption Spectrometer for Atmospheric Cartography ESAENVISAT 2001present retrievals of 02 03 N0 N02 N20 H20 BrO S02 HCHO H2C0 C0 OCLO C02 CH4 httpwwwiupuni quot r quot J 39 39 httpwwwtemisnlproducts MOPI T T Measurements 0f Pollution In The Troposphere NASA Terra l999present retrievals of C0 and CH4 httpwwweosucaredumopitt NASA satellite missions EOS Aura httpauragsfcnasagov EOS Aura Atmospheric Profile Measurements nmin m M can u 39 a a I I I 2 HIRDLS High Resolution Dynamics Limb Sounder MLs Microwave Limb Sounder II OMI Ozone Monitoring lmirument TES Tropospheric Emission Spentromeier D i ii volcanic Polar geopot i 2 my i cloud 39 s i on heigm coniem aerosol ex nclion E x In N m gt o n in 2 u o m E at 5 E o i W 2 3 5 E E 3 E E m g o n a E 93 a Lecture 14 clouds Obiectives 1 Optical interactions of relevance to lasers 2 General principles of lidars 3 Lidar equation 4 Lidar sensing of aerosols and gases 5 Lidar sensing of clouds 6 Lidars in space LITE and CALIPSO Required reading S 841 842 843 844 AdditionaVadvanced reading CALIPSO httpwwwcalipsolarcnasagov 1 Optical interactions of relevance to lasers Laser is a key component of the lidar Lidar LIght Detection And Ranging Laser Light Ampli cation by Stimulated Emission of Radiation Basic Qrincigles of laser stimulated emission in which atoms in an upper energy level can be triggered or stimulated in phase by an incoming photon of a specific energy The emitted photons all possess the same wavelength and vibrate in phase with the incident photons the light is said to be COHERENT The emitted light is said to be INCOHERENT in time and space if the light is composed of many different wavelengths the light is emitted in random directions the light is emitted with different amplitudes there is no phase correspondence between any of the emitted photons Progerties of laser light Monochromaticity Coherence therence intime A TRAIN ZIF CCIHEREHT PHDTCINS Beam divergence All photons travel in the same direction the light is contained in a very narrow pencil almost COLLIMATED laser light is low in divergence usually High irradiance Let s estimate the irradiance of a 1 mW laser beam with a diameter of 1 mm The irradiance power per unit area incident on a surface is F PS 1x10393 W a 1x10393 Inf4 1273 Wmz lt Elastic scattering is when the scattering frequency is the same as the frequency of the incident light eg Rayleigh scattering and Mie scattering Inelastic scattering is when there is a change in the frequency Optical interactions of relevance to laser uni 39 sensing Rayleigh scattering laser radiation elastically scattered from atoms or molecules with no change of frequency Mie scattering laser radiation elastically scattered from particulates aerosols or clouds of sizes comparable to the wavelengths of radiation with no change of frequency Raman Scattering laser radiation inelastically scattered from molecules with a frequency shift characteristic of the molecule Resonance scattering laser radiation matched in frequency to that of a specific atomic transition is scattered by a large cross section and observed with no change in frequency Fluorescence laser radiation matched in frequency to a specific electronic transition of an atom or molecule is absorbed with subsequent emission at the lower frequency Absorption attenuation of laser radiation when the frequency matched to the absorption band of given molecule T Eyes of laser relevant to atmosgh eric remote sensing solid state lasers eg ruby laser 6943 nm gas lasers eg C02 911 pm semiconductor lasers GaAs 820 nm 2 General principles of lidars There are several main types oflidars Backseatter lidars measure backscattered radiation and polarization often called the Mie lidar Efferential Absorption Lidar DIAL is used to measure concentrations of chemical species such as ozone water vapor pollutants in the atmosphere Principles A DIAL lidar uses two different laser wavelengths which are selected so that one of the wavelengths is absorbed by the molecule of interest while the other wavelength is not The difference in intensity of the two return signals can be used to deduce the concentration of the molecule being investigated Raman inelastic backscattering Lidars detect selected species by monitoring the wavelengthshifted molecular return produced by vibrational Raman scattering from the chosen molecules High Spectral Resolution Lidar HSRL measures optical properties of the atmosphere by J quot the D ppl r 39 J J 39 39 39 39 return from the unbroadened aerosol return The molecular signal is then used as a calibration target which is available at each point in the lidar pro le This calibration allows unambiguous measurements of aerosol scattering cross section optical depth and backscatter phase function see S 843 Doppler lidar is used to measure the velocity of a target When the light transmitted from the lidar hits a target moving towards or away from the lidar the wavelength of the light re ectedscattered off the target will be changed slightly This is known as a Doppler shift hence Doppler Lidar If the target is moving away from the lidar the return light will have a longer wavelength sometimes referred to as a red shift if moving towards the lidar the return light will be at a shorter wavelength blue shifted The target can be either a hard target or an atmospheric target the atmosphere contains many microscopic dust and aerosol particles which are carried by the wind Lidars compared to radars Lidar uses laser radiation and a telescopescanner similar to the way radar uses radio frequency emissions and a dish antenna Optically thick cloud and precipitation can attenuate the lidar beam but radar signals can penetrate heavy clouds and precipitation In optically clear air radar return signals may be obtained from insects and birds and from air refractive index variations due to humidity temperature or pressure uctuations Lidar beam divergence is two to three orders of magnitude smaller compared to conventional 5 and 10 cm wavelength radars The combination of the short pulse of the order of 10398 s and the small beam divergence about 10393 to 10394 radiant gives a small volume illuminated by a lidar about a few m3 at ranges of tens of km 3 Lidar equation In general the form of a lidar equation depends upon the kind of interaction invoked by the laser radiation Let s consider elastic scattering Similar to the derivation of the radar equation the lidar equation can be written as PR C h kb exp 2 k d r g 141 R2 2 47 0 1 where C is the lidar constant includes Pt receiver crosssection and other instrument factors Kb 411 in units of km39lsr39l is called the backscattering factor or lidar backscattering coef cient or backscattering coef cient K6 is the volume extinction coef cient and tp is the lidar pulse duration hctp gt Solutions of the lidar e uation In general both the volume extinction coef cient K6 and backscattering coef cient Kb are unknown see Eql4 1 Q It is necessary to assume some kind of relation between Ke and Kb called the extinction to backscattering ratio EXAMPLE Consider Rayleigh scattering Assuming no absorption at the lidar wavelength the volume extinction coefficient is equal to the volume scattering coefficient k k On the other hand Eql322 gives kb 2 kSP 21800 Using the Rayleigh scattering phase function we have 3 P 1800 Z1 cos21800 15 Thus for Rayleigh scattering kbkxP 18015kx15ke 142 To eliminate system constants the range normalized signal variable S can be defined SR 1nR2PrR 143 If S0 is the signal at the reference range R0 from Eq 14 l we have u SR SR0 1nl b 2 krdr or in the differential form d9 1 dkbR 2k R dR E i 144 kbR dR Solution of the lidar equation based on the sloge method assumes that the scatterers are homogeneously distributed along the lidar path so 6 R A m 0 145 dR Thus 2k dR g 146 and K is estimated from the slope of the plot S vs R Limitations applicable for a homogeneous path only T 39 39 based on the 39 39 ts 39 39 39 ratio use a priori relationship between ke and kb typically in the form kb 2 bk 147 where b and n are speci ed constants Substituting Eql47 in Eql44 we have 611339 n dkz R 2k R 148 cm kg R ER with a general solution at the range R S S 0 J eXp n kg 149 1 2 R S S0 1 J eXp dr km R 71 NOTE Eql49 is derived ignoring the multiple scattering Eql49 requires the assumption on the eXtinctiontobackscattering ratio Eql49 is instable with respect to ke some modi cations were introduced to avoid this problem For instance use the reference point at the predetermined end range Rm so the solution is generated for Rlt Rm instead of RgtR0 4 Lidar sensing of aerosols and gases Retrieval of the gas density from DIAL measurements m erential Absorption Lidar DIAL uses two wavelengths one is in the maximum of the absorption line of the gas of interest and a second wavelength is in the region of low absorption For each wavelength the total extinction coefficient is due to the aerosol extinction and the absorption by the gas assumed that Rayleigh scattering is easy to correct for 1w lewd pgkg 1410 where km is the aerosol volume extinction coefficient pg is the density of the absorbing gas and kayg is the mass absorption coefficient of the absorbing gas The two wavelengths are selected so that the aerosol optical properties are the same at these wavelengths ke er ke er and kbaerl1 kbaer Taking the logarithm of both sites of Eq14 1 we have for each wavelength C h kb R 1nltPltRPgt1n FEW 2 1w w 11412 39 quot the at two 39 39 we have R 1nltP1ltRgtPZltR 2j pgltr39kg1rd kwv39ndr39 1413 where P1R and P2R are the normalized power received from the range R at two wavelengths Eq14 13 gives the density of the absorbing gas as a function of range 0 DIAL systems can measure the following gases H20 N02 SO and 03 Elam39c Mi Bulwcmn39nglibux gt gves aemsul mmunrmrbacksmuer mun as a upm39 d by NASA hug mglnet gst nag gbyo WL upemles at me Wavelength n52 um Ranm Elam backzmn39ng Lithugt Enablemasuranems br aemsul ammuun and backsmumng in l Pamgit Raman hdar sysLErns dated saleded species by mummnng me Wavelenng shmed mulecular realm pruduced by mbmuunal Ram smumng mm me chusen mulecule by mnlemles Ey39zkmg themuu ufthe mm at me mtermpbrwayelengm m me 93131 211113 mbbgen Wavelength must ufthe ngerdepmdem taxms drup nut and ne 15 le wnb a quanmy that 15 mm duele pmpummal m me waysrmpbr mixing lm The Ramanhdar equauun canbe wnuen as 8RAAgt WWH mamwao39mzm 1414 where XL and AR are the lidar and Raman wavelengths respectively backscattering coef cient KbR LL4R is linked to the differential Raman backscatter cross section of a gas and molecule number density KeR XL and KeR XR are due to molecular Rayleigh scattering and aerosol extinction In Raman lidars the inelastic Raman backscatter signal is affected by the aerosol attenuation but not by aerosol backscatter gt aerosol extinction pro le can be retrieved Example Raman lidar at DOEARM SGP site NdYAG lidar 355 nm Receiving Wavelengths RayleighAerosol 355 nm Depolarization 355 nm Raman water vapor 408 nm Raman nitrogen 387 nm Aerosol characteristics retrieved from SGP Raman lidar Aerosol Scattering Ratio also called lidar scattering ratio is de ned as the ratio of the total aerosolmolecular scattering to molecular scattering lltbm7tz kba7tz kbymOuz Aerosol Backscattering Coef cient Pro les of the aerosol volume backscattering coef cient kb7t355 nm 2 are computed using the aerosol scattering ratio pro les derived from the SGP Raman Lidar data and profiles of the molecular backscattering coef cient The molecular backscattering coef cient is obtained from the molecular density pro le which is computed using radiosonde pro les of pressure and temperature from the balloonbome sounding system BBSS and or the Atmospheric Emitted Radiance Interferometer AERI No additional data andor assumptions are required Aerosol ExtinctionBackscatter Ratio Pro les of the aerosol extinctionbackscatter ratio are derived by dividing the aerosol extinction pro les by the aerosol backscattering pro les Aerosol Optical Thickness Aerosol optical thickness is derived by integrating the aerosol extinction pro les with altitude AA mum a 7 1quot u n rmwn a 2 4 n m mm mm mm mm mm M um VurrrVupur mm M mm mm Mum mumm mmq 1 I um mm H u m w a m 1 mmuunuan m Am mum MW 4 Figure 141 Examples of retrievals usmg the Raman 11am C02 lidar at 925 m and 106 m measures the backseatterjng coef cient Exmle Jet Propulsion Lab JPL C02 lidar almost continuous operation since 1984 venical resolution is about 200 m throughout the troposphere and lower stratosphere up to about 30km A 10 E W W E 7 E Integration Range E v 7 5 m MSL Tropopause 7 g 10quot 339 39 E 3 is 5 39E g 10 g I i 39g J 0 7 a 76 7 J0 a t E 10 g 3 a E E E H 1077 W W W W W W 11an92 11an93 11an94 lJan95 lJan96 lJan97 lJan98 lJan99 HA 10394 W W 5 Integration Range 7 Tropopause 23 km MSL 7 g 39 I 3 1039s 7 a g 3 J 3 398 o I E a 0 0 E a e d39 n39 f39 I a 76 g 39 39 7 E 10 H W W W W W W W W lJanQZ lJan93 lJan94 lJan95 lJan96 lJan97 lJanQS lJan99 gure 142 Integrated backseatter from the free troposphere upper panel and the lower stratosphere lower panel column above the JPL Pasadena site since the eruption ofthe Philippine volcano Mt Pinatubo in June of 1991 Tratt et al 5 Lidar sensing of clouds 00 4 Height MSL km 039 N lb Wit C11 4 Height MSL km 07 2 O r r r r r r r r r r 10 10210510 10510510 10210510 10510 s107 Return Power Return Power Figure 143 Four typical examples of range corrected lidar backscatter versus altitude ARM Raman lidar 10 min average Sassen et al Fig 143a illustrates a clear sky backscatter which decrease with altitude due to the decrease in molecular density Fig 143b shows a backscatter from cirrus which has a strong increase in backscatter above cloud base and air return above cloud top Backseatter which is totally attenuated in clouds is shown in Fig 143c Compare with clear sky case Fig 143a we can nd a very strong increase in lidar backscatter form clouds Fig 143bc but it is not always observable Fig 143d The other common feature for cloud signal is there is afit decrease regj on in cloud backscatter due to strong attenuation of clouds or transition form cloud to clear region So strong negative and strong positive slopes in lidar backscatter signal are observable in the presence of clouds Cloud boundam detection there is no universal algoritth Common approach analysis ofdPdR ie retuned power vs the range 6 Lidars in space LITE and CALIPSO LITE Lidar Inrspace Technology Experiment httpwwwlitelarcnasagovj o LITE ew on Discovery in September 1994 o LITE was operated for 53 hours resulting in over 40 GBytes of data covering 14 million kilometers of ground track 0 YAG L39L 39 imnlmnnm m Wavelengths of 1064 nm infrared 532 nm visible green and 355 nm ultraviolet The twolaser system provides redundancy in case one laser fails Only one laser operates at atime 8 kilometers permnd 17500 mph 280m aerosols Mulnrlayer cloud system Saharan dust gtr tmn A satellite has been launched m Apnl 2006 http Wwwrca1xpso larc nasa govJ udr r thh 1quot Mn CALIOP Threerchannel Irnagmg Infrared Radwmeter m dee erld Camera WTC resoluuon of 30 meters Table 141 CALIPSO Level 2 Aerosol and Cloud Products Measurement capabilities Data Product Resolution Dam Fmdu and Uncertainties Horizontal Vertical Aerosols Heighi Thickness For layers wilh 0 gt 25 x 10quot km391 srquot 5 km 60 m Opiicai depih r 40 5 km NIA Backscaiier ampbelaaz 20a 30 3 g m gm Exiinclion of 40 jg 33 Em 13262 Clouds Heighl For layers with 0 gt1 x 1039 kmquot sr391 1015 km 30 00 m Thickness For layers wnh r lt 5 13 1 5 km 00 m Opiicai depih r Wiihin a factor of Zfor r lt 5 5 km NIA Backscaiier ampbelacz 20e 30 5 km 50 m Exiinciion Tc Wiihin a factor of 2 for r lt 5 5 km 00 m icewaier phase Layer by layer 5 km 00 m Ice cloud emissivity c 0 03 1 km 39NA ice pariicie size 150 for c gt 0 2 1 km NIA Noie lldar ralio SB o What CALIPSO can see aerosol and thin cloud layers but cannot penetrate through the heavy cloud systems 150002 Version 100 Image Date 0010012000 x10quot 393939hhhhhhhinhinhinhinhthinhhhhhhhh xl 39z xl 393 xl quot w Principles of passive remote sensing using emission and applications WWW Remote sensing of SST Obiectives 1 Radiative transfer with emission 2 Microwave radiative transfer Measurements of atmospheric pathintegrated quantities precipitable water vapor cloud liquid water 3 Remote sensing of seasurface temperature SST Required reading S 71 731 732 72 Additional reading SST products httppodaacjp1nasagovsst Microwave remote sensing data httpwwwremsscom 1 Radiative transfer with emission Atmosphere and surfaces emit infrared and microwave radiation According to the Kirchhoff 5 law emissionabsorption Recall the BeerBouguerLambert law Eq71b Lecture 7 for emission d1 k lids where k8 is the volume extinction coefficient along path ds 0 For a nonscattering medium in LTE the Planck function gives the source function 31 101 Neglecting scattering gt volume extinction coef cient volume absorption coef cient Thus the net change of radiation along path ds is due to the combination of emission and extinction d d extinction d emission and thus the radiative transfer equation in the thermal region is dl k111dsk B1ds 102 or d j k411 BA 103 NOTE EqslO2 103 are often called the differential forms of the radiative transfer equation Recall that by definition dTl k1 sds Let s rearrange terms in Eq103 and multiply both sides by exp1 d1 eXPd expmy eXp T1B1 104 71 and using that dxexp xexp xd1x exp xxdx we have d14exp ri exp r4B drz 105 Integrating the above equation along a path extending from some point s to the end point s it becomes ml 1s e r A I1s39e A j B se r sd rs 106 rs and rearranging terms we have the solution of the radiative transfer in IR J J 31 seT1STJquotld2s 5r 1s 11s39e Wgt T gt1 107 contribution from radiation emitted contribution from radiation incident at s along the path and transmitted to s and transmitted to s Let s consider a planeparallel atmosphere dzuds and 1z p ts Upward intensity I is for 12 u 2 0 or 0 S 9 S 7Z392 Downward intensity I is for 1 S u S 0 or 7I2 S 9 S 7 using that c0s01 c0sn20 and c0s70 1 120 z21t0P t flaunt w ax 114 Z T 12T A i 14T t TT 0 bottom m i I 1 3 1 NOTE For downward intensity p is replaced by p Eq107 gives both the upward intensity in the plane parallel atmosphere t t r 1 14T 714T 76XP t 108 iJeXp T 2B12quotd2quot 1 r l1 and the downward intensity in the plane parallel atmosphere t t T An1M0 140 6XP 109 7 2quot LJ eXp B 2quotd2quot 1 0 o In the atmospheric conditions for IR radiation one can consider that at the surface T T 147 111 BAT 0r 11 7 2 8134711 no thermal incident radiation at the TOA l 11 0 y lt0 0 no dependence on azimuthal angle p Thus Eqs108 and 109 can be rewritten as in the wavenumber domain gt11 239quot T IJryBvr exp 1 Ix 1010 JeXp T T BV2quotd2quot Ill 139 1r 39 13r y Jexp T TBvr39dr 1011 0 ll Eqs10 10 1011 can be expressed in terns of monochromatic transmittance Recall that 139 may exp V 1012 u and the differential form is off 1 eXpTv 1013 d ll ll 0 Multiplication law of transmittance states that when several gases absorb the monochromatic transmittance is a product of the monochromatic transmittances of indiVidual gases T T T T 1014 v12N v1 v2quot39 vN Thus the formal solutions for monochromatic upward and downward in terms of transmittance are Mum BvrTVr r y r 1015 I BAMJIVW pooch I 1 r d1 1 dTV r r IKE0 BAT Mdf 1016 0 d1 2 Microwave radiative transfer According to the RayleighJeans distribution see Lecture 4 Eqs44ab Brightness temperature is linear proportional to the radiance In the microwave surface emissivities are low gt need to account for re ection ie the portion of microwave radiation emitted by the atmosphere toward the ocean is re ected back to the atmosphere and can be polarized depending on the Viewing direction Eq108 can be modi ed to give the brightness temperature 7 measured by a satellite passive microwave detector at a wavenumber v Tb aft experquot m J Tr39exp r39udr39u r 0 1017 Rf experquot no Tr exp r T dT39 0 where Tm is the surface temperature Tam is the atmospheric temperature P 8V 1s the em1ss1v1ty of the ocean surface w1th the g1ven polarlzation state p and R5 1 SVP is re ectivity of the ocean surface with the given polarization state p Let s assume that the absorption by water vapor only in the boundary layer I Tmr exp r dr ml exp rquot W 1018 0 Thus we have from Eq14 17 Tim Tm1 Tv2f18fl 1019 where TVru eXp TV is the transmission function gt Measurements of 39 EL path 39 ated quantities nreci itable water vapor and cloud liquid water Let s consider brightness temperature measured at 1935 GHz and 37 GHz for two measured polarization state horizontal H and vertical V polarization states Using Eq10 19 we have at each frequency ATIW 7 RV RHT Tquot at 1020 where 41 22 The atmospheric transmission can be represented as a combination of transmission for 02 T02 cloud liquid water Tw and water vapor Ta at each frequency 2 2 2 2 T TOZTW Tm 1021 TW eXp kavWLWP u where kavWis the mass absorption coefficient of liquid water cloud drops andLWP is the liquid water path defined as liquid water content L WC Lecture 6 integrated over the path Tm eXp kmw Ll where k7 is the absorption coefficient of water vapor and m is the amount of water vapor integrated over the part called precipitable water From Eq1020 we have kavWLWPkmw ln L 10 22 2 TMIRVRHWOZ I o Eq1022 for two channels gt we have two equations to solve for LWP and as given the Wlues ofTozylg T0237 kw km and R w Problems 1 absorption coef cients 2 R5 are functions of wind speed NOTE The above principle is used in the retrieval algorithm of Special Sensor Microwavelrnager SSMl SSM I is a passive microwave sensor aboard the DM SP satellite series httpwwwrernsscorn Example nfSSMIprnducts Columnar Water Vapor Average for Year 2000 u 2U 40 ED millimeters mrnrce maxrce land nudata a an an m 240 m m Cloud Liquid Water Average for Year 2000 Due n18 thtmetevs mVHEE maXtEE tend nu data a an m m 240 an an 3 Remote sensing of seasurface MT Principles of SSTretrievals from passive infrared remote sensing measure 1R mdiances in the atmospheric Window and correct for contribution from clear sky by using multiple channels called quotsplitWindowquot technique Using Eq1010 we can Write IR radiance at TOA 1 Ti 1 r 4quot mow Em gtexplt7gtzjexplt7gt Bmdr39 1023 0 Let s reWrite this equation using the transmission function TX I exp 7 1 1 y and that 12mm BAmmltmgtBiltTmgtn4mm 10241 Where Tm is an effective blackbody tempemture Which gives the atmospheric emission 31am11 T1rm1 1iexp gt BMW39 1 0 1 1025 We want to eliminate the term with Tm in Eq1024 Suppose we can measure IR radiances 11 and I 2 at two at the adjacent wavelengths 21 and 12 1x 1 B1Tmri71 nu B1 1 T1 71 JO 2 BZYLurTZTZ9BZTajm1T2TZIU NOTE two wavelengths need to be close to neglect the variation in B9Tm Let s apply the Taylor s expansion to 3T at temperature T T am 53 BATWBATWH TTatm 6T Using this expansion for both wavelengths we have 6310 gt Bl T w B1 Tam a T Tatm T 6320 gt 32 T 320 70 Tm 0T and thus eliminating T T m we have 3 T B T 6320 mTlB T B T l m 2 2 arm 1 1 arm Let s introduce brightness temperatures for these two channels T 1 1 and T1 11 BlTb1 and 12 BzTb2 and apply 1031 to BzTb2 and to BZTW 32Tb 2 e 32TammBlTb 2BlTml 39 631T6T 39 and 1026 1027 1028 1029 1030 1031 1032 B T BT aBZltTgt6TBT BT 2 m 2 mmW 1 M 1 mml 1033 Let s substitute the above expressions for BzT 1 2 and to BZTW in Eq1027 B T alum6T B T B T 2 arm 631T6T 1 122 1 W 1034 TBT aBZltTgt6TBT BT BT 1T 2 2 mmW 1 sur 1 aim 2 arm 2 where T1 and T2 are transmissions in the channels 1 and 2 Eq1034 becomes 310m 31TWT2 31Tam1 T2 1035 Using Eq1026 we can eliminate 310111quot 310W 11711 BlTbzl 1036 1 T where 7 T1 and T2 are transmissions in the channels 1 and 2 1 2 Performing linearization of Eq1036 Tsur Tb1 7TbJ T172 1037 The Erincigle at the SST retrieval algorithm SST is retrieved based on the linear differences in brightness temperatures at two IR channels Two channels are used to eliminate the term involving T m and solve for Tsur NOTE Clouds cause a serious problem in SST retrievals gt need a reliable algorithm to detect and eliminate the clouds called a cloud mask One needs to quot 39 39 39 the bulk sea surface temperature and skin sea surface teerrature Bulk 1 15 m depth SST measurements 1 Ships 2 Buoys since the mid1973s buoy SSTs are much lees nosy that ship SSTs Data from buoys are included in the SST retrieval algorithm Skin SST from infrared satellite sensors 0 SR Scanning Radiometer and VHRR Very High Resolution Radiometer both own on NOAA polar orbiting satellites since mid1970 o AVHRR Advanced Very High Resolution Radiometer since 1978 4 channels started on NOAA6 since 1988 5 channels started on NOAAl l 1 Table 10 1 AVHRR CHANNELS AVHRR i Wavelength Channel 11m 1 1 1 1 058 068 1 2 1 072 110 1 1 3 1 355 393 l 4 1 103 113 l 5 7quot 115 125 8 A VHRR M CSST MultiCh auuel SST 2 algorithm SSTa Tb4 TM Tb5c 1038 where a and c are constants l T4 T4 and T5 are transmission function at AVHRR channels 4 and 5 4 5 7 AVHKK NlSST anlinear my ayau39onat myth 01mm 4 0 SST an b M CTw I ssTmmlrw Ia5secsml 10 39 wha39e ssTwlfa rstguess SST Th4 and Th5 arebnghmess my Hature measuredbyAVIIRR channels 4 and 5 Tw Th5 a a aha c are che lclehls lhal calculaled furtwn dlffa39entreglmes hf hhe sel ch rap rah lt hr 07 and ahhlheh se l fvr rap rah gt 0 7 The cnef uems a b and c are eshmaled fmm hegesmh analyses uhhg chlhcalea m all buuy aha salelhle measumhehls called matnhups Alumnus aggth usedlh lhe SST helneval algmlhmlh ATSRA1mgTmnk ScanmngRadmme Ler uh ERSATSR hasA channels l 537 10 2 and l2 hm s51 an Z a 1040 chemclmls a are calculaled fmm a 5 m a hahahvehahsfehmhdel lhslead hflh hm Dbservahvns as m lhe AVIIRR alglmthm NOTE bath algmlhms wm39k fvr thud ee pixels gt dvud mask ls hequhed gt Examples ofSST retrieved 39om AVHRR Yampamium came 10 ls 2o 25 an 35 Temperature CEISius December 1990 5 10 15 20 25 30 35 I l El Nino Temperature Salami December 1997 51015 20 25 30 35 x

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