Spectral parameters of inherent optical property models: method for satellite retrieval by matrix inversion of an oceanic radiance model

Inherent optical property (IOP) spectral models for the phytoplankton absorption coefficient, 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)(lambda(i)) = a(CDOM)(lambda(ref))exp-S(lambda(i)- lambda(ref))] is linear in a(CDOM)(lambda(ref)) and nonlinear in S. Upon linearization by Taylor's series expansion, it is shown that spectral model parameters, such as S, can be concurrently accommodated within the same conventional linear matrix formalism used to retrieve the reference wavelength IOP's. Iteration is used to adjust for errors caused by truncation of the Taylor's series expansion. Employing an iterative linear matrix 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 parameter are within certain specific ranges, (c) accurate retrievals 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 approximately +/-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 x 5 iterative matrix inversion if the starting values for S and g are carefully chosen to be slightly higher than the expected final retrieved values.