## 1 Introduction
[PERSON] et al. [40] developed a three-band ratio for more turbid and productive waters. This supports lakes with a wide range of optically active substances (OAC) and includes \(\lambda_{3}\) (710 nm) in a three-band NIR-red ratio equation. For highly turbid waters, [PERSON] et al. [41] further modified the equation and added a fourth band (\(\lambda_{4}\) = 705 nm) to minimize the impact of absorption and backscattering of TSM [9]. Many other indices have been developed for detecting surface blooms based on specific spectral bands within lower spatial resolution satellites such as MERIS and MODIS, though few studies have adapted these models for sensors such as those onboard Sentinel-2. Previous research has utilized the absorption of phycocyanin at around 620 nm as an indicator for estimating cyanobacteria [42; 43; 44; 45]. However, phycocyanin concentration may be less often seen in studies compared to Chl-a due to challenges associated with laboratory extraction of phycocyanin and its relatively low specific absorption in inland waters [47]. [PERSON] et al. [44] introduced a semi-empirical algorithm employing a band ratio of 709 nm to 620 nm for estimating phycocyanin concentrations, and they also examined the impact of Chl-a absorption at 620 nm. [PERSON] et al. [45] developed an empirical algorithm using 700 nm, which has minimal sensitivity to phycocyanin, and 600 nm for maximum absorption. By selecting 600 nm instead of 617 nm, their algorithm was nearly independent of Chl-a interference. [PERSON] et al. [48] utilized two band ratios (620 nm to 665 nm, and 620 nm to 708.25 nm) to estimate phycocyanin from Ocean and Land Color (OLCI) data for large-scale monitoring. These studies utilized sensors with a higher spectral resolution that feature narrower bands near the phycocyanin absorption peak at 620 nm. However, the large pixel size (300 m for MERIS/OLCI) limits the application of these sensors beyond large waterbodies. [PERSON] et al. [49] developed three empirical models using two-band and four-band ratios from Sentinel-2 data to estimate phycocyanin. They selected the Sentinel-2 bands closest to the phycocyanin peak (560 nm, 665 nm, 705 nm, and 740 nm) and introduced a band ratio model using the 705 nm to 665 nm ratio, which demonstrated the best performance (R\({}^{2}\) = 0.79, RMSE = 44.48). Empirical models have been built to relate different band ratios and indices extracted from remotely sensed data to in situ water quality parameters using statistical techniques such as linear regression, multivariate regression, and nonparametric multiplicative regression (NPMR) [27], as well as machine learning approaches such as support vector machines (SVM; [50]), artificial neural networks (ANN; [24]), and convolutional neural networks (CNN; [51]). These techniques vary in terms of training and calibration requirements, data processing, and the level of complexity. Regression models are popular across many disciplines because of their ease of use and interpretation [52]. Researchers have used a variety of statistical metrics to evaluate water quality retrieval algorithms. Some of the statistical metrics used in previous studies include coefficient of determination (R\({}^{2}\)), mean absolute error (MAE), root mean squared error (RMSE), relative root mean squared error (RRMSE), mean absolute percentage error (MAPE), Nash criterion, Nash-Sutcliffe model efficiency (NSE), and bias [24]. Each of these statistical metrics can be used to compare different models. Of these metrics, R\({}^{2}\), RMSE, and bias are the most applied in previous studies to evaluate different models and compare their accuracy. Cloud contamination is a significant challenge when working with optical remote sensing data. Researchers used a variety of algorithms to detect clouds and cloud shadows in Sentinel-2 images. These algorithms can be broadly classified into three groups: physical rule based, multi-temporal based, and machine learning based [53].