## 2 Study Areas and Datasets  
### Study Areas and In Situ Measurements  
Four inland lakes and reservoirs, including the Guanting Reservoir, Baiyangdian Lake, Panjiakou Reservoir and Dabeiting Reservoir in the Hebei Province of China are selected as the study areas. In situ experiments were implemented to acquire match-up measurements of the GF-5 satellite (Figure 1). Guanting Reservoir is located in Huailai county with an area of 130 km\({}^{2}\), which serves as one of the standby drinking water sources for Beijing. Baiyangdian Lake, the largest lake in North China, is situated in the Xiong'an New Area. Panjiakou Reservoir is located at the junction of Tangshan city and Chengde district, while Dabeiting Reservoir is 30 km downstream of Panjiakou Reservoir. Table 1 lists the basic information for the collected in situ measurements of the study regions. Figure 1: Distributions of the sampling sites in all study regions: (**a**) Guanting Reservoir, (**b**) Dabeiting Reservoir, (**c**) Lake Baiyangdian, and (**d**) Panjiakou Reservoir in North China. The \(Z_{sd}\) values at the sampling sites were measured using a standard 30-cm diameter Secchi disk. Water surface spectra were collected with a FieldSpec HandHeld ASD spectroradiometer according to the above-water method [22; 23; 24], simultaneously with the \(Z_{sd}\) measurement. The water surface radiance (\(L_{u}(\lambda)\)), as well as the downwelling radiance (\(L_{d}(\lambda)\)) and skylight radiance (\(L_{sky}(\lambda)\)) were measured using the ASD spectroradiometer in the range from 400-900 nm at 1-nm intervals. For the \(L_{u}(\lambda)\) measurement, the viewing zenith angle was 40\({}^{\circ}\) downward, and the azimuth angle was 135\({}^{\circ}\) away from the sun's azimuth; for the \(L_{sky}(\lambda)\) measurement, the viewing zenith angle was 40\({}^{\circ}\) upward, and the azimuth angle was the same as the \(L_{u}(\lambda)\) measurement. To acquire the \(L_{u}(\lambda)\), the ASD spectroradiometer was targeted vertically over a reference panel center to measure its reflected radiance \(L_{p}(\lambda)\) at a zenith angle of 0\({}^{\circ}\), and the \(L_{u}(\lambda)\) were then calculated as \(L_{p}(\lambda)/\rho_{p}\). For each sampling site, we conducted spectra measurement in the following order: (1) five measures of \(L_{d}(\lambda)\), (2) ten measures of \(L_{u}(\lambda)\), (3) five measures of \(L_{sky}(\lambda)\), and (4) five measures of \(L_{d}(\lambda)\). As the single-channel-based above-water method requires stable sunlight, the difference among the five \(L_{u}(\lambda)\) measurements cannot exceed 10% in both steps 1 and 4, and so does for the difference between averaged-\(L_{d}(\lambda)\) in step 1 and 4. Measurements not meeting these criteria were discarded. In addition, for \(L_{u}(\lambda)\), we check if unusually large spectra existed in the ten measurements. Unusually large spectra occur possibly due to random solar flares, and were discarded. The average of the remaining spectrum was then taken. The above-water remote sensing reflectance (\(R_{rs}\)) was then calculated as follows:  
\[R_{rs}(\lambda)=\frac{L_{u}(\lambda)-\rho_{sky}(\lambda)L_{sky}(\lambda)}{\pi L _{p}/\rho_{p}}, \tag{1}\]  
where \(\rho_{p}\) is the reflectance of the reference panel calibrated in the laboratory; and \(\rho_{sky}\) is the skylight reflectance determined from the look-up table in Reference [25]. \(\rho_{sky}\) is affected by the wind speed, solar zenith angle, and the viewing geometry, and is thought to be independent of the wavelength. Though some studies [26; 27] propose sophisticated approaches to compute \(\rho_{sky}\) considering the spectral variations of skylight distribution, we choose the method in Reference [25], as it is widely used and easy to implement. Moreover, the error in \(R_{rs}\) caused by small residual errors in \(\rho_{sky}\) mainly exists in the dark blue wavelengths, and is smaller for turbid waters. Figure 2 shows the in situ collected \(R_{rs}\) in the study areas.