# Validation and Calibration of QAA Algorithm for CDOM Absorption Retrieval in the Changjiang (Yangtze) Estuarine and Coastal Waters

^{*}

## Abstract

**:**

_{g}(λ)) can be used as an indicator to trace the distribution and variation characteristics of the Changjiang diluted water, and further to help understand estuarine and coastal biogeochemical processes in large spatial and temporal scales. The quasi-analytical algorithm (QAA) has been widely applied to remote sensing inversions of optical and biogeochemical parameters in water bodies such as oceanic and coastal waters, however, whether the algorithm can be applicable to highly turbid waters (i.e., Changjiang estuarine and coastal waters) is still unknown. In this study, large amounts of in situ data accumulated in the Changjiang estuarine and coastal waters from 9 cruise campaigns during 2011 and 2015 are used to verify and calibrate the QAA. Furthermore, the QAA is remodified for CDOM retrieval by employing a CDOM algorithm (QAA_CDOM). Consequently, based on the QAA and the QAA_CDOM, we developed a new version of algorithm, named QAA_cj, which is more suitable for highly turbid waters, e.g., Changjiang estuarine and coastal waters, to decompose a

_{g}from a

_{dg}(CDOM and non-pigmented particles absorption coefficient). By comparison of matchups between Geostationary Ocean Color Imager (GOCI) retrievals and in situ data, it reveals that the accuracy of retrievals from calibrated QAA is significantly improved. The root mean square error (RMSE), mean absolute relative error (MARE) and bias of total absorption coefficients (a(λ)) are lower than 1.17, 0.52 and 0.66 m

^{−1}, and a

_{g}(λ) at 443 nm are lower than 0.07, 0.42 and 0.018 m

^{−1}. These results indicate that the calibrated algorithm has a better applicability and prospect for highly turbid coastal waters with extremely complicated optical properties. Thus, reliable CDOM products from the improved QAA_cj can advance our understanding of the land-ocean interaction process by earth observations in monitoring spatial-temporal distribution of the river plume into sea.

## 1. Introduction

_{g}to study occurrence and distribution of red tides in coastal waters off South Florida; Bowers et al. [12] used salinity to determinate a

_{g}in an estuary for exploring the river discharge.

_{g}(λ) from spectral measurements of ocean water. Empirical algorithms [13,14,15,16,17,18,19] were mostly based on spectral reflectance ratios to calculate a

_{g}(λ), and these algorithms required adequate data to parameterize the model and may only be valid for specific locations. Algorithms based on statistical modeling [18,20,21,22,23,24], such as optimization (Garver-Siegel-Maritorena, GSM), matrix inversion algorithm, artificial neural network (aNN) and Linear Matrix Inversion (LMI) algorithm, used some semi-analytical methodologies, but required knowledge about specific biochemical parameters [5]. Semi-analytical algorithms [25,26,27] mostly use R

_{rs}(λ) to calculate IOPs and further to estimate biochemical parameters, which incorporate both empirical parameters and bio-optical models. The quasi-analytical algorithm (QAA) developed by Lee et al. [28] was widely applied during the last decade. Several updated versions were presented in following years [29,30,31]. Recent version (QAA_v6) has been presented online by Lee [31].

## 2. Materials and Methods

#### 2.1. Shipborne Samplings and Measurements

_{d}, spectral incident radiance, L

_{s}, total spectral upwelling radiance, L

_{tot}) for estimating R

_{rs}(λ) were measured by Hyperspectral surface acquisition system (HyperSAS, Satlantic Inc.

^{®}, Halifax, NS, Canada). A total of 371 surface data samples was collected. Two radiance sensors were pointed to the sea and sky, respectively, at an optimal zenith angle of 40°, and at an optimal azimuth angle of 135° away from the sun, in order to maximally avoid the wind speed impact and minimize solar glitter effects [46].

^{®}absorption and attenuation meter (ac-s) during downcasts and upcasts as water flowed through the ac-s meter. A total of 479 data samples of a was obtained. b

_{b}(λ, z) values were measured simultaneously by WETLabs

^{®}ECO-BB9 backscattering sensors (at wavelengths of 412, 440, 488, 510, 532, 595, 650, 676, and 715 nm, and at a scattering angle of 117°). 515 data samples of b

_{bp}were collected.

_{rs}, a and b

_{b}were obtained. Furthermore, SPSS software (IBM

^{®}, version 22.0) was used to control data quality. Excluding the sampling data deviating from the mean values more than ±3σ, 144 matchup data were reserved for the analysis. In addition, 159 matchup data of a

_{g}and R

_{rs}were collected. All matchup locations are shown in Figure 1a. Meanwhile, two sets of matchup data were randomly divided into two parts, of which 70% were used to calibrate algorithm, and 30% to validate algorithm.

_{rs}(λ) validation data.

#### 2.2. Data Processing

_{d}(λ), incident spectral radiance, L

_{s}(λ), total upwelling spectral radiance, L

_{tot}(λ), R

_{rs}(λ) is estimated by Sokoletsky and Shen [47]:

_{sky}(λ) stands for a ratio of spectral reflected sky radiance, and L

_{s,sky}(λ) for incident spectral sky radiance. The estimations of ρ

_{sky}(λ), L

_{s,sky}(λ) and R

_{rs}(λ) were detailed in Sokoletsky and Shen [47].

_{nw}(λ), we have used a modified Boss’s method (MBM) which was described in Sokoletsky and Shen [47]. The average of a(λ, z) in depths of 0.5~1.5 m is adopted for the surface data. b

_{bp}(λ) is calculated using a scale factor supplied by the WETLabs Inc. [48]. The specific correction method of b

_{bp}is described in Sokoletsky and Shen [47]. In turbid waters, b

_{bp}at λ < 488 nm measured by ECO-BB9 is generally too low due to absorption effects. Therefore, a spectral power function fitting was conducted, based on b

_{bp}(λ, z) values measured at λ ≥ 488 nm [47]. In this study, the average of b

_{bp}(λ, z) in depths of 0.5 to 1.5 m is adopted for the surface values.

_{g}(λ) was derived as follows [39]:

_{g}(λ) represent uncorrected values of a

_{g}(λ) at wavelength λ, λ in nm; l is the length of cuvette, l = 0.1 m. Further, these initial values were scattering corrected as follows [8]:

_{g}(λ) is the final CDOM absorption coefficient.

#### 2.3. Satellite Images

_{rs}(λ). Afterwards, GOCI images R

_{rs}(λ) were used for CDOM retrieval. Quasi-synchronous matchups between GOCI overpass observations and ground samplings were available during 6 March 2012 and 22 March 2015. A time window between in situ and satellite data was set at ±3 h for the Changjiang estuary, and ±24 h for the outer oceanic area. A mean value from a 3 × 3 pixel box centered at each sampling site is used aiming to reduce sensor and algorithm noise. A total of 28 images were obtained. Locations and time intervals of matchup samples are shown in Figure 1b.

#### 2.4. QAA_v6

_{rs}and IOPs from Gordon et al. [52]:

_{0}= 0.089 and g

_{1}= 0.1245 were accepted in this study in accordance with the QAA_v6. r

_{rs}(λ) has a computable relation with R

_{rs}(λ) according to the following Equation (1) (QAA_v6, step 0),which can be derived from R

_{rs}to obtain IOPs:

_{0}was selected, and then b

_{bp}(λ) and a(λ) were estimated by semi-analytical and analytical algorithms. In this process, a

_{ph}(λ), a

_{g}(λ), and a

_{d}(λ) were not taken into account. In the second part, the total absorption coefficient which was derived from the first part was decomposed into absorption coefficients of its major components.

_{0}) could be estimated from R

_{rs}(443), R

_{rs}(490), R

_{rs}(55X), and R

_{rs}(670) according to empirical formula (QAA_v6, step 2):

_{rs}(670) < 0.0015 sr

^{−1}:

_{0}) is an empirical coefficient relating to the specific study area, h

_{0}= −1.146, h

_{1}= −1.366, h

_{2}= −0.469. Therefore, it is calibrated by fitting Equation (7) by using in situ data in the study area, which is detailed in Section 3.1.

_{b}(λ) is expressed by Lee [31] (QAA_v6, step 5):

_{dg}(λ) and a

_{ph}(λ). The expression for a

_{dg}is given by Lee [31] (QAA_v6, step 9):

_{dg}(λ). According to QAA_v6, S values can be estimated by spectral ratio (QAA_v6, step 8):

#### 2.5. QAA_CDOM

_{g}, the mixture variable a

_{dg}needs to be further decomposed to a

_{g}and a

_{d}. However, the QAA_v6 cannot separate a

_{g}from a

_{dg}so far. In this study, we use QAA_CDOM algorithm proposed by Zhu and Yu [26] and Zhu et al. [27] to separate a

_{g}(443) and a

_{d}(443) by:

_{1}and j

_{2}are calculated by fitting Equation (11) by using in situ data in the study area, which is detailed in Section 3.1.

_{bp}(555) to estimate a

_{p}(443). Therefore, a

_{g}(443) can eventually be obtained by subtracting a

_{p}(443) and a

_{w}(443) from a(443) estimated by the QAA_v6.

#### 2.6. Accuracy Assessment

^{2}). These indices are defined as follows (N is the number of samples):

_{est,i}and X

_{mea,i}are predicted and in situ values of optical parameters, respectively.

## 3. Results

#### 3.1. QAA_cj Calibration

_{0}= 680 nm in Equation(7), Y in Equation (8), a

_{dg}(443) in Equation (9) and S in Equation (10). Details of calibration are described as follows.

^{−4}λ − 9.193 × 10

^{−7}λ

^{2}+ 3.174 × 10

^{−10}λ

^{3}, β(λ) = 1.357 + 8.608 × 10

^{−4}λ − 6.347 × 10

^{−7}λ

^{2}, λ in nm. Equation (17) was derived from the Aas-Højerslev radiative transfer model [47,54,55] at solar zenith angle θ

_{0}= 40°, wind speed = 5 m·s

^{−1}, and the wavelength range of 400 to 800 nm with R

^{2}= 0.9995 and R

^{2}= 0.9903 for α(λ) and β(λ), respectively.

_{0}) formula (step 2 in Table 3). a(λ) was significantly underestimated, when reference wavelength in Equation (7) was accepted as 55X or 670 nm. Through the correlation analysis, it was found that λ

_{0}= 680 nm is the optimal reference wavelength. Based on our in situ data, the following equation relating non-water absorption at 680 nm, a

_{nw}(680), with the spectral ratio R

_{rs}(680)/R

_{rs}(490) was derived as follows (Figure 3):

_{bp}(680) and its corresponding Y values derived from Equation (8). The power regression is:

_{g}(λ) formula (step 7 in Table 3). Though regression analysis, Equation (11) is fitted by in situ data, where it was found that j

_{1}= 4.802 and j

_{2}= 0.8055, with the significance level p < 0.001 (Figure 5).

_{rs}(555)/R

_{rs}(490) and its corresponding S values derived from Equation (10). The power regression is:

#### 3.2. In Situ Data for QAA_cj Validation

_{0}= 670 nm has been selected for the R

_{rs}(λ) dependence in Equation (7) following the QAA_v6 spectral criterion.

_{bp}(λ) by the QAA_v6 (triangles) and QAA_cj (circles) algorithms based on the validation database. It is clear to be seen that values of Y estimated by QAA_cj range from 1.7 to 2.3, which is much closer to the measured values, whereas, the QAA_v6 estimation is largely underestimated (0.3~1).

^{2}are 0.73 and 0.30, respectively. Poor RMSE and bias results are mainly caused by the bias of Y value estimation. In addition, the QAA_v6 algorithm performed better than QAA_cj at 412 and 443 nm, which could be explained by the inaccuracies caused by the empirical Equation (18).

_{g}and a

_{d}have similar absorption features, a

_{g}cannot be extracted from the a

_{dg}by the QAA_v6 algorithm. Therefore, QAA_cj-derived a

_{g}(λ) values were compared only with the QAA_CDOM-derived a

_{g}(λ) values (Figure 8), and the assessment results are shown in Table 5. QAA_cj has a better accuracy in estimating a

_{g}(443) with RMSE, MARE and bias of 0.07, 0.42 and 0.018 m

^{−1}compared with those of 0.25, 2.39 and 0.22 m

^{−1}, respectively, from QAA_CDOM. The retrival accuracy of a

_{g}(λ) at wavelengths of 412 and 490 nm is improved as well (Table 5).

#### 3.3. Satellite Data for QAA_cj Validation

^{2}is larger than 0.8 at 680 nm. It shows that the QAA_cj yielded a better accuracy in estimating a(680) with RMSE and bias of −0.025 and 0.10 m

^{−1}, compared with those of 0.62 and 0.31 m

^{−1}from QAA_v6. However, the inversion result is slightly poor at 745 nm (Figure 9, Table 6).

_{g}(λ), compared with in situ data (Figure 10). It is indicated that estimations from the QAA_CDOM have lower agreement with the in situ values. Meanwhile, QAA_cj has a better consistency in estimating a

_{g}(λ) at 412, 443 and 490 nm, compared with the QAA_CDOM. Remarkably, the retrieval accuracy is optimal at wavelength of 443 nm, at which MARE is 0.14, R

^{2}is 0.70, whereas QAA_CDOM yields MARE = 2.34 and R

^{2}= 0.11 (Table 7).

## 4. Discussion

_{g}and R

_{rs}ratio (using different wavelengths) in Mississippi River and the Baltic. Using R

_{rs}(λ) to calculate a and further to separate out a

_{dg}and a

_{ph}, semi-analytical models, such as GSM [23] and QAA [28], were developed based on IOCCG dataset and in situ data, while Brando and Dekker [5] and Hoge and Lyon [22] developed models using in situ data in Fitzroy Estuary and U.S. Middle Atlantic Bight.

_{g}(λ), on the one hand it could not be estimated by the QAA algorithm and on the other hand it was overestimated by the QAA_CDOM algorithm (Figure 8), while the QAA_cj retrieved value of a

_{g}(443) has RMSE and R

^{2}of 0.07 m

^{−1}and 0.90, respectively, compared with in situ data (Table 5). Nevertheless, the accuracy of a

_{g}(λ) derived from the QAA_cj in highly turbid waters still remains to be a challenge.

_{rs}(λ) to its underwater analog, r

_{rs}(λ). Therefore, in this study, we used the formula proposed by Sokoletsky et al. [57] to calculate r

_{rs}(λ) from R

_{rs}(λ). Sokoletsky and Shen [47] showed that although relations between R

_{rs}(λ) and r

_{rs}(λ) are close for different models, the particular model parameters may play an important role in the inversion results. In addition, we have used only clear and cloudless sky conditions to measure R

_{rs}(λ) to do calculations more simple and closer to remote-sensing results, Figure 2b.

_{0}and g

_{1}) as constants. These parameters are associated with the solar zenith angle and water properties, and vary with water composition scattering properties [62]. Consequently, g

_{0}and g

_{1}have influence on b

_{b}(λ), when using QAA, it will further affect the inversion accuracy of a(λ). Lee et al. [62] partitioned and weighted parameter g according to the molecular (water itself) and particulate contributions to the backscattering coefficient. In this study, however, this approach was not exploited.

_{0}) and Y have an impact on performance of the QAA. Y is a parameter which describes spectral variation of b

_{bp}(λ) [64], and the variation of Y depends on water composition and size of particles according to the Mie theory [65]. Yang et al. [38] found that Y values have a great impact on the retrieval results, particularly in the shorter spectral bands. Figure 6 shows that the QAA_v6 algorithm has a low accuracy in estimating Y, which perhaps caused by the insufficient capability of this algorithm considering the complex optical features of the Changjiang estuarine and coastal waters. The ranges of Y values derived from the QAA_cj and the QAA_v6 are from 1.5 to 2.5 and from 0.3 to 1, respectively (Figure 6). Even though our algorithm for Y (Equation 19) does not yield a reasonable correlation with the measured values (Figure 6), we have chosen to keep it for generalization purposes, and we are planning to improve the Y model in the following study.

_{g}(λ) from the GOCI images using the QAA_v6, QAA_CDOM and QAA_cj algorithms, and presented the comparison results in Figure 9 and Figure 10. As shown in Figure 9, differences between our algorithm and in situ data is smaller than those between the QAA_v6 and in situ data for the whole blue to near infrared spectral range. Similar findings were found for the a

_{g}(λ) retrieving in the blue spectral domain (Figure 10).

_{b}(λ) (from 8% to 14%) depending on wavelength and ocean site. In addition, Zhu et al. [69] compared and verified 15 CDOM retrieval algorithms (empirical, semi-analytical, optimization, and matrix inversion algorithms), and pointed out that the QAA_CDOM algorithm was optimal. The reason of this is that CDOM has negligible backscattering, whereas inorganic particles have strong backscattering, even in longer wavelength [27]. Several researches find that QAA_CDOM has a good accuracy in obtaining the a

_{p}(λ) from b

_{bp}(λ) [26,27,69]. However, QAA_CDOM has some empirical parameters, which are required to be calibrated according to specific study area. Figure 10 shows that after calibration, a

_{g}(λ) has a significant improvement at 412, 443, 490 nm. It seems obvious that better accuracy in a

_{g}(λ) leads to improvement of a retrieval accuracy for a

_{ph}and a

_{d}.

## 5. Conclusions

_{g}(λ), compared with the QAA_v6 and QAA_CDOM. a(λ) derived from QAA_cj is in a good agreement with in situ and GOCI data, where RMSE ranges from 0.35 to 1.17 m

^{−1}, MARE from 0.11 to 0.52, bias from −1.23 to 0.66 m

^{−1}and R

^{2}is from 0.28 to 0.82. As for a

_{g}(λ), RMSE ranges from 0.035 to 0.12 m

^{−1}, MARE from 0.14 to 0.42, bias from −0.0086 to 0.033 m

^{−1}and R

^{2}is from 0.53 to 0.92.

_{g}(λ) retrieval accuracy will help to provide theoretical basis for the release of satellite product and further study on optical properties. Reliable CDOM products can provide information on the internal movements and nutrients structure of Changjiang diluted water and mechanisms of hydrodynamics in the Changjiang estuarine and coastal waters. The trace of CDOM can advance our understanding of the land-ocean interaction processes through monitoring spatial-temporal distribution of the river plume into sea. In the future, we will focus on exploring the relationships between environmental factors and optical parameters, in combination with satellite data and physical models.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Location of sampling stations in the Changjiang estuarine and coastal waters. (

**a**) Samples were collected from 9 cruises in summer (May, July 2011, August 2013 and July 2015) and winter (February, March 2012, March 2013, February 2014 and March 2015); (

**b**) Matchup stations selected for in situ and GOCI images (empty circles and stars represent the matchup time windows within ±24 h, filled circles and stars within ±3 h).

**Figure 2.**(

**a**) Typical spectra of remote-sensing reflectance collected in the Changjiang estuarine and its adjacent coastal waters; (

**b**) The sun zenith angle and weather conditions of in situ R

_{rs}(λ) validation data.

**Figure 3.**Scatter plot of in situ measured a

_{nw}(680) values versus R

_{rs}(680)/R

_{rs}(490) spectral ratios.

**Figure 6.**Comparison of in situ and predicted Y values. The filled squares are in situ Y values, empty circles and triangles denote Y values derived from QAA_cj and QAA_v6, respectively.

**Figure 7.**Comparison of in situ and predicted a(λ) at 443, 555, 680 and 715 nm based on an in situ data set collected from the Changjiang estuarine and coastal waters. The filled circles and empty symbols denote retrievals from algorithms QAA_cj and QAA_v6, respectively.

**Figure 8.**Comparison of in situ and predicted a

_{g}(λ) based on an in situ data set collected from the Changjiang estuarine and its adjacent coastal waters. The filled and empty symbols denote retrievals following QAA_cj and QAA_CDOM algorithms, respectively.

**Figure 9.**A scattering plot of GOCI retrieved a(λ) vs. in situ a(λ) data with using the QAA_cj algorithm (filled symbols) and QAA_v6 algorithm (open symbols) at wavelengths of 443, 555, 680, and 745 nm. The symbol with a filled dot inside represents the match point within the time window of ±3 h.

**Figure 10.**A scattering plot of GOCI retrieved a

_{g}(λ) vs. in situ a

_{g}(λ) data with using the QAA_cj algorithm (filled symbols) and QAA_CDOM algorithm (open symbols) at wavelengths of 412, 443, and 490 nm. The symbol with a filled dot inside represents the match point within the time window of ±3 h.

Symbol | Description | Unit |
---|---|---|

a | Total absorption coefficient, a_{w} + a_{ph} + a_{g} + a_{d} | m^{−1} |

a_{nw} | Non-water absorption coefficient, a − a_{w} = a_{ph} + a_{g} + a_{d} | m^{−1} |

a_{w} | Pure water absorption coefficients | m^{−1} |

a_{ph} | Phytoplankton absorption coefficients | m^{−1} |

a_{g} | CDOM absorption coefficients | m^{−1} |

a_{d} | Non-phytoplankton particulate absorption coefficients | m^{−1} |

a_{p} | Particulate absorption coefficients, a_{ph} + a_{d} | m^{−1} |

a_{dg} | Combined CDOM and non-pigmented particulate absorption coefficient, a_{g} + a_{d} | m^{−1} |

b_{bp} | Particulate backscattering coefficient | m^{−1} |

b_{bw} | Pure seawater backscattering coefficient | m^{−1} |

b_{b} | Total backscattering coefficient, b_{bw} + b_{bp} | m^{−1} |

Y | Power of the spectral particulate backscattering coefficient | |

R_{rs} | Above-surface remote-sensing reflectance | sr^{−1} |

r_{rs} | Below-surface remote-sensing reflectance | sr^{−1} |

S | Exponential slope of the CDOM spectral absorption coefficient | nm^{−1} |

u | Ratio of backscattering coefficient to the sum of absorption and backscattering coefficients, b_{b}/(a + b_{b}) | |

λ_{0} | Reference wavelength | nm |

**Table 2.**Descriptive statistics of water constituent concentrations for the Changjiang estuarine and its adjacent coastal waters (CV is the ratio of standard deviation to the mean).

Min | Max | Median | Mean | Standard Deviation | CV | |
---|---|---|---|---|---|---|

a(443) (m^{−1}) | 0.27 | 8.58 | 1.02 | 1.53 | 1.46 | 0.95 |

b_{bp}(443) (m^{−1}) | 0.014 | 6.85 | 0.14 | 0.38 | 0.77 | 2.05 |

a_{g}(443) (m^{−1}) | 0.029 | 0.65 | 0.12 | 0.17 | 0.13 | 0.74 |

Chl-a (μg·L^{−1}) | 0.082 | 20.32 | 0.95 | 2.02 | 3.19 | 1.58 |

TSM (mg·L^{−1}) | 0.61 | 475 | 13.27 | 40.78 | 63.12 | 1.55 |

Steps | Property | Derivation | Approach |
---|---|---|---|

Step 0 | ${r}_{\mathrm{rs}}\left(\lambda \right)$ | $=\frac{{R}_{\mathrm{rs}}\left(\lambda \right)}{\alpha \left(\lambda \right)+\beta \left(\lambda \right){R}_{\mathrm{rs}}\left(\lambda \right)}$ $\alpha \left(\lambda \right)=0.3638+8.776\times {10}^{-4}\lambda -9.193\times {10}^{-7}{\lambda}^{2}+3.17\times {10}^{-10}{\lambda}^{3};$ $\beta \left(\lambda \right)=1.357+8.608\times {10}^{-4}\lambda -6.347\times {10}^{-7}{\lambda}^{2}$ | Semi-analytical |

Step 1 | $\mathrm{u}\left(\lambda \right)$ | $=\frac{-{\mathrm{g}}_{0}+\sqrt{{\mathrm{g}}_{0}^{2}+4{\mathrm{g}}_{1}{r}_{\mathrm{rs}}\left(\lambda \right)}}{2{\mathrm{g}}_{1}},{\text{}\mathrm{g}}_{0}=0.089,{\mathrm{g}}_{1}=0.1245$ | Semi-analytical |

Step 2 | $a\left(680\right)$ | $={a}_{\mathrm{w}}\left(680\right)+0.9398{x}^{2}+0.865x-0.0852$ $x=\frac{{R}_{\mathrm{rs}}\left(680\right)}{{R}_{\mathrm{rs}}\left(490\right)}$ | Empirical |

Step 3 | ${b}_{\mathrm{bp}}\left(680\right)$ | $=\frac{\mathrm{u}\left(680\right)a\left(680\right)}{1-\mathrm{u}\left(680\right)}-{b}_{\mathrm{bw}}\left(680\right)$ | Analytical |

Step 4 | Y | $=1.75{b}_{\mathrm{bp}}{\left(680\right)}^{-0.05}$ | Empirical |

Step 5 | ${b}_{\mathrm{bp}}\left(\lambda \right)$ | $={b}_{\mathrm{bp}}\left(680\right){\left(\frac{680}{\lambda}\right)}^{Y}$ | Semi-analytical |

Step 6 | $a\left(\lambda \right)$ | $=\frac{\left(1-\mathrm{u}\left(680\right)\right){b}_{\mathrm{b}}\left(\lambda \right)}{\mathrm{u}\left(\lambda \right)}$ | Analytical |

Step 7 | ${a}_{\mathrm{g}}\left(443\right)$ | $=a\left(443\right)-{a}_{\mathrm{p}}\left(443\right)-{a}_{\mathrm{w}}\left(443\right)$ ${a}_{\mathrm{p}}\left(443\right)=4.8024{b}_{\mathrm{bp}}{\left(680\right)}^{0.8055}$ | Empirical |

Step 8 | ${a}_{\mathrm{g}}\left(\lambda \right)$ | $={a}_{\mathrm{g}}\left(443\right){e}^{-S\left(\lambda -443\right)}$, where $S=0.0112{[\frac{{R}_{\mathrm{rs}}\left(555\right)}{{R}_{\mathrm{rs}}\left(490\right)}]}^{1.0401}$ | Semi-analytical |

**Table 4.**Comparison statistics of QAA_cj and QAA_v6 based on in situ dataset collected from the Changjiang estuarine and coastal waters (N is the number of validation data).

Algorithms | N | RMSE (m^{−1}) | MARE | Bias (m^{−1}) | R^{2} | |
---|---|---|---|---|---|---|

$a\left(412\right)$ | QAA_cj | 49 | 1.09 | 0.50 | 0.66 | 0.82 |

QAA_v6 | 49 | 1.08 | 0.48 | −0.79 | 0.71 | |

$a\left(443\right)$ | QAA_cj | 49 | 0.91 | 0.52 | 0.50 | 0.75 |

QAA_v6 | 49 | 0.99 | 0.49 | −0.74 | 0.61 | |

$a\left(490\right)$ | QAA_cj | 49 | 0.42 | 0.34 | 0.027 | 0.73 |

QAA_v6 | 49 | 0.93 | 0.56 | −0.71 | 0.78 | |

$a\left(555\right)$ | QAA_cj | 49 | 0.64 | 0.33 | −0.23 | 0.73 |

QAA_v6 | 49 | 0.93 | 0.60 | −0.68 | 0.53 | |

$a\left(660\right)$ | QAA_cj | 49 | 0.71 | 0.22 | −0.085 | 0.72 |

QAA_v6 | 49 | 0.80 | 0.44 | −0.62 | 0.33 | |

$a\left(680\right)$ | QAA_cj | 49 | 0.54 | 0.18 | −0.084 | 0.75 |

QAA_v6 | 49 | 0.88 | 0.44 | −0.62 | 0.61 | |

$a\left(715\right)$ | QAA_cj | 49 | 0.56 | 0.17 | −0.057 | 0.73 |

QAA_v6 | 49 | 0.95 | 0.44 | −0.78 | 0.30 |

**Table 5.**Comparison statistics between the QAA_cj and QAA_v6 algorithms based on in situ dataset collected from Changjiang estuarine and its adjacent coastal waters (N is the number of validation data).

Algorithms | N | RMSE (m^{−1}) | MARE | Bias (m^{−1}) | R^{2} | |
---|---|---|---|---|---|---|

${a}_{\mathrm{g}}\left(412\right)$ | QAA_cj | 43 | 0.12 | 0.41 | 0.033 | 0.92 |

QAA_CDOM | 43 | 0.41 | 2.40 | 0.34 | 0.61 | |

${a}_{\mathrm{g}}\left(443\right)$ | QAA_cj | 43 | 0.07 | 0.42 | 0.018 | 0.90 |

QAA_CDOM | 43 | 0.25 | 2.39 | 0.22 | 0.56 | |

${a}_{\mathrm{g}}\left(490\right)$ | QAA_cj | 43 | 0.035 | 0.35 | 0.0023 | 0.84 |

QAA_CDOM | 43 | 0.01 | 2.48 | 0.11 | 0.55 |

**Table 6.**Comparison statistics of QAA_cj and QAA_v6 based on in situ dataset and GOCI-derived at a(443), a(555), a(680), a(745) (N is the number of validation data).

Algorithms | N | RMSE (m^{−1}) | MARE | Bias (m^{−1}) | R^{2} | |
---|---|---|---|---|---|---|

$a\left(443\right)$ | QAA_cj | 14 | 0.56 | 0.25 | −0.14 | 0.50 |

QAA_v6 | 14 | 0.76 | 0.49 | −0.42 | 0.046 | |

$a\left(555\right)$ | QAA_cj | 14 | 0.46 | 0.29 | −0.10 | 0.69 |

QAA_v6 | 14 | 0.64 | 0.50 | −0.29 | 0.038 | |

$a\left(680\right)$ | QAA_cj | 14 | 0.35 | 0.11 | −0.025 | 0.80 |

QAA_v6 | 14 | 0.62 | 0.34 | −0.32 | 0.096 | |

$a\left(745\right)$ | QAA_cj | 14 | 1.17 | 0.44 | −1.23 | 0.28 |

QAA_v6 | 14 | 1.47 | 0.68 | −2.11 | 0.029 |

**Table 7.**Comparison statistics of QAA_cj and QAA_v6 based on in situ dataset and GOCI-derived at a

_{g}(412), a

_{g}(443), a

_{g}(490). (N is the number of validation data).

Algorithms | N | RMSE (m^{−1}) | MARE | Bias (m^{−1}) | R^{2} | |
---|---|---|---|---|---|---|

${a}_{\mathrm{g}}\left(412\right)$ | QAA_cj | 30 | 0.029 | 0.16 | 0.0026 | 0.72 |

QAA_CDOM | 30 | 0.46 | 2.37 | 0.36 | 0.26 | |

${a}_{\mathrm{g}}\left(443\right)$ | QAA_cj | 30 | 0.02 | 0.14 | −0.00025 | 0.70 |

QAA_CDOM | 30 | 0.31 | 2.34 | 0.25 | 0.11 | |

${a}_{\mathrm{g}}\left(490\right)$ | QAA_cj | 30 | 0.017 | 0.15 | −0.0086 | 0.53 |

QAA_CDOM | 30 | 0.17 | 2.06 | 0.13 | 0.0001 |

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**MDPI and ACS Style**

Wang, Y.; Shen, F.; Sokoletsky, L.; Sun, X.
Validation and Calibration of QAA Algorithm for CDOM Absorption Retrieval in the Changjiang (Yangtze) Estuarine and Coastal Waters. *Remote Sens.* **2017**, *9*, 1192.
https://doi.org/10.3390/rs9111192

**AMA Style**

Wang Y, Shen F, Sokoletsky L, Sun X.
Validation and Calibration of QAA Algorithm for CDOM Absorption Retrieval in the Changjiang (Yangtze) Estuarine and Coastal Waters. *Remote Sensing*. 2017; 9(11):1192.
https://doi.org/10.3390/rs9111192

**Chicago/Turabian Style**

Wang, Yongchao, Fang Shen, Leonid Sokoletsky, and Xuerong Sun.
2017. "Validation and Calibration of QAA Algorithm for CDOM Absorption Retrieval in the Changjiang (Yangtze) Estuarine and Coastal Waters" *Remote Sensing* 9, no. 11: 1192.
https://doi.org/10.3390/rs9111192