The Nature of Optical Remote Sensing Coefficient

Transcription

1 The Nature of Optical Remote ensing Coefficient Vlaimir I. Haltrin* Naval Research Laboratory, Ocean Optics ection, Coe 7333, tennis pace Center, M , UA ABTRACT The remote sensing coefficient or raiance reflection coefficient is a principal prouct of atmospheric correction algorithms applie to the remotely measure optical images of the ocean. This coefficient contains information about angular structure of light raiance, roughness of the ocean surface, an optical properties of the ater. This presentation analyses remote sensing coefficient an presents it as a prouct of three physically ifferent values or factors. The first factor epens on geometrical parameters of illumination an atmospheric optical properties, the secon factor epens on roughness of the ocean surface, an the thir one epens on the optical properties of seaater. The approach use to erive the thir in-ater factor is vali for all levels of ater turbiity from the clearest open aters to the most turbi aters of river mouths an extremely scattering aters of Yello ea type. Keyors: seaater, light, reflection, remote sensing coefficient, brightness coefficient, raiance coefficient.. INTROUCTION This paper is evote to erive remote sensing coefficient (RC) or raiance reflection coefficient is a principal prouct of atmospheric correction algorithms applie to the remotely measure optical images of the ocean. The RC contains information about angular structure of light raiance, roughness of the ocean surface, an optical properties of the ater. This presentation analyses RC an presents it as a prouct of three physically ifferent values or coefficients. The first coefficient epens on geometrical parameters of illumination an atmospheric optical properties, the secon coefficient epens on roughness of the ocean surface, an the thir coefficient epens on the optical properties of seaater. The approach use to erive the thir in-ater coefficient is vali for all levels of ater turbiity from the clearest open aters to the most turbi aters of river mouths an extremely scattering aters of Yello ea type. It is shon that presente structure of RC allos to increase precision of retrieving seaater optical properties from remotely measure optical images of the ocean.. REMOTE ENING COEFFICIENT By efinition remote sensing coefficient (RC) of the sea or ocean, or brightness/raiance coefficient of the sea or ocean (as it is efine in European literature), is a ratio of upar raiance L + u to onar irraiance E + of light just above the ater surface, rrs L + u E +. () * vihaltrin@nrlssc.navy.mil; Telephone: ; Fax: Remote ensing an Moeling of Ecosystems for ustainability, eite by Wei Gao, avi R. ha, Proceeings of PIE Vol (PIE, Bellingham, WA, 4) X/4/$5 oi: -.7/.55838

2 Equation () coul be reritten as r rs + + L L E L T T u u u + + T T ρθ ( ) ρθ ( ), () E L E E n u here L u is upar raiance just belo the ater surface, E is upar irraiance just belo the sea surface, + T Lu Lu T n is a transmittance of iffuse light ascening from the ater by the avy surface, T is a + transmittance of atmospheric iffuse light by the avy surface, n is the ater inex of refraction, T E E is a transmittance of total atmospheric light by avy sea surface, an ρθ ( ) L E u is raiance coefficient of ater boy of finite epth, an θ is a zenith angle. Here superscripts (+) an (-) enote, respectively, values above an belo the ater surface. The total transmittance of ater surface can be expresse as follos, [ ] T f T + ( f) ( q ) T + q T, (3) f a a here f is a portion of the ater surface covere by foam, T f A is a foam transmittance, A f is a foam albeo, q a is a portion of onar irraiance in atmosphere just above the ater surface that is ue to a irect solar light, T R F is a transmittance of irect solar light by the sea surface free of foam, an R F is a Fresnel reflection coefficient of irect solar light by avy ater surface uncovere by foam. The total raiance (or brightness) coefficient of ater boy ρθ ( ) is connecte ith the total iffuse reflection coefficient R E E by the folloing relationship [], u f R π ρ( θ)cosθsin θθ, R. (4) For Lambertian reflector, ρθ ( ) ρconst an R πρ. The total raiance coefficient ρθ ( ) can be split into to parts, the raiance coefficient for iffuse light ρ, an raiance coefficient for irect solar light ρ, ρθ ( ) ( q ) ρ ( θ) + q ρ ( θ), (5) here q is a portion of onar irraiance in ater just belo the ater surface [-3]. The value q E ( E + E ) can be expresse through the similar value q a as follos. The onar iffuse an irect irraiance just belo the ater surface are, E f A E a E a f f E a ( )( + ) + ( ) T, E f E a T ( ), (6) consequently, q T ( f) T q a. (7) By combining Eqs. (), (5) an (7) e have, Proc. of PIE Vol

3 r rs T T ρ qa( f) T ρ ρ ( θ) n { [ ]} T f ( Af) + ( f) [( qa) T + qa T η( θ) ] R, π n { } (8) here e assume that ρ R π an enote η( θ) ρ( θ) ρ an inherent optical properties of seaater The iffuse transmittance T over zenith angle θ ith the eight proportional to the sky raiance:. The value η is epenent on a zenith angle θ. is a transmittance of irect light T average T T θ, (9) so, Eq. (8) can be reritten as follos: r rs T θ f ( Af) + ( f) ( qa) T + qa T η( θ) R, () π n θ { [ ]} here R is a iffuse reflection coefficient of the ater boy illuminate by iffuse light. Accoring to [, 3] solar to sky light ratio parameter q a is only a function of atmospheric parameters, q a Baτ a a s + e τ µ, () µ s here τ a is a total atmospheric optical thickness, B a is a probability of backscattering of light in atmosphere, an cos Z, ith Z as a solar zenith angle. The foam fraction f is a function of a in spee. Accoring to [] it µ s is expresse through the in spee u as follos: f 5 3, 3. u, u 9m / sec, 5 3, 3. u (. u. 99), u> 9m / sec. () The transmittance of irect light by avy sea surface is expresse through the Fresnel reflection coefficient R F of a flat surface an in spee as follos [4]: { [ ]} T ( Z, u ) a ( u ) R ( F Z ) a ( u ) + R ( F Z ) a ( u ) + a ( u ) R ( F Z ) 3, u < m / sec, (3) here R F cosz n sin Z ( Z) cosz + n sin Z n cosz n sin Z + n cosz + n sin Z, (4) is a Fresnel reflection coefficient of irecte light from clear ater, an coefficients a ( i i,... 3 ) are given by the folloing equations: a( u).( u u ), (5) 366 Proc. of PIE Vol. 5544

4 a( u) u-.77 u, (6) 3 a ( u) u-.398 u u, (7) 3 a ( u) u u. 76 u. (8) 3 The equation for transmittance of iffuse light by avy sea surface accoring to Eqs. (9) an (3) is, T ( u) T a( u) R a( u) + R a( u) + a3 ( u) R, u < m / sec, (9) θ { [ ]} F F F here π / π / RF RF( θ) F( θ) θ, F( θ) θ, () here F( θ ) is a normalize raiance istribution of the sky (ithout incluing the irect sunlight). For Lambertian sky F( θ) π e have the folloing equation for iffuse transmittance: T ( u) ( u)( u+ u ), u < m / sec. (a) For overcast sky F( θ) ( + cos θ) ( 4 + π) (carioi istribution) e have a ifferent equation for iffuse transmittance: T ( u) ( u)( u+ u ), u < m / sec. (b) The ifference beteen values of transmittance given by Eq. (a) an (.b) is about %. The average of transmittance values given by both equations is about T ( u) 9.. The more elaborate proceure to average Fresnel reflection u coefficient shoul inclue an actual raiance istribution of the sky hich is epenent on atmospheric optical properties. 3. NONLINEARITY OF APPARENT OPTICAL PROPERTIE IN REPECT TO GORON PARAMETER Remote sensing coefficient, as e sho belo, is proportional to iffuse reflection coefficient. Both these values are apparent optical properties, that is they are epenent not only on inherent optical properties, but also on conitions of illumination an geometrical an optical structure of the surface an bottom of the sea. iffuse reflection coefficient (RC) of ater boy is an informative part of remote sensing reflectance [5] of light by the ocean. RC contains information on content of issolve an suspene substances in seaater. RC is an apparent optical property that epens not only on inherent optical properties of the seaater, but also on the parameters of illumination. The epenence on inherent optical properties is expresse through the epenence on Goron s parameter, i.e. the ratio of backscattering coefficient b B to the sum of absorption a an backscattering coefficient, g bb /( a+ bb). In the open ocean RC is linearly proportional to g. This linear equation is very goo for the Type I open ocean aters [6]. It is also acceptable for about 9% of coastal aters. Theoretical an numerical analysis sho that the linear relationship can be aequately use only hen Goron s parameter g is relatively small, i.e. g <.. This criterion is alays satisfie in open ocean aters. The available atabase of experimental measurements Proc. of PIE Vol

5 Figure. istribution of occurrences of measure Goron s Figure. epenence of iffuse reflectance coefficient parameter in Yello ea in [7]. errors on Goron s parameteter [7]. sho that in coastal aters Goron s parameter may excee this critical value of.. In some very turbi coastal aters it can even reach values higher than.95. For example, in aters of Yello ea or coastal aters close to river estuaries the percentage of cases hen g >. can reach 5% or more. Until recently e ha no significant cases of in situ measurements that sho existence of sea aters ith high cases of Goron s parameter g exceeing.. Relatively recent measurements mae in by NRL researches ith collaboration of Korean scientists in Yello ea shos that these highly scattering aters exhibit these characteristics [7]. Figure shos a histogram of the frequency of measurements of Goron s parameter in this expeition. In this case more than 5% of measurements correspon to Goron s parameter exceeing critical limit of linear approach. It means that processing of such ata shoul involve nonlinear equations connecting RC ith g. For that reason e ill use a self-consistent raiative transfer approach that takes into account non-linearity of inherent optical properties on Goron s parameter [8-]. 4. RAIANCE REFLECTANCE RATIO AN IFFUE REFLECTANCE OF WATER Accoring to the theory of Ref. [8-] e can rite the raiance reflectance ratio as: here ρ ( θ) κ η( θ) ρ + κcosθ κ ln( κ) ( )[ + ], () µ ( 3 µ ) κ, µ + µ g + g+ g( 4 + 5g), g bb, (3) a + b B a is an absorption coefficient of ater, b B is a backscattering coefficient of light by ater, g is a Goron s parameter, an µ has physical meaning of average cosine of iffuse light insie ater, an θ is a zenith angle measure insie ater boy. If e ant to express Eq. () through a zenith angle ϑ outsie ater, e shoul use the nellius la, 368 Proc. of PIE Vol. 5544

6 Figure 3. epenence of parameter η on vieing angle for ifferent values of Goron s parameter. Figure 4. epenence of parameter η on Goron s parameteter for ifferent vieing angles. sinϑ n sinθ, hich results in substitution in Eq. (): cosθ sin ϑ n. Function η ( θ ) is normalize as follos: π / η ( θ )cos θ sin θ θ. (4) The epenence of factor η on vieing angle an Goron s parameter is shon in Fig. 3 an 4. The iffuse reflectance of shallo sea of arbitrary turbiity an absorption is represente by the folloing equation [8]: R R A R A R e ν zb ( b ) + ( b ) ν z, (5) b ( AR) + ( A R ) Re b b here µ R + µ, R + µ R, ν µ ( a+ b ) µ B, (6) A b is an albeo of a bottom, an z b is a bottom epth, an R is a iffuse reflectance of optically eep sea illuminate by iffuse light. Equations () an (5) take into account multiple scattering of light insie ater an multiple reflection of light from the bottom. It is vali for arbitrary epths ( z b ), arbitrary bottom albeo A b, an arbitrary inherent optical properties of ater, a, an b B. Proc. of PIE Vol

7 5. CONCLUION The result of this paper is an equation that expresses remote sensing reflection coefficient as a function of telve parameters: r ( B, τ, u, A, Z, n, ϑ, ab,, z, A, λ) rs a a f B b b { T ( u) f( u)[ Af( λ)] + [ f( u)][{ qa( Ba, τa)} T ( u) + π n + qa( Ba, τa) T ( Z, u) η( ab, B, ϑ)] } Rab (, B, zb, Ab), (7) here B a is a light backscattering probability in atmosphere, π B p (cos θ)sin θθ p (cos θ)sinθθ a a a π / π (8) (here p a is an atmospheric light scattering phase function, an θ is a scattering angle), τ a is a total optical thickness of atmosphere, u is a in spee at the level of ater surface, A f is an albeo of a in generate foam or hitecaps, Z is a solar zenith angle, n is a refraction inex of ater, ϑ is a vieing zenith angle of an optical receiver, a is an absorption coefficient of light in ater, b B is a backscattering coefficient of light in seaater, z b is a ater epth, A b is a bottom albeo, an λ is a avelength of light. Equation (7) shos spectral (avelength) epenence of RC only through the foam albeo. In reality, the folloing parameters also have spectral epenence on the avelength of light: absorption an backscattering coefficients of ater, bottom albeo, backscattering probability an total optical thickness of atmosphere, an, to some extent, refraction inex of ater. These epenencies are not shon in the right sie of Eq. (7) in orer to make it less bulky. The transmittivity of iffuse light by the avy ater surface T is expresse by Eqs. (), or can be calculate from Eq. (9) using current atmospheric properties. The share of ater surface covere by foam f is compute using Eq. (). The share of irect sunlight in the total light raiance on the ater level q a is compute using Eq. (). The transmittance of irect light by the avy surface T is compute ith Eqs. (3)-(8). The ratio of irect light reflectance to the reflectance of iffuse light η is given by Eqs. ()-(3). An, finally, the iffuse reflectance coefficient of iffuse light by the shallo ater boy is given by Eqs. (5)-(6). Equation (7) is erive to be vali in the hole range of variabilities of optical properties of the ater boy an atmosphere an for arbitrary epth of the ater. It is intene to be use in algorithms of remote processing of optical ata, incluing erivation of ater optical properties, ater epth an bottom albeo. 6. ACKNOWLEGMENT The author thanks continuing support at the Naval Research Laboratory (NRL) through the program VF This article represents NRL contribution PP/733/4/. 7. REFERENCE. V. I. Haltrin, Propagation of light in sea epth. Chapter (p. -6) in the book: Remote ensing of the ea an the Influence of the Atmosphere, Mosco-Berlin-evastopol, Publication of the German emocratic Republic Acaemy of ciences Institute for pace Research, 985 (in Russian). 37 Proc. of PIE Vol. 5544

8 . V. I. Haltrin, an V. A. Urenko cattering of light in the atmosphere an remote sensing of the optical characteristics of seaater. Chapter 3 (p. 63-9) in the book: Remote ensing of the ea an the Influence of the Atmosphere, Mosco-Berlin-evastopol, Publication of the German emocratic Republic Acaemy of ciences Institute for pace Research, 985 (in Russian). 3. V. I. Haltrin, Algorithm for Atmospheric Correction of Airborne AVIRI Ocean Images, in Propagation an Imaging through the Atmosphere II, Proceeings of PIE, Vol. 3433, Luc R. Bissonette, e., (PIE, Bellingham, WA, UA, 998), pp V. I. Haltrin, W. E. McBrie III, an R. A. Arnone, pectral Approach to Calculate pecular Reflection of Light from Wavy Water urface, - pp in Proceeings of.. Rozhestvensky Optical ociety: International Conference Current Problems in Optics of Natural Waters (ONW ), t. Petersburg, Russia,. 5. J. V. R. Zanevel, A theoretical erivation of the epenence of the remotely sense reflectance of the ocean on the inherent optical properties, J. Geophys. Res.,, 3,35-3,4 (995). 6. A. Morel, L. Prieur, Analysis of variations in ocean color, Limnol. Oceanogr.,, 79-7 (977). 7. V. I. Haltrin, an. C. Gallegos, About nonlinear epenence of remote sensing an iffuse reflection coefficients on Goron's parameter, pp in Proceeings of the II International Conference Current Problems in Optics of Natural Waters, ONW 3, Es. Iosif Levin an Gary Gilbert, t. Petersburg, Russia, 38 pp, 3 8. V. I. Haltrin, elf-consistent approach to the solution of the light transfer problem for irraiances in marine aters ith arbitrary turbiity, epth an surface illumination, Appl. Optics, 37, (998). 9. V. I. Haltrin, iffuse Reflectance of the Optically eep ea Uner Combine Illumination of Its urface, in IGAR 97: Proceeing of the 997 International Geoscience an Remote ensing ymposium, Vol. I, (IEEE, ingapore 997), pp V. I. Haltrin, Apparent optical properties of the sea illuminate by un an sky: case of the optically eep sea, Appl. Optics, 37, , (998).. V. I. Haltrin, Monte Carlo Moeling of Light Fiel Parameters in Ocean ith Petzol Las of cattering. in: Proceeings of the Fourth International Conference Remote ensing for Marine an Coastal Environments: Technology an Applications, Vol. I, Publication by Environmental Research Institute of Michigan (ERIM), Ann Arbor, Michigan, UA, pp. 5-58, 997. The reference articles (except, 3, 5, an 6) can be viee an onloae in a PF format from the folloing eb site: < Proc. of PIE Vol