constants except at extreme salinity (Sullivan et al. 2006; Zhang et al. 2009). In
practice, a g and a d are often combined (a dg ) because of the similarity in their
spectral shapes, and the IOPs can be expressed as (IOCCG 2006):
a ph k
ð Þ ¼ a ph 443
ð
Þ a
þ
ph k
ð Þ
a dg k
ð Þ ¼ a dg 443
ð
Þ e
ÀS kÀ443
ð
Þ
b bp k
ð Þ ¼ b bp 443
ð
Þ
443
k
g
ð7:4Þ
where each IOP is expressed as the product of its value at a reference wavelength
(443 nm) and a spectral shape function. The wavelength 443 nm is commonly
chosen because it is the location of a chlorophyll absorption peak, and thus is the
center of a blue band used by all ocean color sensors since the CZCS.
In the open ocean, so-called Case I waters (Morel and Prieur 1977)
1 where
optical properties are dominated by phytoplankton, the terms in Eq. 7.4 tend to
covary with Chl. Thus, both a ph (k) and a ph
+ (k), have been modeled as functions of
Chl (Bricaud et al. 1995, 2004; IOCCG 2006). For example, a ph (k), can be
modeled as:
a ph k
ð Þ ¼ A k
ð ÞChl
B k
ð Þ ;
ð7:5Þ
where A(k) and B(k) are empirical regression coefficients determined from measurements. Bricaud et al. (2004) reported typical values of A(k) and B(k) while
recognizing that they do change with phytoplankton community composition.
Similarly, for phytoplankton-dominated waters b bp (k) has also been modeled as a
function of Chl (Morel 1988; Gordon 1992) although it has been noted that
phytoplankton cannot fully account for the backscattering variability even in the
open ocean (Morel and Ahn, 1990; Antoine et al. 2011). The spectral slope
parameter for a dg , S, varies only slightly with typical values of 0.015–0.018 nm
-1 ,
and the spectral slope parameter for b bp , g, varies inversely with Chl, owing to a
relationship between particle size distributions and the trophic state as indicated by
Chl. Figure 7.1b, c show typical modeled IOP spectra (Eq. 7.4), while Fig. 7.1d
shows how R rs varies with Chl (Eq. 7.3).
While several optical models have been developed to derive R rs using Chl and
other IOPs (e.g., Sathyendranath et al. 1989; Maritorena et al. 2002; IOCCG 2006;
also see Mobley 1994 and references therein), their fundamental principles are the
same and the mathematical expressions are similar to the above. Likewise, inversion
1 The concept of Case I and Case II waters introduced by Morel and Prieur (1977) has been used
extensively by the ocean color community. Case I refers to waters with optical properties
dominated by phytoplankton and their degradation products, whereas Case II waters include all
other water types in which optical properties are influenced by CDOM, inorganic particles, or the
shallow ocean bottom. The concept has been recently revisited by Mobley et al. (2004) and Lee
and Hu (2006), who found that water types can be better described by their different IOPs.
Nevertheless, the terminology of Case I and Case II follows the convention in this context.
7 Oceanic Chlorophyll-a Content
175
practice, a g and a d are often combined (a dg ) because of the similarity in their
spectral shapes, and the IOPs can be expressed as (IOCCG 2006):
a ph k
ð Þ ¼ a ph 443
ð
Þ a
þ
ph k
ð Þ
a dg k
ð Þ ¼ a dg 443
ð
Þ e
ÀS kÀ443
ð
Þ
b bp k
ð Þ ¼ b bp 443
ð
Þ
443
k
g
ð7:4Þ
where each IOP is expressed as the product of its value at a reference wavelength
(443 nm) and a spectral shape function. The wavelength 443 nm is commonly
chosen because it is the location of a chlorophyll absorption peak, and thus is the
center of a blue band used by all ocean color sensors since the CZCS.
In the open ocean, so-called Case I waters (Morel and Prieur 1977)
1 where
optical properties are dominated by phytoplankton, the terms in Eq. 7.4 tend to
covary with Chl. Thus, both a ph (k) and a ph
+ (k), have been modeled as functions of
Chl (Bricaud et al. 1995, 2004; IOCCG 2006). For example, a ph (k), can be
modeled as:
a ph k
ð Þ ¼ A k
ð ÞChl
B k
ð Þ ;
ð7:5Þ
where A(k) and B(k) are empirical regression coefficients determined from measurements. Bricaud et al. (2004) reported typical values of A(k) and B(k) while
recognizing that they do change with phytoplankton community composition.
Similarly, for phytoplankton-dominated waters b bp (k) has also been modeled as a
function of Chl (Morel 1988; Gordon 1992) although it has been noted that
phytoplankton cannot fully account for the backscattering variability even in the
open ocean (Morel and Ahn, 1990; Antoine et al. 2011). The spectral slope
parameter for a dg , S, varies only slightly with typical values of 0.015–0.018 nm
-1 ,
and the spectral slope parameter for b bp , g, varies inversely with Chl, owing to a
relationship between particle size distributions and the trophic state as indicated by
Chl. Figure 7.1b, c show typical modeled IOP spectra (Eq. 7.4), while Fig. 7.1d
shows how R rs varies with Chl (Eq. 7.3).
While several optical models have been developed to derive R rs using Chl and
other IOPs (e.g., Sathyendranath et al. 1989; Maritorena et al. 2002; IOCCG 2006;
also see Mobley 1994 and references therein), their fundamental principles are the
same and the mathematical expressions are similar to the above. Likewise, inversion
1 The concept of Case I and Case II waters introduced by Morel and Prieur (1977) has been used
extensively by the ocean color community. Case I refers to waters with optical properties
dominated by phytoplankton and their degradation products, whereas Case II waters include all
other water types in which optical properties are influenced by CDOM, inorganic particles, or the
shallow ocean bottom. The concept has been recently revisited by Mobley et al. (2004) and Lee
and Hu (2006), who found that water types can be better described by their different IOPs.
Nevertheless, the terminology of Case I and Case II follows the convention in this context.
7 Oceanic Chlorophyll-a Content
175