# A New Algorithm for Simultaneous Retrieval of Aerosols and Marine Parameters
## 2 Data and Methods
### Inherent Optical Properties
#### 2.2.2 Bio-Optical Model  
In the AccuRT algorithm, the inherent optical properties (chlorophyll concentration (CHL), mineral particle concentration (MIN), and absorption by CDOM (\(\alpha_{\text{CDOM}}(443)\)) are adopted from the Coast Colour Round Robin (CCRR) [37] bio-optical model. The model has 3 input parameters: CHL, MIN, and \(\alpha_{\text{CDOM}}(443)\). According to [PERSON] et al. [38], the absorption coefficient for mineral particles at 443 nm and its spectral variation are given by  
\[\alpha_{\text{MIN}}(443)=0.041\times\text{MIN}, \tag{6}\]  
\[\alpha_{\text{MIN}}(\lambda)=\alpha_{\text{MIN}}(443)\exp[-0.0123(\lambda-443 )]. \tag{7}\]  
The absorption coefficient for pigmented (algal) particles is given by [39]  
\[\alpha_{pig}(\lambda)=A_{\phi}(\lambda)\times[\text{CHL}]^{E_{\phi}(\lambda)}. \tag{8}\]  
Here \(A_{\phi}(\lambda)\) and \(E_{\phi}(\lambda)\) are given by [PERSON] et al. [39], and [CHL] is the chlorophyll concentration. The spectral variation of the CDOM absorption coefficient is given by [40]  
\[\alpha_{\text{CDOM}}(\lambda)=\alpha_{\text{CDOM}}(443)\times\exp[-0.0176( \lambda-443)]. \tag{9}\]  
The sum of Equations (7)-(9) gives the total absorption coefficient \(\alpha_{tot}(\lambda)\) due to water impurities  
\[\alpha_{tot}(\lambda)=\alpha_{pig}(\lambda)+\alpha_{\text{MIN}}(\lambda)+ \alpha_{\text{CDOM}}(\lambda). \tag{10}\]  
It should be noted that \(\alpha_{\text{MIN}}(\lambda)\) in Equation (10) caters also for non-algae particles whose absorption does not covary with that of algae particles. The scattering coefficient at 555 nm is given by [38]  
\[\beta_{\text{MIN}}(555)=0.51\times\text{MIN}, \tag{11}\]  
and the spectral variation of the attenuation coefficient is  
\[\gamma_{\text{MIN}}(\lambda)=\gamma_{\text{MIN}}(555)\times(\lambda/\lambda_{ 0})^{-c};\qquad c=0.3749,\qquad\lambda_{0}=555\text{ nm}, \tag{12}\]  
where \(\gamma_{\text{MIN}}(555)=\alpha_{\text{MIN}}(555)+\beta_{\text{MIN}}(555)\).  
The spectral variation of scattering coefficient for mineral particles follows from  
\[\beta_{\text{MIN}}(\lambda)=\gamma_{\text{MIN}}(\lambda)-\alpha_{\text{MIN}} (\lambda). \tag{13}\]  
According to [PERSON] and [PERSON] [41], the attenuation coefficient for pigmented particles at 660 nm wavelength is given by  
\[\gamma_{\text{pig}}(660)=\gamma_{0}\times[\text{CHL}]^{\eta};\qquad\gamma_{0} =0.407,\qquad\eta=0.795, \tag{14}\]  
and its spectral variation is given by [42]  
\[\gamma_{\text{pig}}(\lambda)=\gamma_{\text{pig}}(660)\times(\lambda/660)^{v}, \tag{15}\]  
where  
\[v=\begin{cases}0.5\times[\log_{10}\text{CHL}-0.3]&0.02<\text{CHL}<2.0\\ 0&\text{CHL}>2.0.\end{cases} \tag{16}\]The spectral variation of scattering coefficient for pigmented particles is the difference between Equations (15) and (8)  
\[\beta_{\text{pig}}(\lambda)=\gamma_{\text{pig}}(\lambda)-\alpha_{\text{pig}}( \lambda). \tag{17}\]  
The sum of Equations (13) and (17) gives the scattering coefficient due to water impurities  
\[\beta_{\text{tot}}(\lambda)=\beta_{\text{MIN}}(\lambda)+\beta_{\text{pig}}( \lambda). \tag{18}\]