ApplOpt-38-1657-1999-MatrixInversionRetrieval

Spectral parameters of inherent optical property models: method for satellite retrieval by matrix inversion of an oceanic radiance model Frank E. Hoge and Paul E. Lyon Inherent optical property IOP spec tral model s for the phyt opla nkton abso rpt ion coeffi cient , chromophoric dissolved organic matter CDOM absorption coefficient, and total constituent backscattering TCB coefficient are linear in the reference wavelength IOP and nonlinear in the spectral parameters. For example, the CDOM absorption coefficient IOP a CDOM i a CDOM ref expS i ref is linear in a CDOM ref and nonlinear in S. Upon linea riza tion by Taylor ’s series expan sion, it is shown that spectral model parameters, such as S, can be concurrently accommodated within the same conventional linear matri x formalism used to retrieve t he reference wavelength IOP’s. Iteration i s used to adjust for error s caused by trun cat ion of the Taylor’s series expansion. Empl oyin g an iterat ive linear matri x inversion of a water-leaving radiance model, computer simulations using synthetic data suggest that a no instabilities or singularities are introduced by the linearization and subsequent matrix inversion procedures, b convergence to the correct value can be expected only if starting values for a model para meter are with in certain speci fic rang es, c accu rate retriev als of the CDOM slope S or the phytoplankton Gaussian width g are generally reached in 3–20 iterations, d iterative retrieval of the exponent n of the TCB wavelength ratio spectral model is not recommended because the starting values must be within 5% of the correct value to achieve accurate convergence, and e concurrent retrieval of S and g simultaneously with the phytoplankton, CDOM, and TCB coefficient IOP’s can be accomplished in a 5 5 iterative matrix inversion if the starting values for S and g are carefully chosen to be slightly high er than the expect ed final retrieved v alues. © 1999 Optic al Society of America OCIS codes: 010.4450 , 280.0280 , 300.6550 , 030.5620. 1. Intr odu ctio n It has bee n shown that it is feasi ble to simultane ously retrieve the phy top lankton abso rpt ion coe ffici ent , the chromophoric dissolved organic matter CDOMde- tritus abso rpt ion coef fici ent , and the tot al constitue nt backscattering TCB coef fici ent inherent opt ical properties IOP’s from water-leaving radiances by direct matrix inversion of a radiance model. 1 Spe- cifi call y, the se three IOP ’s, a ph g , a d d , and b bt b , can be readily retrieved from a ph g exp i g 2 2g 2 a d d expS i d b bt b b i n v i a w i b bw i v i (1) by linear matrix inversion. 1 See Ref. 1 for nomen- clature. The IOP spectral model parameters g, S, and n var y spatiall y and tempora lly in the global oceans. Thus a assi gni ng cons tan t values or b empirically derived values for these parameters can lead to sig nifi can t error s in the retrieved IOP’s. A more general approach is to retrieve from the water- lea vin g rad ianc es one or mo re of the g, S, and n parameters simultaneously with the IOP’s. 2. Th eory Retrieval of the IOP spectral model parameters is accomplished by linearizing the models by Taylor’s F. E. Hoge is with the NASA Goddard Space Flight Center, Wallops Flight Facil ity , Wall ops Island , Virgini a 23337. P. E. Lyon is with EG&G Services, Incorporated, Wallops Flight Facil- ity, Wallops Island, Virginia 23337. Received 17 August 1998; revised manuscript received 7 Decem- ber 1998. 0003-693599091657-06$15.00 0 © 1999 Optical Society of America 20 March 1999 Vol. 38, No. 9 A PP LI ED O PT IC S 1 65 7

ApplOpt-38-1657-1999-MatrixInversionRetrieval

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