Evaluation of Uniﬁed Algorithms for Remote Sensing of Chlorophyll-a and Turbidity in Lake Shinji and Lake Nakaumi of Japan and the Vaal Dam Reservoir of South Africa under Eutrophic and Ultra-Turbid Conditions

: We evaluated uniﬁed algorithms for remote sensing of chlorophyll-a (Chla) and turbidity in eutrophic and ultra-turbid waters such as Japan’s Lake Shinji and Lake Nakaumi (SJNU) and the Vaal Dam Reservoir (VDR) in South Africa. To realize this objective, we used 38 remote sensing reﬂectance ( R rs ), Chla and turbidity datasets collected in these waters between July 2016 and March 2017. As a result, we clariﬁed the following items. As a uniﬁed Chla model, we obtained strong correlation (R 2 = 0.7, RMSE = 2 mg m − 3 ) using a two-band model (2-BM) and three-band model (3-BM), with R rs (687)/ R rs (672) and [ R rs − 1 (687) − R rs − 1 (672)] × R rs (832). As a unified turbidity model, we obtained strong correlation (R 2 = 0.7, RMSE = 260 NTU) using 2-BM and 3-BM, with R rs (763)/ R rs (821) and R rs (810) − [ R rs (730) + R rs (770)]/2. When targeting the Sentinel-2 Multispectral Imager (MSI) frequency band, we focused on MSI Bands 4 and 5 ( R rs (740) and R rs (775)) for the Chla algorithm. When optically separating SJNU and VDR data, it is effective to use the slopes of MSI Bands 3 and 4 ( R rs (560) and R rs (665)) and the slopes of MSI Bands 7 and 9 ( R rs (775) and R rs (865)).


Introduction
Fresh water on land, such as in rivers, lakes and reservoirs, accounts for about 0.01% of Earth's water [1]; thus, protecting this resource is a vital global issue. In particular, monitoring water quality to detect turbid water and algal blooms is indispensable [2]. In this research, we focus on the waters of Japan's Lake Shinji and Lake Nakaumi (SJNU), which are well known as brackish water zones with abundant fishery and sightseeing resources such as birds and clams. To protect these resources, water quality monitoring has been conducted at fixed points for a long time [3][4][5][6][7]. However, recent years have seen abnormal phenomena in water bodies such as cyanobacteria bloom, red tide, dysoxic bottom water and the sudden occurrence of seagrass [8,9]. We also focus on a second research site in this study, the Vaal Dam Reservoir (VDR) in South Africa, which is among the largest reservoirs in South Africa. The Vaal Dam was constructed in 1938 and plays a crucial role in supplying irrigation and industrial water to the Johannesburg metropolitan area [10,11]. For this reason, water quality has been conducted for a long time [12,13]. However, recent years have seen a further increase in the importance of water quality monitoring because of problems such as acidic mine drainage [14,15], increased water demand due to urbanization and uneven rainfall distribution caused by climate change [16]. Thus, SJNU and VDR have both similar historical backgrounds and current problems, so it is worth collaborating to improve the water quality monitoring techniques of both sites. Moreover, the current situation cannot be dealt with using conventional point source monitoring; thus, it is vital to establish technology such as remote sensing that can simultaneously monitor wide areas. Conventional water quality remote sensing relies mainly on algorithms dealing with blue and green light, but in optically-complex inland waters, the red and near-infrared parts of the spectrum are often used [17]. For example, methods such as two-band algorithms [18,19], three-band algorithms [20,21] and four-band algorithms [22,23] have been proposed to measure chlorophyll-a (Chla). For measuring turbidity (Turb) or total suspended solids (TSS), which is an indicator of turbidity, methods such as one-band algorithms [24,25] and two-band algorithms [26,27] have been proposed. Furthermore, Chla and turbidity algorithms, such as SCI (Synthetic Chlorophyll Index), which applied fluorescence line height [28] using the fluorescence band for more turbid conditions and a turbidity algorithm [29] using an 810-nm reflection peak under rich colored dissolved organic matter (CDOM) conditions, have been proposed. Several algorithms have been proposed for inland water, but a unified approach has not yet been established.
Based on the current state of satellite sensors, monitoring inland water quality using sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Terra and Aqua satellites, the Geostationary Ocean Color Imager (GOCI) aboard the Communication, Ocean and Meteorological Satellite and the Medium Resolution Imaging Spectrometer (MERIS) aboard the Envisat satellite, which have spatial resolutions of 500 m or better, high frequencies and high spectral resolutions, has become popular since 2000 [30][31][32]. Among these, MERIS, which operated from 2002-2012, used a 600-900 nm band to effectively monitor the quality of optically-complex inland water. Moreover, with an improved spatial resolution, continuous observation of small water bodies is possible with the same spectral performance. The Multispectral Imager (MSI) of the recent Sentnel-2A mission, which was launched in June 2015, has a 10-60-m spatial resolution, a 10-day repeat cycle and uses a 600-900-nm band that can be used for effective water quality monitoring. Additionally, high-resolution hyperspectral imagers, such as EO-1 s Hyperion (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017), the Hyperspectral Imager for the Coastal Ocean (HICO) (2009)(2010)(2011)(2012)(2013)(2014), which was installed on the International Space Station (ISS), and the Hyperspectral Imager Suite, which is scheduled to be operated on the ISS in 2019, also exist. Water quality monitoring for large rivers such as the Mississippi River using airborne hyperspectral sensors has been also conducted [33]. In addition to algorithms that do not depend on band position for inland waters with complex optical properties, these hyperspectral data will become important in the future.
Therefore, in this study, we evaluated recent water quality algorithms using field observation data for spectral reflectance, Chla and Turb) in SJNU and VDR under eutrophic and ultra-turbid conditions to assess algorithm stability. Table 1 shows the research area's basic specifications. SJNU consists of brackish lakes located on the border between Japan's Shimane and Tottori prefectures. The two lakes are connected by the 7.3 km-long Ohashi River and the main freshwater stream flows from the Hii River (accounting for about 90% Lake Shinji's freshwater origin). Freshwater flows from the Hii River, through Lake Shinji and the Ohashi River into Lake Nakaumi and into the Sea of Japan via Miho Bay. The salinity of Lake Shinji and Lake Nakaumi is about 0.3% and about 10%, respectively, with Lake Nakaumi, which is close to the Sea of Japan, having a strong salinity layer developed in some places. Both lakes have an average transparency of about 1 m, with high phytoplankton and suspended solid concentrations. In addition, cyanobacteria (blue-green algae) and red tide blooms often occur in Lake Shinji and Lake Nakaumi, respectively. The SJNU catchment area's average annual rainfall is about 1700-2300 mm.

Study Area and Field Survey
VDR is a freshwater dam reservoir 56 km south of Johannesburg, South Africa. This dam is at the Vaal River drainage system, which has a catchment area entirely situated within South Africa. The name Vaal means gray-brown in Afrikaans, and the VDR is characterized by highly turbid water (known as ultra-turbid conditions). The VDR catchment area's average annual rainfall is about 700 mm.
Field surveys of SJNU were carried out on 15 July and 12 September 2016, and field surveys of VDR were conducted on 12 September and 26 October 2016. To measure Chla and Turb, we used Hydrolab Data Sonde 5× instruments (Chla sensor: range = 0.03-500 mg m −3 , accuracy = ±3%, resolution = 0.01 mg m −3 ; turbidity sensor: range = 0-3000 NTU, accuracy = 1% (<100 NTU), 3% (100-400 NTU), 5% (>400 NTU), resolution = 0.1 NTU), and an MS 720 portable spectral radiometer produced by EKO Ltd. (Guangzhou, China) (spectral range = 350-1050 nm, sampling interval = 3.3 nm) was used to measure remote sensing reflectance (R rs ). We measured spectral irradiance both immediately above the water surface and of solar radiation reflected by a ZB 6010 white board (Japan Color Research Laboratory) three times. We determined the remote sensing reflectance (sr −1 ) by calculating respective average reflectance and divided it by pi. The basic reflectance measurement method and R rs transformation followed the method of Oyama et al. [34]. Mobley [35] and Tan et al. [36] point out the importance of removing sun and sky glint contained in R rs . However, due to equipment and observation time, auxiliary observations such as sky radiance could not be conducted this time, so we did not make corrections for glint.

Chlorophyll-a and Turbidity Algorithms
Various remote sensing algorithms have been suggested to measure Chla and turbidity (or TSS) for inland waters with complex optical properties [17]. For example, the effectiveness of the following 2-band model (2-BM; hereinafter referred to as a C1 model) as a Chla algorithm has been shown using the red and near-infrared bands [18,19].
Recently, semi-analytical analytical models supported by the bio-optical theory have been proposed in waters that cannot be evaluated using Equation (1). For example, a 3-band model (3-BM; hereinafter referred to as a C2 model) and 4-band model (hereinafter referred to as a C3 model) [20][21][22][23] have been proposed. Here, we briefly explain these models according to bio-optical theory. R rs observed immediately above the water surface can be expressed as: a(λ) = a w (λ) + a cdom (λ) + a chla (λ) + a tripton (λ) where b b is the water's backscattering coefficient; a w , a chla , a cdom and a tripton are the absorption coefficients of pure water, phytoplankton, CDOM and inorganic suspended matter. It is relatively easy to remotely estimate Chla in the open ocean because of the strong blue band absorption of Chla. However, Chla and CDOM from terrestrial origin both have strong blue band absorptions, making it difficult to remotely estimate Chla in inland water. Therefore, remote estimation in inland water relies on near-infrared bands, which have relatively small absorption for CDOM and similar a cdom and a tripton values. Only a chla , which is closely related to Chla, can be extracted by removing the influence of CDOM through relatively simple arithmetic operations. Figure 1 shows absorption coefficient spectral characteristics of underwater substances and four basic wavelengths (λ 1 , λ 2 , λ 3 and λ 4 ) typically used for Chla estimation. The C2 model calculates a chla depth by taking the difference between Chla absorption's maximum (λ 1 ) and minimum (λ 2 ) wavelengths, which is the reciprocal number of R rs , and by multiplying Chla by R rs near 740 nm, which is very small. This cancels the influence of b b in the denominator.
However, if the absorption component of the detritus (a d ) value that was omitted in Equation (3) is included, and thus cannot be ignored, Equation (5) may have a large error. Therefore, to alleviate the influence of a d by using wavelengths in which a d is assumed to have about the same range (for example, 720 nm and 750 nm), we replace R −1 (λ 3 ) in Equation (5) with "R −1 (λ 4 ) − R −1 (λ 3 )" to create the following 4-band model.
Because λ 3 and λ 4 are close bands with similar optical characteristics, they are sometimes expressed as the following 3-BM.
In contrast, the turbidity algorithm uses an empirical single-band model (hereinafter referred to as the T1 model) [24,25] and a 2-BM (hereinafter referred to as the T2 model) [26,27] using red to near-infrared bands as follows.
Turb ∝ R rs (λ 5 ) Turb ∝ R rs (λ 6 )/R rs (λ 7 ) where Turb describes turbidity. Furthermore, in waters with a large CDOM influence, a 3-BM (hereinafter referred to as the T3 model) [29] with a high R rs of 810 nm as an index has recently been proposed.

Figure 1.
Typical absorption from Yang et al. [21] for a*chla, a*tripton, aw, a*cdom. The ad is from Kobayashi and Higa (private note) measured in Tokyo Bay.

Accuracy Assessment
To evaluate discrepancies between the model and measured values in Table 3, we calculated the root mean square error (RMSE), which is often used to assess accuracy during water quality remote sensing algorithm evaluation [21].  (11) Here, N is the number of samples; WQpred,i is the predicted value of Chla or turbidity; and WQmeas,i is the measured value of Chla or turbidity for each sample.

Simulated Satellite Data
To monitor Chla and turbidity using satellite data in the future, we simulated Rrs observed from each satellite data band using actual measurement data. Specifically, Rrs of the center wavelength for Sentinel-2 bands was extracted from the measurement Rrs data. However, because the normal Ocean Color sensor's spatial resolution of 1 km is insufficient for monitoring on the scale of lakes and reservoirs, we used the Sentinel-2 MSI, which has a 10-m-30-m resolution. Table 3 shows MSI's performance.  Figure 2 shows detailed sampling points (basic stationary point), and Appendix A lists all Rrs, Chla and turbidity data. Figure 3 shows the acquired spectral reflectance data. Measured Chla and turbidity data at a water depth of 0 m were used. Although SJNU and VDR had nearly identical Chla,  [21] for a* chla , a* tripton , a w , a* cdom . The a d is from Kobayashi and Higa (private note) measured in Tokyo Bay.

Accuracy Assessment
To evaluate discrepancies between the model and measured values in Table 3, we calculated the root mean square error (RMSE), which is often used to assess accuracy during water quality remote sensing algorithm evaluation [21].
Here, N is the number of samples; WQ pred,i is the predicted value of Chla or turbidity; and WQ meas,i is the measured value of Chla or turbidity for each sample.

Simulated Satellite Data
To monitor Chla and turbidity using satellite data in the future, we simulated R rs observed from each satellite data band using actual measurement data. Specifically, R rs of the center wavelength for Sentinel-2 bands was extracted from the measurement R rs data. However, because the normal Ocean Color sensor's spatial resolution of 1 km is insufficient for monitoring on the scale of lakes and reservoirs, we used the Sentinel-2 MSI, which has a 10-m-30-m resolution. Table 3 shows MSI's performance.  Figure 2 shows detailed sampling points (basic stationary point), and Appendix A lists all R rs , Chla and turbidity data. Figure 3 shows the acquired spectral reflectance data. Measured Chla and turbidity data at a water depth of 0 m were used. Although SJNU and VDR had nearly identical Chla, VDR has turbidity values about 100-and 1000-times greater than SJNU, as shown in Table 4.

Chla Algorithm
Determining the Chla algorithm's optimum wavelength position is vital for regional dependency reasons. Previous studies have confirmed changes in R 2 and RMSE values by moving the wavelength within a certain range [20,23]. Here, we selected the optimal band with the minimum RMSE as these studies; however, we tried all combinations of 1 nm in the 2-BM. Figure 4 shows the Chla results from the C1 model in the SJNU and VDR. Figure 4a shows the correlation coefficient matrix [Rrs(λ1)/ Rrs(λ2)] and measured Chla derived every 1 nm in the 400-900-nm range. Rrs values at 687 nm and 672 nm are the highest correlated (R 2 = 0.69, RMSE mg m −3 ), and relatively strong correlation was obtained only in the narrow area noted by the box labeled "A." Figure 4b shows the optimal [Rrs(687)/Rrs(672)] correlation and measured Chla. Figure 4c,d shows the RMSEs of variation between [Rrs(λ1)/Rrs(672)] or [Rrs(687)/Rrs(λ2)] and measured Chla when λ1 or λ2 is in the 600-900-nm range. Thus, in this model, we obtained a relatively stable RMSE of 1.95 ± 0.05 mg m −3 when λ3 was about 740-900 nm, and the RMSE increases abruptly at wavelengths shorter than 740 nm. Figure 5 shows the Chla results from the C2 model for in SJNU and VDR. Figure 5a shows RMSE variation between [Rrs −1 (687) − Rrs −1 (672)] × R(λ3) and measured Chla when λ3 is in the 600-900-nm range. Thus, in this model, we obtained a relatively stable RMSE of 1.95 ± 0.05 mg m −3 when λ3 was about 740-900 nm, and the RMSE increases abruptly at wavelengths shorter than 740 nm. Figure 5b shows the optimal correlation between [Rrs −1 (687) − Rrs −1 (672)] × R(832) and measured Chla. As a result, we obtained a relatively high correlation (R 2 = 0.73, RMSE = 1.96 mg m −3 ) similar to that in Figure 4b. Moreover, compared the C2 model shows less variation that the C1 model when Chla concentrations are low (<5 mg m −3 ). Figure 6 shows the Chla results of the C3 model in SJNU and VDR. Figure 6a shows RMSE variation between [Rrs −1 (687) − Rrs −1 (672)] × [R(λ4) − R(832)] and measured Chla when λ4 is in the 600-900-nm range. Figure  6b shows the optimal correlation between

Chla Algorithm
Determining the Chla algorithm's optimum wavelength position is vital for regional dependency reasons. Previous studies have confirmed changes in R 2 and RMSE values by moving the wavelength within a certain range [20,23]. Here, we selected the optimal band with the minimum RMSE as these studies; however, we tried all combinations of 1 nm in the 2-BM. Figure 4 shows the Chla results from the C1 model in the SJNU and VDR. Figure 4a shows the correlation coefficient matrix [R rs (λ 1 )/ R rs (λ 2 )] and measured Chla derived every 1 nm in the 400-900-nm range. R rs values at 687 nm and 672 nm are the highest correlated (R 2 = 0.69, RMSE mg m −3 ), and relatively strong correlation was obtained only in the narrow area noted by the box labeled "A." Figure 4b shows the optimal [R rs (687)/R rs (672)] correlation and measured Chla. Figure 4c,d shows the RMSEs of variation between [R rs (λ 1 )/R rs (672)] or [R rs (687)/R rs (λ 2 )] and measured Chla when λ 1 or λ 2 is in the 600-900-nm range. Thus, in this model, we obtained a relatively stable RMSE of 1.95 ± 0.05 mg m −3 when λ 3 was about 740-900 nm, and the RMSE increases abruptly at wavelengths shorter than 740 nm. Figure 5 shows the Chla results from the C2 model for in SJNU and VDR. Figure 5a shows RMSE variation between [R rs −1 (687) − R rs −1 (672)] × R(λ 3 ) and measured Chla when λ 3 is in the 600-900-nm range. Thus, in this model, we obtained a relatively stable RMSE of 1.95 ± 0.05 mg m −3 when λ 3 was about 740-900 nm, and the RMSE increases abruptly at wavelengths shorter than 740 nm. Figure 5b shows the optimal correlation between [R rs −1 (687) − R rs −1 (672)] × R(832) and measured Chla. As a result, we obtained a relatively high correlation (R 2 = 0.73, RMSE = 1.96 mg m −3 ) similar to that in Figure 4b. Moreover, compared the C2 model shows less variation that the C1 model when Chla concentrations are low (<5 mg m −3 ). Figure 6 shows the Chla results of the C3 model in SJNU and VDR. Figure 6a shows RMSE variation between [R rs −1 (687) − R rs −1 (672)] × [R(λ 4 ) − R(832)] and measured Chla when λ 4 is in the 600-900-nm range. Figure 6b shows the optimal correlation between [R rs −1 (687) − R rs −1 (672)] × [R −1 (600) − R −1 (832)] and measured Chla. From these results, we determined that the RMSE within this wavelength range was 3.1-3.7 mg m −3 , and that estimation accuracy decreased in every band compared to the C2 model shown in Figure 4.
Water 2018, 10, x FOR PEER REVIEW 8 of 18 and measured Chla. From these results, we determined that the RMSE within this wavelength range was 3.1-3.7 mg m −3 , and that estimation accuracy decreased in every band compared to the C2 model shown in Figure 4.  Table 5 shows the optimal Chla model produced using C1, C2 and C3 as summarized above. The Chla estimation error is smaller than the RMSE in the order of C2, C1 and C3.

Turbidity Algorithm
As with the Chla algorithm, it is crucial to choose the turbidity algorithm's optimal wavelength. Here, we performed optimal wavelength selection and evaluation using the same methods as were used with the Chla algorithm.  Table 5 shows the optimal Chla model produced using C1, C2 and C3 as summarized above. The Chla estimation error is smaller than the RMSE in the order of C2, C1 and C3.

Turbidity Algorithm
As with the Chla algorithm, it is crucial to choose the turbidity algorithm's optimal wavelength. Here, we performed optimal wavelength selection and evaluation using the same methods as were used with the Chla algorithm. Figure 7 shows the turbidity results of the one-band model (T1) in SJNU and VDR. Figure 7a shows RMSE variation between R rs −1 (λ 5 ) and measured turbidity when λ 5 is in the 400-900-nm range. Figure 7b shows the optimal correlation (R 2 = 0.17, RMSE = 443 NTU) between R rs (814) and measured turbidity. This model's estimation accuracy of 500 NTU or less was extremely bad.
Water 2018, 10, x FOR PEER REVIEW 9 of 18 Figure 7 shows the turbidity results of the one-band model (T1) in SJNU and VDR. Figure 7a shows RMSE variation between Rrs −1 (λ5) and measured turbidity when λ5 is in the 400-900-nm range. Figure 7b shows the optimal correlation (R 2 = 0.17, RMSE = 443 NTU) between Rrs(814) and measured turbidity. This model's estimation accuracy of 500 NTU or less was extremely bad.   Figure 8a shows the correlation coefficient matrix between [Rrs(λ8)/Rrs(λ9)] and measured turbidity. We obtained a relatively strong correlation only in the narrow area indicated by the area labeled "B" in the figure. Figure 8b shows the optimal correlation (R 2 = 0.72, RMSE = 257 NTU) between [Rrs(821)/Rrs(763)] and measured turbidity. SJNU data (10 NTU or less) do not appear to be detected in this model. Figure 8c,d shows RMSE variations between [Rrs(λ1)/Rrs(763)] or [Rrs(821)/Rrs(λ9)] and measured turbidity when λ1 or λ2 is in the 400-900-nm range. We obtained a low RMSE value in combination with 763 nm between 740 nm and 820 nm (RMSE = 400 NTU or less). In contrast, the band with low RMSE in combination with 821 nm is between 740 nm and 770 nm (RMSE = 400 NTU or less).  Figure 7 shows the turbidity results of the one-band model (T1) in SJNU and VDR. Figure 7a shows RMSE variation between Rrs −1 (λ5) and measured turbidity when λ5 is in the 400-900-nm range. Figure 7b shows the optimal correlation (R 2 = 0.17, RMSE = 443 NTU) between Rrs(814) and measured turbidity. This model's estimation accuracy of 500 NTU or less was extremely bad.   Figure 8a shows the correlation coefficient matrix between [Rrs(λ8)/Rrs(λ9)] and measured turbidity. We obtained a relatively strong correlation only in the narrow area indicated by the area labeled "B" in the figure. Figure 8b shows the optimal correlation (R 2 = 0.72, RMSE = 257 NTU) between [Rrs(821)/Rrs(763)] and measured turbidity. SJNU data (10 NTU or less) do not appear to be detected in this model. Figure 8c,d shows RMSE variations between [Rrs(λ1)/Rrs(763)] or [Rrs(821)/Rrs(λ9)] and measured turbidity when λ1 or λ2 is in the 400-900-nm range. We obtained a low RMSE value in combination with 763 nm between 740 nm and 820 nm (RMSE = 400 NTU or less). In contrast, the band with low RMSE in combination with 821 nm is between 740 nm and 770 nm (RMSE = 400 NTU or less).   Figure 8a shows the correlation coefficient matrix between [R rs (λ 8 )/R rs (λ 9 )] and measured turbidity. We obtained a relatively strong correlation only in the narrow area indicated by the area labeled "B" in the figure. Figure 8b shows the optimal correlation (R 2 = 0.72, RMSE = 257 NTU) between [R rs (821)/R rs (763)] and measured turbidity. SJNU data (10 NTU or less) do not appear to be detected in this model. Figure 8c,d shows RMSE variations between [R rs (λ 1 )/R rs (763)] or [R rs (821)/R rs (λ 9 )] and measured turbidity when λ 1 or λ 2 is in the 400-900-nm range. We obtained a low RMSE value in combination with 763 nm between 740 nm and 820 nm (RMSE = 400 NTU or less). In contrast, the band with low RMSE in combination with 821 nm is between 740 nm and 770 nm (RMSE = 400 NTU or less).    Table 6 shows the optimal turbidity model using the T1, T2 and T3 models summarized above. Comparing RMSE values shows that the turbidity estimation error is small in the order of T2, T3 and T1. correlation between R rs (814) and measured turbidity (Turb). Figure 9 shows the turbidity results of the three-band model (T3) in SJNU and VDR. Figure 9a shows the RMSE variation between R rs (λ 8 ) − [R rs (770) + R rs (840)]/2 and measured turbidity when λ 8 is in the 400-900-nm range. We obtained a relatively low RMSE (RMSE = 400 NTU or less) by tuning λ 8 between 780 nm and 840 nm. Figure 9b shows the RMSE variation between R rs (810) − [R rs −1 (λ 9 ) + R rs (840)]/2 and measured turbidity when λ 9 is the 400-900-nm range and R rs (810) − [R rs (770) + R rs (λ 10 )]/2 and measured turbidity when λ 10 is in the 400-900-nm range. For λ 9 , we obtained a band with relatively low RMSE (RMSE = 300 NTU or less) between about 730 nm and 770 nm. In contrast, the relatively low RMSE (RMSE = 300 NTU or less) band for λ 10 is between about 720 and 740 nm. Figure 9c shows the optimal correlation (R 2 = 0.58, RMSE = 316 NTU) between R rs (830) − [R rs (770) + R rs (840)]/2 and measured turbidity. Figure 9d shows the optimal correlation (R 2 = 0.70, RMSE = 267 NTU) between R rs (810) − [R rs (730) + R rs (770)] and measured turbidity. Figure 9d seems to be more aggregated data of SJNU compared to Figure 9c. Table 6 shows the optimal turbidity model using the T1, T2 and T3 models summarized above. Comparing RMSE values shows that the turbidity estimation error is small in the order of T2, T3 and T1.    Table 6 shows the optimal turbidity model using the T1, T2 and T3 models summarized above. Comparing RMSE values shows that the turbidity estimation error is small in the order of T2, T3 and T1.

Algorithm Evaluation Using Simulated Sentinel-2 Data
We evaluated the Chla and turbidity algorithms for satellite observation bands (bands close to the tuned wavelength) using C1, C2, T2 and T3. Figure 10 shows Chla and turbidity results for the 2-BM and 3-BM using the Sentinel-2 MSI band only. Figure 10a shows the correlation between R rs (705)/R rs (665) and measured Chla, and Figure 10b shows the correlation between R rs (775)/R rs (740) and measured turbidity. Total R 2 was low at 0.25 and 0.49 for Chla and turbidity, respectively (RMSE: 3.1 mg m −3 and 347 NTU, respectively); however, R 2 slightly improved to 0.51 and 0.77 for Chla and turbidity, respectively (RMSE: 1.5 mg m −3 and 223 NTU, respectively) for the VDR. Figure 10c shows the correlation between [R rs −1 (705) − R rs −1 (665)] × R(842) and measured Chla, and Figure 10d shows the correlation between R(810) − [R rs (730) + R(770)]/2 and measured turbidity. R 2 was not so high at 0.25 and 0.49 for Chla and turbidity, respectively (RMSE = 3.3 mg m −3 and 348 NTU, respectively). However, the correlation improved for the case of VDR data only. Strong correlations cannot be obtained for all data, as shown in Figure 10a,b; however, the correlation becomes remarkably high only when data are confined to VDR. In such a case, VDR's spectral reflectance characteristics can be determined mechanically and used as an algorithm with more versatility. We then examined spectral characteristics by separating data from SJNU and VDR. Figure 11a shows the average spectral reflectance characteristics (MSI band only) of all R rs data in SJNU and VDR. Here, based on the shape of Slope 1 (the slope of R rs at 705 nm and 740 nm), Slope 2 (the slope of R rs at 775 nm and 865 nm) and Slope 3 (the slope of R rs at 775 nm and 865 nm), we focused on the slope of R rs between the bands. Figure 11b-d shows scatterplots for Slope 1 and Slope 2, Slope 1 and Slope 3 and Slope 2 and Slope 3, respectively. These figures make it clear that data from SJNU and VDR are clearly separated by slope combinations. In particular, in the Slope 1 and Slope 3 scatterplots shown in Figure 11b, SJNU and VDR data were clearly divided between the 1:1 line.
Strong correlations cannot be obtained for all data, as shown in Figure 10a,b; however, the correlation becomes remarkably high only when data are confined to VDR. In such a case, VDR's spectral reflectance characteristics can be determined mechanically and used as an algorithm with more versatility. We then examined spectral characteristics by separating data from SJNU and VDR. Figure 11a shows the average spectral reflectance characteristics (MSI band only) of all Rrs data in SJNU and VDR. Here, based on the shape of Slope 1 (the slope of Rrs at 705 nm and 740 nm), Slope 2 (the slope of Rrs at 775 nm and 865 nm) and Slope 3 (the slope of Rrs at 775 nm and 865 nm), we focused on the slope of Rrs between the bands. Figure 11b-d shows scatterplots for Slope 1 and Slope 2, Slope 1 and Slope 3 and Slope 2 and Slope 3, respectively. These figures make it clear that data from SJNU and VDR are clearly separated by slope combinations. In particular, in the Slope 1 and Slope 3 scatterplots shown in Figure 11b, SJNU and VDR data were clearly divided between the 1:1 line.   of all R rs data in SJNU and VDR; (b) relationship between Slope 1 (R rs (560)/R rs (665)) and Slope 2 (R rs (705)/R rs (740)); (c) relationship between Slope 1 (R rs (560)/R rs (665)) and Slope 3 (R rs (775)/R rs (865)); (d) relationship between Slope 2 (R rs (705)/R rs (740)) and Slope 3 (R rs (775)/R rs (865)).

Evaluation of Chla Algorithm
As summarized in Table 5, we found the C1 and C2 models to be effective in estimating Chla at the two sites (R 2 is about 0.7, RMSE is about 2.0 mg m −3 ). The four-band model, which is more suitable for detritus-rich water conditions, was found to not be significant under this study's conditions. We selected 672 nm and 687 nm as the optimal bands for the C1 model, adding 832 nm to these wavelengths for the C2 model. The wavelengths used in the C1 model for water on land were λ 1 (650-680 nm; red) and λ 2 (650-720 nm; near infra-red) for a Chla range of about 0-100 mg m −3 [37][38][39][40]. Similarly, for the C2 model, λ 1 was 660-670 nm; λ 2 was 700-730 nm; and λ 3 was 740-760 nm [20,39,40]. The RMSE obtained in these past studies was about 8-10 mg m −3 for a Chla range of 0-100 mg m −3 . The Chla range in our study was about one-fifth of those, so it is very harmonious that RMSE was around 2 mg m −3 . However, as seen in Figure 4, the wavelength range that can estimate Chla with such RMSE in an algorithm that can be used for both SJNU and VDR is very narrow (about 672 ± 1 nm and 687 ± 1 nm).

Evaluation of Turbidity Algorithm
The T2 and T3 models were effective (R 2 = 0.7, RMSE = 260 NTU), as summarized in Table 6. Furthermore, we selected 821 nm and 763 nm as the optimal bands for T2 and 730 nm, 810 nm and 770 nm as the optimal bands for T3. In previous research, many models used a single band in the red to near-infrared as typified by Chen et al. [24], but when turbidity is extremely high and eutrophic, such as in a watershed, 2-BMs are often used. For example, the combination of 550 nm and 850 nm in France's Gironde Estuary (TSS: 13-985 g m −3 ) by Doxaran et al. [27], that of 551 nm and 678 nm (MODIS Bands 12 and 14) in China's Yellow River (TSS: 2-1897 mg L −1 ) by Qiu [41] and that of 555 nm and 645 nm in China's Yangtze River (TSS: 1-300 mg L −1 ) by Hou et al. [42] were used for 2-BMs. These studies obtained very high correlations with R 2 values of 0.8 or more. Because our research sites also have extremely high turbidity and eutrophic water areas, the 2-BM seemed more suitable than a single-band model. Additionally, estimating only turbidity by using a near-infrared wavelength of about 740 nm or more, which is hardly affected by Chla absorption, can be considered appropriate as seen in Figure 1. In contrast, Kutser et al. [29] used bands of 770 nm, 810 nm and 840 nm (T3 model of this study), proposing a new 3-BM targeting the peak near 810 nm in CDOM-rich water areas. This method originally estimates the 810-nm height using the average height of 770 nm and 840 nm as a baseline. The result this time took the average value at 730 nm and 770 nm as the baseline; however, as this idea has just recently been announced, further discussion about which position to use as a baseline will be needed.

Feasibilities of Chla and Turbidity Estimation Using the Sentinel-2 MSI Band
In this study, we investigated whether Chla and turbidity can be estimated by MSI's band, assuming the recently-launched Sentinel-2 MSI, which has high spectral and spatial resolution. As shown in Figure 10, we found no correlation when using all data where both water zones were mixed such that R 2 was greater than 0.5 for both Chla and turbidity. However, when only the VDR data were used, we observed a significant correlation (R 2 = 0.51, RMSE = 9.8 mg m −3 , N = 38) in the 2-BM using 705 nm and 665 nm (MSI Bands 4 and 5). The 2-BM using 775 nm and 740 nm to measure turbidity found a significant correlation (R 2 = 0.77, RMSE = 223 NTU, N = 38). SJNU had much lower turbidity measurements than VDR; thus, we found it extremely difficult to find a unified algorithm. Recently, Chen et al. [43] conducted a Chla estimation study targeting MSI bands by measuring the spectral reflectance of Lake Huron (Chla range of 2-52 mg m −3 ) obtaining 705 nm and 665 nm. In the 2-BM we used, we obtained a correlation of R 2 = 0.49 and RMSE = 9.97 mg m −3 . In addition, Ha et al. [44] obtained 2-BM R 2 values of 0.68 using 560 nm and 665 nm and R 2 =0.29 using 705 nm and 665 nm for Vietnam's Lake Ba Be (Chla range of 1-6 mg m −3 ). This difference indicates the 705-nm and 665-nm frequencies in the 2-BM as more effective in water areas with advanced eutrophication.
As described above, when the Chla and turbidity algorithms are only effective with VDR data, being able to limit the algorithms that can be used based on spectral characteristics beforehand is convenient. In this case, as shown in Figure 11, it is relatively easy to separate data using the spectral reflectance slope of the 2-BM (specifically the slope of MSI Bands 3 and 4 [R rs (560) and R rs (665)] and the slope of MSI Bands 7 and 9 [R rs (775) and R rs (865)]. Such spectroscopic separation is often used during remote sensing of red tide. For example, Takahashi et al. [45] proposed a method for separating red tide and non-red tide data by treating normalized water-leaving radiance spectral characteristics as almost equal to R rs and using the slope of 443 nm and 490 nm and the slope of 490 nm and 555 nm, giving us a method to use. Although different from the subjects in this study, it can be said that the method for separating watershed properties using reflectance gradients can be used as a general and practical method in waters other than SJNU and VDR.

Conclusions
We acquired unified Chla and turbidity remote sensing algorithms based on recent Chla and turbidity algorithms using spectral reflectance data acquired by field surveys of SJNU and VDR and evaluating significantly different spectral characteristics. In addition, we also considered Chla and turbidity estimation using Sentinel-2 MSI frequency bands. As a result, we clarified the following items.
The method using the slopes of R rs (560) and R rs (665) and the slopes of R rs (775) and R rs (865) (that is, judgment above and below the 1:1 line) was effective at spectrally separating SJNU data and VDR data.
Validation of these models by applying them to actual MSI data is a crucial step in assessing model viability and accuracy using space-borne satellite images. Additionally, continuous monitoring of water quality changes in the VDR and SJNU through mapping will help dam water management.
Author Contributions: Y.S. was the director of the field survey and this paper. H.Y. and M.A.M.A.E. were the project leaders in the planning and implementation of field campaigns for this research project. Y.Y., S.S., E.A. and J.G.C. performed the field survey execution and analysis, respectively.