356
A. Dekker, V. Brando, J. Anstee, S. Fyfe, T. Malthus and E. Karpouzli
As more spectral bands become available it becomes possible to determine more variables. In theory, if we have two spectral bands (containing some
uncorrelated information) then two variables can
be directly retrieved, with three spectral bands three
variables can be directly retrieved, and so on. These
variables do need to have a measurable influence
(from an aircraft or space sensor) on the spectral
band reflectances!
To obtain bottom reflectance (R b ), we would need
to invert Eq. (11) and to do this we would need to be
able to determine two reflectances (R(0−, H ) and
R ∞ ), four vertical attenuation coefficients (K d , K u ,
κ B , and κ C ) and the water column depth, which would
require a minimum of eight spectral bands for direct
inversion calculations. Since the vertical attenuation coefficients are spectrally similar and potentially
spatially variable (e.g. Karpouzli et al., 2003), it is
difficult to determine these directly from remotely
sensed image bands.
A solution to this problem is to look at the inherent optical properties of absorption, scattering, or
preferably backscattering of each of the components
of the water. The spectral shapes of these components are more specific and thus have a better chance
of being estimated from spectral information. The
vertical attenuation coefficients can then be calculated from the inherent optical properties. Inversion
of an 8 band, 8 variable set of equations (that contain
some nonlinear effects) is virtually impossible, especially if one realizes that all the remote sensing data
contain some level of noise. Solutions are possible;
but these will be discussed only after considering another pathway to understanding the underwater light
climate and the detection of substratum reflectance:
the Radiative Transfer of Energy theory (RT) based
modeling approach (see Chapter 12 for introduction
to RT theory and Chapter 13 for the application of
RT theory to seagrass canopy light interactions).
4. Numerical Modeling of the Underwater
Light Field
The fundamental principles of all optical processes
are incorporated within Radiative Transfer of Energy theory (RT). RT explains how the radiometric
properties, i.e. the radiance and irradiance, change in
the water column due to the optical properties of the
medium. Mobley (1994) and the software package
Hydrolight based on that book are the current stateof-the-art tools for exact modeling of the underwater
light field. The Hydrolight model does require accurate input on sun position and atmospheric conditions (including wind speed at the surface), inherent
optical properties of each of the optical components
and substratum or benthic vegetation reflectance.
Once these are available, it will calculate all apparent
optical properties such as attenuation coefficients,
reflectances from just above the substratum to those
above the air–water interface, and so on. The average cosines and diffuse inherent optical properties
can also be calculated. Since the user may define
many layers of water with differing optical properties, all conceivable permutations of water columns
can be calculated.
Unfortunately, it is not possible to directly invert
an RT model to derive the variables of interest because the calculations involve tracing the fates of
fluxes of photons through few to many interactions
with the pure water, its constituents and the substratum and its vegetation cover.
B. Analytical and/or Radiative Transfer-Based
Inversion Schemes for Remote Sensing
of Seagrasses
Two main pathways are therefore available for inverting a remote sensing image to produce a benthic
map, e.g. a map of seagrass distribution or some
other benthic map.
One approach is to use the analytical model for
inversion, whereby the forward analytical model is
parameterized by, amongst others, the RT simulations. The analytical inversion methods are fast and
traceable, although the results will always be based
on the necessary simplifications inherent in analytical equations.
The other approach is to use inversion methods
such as matching remotely measured spectra with
lookup tables or neural network inversions, requiring significant computing time either in their preparation or in applying them to a remote sensing image. Increased computing power will make this task
easier in the future. Louchard et al. (2003) applied
the lookup table approach using matching spectra to
airborne imaging spectrometry data over Lee Stocking Island in the Bahamas and were able to determine water column depth as well as three sediment
classes, five cover classes of Thalassia testudinum
(in steps of 20%) and coral cover and coral rubble.
Dierssen et al. (2003) using the same hyperspectral
airborne data over Lee Stocking Island were able to
A. Dekker, V. Brando, J. Anstee, S. Fyfe, T. Malthus and E. Karpouzli
As more spectral bands become available it becomes possible to determine more variables. In theory, if we have two spectral bands (containing some
uncorrelated information) then two variables can
be directly retrieved, with three spectral bands three
variables can be directly retrieved, and so on. These
variables do need to have a measurable influence
(from an aircraft or space sensor) on the spectral
band reflectances!
To obtain bottom reflectance (R b ), we would need
to invert Eq. (11) and to do this we would need to be
able to determine two reflectances (R(0−, H ) and
R ∞ ), four vertical attenuation coefficients (K d , K u ,
κ B , and κ C ) and the water column depth, which would
require a minimum of eight spectral bands for direct
inversion calculations. Since the vertical attenuation coefficients are spectrally similar and potentially
spatially variable (e.g. Karpouzli et al., 2003), it is
difficult to determine these directly from remotely
sensed image bands.
A solution to this problem is to look at the inherent optical properties of absorption, scattering, or
preferably backscattering of each of the components
of the water. The spectral shapes of these components are more specific and thus have a better chance
of being estimated from spectral information. The
vertical attenuation coefficients can then be calculated from the inherent optical properties. Inversion
of an 8 band, 8 variable set of equations (that contain
some nonlinear effects) is virtually impossible, especially if one realizes that all the remote sensing data
contain some level of noise. Solutions are possible;
but these will be discussed only after considering another pathway to understanding the underwater light
climate and the detection of substratum reflectance:
the Radiative Transfer of Energy theory (RT) based
modeling approach (see Chapter 12 for introduction
to RT theory and Chapter 13 for the application of
RT theory to seagrass canopy light interactions).
4. Numerical Modeling of the Underwater
Light Field
The fundamental principles of all optical processes
are incorporated within Radiative Transfer of Energy theory (RT). RT explains how the radiometric
properties, i.e. the radiance and irradiance, change in
the water column due to the optical properties of the
medium. Mobley (1994) and the software package
Hydrolight based on that book are the current stateof-the-art tools for exact modeling of the underwater
light field. The Hydrolight model does require accurate input on sun position and atmospheric conditions (including wind speed at the surface), inherent
optical properties of each of the optical components
and substratum or benthic vegetation reflectance.
Once these are available, it will calculate all apparent
optical properties such as attenuation coefficients,
reflectances from just above the substratum to those
above the air–water interface, and so on. The average cosines and diffuse inherent optical properties
can also be calculated. Since the user may define
many layers of water with differing optical properties, all conceivable permutations of water columns
can be calculated.
Unfortunately, it is not possible to directly invert
an RT model to derive the variables of interest because the calculations involve tracing the fates of
fluxes of photons through few to many interactions
with the pure water, its constituents and the substratum and its vegetation cover.
B. Analytical and/or Radiative Transfer-Based
Inversion Schemes for Remote Sensing
of Seagrasses
Two main pathways are therefore available for inverting a remote sensing image to produce a benthic
map, e.g. a map of seagrass distribution or some
other benthic map.
One approach is to use the analytical model for
inversion, whereby the forward analytical model is
parameterized by, amongst others, the RT simulations. The analytical inversion methods are fast and
traceable, although the results will always be based
on the necessary simplifications inherent in analytical equations.
The other approach is to use inversion methods
such as matching remotely measured spectra with
lookup tables or neural network inversions, requiring significant computing time either in their preparation or in applying them to a remote sensing image. Increased computing power will make this task
easier in the future. Louchard et al. (2003) applied
the lookup table approach using matching spectra to
airborne imaging spectrometry data over Lee Stocking Island in the Bahamas and were able to determine water column depth as well as three sediment
classes, five cover classes of Thalassia testudinum
(in steps of 20%) and coral cover and coral rubble.
Dierssen et al. (2003) using the same hyperspectral
airborne data over Lee Stocking Island were able to