## 4 Discussion  
### Performance of the OLCI K\({}_{d}\)(490) Algorithm  
#### 4.1.1 Challenges in Estimating K\({}_{d}\)(490) Using Satellite Data  
It is difficult to obtain highly accurate \(R_{\rm rs}\) from satellite images in extremely turbid inland waters due to the complex optical conditions from elevated concentrations of optically active substances and algal blooms [34; 53]. This is further complicated when turbid atmospheric conditions from elevated aerosol concentrations are present. The accuracy of estimating the \(R_{\rm rs}\) band ratios is critical to the newly developed \(K_{\rm d}\)(490) algorithm because the input parameters of this algorithm are two \(R_{\rm rs}\) band ratios (\(R_{\rm rs}\)(681)/\(R_{\rm rs}\)(560) and \(R_{\rm rs}\)(754)/\(R_{\rm rs}\)(560)). The sensitivity of this algorithm to the input parameters was analyzed (Figure 9a), and the results indicate that this algorithm is highly sensitive to \(R_{\rm rs}\)(681)/\(R_{\rm rs}\)(560) and less sensitive to \(R_{\rm rs}\)(754)/\(R_{\rm rs}\)(560). The \(\rm RMSE_{\rm rel}\) of \(K_{\rm d}\)(490) increases to 64.32% when \(R_{\rm rs}\)(681)/\(R_{\rm rs}\)(560) is underestimated or overestimated by 30%, whereas it increases to 24.49% when \(R_{\rm rs}\)(754)/\(R_{\rm rs}\)(560) is underestimated or overestimated by 30%. Fortunately, the accuracies of the two \(R_{\rm rs}\) band ratios are quite high (Figure 9b; R\({}^{2}\) > 0.65, \(\rm RMSE_{\rm rel}\) < 39.00%, MNB < 27.00% and NRMS < 29.00%), especially that of the \(R_{\rm rs}\)(681)/\(R_{\rm rs}\)(560) band ratio (R\({}^{2}\) = 0.86, \(\rm RMSE_{\rm rel}\) = 13.58%, MNB = 3.79% and NRMS = 13.18%), as the \(R_{\rm rs}\) band ratios can decrease the effect of the atmospheric correction [54]. In general, the effects of the atmospheric correction's uncertainty are small, and the 6S atmospheric correction for the OLCI over Lake Taihu is considered to be appropriate for us to focus our study on the retrieval and validation of \(K_{\rm d}\)(490).  
Atmospheric correction was also performed based on the aerosol parameters measured at an AERONET station in conjunction with the 6S radiative transfer model. However, aerosols were measured at only one station near Meiliang Bay (Figure 1). As a result, the measurements cannot effectively characterize the distribution of aerosols across all of Lake Taihu, which will also affect the accuracy of the results obtained from the atmospheric correction and estimation of \(K_{\rm d}\)(490). Here, we use the measurements taken on 14 March 2017, as an example. On this date, the AOD(550) acquired at the AERONET station is 0.3493. Let us assume that the actual AOD(550) ranges from 0.1 to 1.5 (Figure 9c,d). The OLCI-derived \(R_{\rm rs}\) band ratios (\(R_{\rm rs}\)(681)/\(R_{\rm rs}\)(560) and \(R_{\rm rs}\)(754)/\(R_{\rm rs}\)(560)) and the OLCI-derived \(K_{\rm d}\)(490) both increase as the input AOD(550) increases. When AOD(550) > 1.0, \(K_{\rm d}\)(490) increases rapidly as AOD(550) increases, the absolute relative error (abs(\(K_{\rm d}\)(490)\({}_{\rm AERONET}\)-\(K_{\rm d}\)(490)\({}_{\rm simulation}\))/\(K_{\rm d}\)(490)\({}_{\rm AERONET}\)) also increases rapidly. When 0.1 < AOD(550) < 0.8 (within the spatial variation for Lake Taihu), the absolute relative error is within 10% and is thus acceptable.  
Figure 8: Temporal variations of the OLCI-derived \(K_{\rm d}\)(490) at four virtual stations in different lake segments from November 2016 to April 2017. Note that the data influenced by algal blooms and cloud are excluded.