Hyperspectral remote sensing for shallow waters I A semianalytical model

Abstract

For analytical or semianalytical retrieval of shallow-water bathymetry and/or optical properties of the water column from remote sensing, the contribution to the remotely sensed signal from the water column has to be separated from that of the bottom. The mathematical separation involves three diffuse attenuation coefficients: one for the downwelling irradiance (K(d)), one for the upwelling radiance of the water column (K(u)(C)), and one for the upwelling radiance from bottom reflection (K(u)(B)). Because of the differences in photon origination and path lengths, these three coefficients in general are not equal, although their equality has been assumed in many previous studies. By use of the Hydrolight radiative-transfer numerical model with a particle phase function typical of coastal waters, the remote-sensing reflectance above (R(rs)) and below (r(rs)) the surface is calculated for various combinations of optical properties, bottom albedos, bottom depths, and solar zenith angles. A semianalytical (SA) model for r(rs) of shallow waters is then developed, in which the diffuse attenuation coefficients are explicitly expressed as functions of in-water absorption (a) and backscattering (b(b)). For remote-sensing inversion, parameters connecting R(rs) and r(rs) are also derived. It is found that r(rs) values determined by the SA model agree well with the exact values computed by Hydrolight (~3% error), even for Hydrolight r(rs) values calculated with different particle phase functions. The Hydrolight calculations included b(b)/a values as high as 1.5 to simulate high-turbidity situations that are occasionally found in coastal regions.

A semianalytical ocean color inversion algorithm with explicit water column depth and substrate reflectance parameterization

“…In optically complex waters, the optical properties of the water column are typically influenced by nonalgal particulate matter, colored dissolved organic matter, and phytoplankton [IOCCG, 2000], and unlike oceanic waters, the nonalgal constituents do not necessarily covary with respect to phytoplankton abundance. Regarding optically shallow waters, these can be characterized as zones in which light reflected from the seafloor influences the waterleaving radiance signal [Lee et al, 1998] thereby confounding contemporary ocean color algorithms developed for optically deep waters [Cannizzaro and Carder, 2006;Qin et al, 2007;Zhao et al, 2013] (see Appendix A for further discussion). Whilst a range of ocean color algorithms have been developed and proven effective within optically complex waters [Doerffer and Schiller, 2007;Smyth et al, 2006;Werdell et al, 2013a], only a few approaches for optically shallow waters have been published [Barnes et al, 2014Brando et al, 2012] with none in operation that explicitly use pre-existing water column depth and benthic albedo data sets to improve IOP retrievals.…”

“…Many recent approaches such as the Hyperspectral Optimization Process Exemplar (HOPE), a semianalytical inversion algorithm developed by Lee et al [1998], and the Comprehensive Reflectance Inversion based on Spectrum matching and Table Look up (CRISTAL), a spectral matching look-up-table algorithm developed by Mobley et al [2005], have been developed for simultaneous retrieval of bathymetry, benthic types, and IOPs. The HOPE algorithm and its variants (e.g., Goodman and Ustin, [2007]; ALUT-Hedley et al…”

“…The spectral shape of a / (k) used within an SAA is often normalized to 1.0 at 443 nm. The normalized phytoplankton absorption coefficient, a à / ðkÞ, can be a single fixed spectral shape [Maritorena et al, 2002] or modeled using basis vectors [Bricaud et al, 1998;Ciotti and Bricaud, 2006;Lee et al, 1998]. The resulting parameterization of a / (k) within an SAA thus takes the form a / ðkÞ5Pa à / ðkÞ ðm 21 Þ;…”

“…These were further refined by Lee et al [1998] to explicitly incorporate IOPs and both solar and sensor geometries, r rs k ð Þ % r dp rs k ð Þ2r dp…”

“…is the upwelling diffuse attenuation for radiance scattered from the water column, and k B d ðkÞ is the upwelling diffuse attenuation coefficient for radiance reflected off the benthos [Lee et al, 1998]. The diffuse attenuation coefficients are functions of the IOPs and solar and sensor geometries and are expressed according to Lee et al [1998Lee et al [ , 1999 as…”