## 3 Inherent Optical Properties (IOPs)
### Scattering Phase Function for Particles
#### 3.6.2 The SBC and GSM Bio-Optical Models  
Based on field measurements conducted in the Santa Barbara Channel and compiled in the NOMAD data base [69], [PERSON] et al. [70] constructed a local bio-optical model representative for the SBC coastal waters. Another frequently used bio-optical model is the GSM model [71; 72], which is included in NASA's SeaDAS software package. GSM is a global model which has the same structure as the SBC model, but with different coefficients.  
In the SBC model, the water body, in addition to pure water, is assumed to be described by three parameters that can be varied: (i) the chlorophyll concentration [CHL] (a proxy for the concentration of pigmented particles), the CDOM absorption coefficient at 443 nm [\(\alpha_{\text{CDOM}}(443)\)], and the total scattering coefficient at 443 nm [\(\beta_{\text{tot}}(443)\)]. The IOPs of the SBC model are described by:  
\[\alpha_{\text{Pig}}^{\text{SBC}}(\lambda) =a_{1}^{\text{SBC}}(\lambda)[\text{CHL}]^{a_{2}(\lambda)} \tag{105}\] \[\alpha_{\text{CDOM}}^{\text{SBC}}(\lambda) =\alpha_{\text{CDOM}}^{\text{SBC}}(443)\exp[-S(\lambda-443)]; \qquad S=0.012\] (106) \[\beta_{\text{tot}}^{\text{SBC}}(\lambda) =\beta_{\text{tot}}^{\text{SBC}}(443)(\lambda/443). \tag{107}\]  
Similarly, for the GSM model the IOPs are described by  
Figure 2: Rayleigh, Fournier-Forand, and Petzold scattering phase functions used to represent scattering by water molecules, pigmented particles, and non-algal particles, respectively, in the CCRR bio-optical model. To generate the FF scattering phase function the values \(\xi=3.38\) and \(\bar{m}_{t}=1.068\) were used.  
\[\alpha^{\text{GSM}}_{\text{pig}}(\lambda) =a^{\text{GSM}}_{1}(\lambda)[\text{CHL}] \tag{108}\] \[\alpha^{\text{GSM}}_{\text{CDOM}}(\lambda) =\alpha^{\text{GSM}}_{\text{CDOM}}(443)\exp[-S(\lambda-443)];\qquad S =0.0206\] (109) \[\beta^{\text{GSM}}_{\text{tot}}(\lambda) =\beta^{\text{GSM}}_{\text{tot}}(443)(\lambda/443)^{1.0337}. \tag{110}\]  
Please note that the wavelength dependent factors \(a^{\text{SRC}}_{1}(\lambda)\) and \(a_{2}(\lambda)\) in Equation (105) as well as \(a^{\text{GSM}}_{1}(\lambda)\) in Equation (108) are determined from field measurements compiled in the NOMAD data base. For simplicity we will assume here that \(\alpha^{\text{SRC}}_{\text{pig}}(\lambda)=\alpha^{\text{GSM}}_{\text{pig}}( \lambda)\equiv\alpha^{\text{CCRR}}_{\text{pig}}(\lambda)\), so that the difference between the three models lies in the treatment of scattering and CDOM absorption.  
For both the SBC and GSM models, CDOM represents a combination of colored dissolved organic matter and mineral particles. Hence, values of \(\alpha^{\text{SRC}}_{\text{CDOM}}(443)\) in Equation (106) and \(\alpha^{\text{GSM}}_{\text{CDOM}}(443)\) in Equation (109) should be compared to the sum \(\alpha^{\text{CCRR}}_{\text{CDOM}}(443)+0.041\times 0.75\) MIN. The total suspended particle scattering coefficient is \(\beta^{\text{SBC}}_{\text{tot}}(\lambda)\) and \(\beta^{\text{GSM}}_{\text{tot}}(\lambda)\) in the SBC and GSM model, respectively, each being comparable to \(\beta_{\text{tot}}(\lambda)=\beta_{\text{MIN}}(\lambda)+\beta_{\text{pig}}(\lambda)\) in the CCRR model.  
The most significant difference between these three models is that the SBC and GSM models do not separately include mineral particles although the total scattering coefficient does include the total suspended particle scattering. Another difference is that the CCRR model is based on three different reference wavelengths, namely 443 nm for \(\alpha_{\text{MIN}}\), 555 nm for \(\gamma_{\text{MIN}}\), and 660 nm for \(\alpha_{\text{pig}}\), while the SBC and the GSM models are based only on 443 nm as a reference wavelength. In the SBC and GSM models one may use the FF scattering phase function for pigments, but other scattering phase functions, such as the Petzold scattering phase function may work better in coastal areas.