Chapter 15 Remote Sensing of Seagrasses
353
either reached the substratum and is reflected from
it, or the light that is scattered upward in the water
column and travels upward, is defined as the attenuation with decreasing depth (κ). Unfortunately, κ
cannot be measured directly but must be estimated
through RT modeling. These important variables of
the underwater light field determine the fate of light
that passes into, and out, of the water column after
interacting with the water column and the substratum (cf. Chapter 13). The resultant light traveling in
an upward direction may ultimately be detected and
measured by a remote sensor.
IV. Optically Deep and Shallow Waters:
Physical Definitions
Chapter 12 presented an introduction to the fundamental principles of the interaction of light in water. A more detailed explanation is essential for understanding the signal measured by remote sensing
over a seagrass area. Here, we expand these concepts making use of all the quantities and variables
defined in Chapter 12. Dekker et al. (2001) have presented a comprehensive review of the remote sensing
of aquatic ecosystems: the following discussion, on
the analytical model of the underwater light field, is
based on that review.
A. Optically Deep Waters
In order to understand the relationship between the
subsurface irradiance reflectance over a water body
and related substratum visibility it is necessary to
first understand the subsurface irradiance reflectance
of a water body where only the water column is visible, i.e. in optically deep waters. Very clear natural
waters may be 30, 40 or more than 50 m deep before the water can be considered optically deep. In
waters with very high concentrations of absorbing
and scattering substances such an ‘optically deep’
water body may occur when the benthic vegetation
or substratum is only submerged under half a meter
of water. Thus, benthic vegetation may be detectable
to depths of tens of meters in the clearest waters but
only to tens of centimeters in high light absorbing
and scattering waters.
We refer to Aas (1987) for a complete derivation
of the analytical model for the irradiance reflectance
over an optically deep water body. The reason for
choosing this model is that it acts as a reference for
understanding all other models of this kind found in
the literature (Dekker et al., 2001). In terms of the
backscattering and absorption coefficients, the Aas
(1987) analytical model for irradiance reflectance
can be written as
R(0−) =
r d ¯
µ u
¯
µ u + ¯
µ d
b b
a + kb b
,
k =
r d ¯
µ u + r u ¯
µ d
¯
µ u + ¯
µ d
(1)
To specify the model in Eq. (1), four parameters
are required, namely ¯
µ d , ¯
µ u , r d , and r u , where r u and
r d are the shape factors for up and downward scattering, respectively (the average cosines for downwelling and upwelling light ¯
µ d , ¯
µ u are explained in
Chapter 12). The shape factors describe the difference between the backward and upward scattered
fraction of light and the forward and downward fractions of light. For vertically incident irradiance these
are unity. Despite the approximations applied in this
model (Aas, 1987), it may be expected to yield quite
accurate results for turbid waters.
B. Optically Shallow Waters
The discussion of the analytical model for optically
shallow waters was based mainly on Maritorena et al.
(1994), slightly adapted and reformulated to ensure
consistency in terminology and definitions. Maritorena et al. (1994) present a clear discussion of the
physics of an optically shallow water body where
part of the reflectance at the surface is composed of
a bottom signal, using an approach derived from the
two-flow equations. The following text is mainly derived from their text; however, the notation has been
adapted for consistency.
In optically shallow waters, E u (0−) can be defined
as the sum of E u (0−) C , the upwelling irradiance
originating from within the water column (where
none of the photons have interacted with the substratum), and E u (0−) B , the upwelling irradiance reflected from the substratum (where each of the photons have interacted with the substratum):
E u (0−) = E u (0−) C + E u (0−) B
(2)
To estimate the first term of the right hand side
consider an infinitely thin layer of thickness dZ at
depth Z , where the downwelling irradiance is E d (Z ).
353
either reached the substratum and is reflected from
it, or the light that is scattered upward in the water
column and travels upward, is defined as the attenuation with decreasing depth (κ). Unfortunately, κ
cannot be measured directly but must be estimated
through RT modeling. These important variables of
the underwater light field determine the fate of light
that passes into, and out, of the water column after
interacting with the water column and the substratum (cf. Chapter 13). The resultant light traveling in
an upward direction may ultimately be detected and
measured by a remote sensor.
IV. Optically Deep and Shallow Waters:
Physical Definitions
Chapter 12 presented an introduction to the fundamental principles of the interaction of light in water. A more detailed explanation is essential for understanding the signal measured by remote sensing
over a seagrass area. Here, we expand these concepts making use of all the quantities and variables
defined in Chapter 12. Dekker et al. (2001) have presented a comprehensive review of the remote sensing
of aquatic ecosystems: the following discussion, on
the analytical model of the underwater light field, is
based on that review.
A. Optically Deep Waters
In order to understand the relationship between the
subsurface irradiance reflectance over a water body
and related substratum visibility it is necessary to
first understand the subsurface irradiance reflectance
of a water body where only the water column is visible, i.e. in optically deep waters. Very clear natural
waters may be 30, 40 or more than 50 m deep before the water can be considered optically deep. In
waters with very high concentrations of absorbing
and scattering substances such an ‘optically deep’
water body may occur when the benthic vegetation
or substratum is only submerged under half a meter
of water. Thus, benthic vegetation may be detectable
to depths of tens of meters in the clearest waters but
only to tens of centimeters in high light absorbing
and scattering waters.
We refer to Aas (1987) for a complete derivation
of the analytical model for the irradiance reflectance
over an optically deep water body. The reason for
choosing this model is that it acts as a reference for
understanding all other models of this kind found in
the literature (Dekker et al., 2001). In terms of the
backscattering and absorption coefficients, the Aas
(1987) analytical model for irradiance reflectance
can be written as
R(0−) =
r d ¯
µ u
¯
µ u + ¯
µ d
b b
a + kb b
,
k =
r d ¯
µ u + r u ¯
µ d
¯
µ u + ¯
µ d
(1)
To specify the model in Eq. (1), four parameters
are required, namely ¯
µ d , ¯
µ u , r d , and r u , where r u and
r d are the shape factors for up and downward scattering, respectively (the average cosines for downwelling and upwelling light ¯
µ d , ¯
µ u are explained in
Chapter 12). The shape factors describe the difference between the backward and upward scattered
fraction of light and the forward and downward fractions of light. For vertically incident irradiance these
are unity. Despite the approximations applied in this
model (Aas, 1987), it may be expected to yield quite
accurate results for turbid waters.
B. Optically Shallow Waters
The discussion of the analytical model for optically
shallow waters was based mainly on Maritorena et al.
(1994), slightly adapted and reformulated to ensure
consistency in terminology and definitions. Maritorena et al. (1994) present a clear discussion of the
physics of an optically shallow water body where
part of the reflectance at the surface is composed of
a bottom signal, using an approach derived from the
two-flow equations. The following text is mainly derived from their text; however, the notation has been
adapted for consistency.
In optically shallow waters, E u (0−) can be defined
as the sum of E u (0−) C , the upwelling irradiance
originating from within the water column (where
none of the photons have interacted with the substratum), and E u (0−) B , the upwelling irradiance reflected from the substratum (where each of the photons have interacted with the substratum):
E u (0−) = E u (0−) C + E u (0−) B
(2)
To estimate the first term of the right hand side
consider an infinitely thin layer of thickness dZ at
depth Z , where the downwelling irradiance is E d (Z ).