First-Derivative Analysis for Estimating Water Quality and Optical Metrics in Shallow Coastal Waters

The study quantifies correlations between remote sensing reflectance (Rrs), first derivatives (FDs), and water quality and optical metrics: chlorophyll-a (Chl-a), phaeopigments (Pha), total suspended matter (TSM), coloured dissolved organic matter (CDOM), and the scalar ambient attenuation coefficient for photosynthetically active radiation, K0(PAR). Data from 14 stations (n = 23) along the German Baltic coast during summers of 2022 and 2023 established a summer-specific optical baseline. Rrs was pre-processed using 10-point moving average (10MA) smoothing or discrete wavelet transformation (DWT) before computing FD. Results show moderate to strong correlations for estimating variables using simple algorithms. Chl-a and Pha are best estimated using the FD peak at 685 nm (R2 of 0.67 and 0.69, respectively), though retrieval highly depends on localized nutrient enrichment. TSM estimation was optimized via a DWT baseline peak algorithm (670 to 750 nm), yielding a physically consistent positive correlation (R2 = 0.17) over stronger inverse models. CDOM and K0(PAR) are optimally retrieved at 689 nm and 629 nm (R2 = 0.51 and 0.48, respectively). Signal processing significantly affects results, and the 600–850 nm window is proved highly sensitive. This approach mitigates wind and wave effects, demonstrating the utility of high-resolution in situ spectra free from atmospheric interference.