Atmospheric Effects on Remotely Sensed Data from Space

ATMOSPHERIC EFFECTS ON REMOTELY SENSED DATA FROM SPACE Sueo Veno and Sonoyo Mukai Kanazawa Institute of Technology, P. O. Kanazawa-South, Japan 921

ABSTRACT The systematic variations a ssociated with the target - background discrimination in a satel lite sen sor are caused by atmospheric effects . In other words, the apparent radi ance of surface features wnich an orbiting spacecraft measures differs from the intri nsic surface radiance of the object , because of the presence of intervening Earth ' s atmo sphere bounded by a reflectin ~ bottom . The n , an a llowance of radiometric correction due to atmospheric effects can improve the accuracy of pattern recognition and image interpretation in remote sensing_ To what extent the atomosphere affects the radiation emanat ing from the surface objects should be evaluated. In the present paper, based on the radi ative transfer model, from the analytical aspects we show how to validate the atmosphe ric model and to compute the path l'adiance, transmit t ed radiance and contrast transmi tt ance expressed in terms of the scattering and transmission functions of the free atmo s phere . IN'l'RODUCTION In recent years, with the advent of LAiElGA7' Skylab , and other advanced Earth mon.itc)j'i· 'i" spacecrafts, it bec~ne increasingly important to eval uate the extent of the atmospheric effects on the remotely sensed data because the presence of Earth ' s atmosphere diminishes the ability of target - background discrimination in remote sensing . To insure the usefulness of glogal monitorinG, it is therefore necessary to determine the atmospheric effects due to scattering, absorption and reflection on the radiation emanating from the Earth- atmosphere system . In section 2 , the theory of radiative trans fer in the terrestrial atmosphere is presented, and the scattering and transmission fun ctions are formulated, a llowing for (Ref . 1 , 2,3 , 4 , 5 , 6 , 7)the optical inhomogene i ty , and the diffuse reflector at the bottom(Ref. 4 , 8 , 9 , 10 , ) . Such an initial - value solution permi ts us to determine numerical values with the aid of high- speed digital computer . Then, the required total radiance , path radiance and transmitted radiance are determined in specified channels. Furthermore , it is shown how to compute analytically the contrast

transmittance and the averar:e background albedo expressed in terms of ~uch [ lobal functions as the scatterinr: ~nd transmission functions . In section ::1 , b;].ft:d !)n l: }: e i..'!.t: l(':; l ·'~. t::l · ic .L~l'~el consisting of a compos i te laye r , the atmoop heric scattering effects on radiances are evaluated, allol"ing for the Rayleif,h molecular scattering and the continental and mari time types of aerosols . furthermore , the ve rification of such an atmo:;plleric model is elucidat ed with the aid of t.he contrast tran mittance and the equivalent diffuse reflect ance of tar get materials . ThE RADIATJ. VE TRA;JSFER ,';!ODEL

~~athema tic al

Formulation

The scattering effect on the radiation fiel d in hazy atmosphe res is evaluated by solving the equation of radiative transfer with the boundary condition s . Suppose that parallel rays of a net flux TIF per unit area normal to the direction of propa 0 a tion fall in th e direction - ~o on the top of a plane - parallel , inhomogeneous, anisotropically s cattering atmosphere of otical thic kn ess X, whose flat bottom surface r eflects the raiiation in ac cordance with the g iven bidirectional reflec tance . Let the intensity of un~(llin~ radiation at lev el t (O~tC) in th e ,1irection + ~ be denot erl by I(t , +rl), ctncl si,nilarly , let the inten sity of downwellin c ,ad iation a t level t in the direction - Q be denoted by I (t ,-rl ), In the above + ~ stands for ( + v , ~ ) , where v(O'v,l) represents the cosine of the polar angle measured from the upwards normal at the top and ~(0'~'2TI) is the azimuth re ferred to a suitably chosen ho r i zontal axis . Furthermore , let the normalized ph~se func tion be denoted by P(t ;~,12 ' )drl.'/:;IT, which repre s ents the probability of scatterin g ra diation from the direction ~' into the direction ~ within a solid angle d~' . I t is ass umed that P- function is an arbitrary [i v e n function of optical level t in the case of pure scattering . The equation of transfer appropriate to the present case takes the form vI~·

(t , ~ ) + I =f F(t 2'[

423

; )l , )) ' ) I

( t , ~, ) drl ' /4 TI , (1)

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S . Vena and S. Mukai

where the subscript t represent s differenti at ion with respect t o t , dS"l ' '-'dv' d ', and the optical height i s defined by t

= Jga(z)dz .

shown that the S- function satisfies an integro-differential equation as bel ow(Ref .lO ):

(2)

In Eqs . (2) a(z) is the volume extinction coefficient at geometrical a lt itude z . Eq.(l) should be solved subject to the boundary conditions

+J p(x ; S"l , S"l ' )S(x;S"l'S"l0 , A)dS"l ' /4Trv ' 2"TT

+J (3)

I(x, - S"l)

2"TT

-

-

J S(x ; S"l , S"l ' , A)p(x ;-n ' , nil) 2"

~

-

(8) (4)

where 0(S"l-S"l0) = o(v -u ) 0(4) - 4>0 ) , and k(S"l , S"l ' ) is the bidirectional reflectance r epresenting the probability that a photon incident on the bottom in the direction - S"l' uill be reflected into the dire ction +S"l within an unit solid angle. In the case of a diffuse reflector it becomes A(v ' )v/Tr , whereas A(v ' ) r educes to a constant A for a perfect diffuse reflector ,i. e . for a Lambert 's law refl ector. On the other hand ,in the case of a specular r eflector it is given by k(S"l , S"l ' )

A(v ' ) o(v - v') 0(4)' - 4> +Tr ) . (6)

In the real case , the bidirectional reflect·· ance may be considered to be a hybrid of both albedos . In Eqs.(5) and (6) A- function is ca lled an albedo of the reflecting surface , designating the ratio of the total ene~gy reflected by the surface to the incident energy of skylight and attenuated direct sunlight . The Sc attering and Transmission Functions I t is diffic ult to solve ri gorously the twopoint boundary value problem given by Eq . (l) with Eqs. (3) and (4). Then , in "hat follow s , we present the initial value solution by an inval'iant imbedding method (Ref.l , 2 , 3 , 4 , 5 , 6 , 7) .

The i ntensity of radiation diffusely reflect ed by the atmosphere bounded by a d if fuse reflector is expressed in terms of the scat tering function

together with the initial condition 4A(u)vu. JII or(:.or to discuss explicitly theal b~c1o co efficient A of the diffuse reflector , we need the scattering and transmission functions of a fr ee atmosphere as below: For monodirect ional illumination of the top the scatteri ng function s(~;n , S"l ) is governed by Eq . (8) , whose S(~ ;S"l, S"lo , A~ is replaced by S (~;S"l , S"lo) ' tocether with the initial condition

o

(10)

Furthermore , an initial - value solution of the transmi s sin function T(X;S"l , S"lo) fulfills an integro- differential equation exp( - ~/v)

xp(x.; - n ' ,-S"l0)dn ' /4Trv ' +J2"TT J211 T(x;S"l ,n ' ) _. xp(~; - S"l ' , n")s(~;S"l" , S"lo)dS"l 1 tJ.S"l "/(1 611 2V'V") (ll)

Eq. (11) should be solved subject to the ini tial condition

o

(12)

The scattering and transm i ssion functions satisfy the principle of reciprocity . These relations take the form wher e S-function represents the scattering function for the bounded atmosphere . It i s

Atmospheric effects on remotely sensed data from space

425

(13) + J T(x;rl ' ,rlo )drl ' /4TI . 2TI -

(18)

(14) where T*(~;n,no) is the transmission function for monodirectional illumination of the bott om from below . A system of the scattering and transmission functions for imhomogeneous atMospheres stems from the polarity of multiple scattering processes . It is of interest to mention that the order- of-scattering theory (Ref. 11) and adding procedure (Ref . 12,13,14) are usable for the numerical solution of Eqs. (8) and (11) . Some of such numerical resul ts are used for eval uation of atmospheric effects on the classification of remotely sensed Earth imageries (Ref.15) .

Since the target is assumed to be small,Eq . (17) will provide a good approximation to the val ue of radiance reflected f r om the object space surrounding the target. Then, the interaction term G(~;n,rlo , A) is given by (19) where

+J T*(x;rl,rl')drl'/(4TIv)], 2TI

Radiance In recent years, based on the radiative transfer model, atmospheric effects on multispectral scanner data have approximately been evaluated by several author s (Ref.16,17,18, 19,20) making use of the observed value of radiance, albedo and contrast . Furthermore, an allowance for the polarization has also been made by several authors (Ref . 21 . 22 , 23 , 24,12,25,26,14). The total spectral radiance I(~, + n) consists of two compon ents ,i,e, the path radiance FS(A;n,n o )/4v and transmitted radianc e G(~ ;n, no , A) as below:

-

Assuming that the target mater i al and background are together diffuse reflectors, the albedo A takes the form

(2l)

(15) where G- function repre sents the inten s ity of raQiation directly and diffusely tran smitted from the bottom. Then , G-function is expressed in terms of the sc attering and transmi ssion functions of a free atmosphere and al bedo A G(~;rl,rlo,A)

= I(O, +rl)exp( - ?S/v)

+/ T*(~;n,n')I(0,+n ' )drl ' /(4TIv), 2TI

(16)

where I(O, +n) is called the intrinsic radiance. On the right-hand side of Eq.(16) the first term represents the int",nsity of radi ·· ation directly transmitted from the bottom, and the second term denotes the intensity of radiation diffusely transmitted from the bottom. In a manner similar to that given by Chandrasekhar (cf . Ref.l) the first approxi mation of I(O, +rl) is expressed in the form I(O, +rl)

where S(x ; rl,rlo,A), S(x;rl,rl o ), and f- function are give~ by Eqs . (8),T9),(10) and (20), res pectively . Eq.(21) shows that, once the opti cal thickness of the free atmosplJere has been validated, the albedo is expressed in terms of the scattering function of the bounded atmosphere, and the scattering and transmi -· ssion funct ions of the free atmosphere . The equation is useful for evaluation of the al bedo for the specified target mater ial, whereas the atmo spheric effects due to the background surrounding the target on the total radiance is not included, because of the onc ·-d imensionaJ. treatment. In this context mult idimensional procedure should be referred (Ref . 27 ,28 , 29). Apparent Contra st The contrast of radiance between a target material and its background at level t is usually defined to be:

(17) (22 )

where exp( - ~/u)u

IFAC S.E.S.-·O·

(20)

When the target is assumed horizontall y and

426

S. Ueno a nd S. Mukai

vertically to be small compared with the bac):ground , the apparent contrast C(~ ; rI , rlo) is expressed in terms of the contrast t r ansmit tance i\ ~; rI , rlo) and the intrinsic surface contrast C(O ; rI , rl o ) as below: (23) ·\·7hereas the target material may not inherent l y be diffuse , for simplicity we assume that the target and background are together per fect diffuse reflectors . Then , in the first approximation the contrast transmittance Y takes the form

where S- and f - function s are given by E~s . (8), (10) , and (20) . Furthermore , denoting the albedo of the target and background by It and Ib respectively, the intrinsic surface contrast is expr essed in the form (25 )

It is or interest to mention that in Eq . (24) Y- function depends on the wave- length , the optical thi~knes s , the direction of incidence and reflection , and the diffuse background albedo, being concerned with no target charac teristics , bec~use of the first approximation . Calculation of Y- function can be made by us ing quantities g enerated with ou; radiative transfer model for a variety of atmospheric and observational conditions , whereas atmos pheric state depends on the visual range(Ref . 30) . ATMOSPHERIC EFFECTS ON RADIANCE Atmosphe ric t··l odel Terre st rial a t mosphe re consists of semipermanent gas es such as nitrogen, oxygen and ar gon in addition to highly va riable components such as o zone , water vapor , and particulates . The aerosol in atmosphe res consists of man made .:1r.1

~1 :~7/l.l l·~f l

!1:-'rt ir:J

~~ .

r~C~I C

.nsn: - :!:f,.'ie co -

n'·r i b·.lt :!J" ; is added to the natural back-· gr ound( i.e. , water droplets , forest f ires a nd volcanic dust , smoke particle s , sea spray , and fumes) that is gen erally considered to be responsible for determination of c limatic chang es . However , from the extreme value of man- made part i culates(Ref . 20) , it is shown that on a gl obal scale most of the particu·· lates are of nat l~ral orig in , whereas on a local scale the man - made contribution due to th~ i:l ,~u.;~.ri8.1 activiti ,,:s , increased culti vc'.-· tion of land and others far exceeds the natu-

ral ones . For the purpose of remote sensing in the v isible region , we require little information on the atmospheric content of gases such as water vapour , ozone and carbon dio-· xide , because of their negli gible contribution due to absorptio n. Thus , in our model the multiple scattering processes are consi dered to be a primary attenuating agent . To evaluate the atmospher ic scattering e ffect on the remotel y sensed data , we need a simplif ied model which cove rs a wide range of atmospheric and surface conditions with a mi nimized computat ional effort. The model under consideration consists of double layers , each of which is a hybrid of the Rayl e i gh scattering and hazy atmospheres . Whe r eas the aerosol in uppe r layer is stratospheric type , in lower layer bounded by a diffuse r eflector the aerosol is of maritime type , because of the local geographic surround ings under cons ideration . This may be considered a valid approx i mation . Whereas the tropospheric aerosols are hi ghly variable in nature , the well - known scattering properies of Raylei gh atmosphere do not vary apprec illbl:r . In general, a haze mod.el con"j.3ts of stratospheric and mariti me type hazes (Ref . buti on and index of refraction . It permits us to compute the scattering properties of ha-.e by the Mie theory . Our model used in evaluation was desi gned to represent a hybrid of continental and maritime type hazes (Ref . 31) . Furthermore , we uti liz e such an optical depth- height - wave- length relationsh i p as determined by Elterman(Re . 32) for several vist
model validation

In this section the procedure used to verify the atmosphe r ic model is discussed . The radiative transfer model was formulated for computing scattering effe cts on the spacec raft scanner data. In Eq . (21) path radiance , transmittance term f - function , and the toal optical th ickne ss for the Raylei gh and aerosol atmospheric model , whereas the total spect r a l radiance is obtained from a calibrated sens ing dev ice aboard the s8.t ellite , i . e . , the co unt rate l'1 ul tiplied by the radiance for bit

Atmospheric effec t s on remotely sensed data from space of count rate in the considered channel. Then, Eq.(21) permits us to evaluate the albedo A whose value should be compared with the observed ones in the specifed test - site . In such a way the equivalent diffuse reflectances of the target material and background are determined . If the target is not inherently perfect diffuse, then tl,e albedo A of the target material will ge nerally change with the angles of incidence and reflection. Such validation procedure requires a rather appreciable amount of information to be di rectly available,i.e., the multispectral data, ground truth and environmental data . In our case the average background spectral albedo is the average hemi-spherical spectral reflectance of the terrain surrounding the object under consideration, estimated from the ground truth information . Alternatively , Eq . (23) is also available for verification since the computational value of contrast tramsmittamce can be compared with the ratio of the intrinsic surface contrast to the apparent contrast. This can be estimated from the remotly sen sed data and ground truth in formation . CONCLUSIONS In the present paper we have shown that an initial - value solution of the transfer equation is useful for the evaluation of scatter ing effects on the spacecraft scanner data, assuming a plane- parallel, inhomogeneous, anisotropically scattering atmosphere bounded by a diffuse reflector. Absorption effect by molecular gases and aero sols will be taken into account afterwards . Some of numerical results according to the present scheme in adding procedure has been applied to the digital processing of multi spectral scanner data (Ref.15). Furthermore, the variety of numerical examples on radiance, contrast transmittance, and others will be discussed subsequently. It is recognized that an influence of background albedo on target radiance affects seriously digital processing of remote ly sensed data. Particularly , in the case of hiGh reflectance of the background surrounding the target of l ow albedo the change in spectral radianc e from the case to the case with the low albedo of background material will be quite appreciable. In other ,"ol'ds this effect will give rise to noticeable classification inaccuracies. '.-Ihereas in our preceding paper (Ref . 27 ,28) an initial value solution of multidimensional transfer equation,i.e. an integro- differential equation of the scattering and transmission function, has been fully discussed, for simplicity in the present paper we have not discussed the effect of nonuniform reflectance of the background cn the target radiance. In our subsequent paper we shall treat with the change in atmospheric effects due to changes in elevation and an rough surface . Furthermore, the effects of horizontal and vertical distribution of clouds will be taken into account, allowing for the shadow ef~ect . With these refinements stated above, a considerable im-

provement will result in the ability of r get - background discrimination .

427 ta~

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