AN ALGORITHM TO ESTIMATE CONCENTRATIONS OF SUSPENDED PARTICLES IN SEAWATER FROM SATELLITE OPTICAL IMAGES

Transcription

1 Poceedings of the II Intenational Confeence Cuent Poblems in Otics of Natual Wates, ONW 003, Eds. Iosif Lein and Gay Gilbet, St. Petesbug, Russia, 003, 38. AN ALGORITHM TO ESTIMATE CONCENTRATIONS OF SUSPENDED PARTICLES IN SEAWATER FROM SATELLITE OPTICAL IMAGES V. I. Haltin, and R. A. Anone Naal Reseach Laboatoy, Ocean Sciences Banch, Code 7330, Stennis Sace Cente, MS , USA web age: htt://haltin.feeshell.og Abstact: A new method to etiee concentations of susended oganic and inoganic aticles in seawate fom satellite images is oosed. The method uses as inut images of scatteing and backscatteing coefficients in seeal satellite channels as well as an image of concentation of chloohyll. All these thee oeties ae deied using an atmosheic coection algoithm and algoithms to deie inheent otical oeties fom emote sensing eflectance. The oosed method is based on seeal aoaches deeloed eiously by Twadowski et al., an de Hulst, and Eans and Founie and is based on Mie theoy. The oututs to this method ae images of concentations of oganic and teigenic factions of susended matte in seawate. 1. Intoduction In this ae we descibe an aoach to estimate concentations of susended scatteing aticles in seawate using sectal infomation obtained in otical channels fom a satellite. Modeling esults by aious authos (Foand and Founie [1], Twadowski and othes[]) show that sectal deendence of aticula scatteing and extinction (attenuation) coefficients ae closely connected with the shae of aticle size distibution in seawate. In the fist aoximation the shae of size distibution may be eesented in the fom of Junge distibution. The sectal shae of scatteing o aticula extinction (o scatteing) coefficient allows us to obtain a Junge aamete which is a key to comute an effectie efactie index of seawate with susended scatteing aticles. The alue of effectie efactie index allows us to estimate shaes of oganic and teigenic factions of scattees. The total concentation of scatteing matte is estimated though the total scatteing coefficient and a scatteing efficiency by abitay size aticle aeaged oe estoed size distibution (Eans and Founie, [3] an de Hulst [4]). The actual ealization of the aoach is imlemented as a FORTRAN code and tested with an otical satellite data of sea wate eflection in the Gulf of Mexico (Mississii Bight aea). The inuts to the oosed algoithm ae images of aticle extinction c, scatteing b and og backscatteing b B coefficients, and oututs ae images of concentations of oganic C and te teigenic C factions of susended matte. The inut images ae obtained fom the images of emote sensing eflectance s in seeal bands of a satellite otical senso. We used algoithms of K. L. Cade [5] and R. A. Anone [6] to obtain alues of extinction, scatteing and backscatteing coefficients fom the alues of emote sensing eflectance. The sectal emote sensing eflectance [7] was obtained fom the sectal alues of adiances of the ocean-atmoshee system using an atmosheic coection algoithm deeloed by Howad R. Godon [8]. 71

2 Poceedings of the II Intenational Confeence Cuent Poblems in Otics of Natual Wates, ONW 003, Eds. Iosif Lein and Gay Gilbet, St. Petesbug, Russia, 003, 38.. Deiation of effectie efactie index of wate with scattees The fist ste in the algoithm is to obtain the sloe γ in the sectal deendency of aticula extinction coefficient c ~ λ γ using a linea inteolation method in a log-log scale. The next ste is to estoe main oeties of size distibution of aticles susended in seawate. While ealistic aticle size distibutions N ()(whee is a aticle adius) ae quite unique and only in ey ae cases may be descibed by some theoetical kind of size distibution, they ae in geneal, if lotted on a log-log scale: i. e. log N ( ) esus log( ), exhibit a linea behaio. It means, that in the fist aoximation they can be descibed as a Junge (hyebolic) distibution, N ()~ ν, with ositie alue of aamete ν. The extensie study of inheent otical oeties of seawate with scattees distibuted accoding to Junge law was accomlished by Twadowski et. al. []. Among othe esults these authos obtain emiical elationshi between sloe of aticula extinction coefficient and Junge aamete, as well as elationshi that connects effectie efactie index of seawate n w with Junge aamete ν and backscatteing b b coefficient. Accoding to Twadowski et al. [] the elationshi between aticula extinction sloe γ and Junge aamete ν is linea: c ( λ) = A cλ γ, ν = γ +3, = µ m, = 76µ m, (1) hee min and max ae minimum and maximum adii in aticles size distibution. The simila esult was obtained ealie by Foand and Founie [1] who imlied a Junge distibutions of scattees with infinite limits. They obtained the simila esult fo the case of aticula scatteing coefficient: b min ( λ) = A λ γ, ν = γ + 3, = 0, =. () b We tested both egessions (1) and () and found that egession (1) oduces moe eliable esults. The effectie efactie index of susended aticles is connected with backscatteing obability by aticulate matte B = bb / b, whee b b is a aticula backscatteing coefficient, by the following egession [] obtained fom esults of modeling using Mie theoy: γ n ( B, γ) = 1+ B γ γ min max max [ ]. (3) So, the equations (1) and (3) allow us to estoe the aamete of the size distibution ν and effectie efactie index of scattees. 3. Estimation of concentation of oganic and teigenic factions of scattees The total concentation of aticula matte C could be found fom the following elationshis: C = C ρ, C = N V, (4) tot 7

3 Poceedings of the II Intenational Confeence Cuent Poblems in Otics of Natual Wates, ONW 003, Eds. Iosif Lein and Gay Gilbet, St. Petesbug, Russia, 003, 38. hee C is a olume concentation of aticula matte, ρ is a mass density of aticles, N tot is a total numbe of aticles e unit olume, V is an aeage olume of one scatteing aticle which can be obtained using the following equation: V 4 max 3 max = π f() d, f d 3 () = 1, (5) min min hee f() is a nomalized size distibution of aticles. Taking into account that total numbe of scatteing aticles can be exessed though the aticula scatteing coefficient [4], Ntot = b max π Qsc nw x f d (, ) ( ), (6) min whee Q sc is a scatteing efficiency. We can ewite Eqs. (4)-(6) as follows: C = 4 b S 3 S q max 3 max, S = f() d, Sq = f() Qsc() d. (7) min Integals S and S q also may be used to obtain a secific scatteing coefficient of aticula matte: b S 0 3 q b = =. (8) C 4 ρ S The scatteing efficiency Q sc of aticles susended in seawate deends on effectie efactie index n w of seawate and size aamete, x = π λ, whee λ is a waelength of light in acuum. The alue Q sc can be comuted numeically using Mie theoy [4]. This aoach while haing sueio accuacy is not good fo ou uoses due to its slowness. Fo that eason we hae chosen to use an analytic exession fo Q sc oosed by Eans and Founie [3]: min hee QR Qsc( nw, x) = µ 1/ µ, (9) 1 Q QT 8 QR( nw, x)= x 3 [ + ( R ) ] 4 n n w w 1 +, (10) Q( nw, x) = sin cos 1 ρ ρ, ρ ρ ρ = x( n w 1), (11) / T( x) = ex( x 3 ), (1) 73

4 Poceedings of the II Intenational Confeence Cuent Poblems in Otics of Natual Wates, ONW 003, Eds. Iosif Lein and Gay Gilbet, St. Petesbug, Russia, 003, / 4 µ( nw, x) = + ( nw 1) + ( nw 1) + ( nw ) + ( nw ) x (13) Equations (9)-(13) gie us a ey good aoximation to scatteing efficiency, esecially when used late fo monodisesed scattees. The testing of algoithm to estoe concentations of scattees based on Eqs. (4)-(13) oes that it is stable and eliable. The next final touch to ou algoithm is to seaate oganic and inoganic comonents of susended matte. The final ste in this algoithm is to seaate oganic and teigenic factions of susended matte. The simlest aoach is to assume that scatteing aticles consist of two factions, oganic and teigenic, with diffeent efactie indices and the same size distibutions. In this case an effectie efactie index of susended aticles is detemined by og og og te n = α n + ( 1 α ) n. (14) hee α og is a shae of oganic matte in susended scatteing faction. Consequently, α og = n n te te n n og. (15) And, coesondingly, the concentations of oganic and inoganic factions of susended matte ae: C te og te = α ρ C, C = ( 1 α ) ρ C. (16) og og og Accoding to Refs. [, 9, 10] elatie efactie index of oganic faction can be acceted as n og = 104. (hytolankton cells), and fo teigenic faction as n te = (quatz-like inoganic matte), and mass densities: ρ te = g / dm (o g / l), ρ og = g / dm (o g / l). Figues 1-4 show esults of samle comutation using oosed algoithm. Figues 1 and eesent 300x300 ixels SeaWIFs images of two inut aametes, emote sensing eflectance s in Band 3 (490 nm) and scatteing coefficient of aticles b the same sectal band. Figues 3 and 4 dislay outut images of the shae of oganic matte α og and concentation of teigenic at of the scattees C te geneated using oosed algoithm. 4. Conclusion We oosed hee a new method to etiee concentations of susended oganic and inoganic aticles in seawate fom satellite images. The method uses as inut alues of extinction, scatteing and backscatteing coefficients in seeal satellite channels. The oututs to this method ae concentations of oganic and teigenic factions of susended matte in seawate. 74

5 Poceedings of the II Intenational Confeence Cuent Poblems in Otics of Natual Wates, ONW 003, Eds. Iosif Lein and Gay Gilbet, St. Petesbug, Russia, 003, 38. Figue 1. Remote sensing eflectance (490 nm). Figue. Scatteing coefficient (490 nm). Figue 3. Shae of oganic matte. Figue 4. Concentation of teigenic matte. 5. Acknowledgments The authos thank continuing suot at the Naal Reseach Laboatoy (NRL) though the Volume Scatteing Functions VSF ogam. This aticle eesents NRL contibution PP

6 Poceedings of the II Intenational Confeence Cuent Poblems in Otics of Natual Wates, ONW 003, Eds. Iosif Lein and Gay Gilbet, St. Petesbug, Russia, 003, Refeences 1. J. L. Foand and G. R. Founie, Paticle distibutions and index of efaction estimation fo Canadian wates, SPIE, Vol. 3761, Dene, Coloado, USA, (1999).. M. S. Twadowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Banad, and R. V. Zaneeld, A model fo estimating bulk efactie index fom the otical backscatteing atio and the imlications fo undestanding aticle comosition in case I and case II wates, J. Geohys. Res., 106, (001). 3. B. T. N. Eans, and G. R. Founie, Simle aoximation to extinction efficiency alid oe all size aametes, Al. Otics, 9, (1990). 4. H. C. an de Hulst, Light Scatteing by Small Paticles, 470., (Doe Publications, New Yok, N.Y., 1981). 5. K. L. Cade, F. R. Chen, Z. Lee, and S. K. Hawes, MODIS Ocean Science Team Algoithm Theoetical Basis Document: Case Cloohyll a, esion 5, Reot No. ATBD 19, (Maine Science Deatment, Uniesity of South Floida, St. Petesbug, Floida, USA, 1999). 6. R. A. Anone, An algoithm to etie scatteing, backscatteing, and beam attenuation coefficients fom the alues of emote sensing eflectance, iate communication, J. V. R. Zaneeld, A theoetical deiation of the deendence of the emotely sensed eflectance of the ocean on the inheent otical oeties, J. Geohys. Res., 100, 13,135-13,14 (1995). 8. H. R. Godon, Radiatie tansfe in the atmoshee fo coection of ocean colo emote sensing, in Ocean Colou: Theoy and Alications in the Decade of CZCS Exeience, V. Baale and P. M. Schlittenhadt, eds., (Kluwe Publishes, Bussels and Luxemboug, ISBN , 1993). 9. V. I. Haltin, Chloohyll based model of sea wate otical oeties, Alied Otics, 38, , (1999). 10. K. S. Shifin, Physical Otics of Ocean Wate, (Ameican Institute of Physics, New Yok, 1988). 76