## 4 Discussion  
### Advantages and Disadvantages of the \(n_{\rm p}\) Model  
The \(n_{\rm p}\) model proposed in this study is a proof-of-concept remote sensing method for retrieving particulate refraction from GOCI satellite measurements in the study area. It is essentially dependent on the accurate retrievals of \(TSM\) and \(b_{\rm bp}\), which are achieved by establishing stable empirical models. The variety of field measurements from the four cruises represents a prominent advantage in this study and provides a steady basis for developing the TSM and \(b_{\rm bp}\) empirical models. As shown in Figure 12, a leave-one-out cross-validation (LOO-CV) [38; 39] was conducted to evaluate the performances of the TSM and \(b_{\rm bp}\) models. Briefly, we randomly selected one sample from the full dataset (sample number, \(n\)) that served for the validation of the model, while the remaining \(n-1\) samples were trained for model calibration. Based on the LOO-CV method, all samples were tried for one round, deriving relatively low and acceptable predictive errors. Thus, relatively accurate TSM and \(b_{\rm bp}\) retrievals, as well as their close relationships with \(b_{\rm p}\) and \(c_{\rm p}\), provided a feasible route for achieving the estimation of \(n_{\rm p}\) in the study areas. Another advantage lies in that there are more adequate remote sensing signals for model inputs when compared with the remote sensing method proposed by [PERSON] et al. (2015) [5], which utilizes a single band reflectance (i.e., a green band at 551 nm) to derive the intermediate and target parameters. In addition to green band reflectance (555 nm), this study introduced red band reflectance, i.e., 660 nm, as another input, which assures more adequate valid remote sensing information that could potentially derive better outputs.  
The developed \(n_{\rm p}\) model may show limitations when it is applied to other coastal water areas. This is due to different optical properties that may vary with the change of study area because of the diversity and dynamics of in-water constituents [24; 40; 41; 42; 43; 44]. Such local characteristics on water conditions generally determine region-specific empirical relationships between TSM (and \(b_{\rm bp}\)) and remote sensing reflectance and between \(b_{\rm p}\) (and \(c_{\rm p}\)) and TSM [16; 17; 45; 46]. Nevertheless, these so-called limitations should not hinder the use of the proof-of-concept method proposed in this study for other regions. The same method with necessary local parameterizations can be employed to derive the particulate refraction using remote sensing data only if valid regional data can be obtained. However, in future, detailed investigations are still required to thoroughly assess the model's applicability in various coastal water conditions. In addition, this study mainly focused on developing a method for estimating \(n_{\rm p}\) from satellite data; thus, we used GOCI data as a case study. The applicability of the method to other satellite sensors is not clear, and further studies are also required to apply the similar method of this study to develop \(n_{\rm p}\) estimation models specifically for MODIS, Visible infrared  
Figure 12: Comparison between in situ and modeled (**A**) TSM and (**B**) \(b_{\rm bp}(488)\) for the leave-one-out cross-validation. The colors indicate different cruise datasets.  
Imaging Radiometer (VIIRS), Landsat, etc., according to their band specifications, and then compare and cross-validate their performances.