Retrieval of absorption coefficients for a drinking water source using a green–red band quasianalytical algorithm

Abstract. This study proposed a green–red band quasianalytical algorithm, QAA-GRI, and evaluates its performance using an in situ dataset from Lake Qiandaohu, a drinking water source, in China. First, by shifting the reference wavelength from 555 to 510 nm, a green–red index (GRI) can be calculated from remote sensing reflectance at 510, 560, and 620 nm, and the index was then used to retrieve the total absorption coefficients at the reference band, a  (  510  )  . Second, a semianalytical model based on a  (  510  )   and the GRI was deduced to establish the QAA-GRI, replacing the empirical model in quasianalytical algorithm version 5 (QAA-v5). The QAA-GRI was applied to retrieve absorption coefficients from an in situ dataset of Lake Qiandaohu, and the QAA-GRI’s performance was compared with that of QAA-v5 and another red–green QAA-based approach (QAA-RGR). The results demonstrate that, for this dataset, the QAA-GRI exhibited better performance (R2  =  0.81, mean absolute percentage error, MAPE  =  15.7  %  ), which indicated a clear improvement in the accuracy of absorption coefficient retrieval, compared with QAA-v5 (R2  =  0.56, MAPE  =  21.2  %  ) and QAA-RGR (R2  =  0.67, MAPE  =  22.6  %  ). In addition, to illustrate the QAA-GRI’s assumptions and its applicability, the QAA-GRI was also applied to an in situ dataset from Taihu Lake, a highly turbid and eutrophic water source. As predicted, when applied to Taihu Lake, the QAA-GRI did not perform as well as it did when applied to Lake Qiandaohu because of the former’s extremely high turbidity, which can cause greater uncertainty with regard to backscattering coefficients. This study suggests that the QAA-GRI is better suited to the retrieval of absorption coefficients from drinking water resources. Our algorithm will also have potential applications to satellite data from the Medium Resolution Imaging Spectrometer or Ocean and Land Color Instrument.

Retrieval of absorption coefficients for a drinking water source using a green-red band quasianalytical algorithm the absorption coefficients at the reference band of 510 nm. This model, which expresses more physical properties than previous models, offers more potential for deriving absorption coefficients than the original empirical model used in the QAA. Our results indicate that the proposed approach provides an effective alternative for investigating the IOPs of drinking water sources, as well as theoretical insight into other water bodies with similar optical type.
2 Materials and Methods

Study Area
Lake Qiandaohu (118°34′ to 119°15′ E, 29°22′ to 29°50′ N), meaning Thousand Island Lake in Chinese, is a freshwater lake in Zhejiang Province, China, and is part of Xin'an Jiang Reservoir. The lake also attracts tourists, who come for its clear water and numerous islands [ Fig. 1(a)]. The water quality of Lake Qiandaohu is described as oligotrophic, although it has been trending toward mesotrophic. 23 The mean total phosphorus, total nitrogen, and Secchi depth of Lake Qiandaohu are 0.025 mg∕L, 1.042 mg∕L, and 4.7 m, respectively, and the magnitude of absorption by particulates and CDOM is low (as detailed in Table 1). The lake has a surface water area of 580 km 2 and a mean depth of 37 m at its normal water level. It is a long and narrow reservoir with more than 80 bays. The reservoir was constructed in 1959 and has served a variety of purposes, including as the drinking water supply for more than 9.0 million people in Hangzhou city. In comparison, Taihu Lake (118°34′ to 119°15′ E and 29°22′ to 29°50′ N) is the third largest lake in China [ Fig. 1(b)]. Its water surface area and mean water depth are 2340 km 2 and 1.8 m, respectively. Lake Taihu's eutrophication, high levels of TSM, and algal bloom have caused significant concern and motivated several studies; these factors also cause the IOPs of Taihu Lake to be very different from those of Lake Qiandaohu.

Field Sampling and Laboratory Measurements
Field samples were collected from Lake Qiandaohu during nine campaigns from June 2015 to June 2016 (June 1-3, July 7-10, August 4-7, October 9-12, November 3-7, and December 1-4, 2015; March 1-5, May 3-7, and June 1-3, 2016). The sampling dates and location are shown in Fig. 1(a). A total of 144 water samples were collected, among which 63 samples [at lettered stations in Fig. 1(a)] were collected for optical analysis. Another field campaign was conducted at Taihu Lake on May 15-26, 2015, from 38 sampling stations, the distribution of which can be seen in Fig. 1(b). Water samples were collected from depths above 0.5 m, and then filtered on 0.45-μm Whatman glass fiber GF/F filters. The filtered samples were stored in a dark container with liquid nitrogen and taken to the laboratory for chlorophyll-a (Chl-a) concentration analysis within 6 h. The Chl-a was extracted from the filtered samples in hot (80°C) 90% ethanol, the extract was cleared by centrifugation, and the Chl-a concentration was then determined fluorometrically using a Turner fluoroprobe with two replicated measurements following the EPA Method. 26

Absorption Measurements
Several studies 27,28  E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 1 5 1 aðλÞ ¼ a w ðλÞ þ a ph ðλÞ þ a NAP ðλÞ þ a CDOM ðλÞ; (1) where a w ðλÞ is rather constant, as reported by Pope and Fry. 29 The methods for laboratory measurements of a p ðλÞ, a ph ðλÞ, a NAP ðλÞ, and a CDOM ðλÞ are described in detail by Babin et al. 30 and in our previous study. 22 For this study, water samples were processed onboard the ship immediately after collection. CDOM samples were first filtered through a 47-mm diameter Whatman GF/F filter with a pore size of 0.7 μm, and then refiltered through 47-mm diameter millipore polycarbonate filters with pore sizes of 0.22 μm, before being stored in the darkness in a refrigerator. For the particle samples, water volumes of 50 to 500 mL were filtered through 25-mm-diameter Whatman GF/F filters and then kept in a container with liquid nitrogen. These treated samples were (b) (a) Fig. 1 (a) Location of Lake Qiandaohu, and distribution of sampling sites during nine cruises in Lake Qiandaohu; water quality parameters were collected at all stations, and optical sampling, including absorption and remote sensing reflectance measurements, was conducted at the 12 lettered stations. (b) Location of Taihu Lake, and distribution of sampling sites in Taihu Lake on May 2015.
later taken back to the laboratory for analysis of optical variables. The absorption coefficients of CDOM, a CDOM ðλÞ, were measured over 250 to 860 nm in 1-nm increments using a Perkin Elmer (PE) lambda-35 spectrophotometer. Then, a p ðλÞ, a ph ðλÞ, and a NAP ðλÞ were determined according to the quantitative filter technique, 31 calculated from their absorbances measured over 300 to 800 nm in 1-nm increments using a PE lambda-950 spectrophotometer.

Remote Sensing Reflectance Measurements
Synchronous with the water sampling, remote sensing reflectance above the water surface was measured using an ASD field spectrometer (Analytical Spectral Devices, Inc., Boulder Colorado), with a spectral range of 350 to 1050 nm and a spectral resolution of 1.58 nm. For a detailed discussion of in situ spectral measurements above water, see Fargion and Mueller. 32 Remote sensing reflectance measurements for Lake Qiandaohu were collected only at those stations identified by letters in Fig. 1(a). All measurements of reflectance were performed between 9:30 and 15:00 local time. The radiance of water, sky, and a standard Spectralon reflectance plaque was measured 20 times for each target. The radiance spectra from 20 scans of each target were averaged, and then the remote sensing reflectance, R rs ðλÞ, was calculated from the average according to the following equation: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 3 3 7 where L w ðλÞ is the water-leaving radiance, E d ð0 þ ; λÞ is the downward irradiance, L sw ðλÞ is the total radiance from the water surface, L sky ðλÞ is the diffused radiance from the sky, L p ðλÞ represents the radiance of the reference panel, ρ p represents the reflectance of the Spectralon plaque with Lambertian characteristics, and r refers to sea surface skylight reflectance, which is not spectrally constant and is determined by the surface wind speed and the spectral distribution of skylight. Therefore, for this study, an average value of 0.026 in cloudy calm weather, and a value of 0.024 in sunny calm weather, was used according to Cui et al. 33 Prior research has indicated that bottom reflectance affects the water surface reflectance in shallow waters. 34 However, in this paper, when calculating R rs ðλÞ, this effect was considered negligible because Lake Qiandaohu is an optically deep lake, where light cannot penetrate to the bottom.

Algorithm Development
In QAA-v5, as reported by Lee et al., 16 the wavelength of 555 nm is used as the reference wavelength. However, Lee et al. 4 indicated that the reference wavelength should be shifted to a longer wavelength for high-absorption waters. Le et al. 17 proposed a QAA-710 algorithm, in which 710 nm was used as the reference band for highly turbid waters. Chen et al. 19 modeled the empirical relationship between að555Þ and the ratio of R rs ð640Þ to R rs ð555Þ, substituting the empirical model (step 2) in QAA_v5. Here, to adapt the general structure of the QAA for application to drinking water sources, we propose replacing the original empirical model with a semianalytical model of the relationship between að510Þ and a green-red index (GRI). In the proposed model, 510 nm is chosen as the reference band, and the derivation of að510Þ is presented step-by-step based on several reasonable assumptions.

QAA-GRI algorithm
Although spectral remote sensing reflectance, R rs ðλÞ, can be estimated from the ratio of waterleaving radiance, L w ðλÞ to downward irradiance, E d ð0 þ ; λÞ, as in Eq. (2), Gordon et al. 35 and Carder et al. 36 have shown that in a homogeneous water body, R rs ðλÞ can also be defined in terms of IOPs, namely total absorption [aðλÞ] and backscattering [b b ðλÞ] coefficients as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 6 0 3 where f∕Q ratio is a coefficient dependent on the geometry of the light field from the water body, spectrally related to the sun's zenith angle and the volume scattering function. 37 The variation in f∕Q is not significant according to Loisel and Morel;38 its value changes at maximum by ∼20%.
For proper viewing angles in the remote sensing domain and with a solar zenith angle <60 deg, the variation of f∕Q is quite small (below 10%). Therefore, as a first approximation, the f∕Q ratio is assumed to be spectrally invariant in the band range from 500 to 650 nm. To obtain a function directly related to a pc ðλÞ, we adjust Eq. (3) as follows: where aðλÞ ¼ a w ðλÞ þ a pc ðλÞ, and a pc ðλÞ can be expressed as a pc ðλÞ ¼ a p ðλÞ þ a CDOM ðλÞ. We also assume that the difference in a pc ðλÞ between the 560-and 620-nm bands is small. Thus, as a second approximation, the following assumption can be made for each a pc ðλÞ spectrum E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 6 ; 3 9 2 a pc ð560Þ ¼ a pc ð620Þ: In addition, the spectral dependence of b b ðλÞ is considered to be weak, and its variation between 500 and 650 nm is supposed to be small, especially in drinking water sources. 39,40 From this point onward, b b ðλÞ is assumed to be equal in the three bands of 510, 560, and 620 nm for drinking water sources. Based on this assumption, we can obtain the following relationship between the three bands: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 2 9 9 To isolate b b ð560Þ or b b ð620Þ from Eq. (4) by minimizing the effects of b b , we first remove b b from the denominator of Eq. (4) using the other two values of R rs at 560 and 620 nm. By subtracting R −1 rs ð620Þ from R −1 rs ð560Þ, we therefore remove a pc from the denominator of Eq. (4), obtaining E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 1 1 6 ; 2 1 9 where Next, R rs ð510Þ is used to remove b b ð560Þ and Q∕f from Eq. (7). R rs ð510Þ also satisfies Eq. (4) E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 9 ; 1 1 6 ; 6 7 5 Because b b ð510Þ ≪ a w ð510Þ þ a pc ð510Þ for drinking water sources, b b ð510Þ in the denominator of Eq. (9) can be neglected. Multiplying the reciprocal of Eq. (8) and the reciprocal of Eq. (9) by 0.213, we obtain an approximation of the green-red retrieval index (GRI), as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 0 ; 1 1 6 ; 5 9 2 Once the absorption coefficient at the reference band, að510Þ, is obtained, the QAA-GRI algorithm can be developed based on the general framework of the QAA (see Sec. 3.3).

Accuracy assessment
Two indices, the root mean square error (RMSE) and the mean absolute percentage error (MAPE), were used to assess the accuracy of the QAA-GRI algorithm. The RMSE is defined as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 1 ; 1 1 6 ; 4 5 0 where n is the number of observations, a measured;i and a retrieved;i are the measured and retrieved absorption coefficients at each station i, respectively. The MAPE compares the differences between the measured and retrieved absorption coefficients at all stations, and is calculated as the following: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 2 ; 1 1 6 ; 3 5 6 MAPE ¼ X ja retrieved;i − a measured;i j a measured;i ∕n: 3 Results

Water Quality and Absorption Properties
The descriptive statistics of water quality (including Chl-a and turbidity) for all stations, as well as remote sensing reflectance and absorption coefficients of particles and CDOM at the lettered stations of Lake Qiandaohu are shown in Table 1. Variations in the concentrations of optically active constituents and absorption coefficients were found in the dataset from Lake Qiandaohu. For the whole dataset, the turbidity, which represents the TSM concentration, was small, ranging from 0.35 to 20.5 NTU, with an average of 2.27 NTU. Therefore, Lake Qiandaohu is not turbid. The concentration of Chl-a ranged from 0.37 to 30.35 μg∕L, with an average value of 5.62 μg∕L, indicating that the trophic level of Lake Qiandaohu remains low. The sums of spectral absorption coefficients of particles and CDOM, a pc ðλÞ, matched with the corresponding remote sensing reflectance, are shown in Fig. 3(a), from which peaks at 675 nm can be observed due to the strong absorption of Chl-a. The magnitude of a pc ðλÞ was quite low, ranging from 0 to ∼1.5 m −1 , with only slight variation. Therefore, Lake Qiandaohu can be characterized as relatively low-absorption water based on its optical properties. Figure 2(a) shows the average a p ðλÞ, a ph ðλÞ, and a NAP ðλÞ between 400 and 700 nm, which indicate that the CDOM absorption generally dominated the total absorption of Lake Qiandaohu.
The absorption by pure water at wavelengths >550 nm dominated the total absorption. As shown in Table 1, the absorption coefficient of particles at 440 nm, a p ð440Þ, ranged from 0.045 to 0.548 m −1 ; the CDOM absorption coefficient at 440 nm, a CDOM ð440Þ, ranged from 0.134 to 0.435 m −1 ; the phytoplankton absorption coefficient at 675 nm, a ph ð675Þ, ranged from 0.008 and 0.242 m −1 , and its magnitude had a direct relationship with Chl-a concentration. Figure 2(b) shows the absorption budget derived from the in situ data using a ternary plot at five different wavelengths. Spectral changes in the ternary plot reveal interesting, although expected, patterns. In the ternary plots at 440, 510, and 560 nm, the majority of our data show that the relative contribution of CDOM dominated other constituents in Lake Qiandaohu. The relative contribution of NAP absorption never exceeded 50% among the three constituents considered. However, the relative contribution of NAP absorption increased at 620 nm, and the phytoplankton absorption was dominant at 675 nm.

Remote Sensing Reflectance
The reflectance collected on April 6-9, 2016, was not considered because a rainstorm on April 2-3, 2016, contaminated Lake Qiandaohu with the heavy soil erosion. Therefore, the remaining 47 spectra of remote sensing reflectance are shown in Fig. 3(b). The shapes of the spectra were generally similar to many case 2 waters, although they were closer to case 1 than those from Taihu Lake [ Fig. 8(b)]. 41,42 The remote sensing spectrum of Lake Qiandaohu showed a low magnitude (ranging from 0 to 0.014 sr −1 ), high variability in the blue and green regions, and a near-zero value in the near-infrared red (NIR) region. Furthermore, there was a weak trough around 440 nm, which is a typical characteristic of oligotrophic waters. 43 The reflectance  showed a peak around 550 nm, where the absorption of phytoplankton pigments was minimal, and the magnitude of reflectance in this range was mainly controlled by scattering of phytoplankton and NAP. The magnitudes of R rs ð550Þ are given in Table 1, ranging from 0.003 to 0.013 sr −1 , with an average value of 0.006 sr −1 . The reflectance spectrum showed a weak trough at 665 nm, which was caused by the Chl-a absorption maximum; this magnitude was affected by the Chl-a concentration and fluorescence contribution. 44 The reflectance peak at 680 nm resulted from the minimal combined absorption of phytoplankton, NAP, and water. 45 In the NIR band, the reflectance reached a minimum, approaching zero, which was caused by the increasing absorption by water and a relatively small scattering by NAP due to the low concentration of TSM. Unlike drinking waters, the reflectance in the NIR range of turbid waters would not be negligible because of the scattering that results from the high concentration of sediments. 46

QAA-GRI Calibration in Lake Qiandaohu
In this study, the QAA-GRI is proposed specifically to retrieve aðλÞ from drinking water source, Lake Qiandaohu in this case, by establishing a relationship between að510Þ and the GRI. Figure 3(a) shows that the a pc ðλÞ spectrum measured in Lake Qiandaohu is almost flat in the 560-to 650-nm range, and Fig. 4(a) shows that the a pc ðλÞ variation is rather small in this range. Moreover, the absorption values in this range are much smaller than those in the blue and red bands. Figure 4(b) shows that the values of a pc ð620Þ − a pc ð560Þ in Eq. (7) at all the Lake Qiandaohu stations were small, with an average far less than the value of a w ð620Þ − a w ð560Þ, which was 0.213 m −1 . Therefore, the value of a pc ð620Þ − a pc ð560Þ accounted for only a small proportion (approximately one-fifth) of the numerator of Eq. (7) and can be considered negligible, validating Eq. (7). Based on this analysis and Eq. (7), we considered the rapid decrease of R rs from 560 to 620 nm, shown in Fig. 3(b), to be mainly caused by the strong absorption of pure water, rather than by particles and CDOM. These results supported the assumption used to derive the QAA-GRI: a pc ð560Þ ¼ a pc ð620Þ. Hence, the QAA-GRI could be cautiously calibrated based on the in situ dataset collected from Lake Qiandaohu. Figure 5 shows the relationship between the GRI and að510Þ (R 2 ¼ 0.78) using the in situ data measured from Lake Qiandaohu. Based on these data, the following equation relating the total absorption coefficients at 510 nm, að510Þ, with the GRI was obtained E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 3 ; 1 1 6 ; 3 6 3 að510Þ ¼ 0.5712 × GRI þ 0.081: (13) It should be noted that Eq. (13) overestimates að510Þ for oceanic waters. When the GRI approaches zero, as in oceanic cases, the að510Þ derived by Eq. (13) is more than two times a w ð510Þ, which is not supported by ocean optics. Therefore, the condition that GRI > 0.05 is required to ensure that Eq. (13) will provide the accurate estimations for inland waters. Because the reference band used in the original QAA was shifted from 555 to 510 nm, the coefficients of the spectral slope (Y) calculation (step 4) were fine-tuned with an optimization algorithm. 47 The newly developed algorithm for retrieving aðλÞ, QAA-GRI, is summarized in Table 2.

Performance of QAA-GRI Algorithm for the In Situ DataSet in Lake Qiandaohu
This subsection presents the performance of the QAA-GRI algorithm in relation to the in situ dataset collected in Lake Qiandaohu. Figure 6 shows a scatterplot of the aðλÞ derived by the QAA-GRI and from in situ measurements at specific wavelengths. These results demonstrate that the QAA-GRI algorithm performs well in this case. Moreover, the correlation coefficients of the QAA-GRI results at 460, 490, and 510 nm are slightly higher than those at 560 nm.  4 which indicated that the accuracy of aðλÞ retrieval around the reference band is highest, and the retrieval uncertainties tend to increase in the blue bands because of the high magnitude of aðλÞ and the complex interactions among CDOM, NAP, and phytoplankton within this range.

Comparison with Different Algorithms
Three different algorithms for the retrieval of absorption coefficients, QAA-v5, QAA-RGR, and QAA-GRI, were applied to the same dataset from Lake Qiandaohu for comparison. Figure 7 shows scatterplots of the estimated and measured aðλÞ at different wavelengths for all three algorithms. The regression analysis clearly indicates that the newly developed QAA-GRI algorithm shows the best performance at all five wavelengths, with the highest R 2 value of 0.81, whereas QAA-v5 and QAA-RGR yield R 2 values of 0.56 and 0.67, respectively. The MAPE values for QAA-v5, QAA-RGR, and QAA-GRI are 21.2%, 22.6%, and 15.7%, respectively. This result is attributed to the fact that the performance of QAA-v5 and QAA-RGR strongly depends on the accuracy of að555Þ; however, these algorithms apply a simple empirical approach based on band ratio methods that can reduce some errors in R rs measurements but do not eliminate them. However, the band difference approach used in the QAA-GRI is less  sensitive to errors than the band ratio methods. 48 The QAA-RGR has a slightly higher R 2 value compared with that of the QAA-v5; however, the former clearly underestimates aðλÞ compared with the other two algorithms. This probably is because the QAA-RGR estimates Y using a "local-specific" model of b b ð555Þ; however, b b ð555Þ is associated with more uncertainty than the band ratio of r rs used in QAA-v5 and QAA-GRI, and thus leads to a lower b b ðλÞ retrieval. Therefore, the underestimation of aðλÞ by the QAA-RGR can be regarded as due to systematic errors, and its R 2 value can still be used to evaluate the algorithm performance. The statistical parameters for the estimated and measured aðλÞ at 460, 490, 510, and 560 nm are given in Table 3. For the derivation of að620Þ, the QAA-GRI yields a smaller RMSE and MAPE compared with the other two algorithms, which means that the relationship between the retrieved and measured values is closer to 1∶1 line, as can also be observed from Fig. 7(c). This results occur because step 2 of the proposed model (see Table 2) results in a more accurate aðλÞ retrieval at the reference band for the in situ data of Lake Qiandaohu, which in turn significantly improves the low magnitude að620Þ retrieval. These results show that both QAA-v5 and QAA-RGR do not perform satisfactorily; however, the proposed QAA-GRI can derive more accurate estimates of absorption coefficients, particularly for waters with relatively low-absorption coefficients.

Comparative Evaluation of Applying QAA-GRI to Taihu Lake
Several studies have indicated that QAA-v5 and QAA-RGR cannot be applied directly to Taihu Lake. To independently evaluate the QAA-GRI in relation to the wider range of values presented by highly turbid waters, we applied the proposed algorithm to the 38 measurements of remote sensing reflectance and absorption coefficients collected in Taihu Lake. The in situ measurements of remote sensing reflectance [R rs ðλÞ] and absorption spectra of a pc ðλÞ in Taihu Lake are shown in Figs. 8(a) and 8(b), respectively. The R rs ðλÞ of Taihu Lake can be seen to be typical of inland eutrophic waters; its magnitude is more than three times higher than that in Lake Qiandaohu [ Fig. 3(b)], and the a pc ðλÞ is five times higher. Furthermore, the Chl-a concentration Table 3 Comparison of QAA-v5, QAA-RGR, and QAA-GRI aðλÞ retrieval performance relative to measured data from Lake Qiandaohu at 460, 490, 510, and 560 nm. and absorption coefficients vary significantly (Table 4), with larger values than those in Lake Qiandaohu (Table 1). In Taihu  These results provide further evidence of the high turbidity and large spatial variations in Taihu Lake. As predicted, the performance of the QAA-GRI at five specific wavelengths in Taihu Lake (R 2 ¼ 0.45) is poorer than that in Lake Qiandaohu (R 2 ¼ 0.81). This result is attributed to the poor applicability of the QAA-GRI algorithm to Taihu Lake, which does not satisfy the assumptions used in the algorithm. The absorption coefficients of particles and CDOM in Taihu Lake were significantly higher than those in Lake Qiandaohu; therefore, the assumption applied in relation to Eq. (5) does not hold true, and the a pc ðλÞ difference between 560 and 620 nm in Taihu Lake could not be disregarded. Figure 9(b) also shows that a pc ð620Þ − a pc ð560Þ had a similar magnitude for all data from Taihu Lake, or even exceeded a w ð620Þ − a w ð560Þ in the numerator of Eq. (7). Furthermore, in highly turbid water with eutrophication, the assumption used in Eq. (6) may be invalid. Several studies have indicated that the backscattering coefficient in the blue and red bands may vary significantly for highly turbid waters. 49,50 In addition, the magnitude of backscattering coefficients of particles in highly turbid waters is relatively larger than that in clear waters, and therefore could not to be ignored in the denominator of Eq. (7). Therefore, the two assumptions used in the QAA-GRI algorithm are not valid in highly turbid waters, and therefore the QAA-GRI could not perform as well for Taihu Lake as for Lake Qiandaohu.

Factors Influencing QAA-GRI Application
There are a few prerequisites for successful application of the newly developed QAA-GRI algorithm. One assumption is that a pc ð560Þ equals approximately a pc ð620Þ, or equivalently, that  að560Þ equals að620Þ because aðλÞ ¼ a w ðλÞ þ a pc ðλÞ where a w ðλÞ is a constant. This assumption requires that the difference between a pc ð560Þ and a pc ð620Þ be small. Therefore, when using the QAA-GRI algorithm, one should analyze the absorption spectra of the total particulate and CDOM. The key to the successful application of the QAA-GRI is that Eq. (14) must be satisfied, particularly that "≪" is fulfilled. Fortunately, this requirement for Eq. (14) is satisfied in most drinking water resources, which have low TSM concentrations For the two cases discussed above, the average value of a pc ð560Þ − a pc ð620Þ for all the measurements of Lake Qiandaohu is ∼0.034 m −1 , which is much smaller than one-sixth of the a w ð620Þ − a w ð560Þ value, 0.213 m −1 [blue line in Fig. 4(b)]. However, the average magnitude of a pc ð560Þ − a pc ð620Þ for the measurements of Taihu Lake is 0.279 m −1 , even exceeding 0.213 m −1 , as shown in Fig. 9(b). Therefore, for waters with different optical properties, if the magnitude of a pc ð560Þ − a pc ð620Þ accounts for only a small proportion of Eq. (7) numerator, the value of a pc ð560Þ − a pc ð620Þ could be considered negligible because its value is much smaller than a w ð620Þ − a w ð560Þ. In contrast, if the value of a pc ð560Þ − a pc ð620Þ cannot be neglected, the assumption used in Eq. (7) would be invalid, as in the case of Taihu Lake.
Another necessary assumption used in the QAA-GRI is that the backscattering coefficients at 510, 560, and 620 nm have little variation; thus, b b was considered to be approximately the same at these wavelengths. In moderately turbid waters, such as Lake Qiandahu, b b is typically weak, and its magnitude is much lower than the magnitude of the total absorption coefficients. Therefore, the approximate equation, b b ð510Þ ¼ b b ð560Þ ¼ b b ð620Þ, holds true in this water body. Conversely, b b in Taihu Lake has a relatively large magnitude, and its values between 510 and 650 nm vary significantly. 49 Therefore, the backscattering coefficients, b b , can be considered neither negligible nor equal, and the QAA-GRI may generate large estimation errors when retrieving the total absorption coefficient, aðλÞ, in highly turbid waters such as those of Taihu Lake.
Because these conditions must be satisfied to apply the QAA-GRI, appropriate bodies of water must be identified to apply the proposed algorithm. However, in situ IOPs are difficult to obtain for local water bodies, and the most relevant parameter that can be obtained from ocean color satellite data is remote sensing reflectance. Therefore, the following criterion is recommended for detecting waters where QAA-GRI can be successfully applied, based on a combination of the GRI and R rs indices: when the R rs peak is at ∼560 nm, R rs ð560Þ < 0.015, and GRI > 0.05, the QAA-GRI can be applied to these inland waters. The R rs index indicates that the water is not highly turbid and Eq. (14) holds true; the GRI index excludes waters with optical properties similar to those of oceanic waters, and some coastal waters. 51

Conclusions
A GRI based on remote sensing reflectance at three bands (510, 560, and 620 nm) was proposed in this study. With a semianalytical model that establishes a relationship between að510Þ and the GRI, the proposed QAA-GRI was developed to derive the total absorption coefficients for drinking water sources analytically. Two independent bio-optical datasets were used to evaluate the applicability and accuracy of the QAA-GRI in retrieving absorption coefficients from two different types of inland waters. Encouraging results were achieved when the algorithm was applied to Lake Qiandaohu (R 2 ¼ 0.81, MAPE ¼ 15.7%).
The QAA-GRI could potentially be successfully applied to oceanic waters because the assumptions upon which the QAA-GRI is based are also satisfied in these waters. If this is the case, the relationship between að510Þ and the GRI must be modified to accommodate the broader range of oceanic dataset. Therefore, further studies are required to extend the application of QAA-GRI, and we eagerly anticipate applying the QAA-GRI to the Ocean and Land Color (OLCI) satellite data in the near future because the three characteristic bands used in QAA-GRI can be found exactly in this instrument.