## 5 System Model
### [PERSON]'s Single-Parameter IOP Model Based on Concentration of Chlorophyll-\(a\)  
[PERSON]'s model is widely adopted for UOWC performance analyses, being derived from in situ measurements, which link the IOPs of seawater to the Chl-\(a\) concentration. It has been verified for Chl-\(a\) concentrations ranging between 0-12 mg m\({}^{-3}\), within which are the concentrations of the profiles of stratified water bodies presented in [PERSON] et al. [56]. Prior to this model's application, the depth \((z)\)-dependent variation of Chl-\(a\), \(C_{c}(S,z)\), for each classification profile \(S\), needs to be evaluated, as given in Section 4.2. The absorption coefficient \(a(S,\lambda,z)\) may be derived with (8), where \(a_{w}(\lambda)\) is the pure water absorption coefficient adopted from [PERSON] et al. [57]; \(a_{c}^{0}(S,\lambda,z)\) is the specific absorption coefficient of Chl-\(a\) determined by (9) and the values for empirical constants \(A\) and \(B\) are available in Pope and Fry [58]; \(C_{c}^{0}\) is the total reference concentration of Chl-\(a\) (1 mg m\({}^{-3}\)); \(a_{h}^{0}\) is the specific absorption coefficient of fulvic acid at 35.959 m\({}^{2}\) mg\({}^{-1}\); \(k_{f}=0.0189\) nm\({}^{-1}\); \(a_{h}^{0}\) is the specific absorption coefficient of humic acid at 18.828 m\({}^{2}\) mg\({}^{-1}\); \(k_{h}=0.01105\) nm\({}^{-1}\); and \(C_{f}\) and \(C_{h}\) are the concentrations of fulvic and humic acids in mg m\({}^{-3}\), calculated using (10) and (11), respectively. \[a(S,\lambda,z)=a_{w}(\lambda)+a_{c}^{0}(S,\lambda,z)\bigg{(}\frac{C_{c}(S,z)} {C_{c}^{0}}\bigg{)}^{0.602}+a_{f}^{0}C_{f}(S,z)e^{-k_{f}\lambda}+a_{h}^{0}C_{ h}(S,z)e^{-k_{h}\lambda} \tag{8}\]  
\[a_{c}^{0}(S,\lambda,z)=A(\lambda)C_{c}(S,z)^{-B(\lambda)} \tag{9}\]  
\[C_{f}(S,z)=1.74098C_{c}(S,z)e^{0.12327(\frac{C_{c}(S,z)}{C_{c}^{0}})} \tag{10}\]  
\[C_{h}(S,z)=0.76284C_{c}(S,z)e^{0.03092(\frac{C_{c}(S,z)}{C_{c}^{0}})} \tag{11}\]  
Note that the above models and the following are computable only for the 400-700 nm range limited by the coefficient availability in the reference studies. However, this is sufficient as this bandwidth covers a full span of the visible spectrum used in UOWC due to limitations posed by attenuation (wavelengths less than 400 nm or greater than 700 nm are highly attenuated in seawater) and hardware (semiconductor photodetectors are much less sensitive to wavelengths less than 400 nm). The scattering coefficient \(b(S,\lambda,z)\) is derived from (12), where \(b_{w}(\lambda)\) is the scattering coefficient of pure water calculated with (13); \(b_{s}^{0}(\lambda)\) and \(b_{h}^{0}(\lambda)\) are the specific scattering  
Figure 6: The system model. coefficients of small and large suspended particles, respectively, in m\({}^{2}\) g\({}^{-1}\); and \(C_{s}(S,z)\) and \(C_{l}(S,z)\) are the concentrations of small and large particles in g m\({}^{-3}\), calculated using (16) and (17), respectively. \[b(S,\lambda,z)=b_{w}(\lambda)+b_{s}^{0}(\lambda)C_{s}(S,z)+b_{l}^{0}(\lambda)C_{ l}(S,z) \tag{12}\]  
\[b_{w}(\lambda)=0.005826\left(\frac{400}{\lambda}\right)^{4.322} \tag{13}\]  
\[b_{s}^{0}(\lambda)=1.151302\left(\frac{400}{\lambda}\right)^{1.7} \tag{14}\]  
\[b_{l}^{0}(\lambda)=0.341074\left(\frac{400}{\lambda}\right)^{0.3} \tag{15}\]  
\[C_{s}(S,z)=0.01739C_{c}(S,z)e^{0.11631\left(\frac{C_{s}(S,z)}{C_{s}^{2}}\right)} \tag{16}\]  
\[a_{c}^{0}(S,\lambda,z)=A(\lambda)C_{c}(S,z)^{-B(\lambda)} \tag{9}\]0  
Backscattering may be determined using (18), where \(B_{s}\) (0.039) and \(B_{l}\) (0.0064) are the probabilities of scattering by small and large particles, respectively. It is needed for the evaluation of underwater reflectance; an AOP used in modeling ambient light. \[a_{c}^{0}(S,\lambda,z)=A(\lambda)C_{c}(S,z)^{-B(\lambda)} \tag{9}\]1  
The linear sum of \(a(S,\lambda,z)\) and \(b(S,\lambda,z)\), as in (1), is used to determine the spectral attenuation \(c(S,\lambda,z)\) for each profile. Figure 7 shows the depth-spectral distribution of attenuation for profiles S2 and S8.