Total phosphorus (TP) is a significant indicator of water eutrophication. As a typical macrophytic lake, Lake Baiyangdian is of considerable importance to the North China Plain’s ecosystem. However, the lake’s eutrophication is severe, threatening the local ecological environment. The correlation between chlorophyll and TP provides a mechanism for TP prediction. In view of the absorption and reflection characteristics of the chlorophyll concentrations in inland water, we propose a method to predict TP concentration in a macrophytic lake with spectral characteristics dominated by chlorophyll. In this study, water spectra noise is removed by discrete wavelet transform (DWT), and chlorophyll-sensitive bands are selected by gray correlation analysis (GRA). To verify the effectiveness of the chlorophyll-sensitive bands for TP concentration prediction, three different machine learning (ML) algorithms were used to build prediction models, including partial least squares (PLS), random forest (RF) and adaptive boosting (AdaBoost). The results indicate that the PLS model performs well in terms of TP concentration prediction, with the least time consumption: the coefficient of determination (R²) and root mean square error (RMSE) are 0.821 and 0.028 mg/L in the training dataset, and 0.741 and 0.029 mg/L in the testing dataset, respectively. Compared with the empirical model, the method proposed herein considers the correlation between chlorophyll and TP concentration, as well as a higher accuracy. The results indicate that chlorophyll-sensitive bands are effective for predicting TP concentration.

Water reflectance anisotropy has serious implications for the remote sensing of water surfaces. The ${\bm{f}^{\prime}}/{\bm{Q}}$ factor serves as a crucial bridge connecting the inherent and apparent optical properties of turbid water bodies; ${\bm{f}^{\prime}}/{\bm{Q}}$ varies not only with angular geometry and inherent optical properties (IOPs), but also with wavelength. However, there was limited research on ${\bm{f}^{\prime}}/{\bm{Q}}$ in turbid water bodies. This research conducted preliminary exploration on ${\bm{f}^{\prime}}/{\bm{Q}}$ in inland turbid water bodies based on measurements of in-situ multi-angle bidirectionality reflectance, including 17 angles and 251 bands when the solar zenith angle ( ${{\bm{\theta }}}_{\bm{s}}$ ) was between 40° and 50°. This study indicated that ${\bm{f}^{\prime}}/{\bm{Q}}$ exhibited highly sensitivity in the wavelength range of 690–750 nm with a peak near 727 nm, as well as angular geometry played an important role in the BRDF. The ${\bm{f}^{\prime}}/{\bm{Q}}$ varied over the range of 0.13–0.18 sr ⁻¹ , variation of 0.06 sr ⁻¹ across different bands, when viewing zenith angle ( ${{\bm{\theta }}}_{\bm{v}}$ ) and particle backscattering ratio ( ${{\tilde{\bm{b}}}}_{{\bm{bp}}}$ ) were 0 and 0.0183, respectively; higher than the range observed for the ocean (0.08–0.15 sr ⁻¹ ). The variability in ${\bm{f}^{\prime}}/{\bm{Q}}$ as a function of wavelength must be accounted for in turbid waters. The ${\bm{f}^{\prime}}/{\bm{Q}}$ was correlated with the IOPs in the range of 690–750 nm, with coefficient of determination ( R ² ) values higher than 0.94 and root mean square error (RMSE) values lower than 0.004. Our findings are of great significance for understanding the relationship between inherent and apparent optical properties in inland water bodies, for BRDF studies, and for improving the accuracy of satellite product retrieval.

The bidirectional reflectance distribution function (BRDF) factor ƒ′ provides a bridge between the inherent and apparent optical properties (IOPs and AOPs) of inland waters. The previous BRDF studies focused on ocean waters, while few studies examine inland waters. It is meaningful to improve the theory of remote sensing of water surface and the accuracy of image derivation in inland waters. In this study, radiative transfer simulation was applied to calculate the ƒ′ values using appropriate IOPs based on in situ combined with realistic boundary conditions (N = 11,232). This study shows that ƒ′ factor varied over the range of 0.33–16.64 in Lake Nansihu, a finite depth water, higher than the range observed for the ocean (0.3–0.6). Our results demonstrate that the factor ƒ′ depends on not only solar zenith angle (${\theta }_s$) but also the average number of collisions ($\stackrel{-}{n}$) and particulate backscattering ratio (${\tilde{b}}_{bp}$). The ƒ′ factor shows a continuous geometric increase as the solar zenith angle increases at 400–650 nm but is relatively insensitive to solar angle in the 650–750 nm range in which ƒ′ increases as ${\tilde{b}}_{bp}$ and $\stackrel{-}{n}$ decreases. To account for these findings, two empirical models for ƒ′ factor as a function of ${\theta }_s$, $\stackrel{-}{n}$ and ${\tilde{b}}_{bp}$ are proposed in various spectral wavelengths for Lake Nansihu waters. Our results are crucial for obtaining Hyperspectral normalized reflectance or normalized water-leaving radiance and improving the accuracy of satellite products.

The Q -factor is a key parameter characterizing the bidirectional structure of apparent optical properties, yet its variability in optically complex lakes has not been adequately characterized. This study quantitatively assesses and decouples the respective influences of inherent optical properties (IOPs) and angular parameters on the radiative regime, using data from 202 in situ stations with 208 b ~ _bp in Lake Taihu and over 30 million radiative transfer simulations. The results show that Q values range from 0.3 to 6.0 and Q -nadir ( Q _n ) exhibits spectral variations primarily driven by the particle backscattering ratio ( b ~ _bp ), particularly in waters with an average number of collisions at 720 nm ( n ¯ ₇₂₀ ) below 6.0 (Type 2 waters). In these waters, Q _n displays an inverted Gaussian pattern in the red spectral region (670–720 nm), likely associated with solar-induced chlorophyll fluorescence (SICF), and increases with b ~ _bp , opposite to the trends observed at other wavelengths and in extremely turbid waters ( n ¯ ₇₂₀ >6.0). Q increases with the solar zenith angle and decreases with increasing viewing zenith angle ( θ _v ). Coupled Q -factor models are proposed across the 400–750 nm spectral range at 5 nm intervals for optically deep lakes and yield R ² values exceeding 0.85 and 0.71, with RMSE below 0.055 and 0.219 sr, respectively, when compared with Hydrolight simulated Q _n and Q -factor ( θ _v ≤60 ^∘ ). Sensitivity analyses further reveal that wind speed and aerosol type have limited effects on Q _n , whereas isotropic SICF emissions in Type 2 waters suppress angular variability and induce a maximum relative difference of approximately 6.0% in Q _n at 680 nm. This study enhances the capability of multi-angle and hyperspectral remote sensing to model radiance distribution in optically complex deep lakes.

Picophytoplankton and nanophytoplankton play a central role in ocean primary production, carbon cycling, and food-web dynamics. Their highly dynamic distributions, however, make in situ measurements insufficient for large-scale monitoring. Satellite remote sensing provides continuous, large-scale optical observations, enabling the estimation of phytoplankton abundances and their spatiotemporal variability across regional to basin scales. In the Kuroshio Extension region of the western North Pacific, we combined high-frequency underway flow cytometry measurements of Synechococcus (SYN), Prochlorococcus (PRO), picoeukaryotes (PEUK), and nanoeukaryotes (NEUK) with Sentinel-3/OLCI reflectance spectra. By treating reflectance as a continuous spectral function, we extracted key spectral features, including blue-to-green band ratios and red-edge characteristics, to empirically estimate group-specific abundances. The resulting OLCI-derived products capture the spatiotemporal variability of pico- and nanophytoplankton communities and their responses to mesoscale and submesoscale physical processes.