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Chlorophyll-a concentrations inversion based on the modified Quasi-Analytical Algorithm and Sentinel-3 OLCI in Daihai Lake, China

The Quasi-Analytical Algorithm (QAA) is effective in retrieving water inherent optical properties (IOPs) from remote sensing spectral reflectance and has wider applications in studies of the open ocean and coastal waters than of inland waters. This research aimed to modify the QAA model based on measured field spectral reflectance and absorption coefficients to render it applicable to studies of Daihai Lake, China. The improvements mainly included the reference wavelength selection, the power index of the particle backscattering coefficient and the exponential slope of the absorption coefficient of the colored detrital matter estimation. The average relative error between the inversed and measured absorption coefficients was less than 20%. A linear model was established between the phytoplankton absorption coefficient at a wavelength of 674 nm (aph(674)) and the chlorophyll-a (Chl-a) concentration, with a determination coefficient of 0.88. Additionally, the modified Quasi-Analytical Algorithm (MQAA) model was applied to the Ocean and Land Color Instrument (OLCI) data aboard the Sentinel-3 satellite. Finally, a spatial distribution map for the Chl-a concentrations in Daihai Lake on August 10, 2017 was drawn and the mid-eutrophication area was found to occur in the north and border.


INTRODUCTION
Water inherent optical properties (IOPs) mainly consist of the absorption coefficients of pure water a w (λ) (abbreviations are listed in Table 1), phytoplankton a ph (λ), non-algal particles a nap (λ), colored dissolved organic material a CDOM (λ), the backscattering coefficients of the pure water b bw (λ), and particulate matter b bp (λ), without the influence of external light. Therefore, accurate retrievals for the IOPs for the water constituent are essential for water quality inversion using remote sensing data.
To inverse the water IOPs from the remote sensing reflectance, semi-analytical algorithms based on the light radiation transfer principle have been put forward. These algorithms included the Shallow Water Inversion Model (SWIM) (McKinna et al. 2015), the Generalized Inherent Optical Properties (GIOP) (Werdell et al. 2013), Garver-Siegel-Maritorena Model (GSM) (Wang et al. 2016), and the Quasi-Analytical Algorithm (QAA) (Munnooru et al. 2019). Among these, the QAA model has the widest application for the study of ocean and coastal waters. The conversion relationship of the remote sensing reflectance above and below the water surface was constructed using the Hydrolight radiative transfer numerical model with consideration of the absorption and backscattering coefficients of the water constituent. The QAA model was first built and validated for multiband data (Barnes et al. 2002), for example, Moderate Resolution Imaging Spectroradiometer (MODIS) and Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) data for deep waters, then was applied to hyperspectral data and later extended to shallow waters (Barnes et al. 2017). The optical parameters that influence the model accuracy include the estimated absorption coefficient at the reference wavelength, the extrapolated backscattering coefficient of the particles, and the assumed absorption coefficients ratio for the specific wavelengths (Lee et al. 2010). Therefore, for lakes with specific water quality characteristics, the typical characteristic wavelength should be selected according to the satellite data source through the field measurement of spectral parameters to reduce the influence of uncertainty. In addition, some studies showed that the remote sensing data acquisition may also increase the uncertainty of the inversion model (Liuzzo et al. 2020). Before inversion, it is necessary to adopt appropriate methods to preprocess remote sensing data to reduce the errors caused by data acquisition.
QAA algorithm has showed the advantages in reversion of inherent optical properties of water bodies; However, it requires specific bands, such as 413 nm, 443 nm, 490 nm, 555, 640 and 667 nm, and 670 nm wavelength, etc. The two wavelengths, 413 and 443 nm, are mainly used for total absorption coefficient decomposition for the phytoplankton pigment and CDM strong absorption, and the reflectance peak above the water surface is mostly near 555 nm. Most satellite sensors don't include 413 nm wavelength for the atmosphere's strong absorbance of sunlight and weak receiving signal for the sensors. Thus, due to its requirement for specific wavelengths, QAA algorithm is mainly applied to hyperspectral data measured on water surface and medium spectral remote sensing data in MERIS, MODIS, Sea WIFS, etc.
In the past decade, the QAA model has been applied to inland water bodies such as the aquaculture ponds in Mississippi State (Mishra 2014), the Great Lakes (Becker et al. 2009), and Liaohe River (Deng et al. 2019). However, as the spectral characteristic and the IOPs of inland waters are different from the open ocean and coastal waters, the QAA model still requires modifications before it can have wider applications. Huang et al. (2014aHuang et al. ( , 2014b selected 710 nm as the reference wavelength in Poyang Lake and developed an optimization model after the spectral classification of four inland lakes in China (Huang et al. 2014a(Huang et al. , 2014b. Yang et al. (2013) enhanced the spectral slope of the particles' backscattering coefficients and the chlorophyll-a (Chl-a) absorption coefficient at a wavelength of 443 nm. Li et al. (2013) chose 778 nm as the reference wavelength. Ma et al. (2006) calibrated the conversion coefficient of the remote sensing reflectance above and below the water surface in Taihu Lake. Pitarch et al. (2019) Absorption coefficient of the colored detrital matter, sum of the non-algal particles and the colored dissolved organic material, a nap (λ) þ a CDOM (λ)

Uncorrected Proof
Vanhellemont (2021) presented the QAA-RGB, a universal three-band absorption and backscattering retrieval algorithm for high resolution satellite sensors. Thus far, no better progress has been made in customizing the QAA model for inland waters.
Chlorophyll-a content in water is closely related to the eutrophication level and it shows spectral characteristics similar to terrestrial vegetation in remote sensing images. The spectral curve of Chlorophyll-a shows absorption peaks in blue wave segment and red band respectively, with a very prominent reflection peak in the near-infrared band which isobviously different from other components of water body. Previous studies on chlorophyll-a concentration have been carried out by using multisource remote sensing data and integrating multiple methods, and the accuracy has been constantly improved. The remote sensing inversion methods for Chl-a concentrations can be broadly classified into two types, one type is the empirical model based on reflectivity, and the other type is the semi-analytical model based on absorption coefficient. The empirical models are based on band combinations, vb such as the double-band model (Pulliainen et al. 2001), three-band model (Bi et al. 2018), four-band model (Shen et al. 2010). The semi-analytical models are based on the phytoplankton absorption coefficient. The relationship between the Chl-a concentration and the phytoplankton absorption coefficient for the power and linear (Sun et al. 2012) models varies in different inland waters. In this study, the measured data including the in-situ remote sensing reflectance R rs (λ), the absorption coefficient of the non-water a n-w (λ), non-algal particles a nap (λ), colored dissolved organic material a CDOM (λ), and the phytoplankton absorption coefficient a ph (λ) were employed to modify the QAA model for the inversion of the IOPs and Chl-a concentration for Daihai Lake. After applying the MQAA model to the Sentinel-3 OLCI satellite data, the Chl-a concentration spatial distribution for August 10, 2017 was derived. Technical route of research was shown in Figure 1.
There were many parameters and symbols used in the study. In order to facilitate the understanding of the model method, the abbreviations of relevant parameters were explained in Table 1.

Study area
Daihai Lake is located at 112°37 0 -112°46 0 E, 40°32 0 -40°37 0 N ( Figure 2). It is a typical inland lake in a semiarid area of Liangcheng County, Ulancha City, Inner Mongolia Autonomous Region, North China. The depth of the lake ranges from 4-16 m, with an average depth of 7 m. It is characterized as a light saltwater lake. The surface altitude is about 1,223 m and the average annual temperature is 5°C. The water supply mainly depends on the intermittent rivers to the west, namely the Gongba River, Wuhao River, Buliang River, Tiancheng River and Muhua River. The icebound period lasts from late November to next April. In the past decades, the lake area has declined year by year due to low annual rainfall (427 mm) and high annual evaporation (1,938 mm).
Daihai Lake belongs to Mengxin Lake System. Most of the lakes developed from relatively independent inland basin water systems. Under arid and semi-arid climate conditions, strong solar irradiation and scarce rainfall supplement, coupled with Uncorrected Proof vigorous evaporation, made Daihai lake water supply of the river system exceed its income, resulting in degradation (Liang et al. 2017). In addition, reclamation activities such as vegetation destruction and inappropriate grassland protection, as well as the utilization of supplementary water resources, seriously damaged the water and salt balance under normal conditions, resulting in salinity (Xi et al. 2012). The discharge of industrial wastewater, domestic sewage, farmland drainage, etc., leads to organic pollutants entering Daihai lake water bodies and enriching, which can seriously lead to eutrophication (Zeng & Wu 2010). In recent 20 years, the water pollution in Daihai Lake was serious, and the concentrations of COD Mn , BOD 5 and TP exceeded the standard in varying degrees (Liang et al. 2021). The water quality in Daihai Lake is alkaline, and the degree of alkalization is still increasing (Zhou et al. 2006).

Data sources
According to the characteristics of water quality change and satellite transit time, a field survey and water sample collection were conducted in Daihai Lake on August 10th, 2017 from 10: 00 am to 12: 00 am. The actual sampling points are selected according to the principle of uniform distribution in the region and obvious difference in water quality characteristics. A total of 40 water samples were selected. The spectral reflectance of water surface at water sample points was collected by ASD Field Handheld 2 spectrometer, and the water about 10 cm below the water surface was collected by sampling bottle. The collected water was sealed and stored in dark bottles, and the absorption coefficient and Chl-a concentration of water samples were determined under laboratory conditions. To reduce the error, the reflectivity of each sampling point was collected five times, and the average value of the reflectivity was taken as the reflectivity. Five groups of water samples were also collected at each sampling point, and the measured average Chl-a concentration was taken as the Chl-a concentration at the sampling point. The distribution of sampling points was shown in Figure 2.
The above water measurement method was employed using an azimuth angle of 135°and an elevation angle of 40°to avoid the influence of mirror reflections from the water and the diffuse light scattering from the sky. The measured radiances included the water (L sw (λ), W/(m 2 .nm.sr)), the diffuse light scattering from the sky (L sky (λ), W/(m 2 .nm.sr)), and the standard white board (L p (λ), W/(m 2 .nm.sr)) with a reflectance (ρ p ) of 100% using an ASD Field Handheld 2 spectrometer with a wavelength range from 325-1,075 nm and a 1 nm interval. The reflectance on the air-water interface (r) was taken as 0.025 using the 5 m/s wind speed conditions determined on-site. The remote sensing reflectance above the water (R rs (λ) Figure 3) was calculated as follows (Tang et al. 2004): Acetone method and ethanol method were the main methods for extracting Chl-a (Chen & Gao 2000). Spectrophotometry (Lorenzen 1967) and fluorescence (Yentsch & Menzel 1963) were the two main methods for the determination of Chl-a.

Uncorrected Proof
Water quality -Determination of Chl-a -Spectrophotometric method (HJ897-2017) is a standard document formulated by the Ministry of Ecology and Environment of the People's Republic of China. This document regulates the determination of Chl-a, which can be downloaded from the website http://www.mee.gov.cn/ywgz/fgbz/bz/bzwb/jcffbz/201712/ t20171227_428728.shtml. In the study, Chl-a concentrations were determined according to the requirements of this standard. The water samples were filtered through GF/F membranes, and then frozen for 48 h at À20°C. After chlorophyll extraction by acetone, the absorbance of the membrane and acetone were measured at wavelengths of 665 and 750 nm, respectively, using a TU-1810 ultraviolet-visible spectrophotometer and then twice after a drop of 1% hydrochloric acid (Clevers & Gitelson 2013). Then the Chl-a concentrations were measured by spectrophotometry.
The absorbances of the non-water (OD n-w (λ)), non-algal particles (OD nap (λ)), and the colored dissolved organic material (OD CDOM (λ)) were measured using a TU-1810 ultraviolet-visible spectrophotometer. With pure water as the baseline, the absorbances of the water samples before and after filtration were measured and labeled as non-water and colored dissolved organic material, respectively. The absorption coefficients of the non-algal particles were derived using the quantitative filter technique. After extraction by ethanol, the absorbance of the filtered GF/F membrane was measured as the non-algal particle. The corresponding absorption coefficients were obtained from the absorbances as follows: a n-w (l) ¼ 2:303OD n-w (l)=L (2) where L (m), S (m 2 ), and V (m 3 ) represent the optical path with a value of 0.01, the membrane filter area, and water sample volume, respectively. a n-w (λ) represents the absorption coefficients of non-water. a nap (λ) represents the absorption coefficients of non-algal particles; a CDOM (λ) represents the absorption coefficients of colored dissolved organic material. After adding a nap (λ) and a CDOM (λ), the a CDM (λ) was derived as shown in Figure 4. Finally, the a ph (λ) (Figure 5) was obtained by subtracting a CDM (λ) from a n-w (λ) (Figure 6).
The Sentinel-3 satellite carrying the 21 band OLCI sensor (Table 2) with a spatial resolution 300 m was launched in February 2016. The satellite was intended as a substitute for the medium-spectral resolution imaging spectrometer (MERIS) for the purpose of land and ocean observation (Zhang et al. 2009). The Sentinel-3 OLCI data from August 10, 2017 were downloaded from the website https://scihub.copernicus.eu/s3/#/home. To reduce the inversion error caused by remote sensing data, the data were preprocessed for geometric positioning, calibration, and atmospheric corrections using the Fast Lineof-sight Atmospheric Analysis of Hypercubes (FLAASH) model and a resampled spatial resolution of 30 m.    QAA algorithm was proposed based on the radiation transmission model of water body and it is applied to the optical deepwater area with several improvements and modifications. The basic idea of this algorithm is to establish the quantitative relationship between remote sensing reflectivity and inherent optical quantity of water body. Firstly, the total absorption coefficient of the effluent body is retrieved, and the reflectance of the water surface is calculated from the reflectance above the water surface. Then the total absorption coefficient of the water body at the reference band is determined by the empirical inversion model, and the total backscattering coefficient at the reference wavelength is obtained. Combined with the empirical values of power exponent, the backscattering coefficient at full wavelength is obtained, and then the total absorption coefficient at full wavelength is inversely derived. Based on the above, the total absorption coefficient decomposition was carried out. The phytoplankton pigment absorption coefficient ratio between 413 and 443 nm was estimated by the experience formula. With the measured CDM absorption coefficient, the slope index was fitted out. After solving the total absorption coefficient equations, the absorption coefficients for phytoplankton pigment and CDM at the wavelengths 413 and 443 nm were derived. On the basis of slope index, the CDM absorption coefficient at other wavelengths can be extrapolated. Finally, the phytoplankton pigment absorption coefficient at all wavelengths can be get.
The basic steps of QAA algorithm are divided into 12 steps, including three-step and half-analysis relationship, four-step analysis relationship and five-step empirical relationship, which can be applied to the measured hyperspectral of water surface and spectral data in multiple categories on board.
The bio-optical model served as the basis for the QAA model mainly used for determining the absorption coefficients a(λ) and backscattering coefficients b b (λ) of the water components shown below:

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The above water reflectance R rs (λ) was converted to the subsurface reflectance r rs (λ) empirically using the equation below: r rs (l) ¼ R rs (l) 0:52 þ 1:7R rs (l) The dependence of the subsurface reflectance r rs (λ) on the total absorption a(λ) and backscattering coefficient b b (λ) based on the mechanism analysis was shown below: where the values of g 0 and g 1 were 0.0895 and 0.1247, respectively. The relationship between the backscattering coefficient b b (λ) and the wavelength was in accordance with the power function with Y as the unknown as follows: For the absorption coefficient decomposition, two variables, namely the ratios of the absorption coefficients at wavelengths of 413 and 443 nm, respectively for the phytoplankton and the colored detrital particles were introduced as follows: The two variables were expressed with the undetermined S CDM (λ) as the equations: b ¼ 0:71 þ 0:06 0:8 þ r rs (443)=r rs (560) The absorption coefficient of the colored detrital material a CDM (λ) declines in exponent regularity with the wavelength as follows:

MQAA model
Based on the QAA model and the measured a n-w (λ), a CDM (λ), a ph (λ), the reference wavelength was reselected and the linear fitting models for the Y and S CDM estimation was established. The difference between the absorption coefficients of pure water and the water samples provides the basis for estimating the total absorption coefficient and this difference was quite small at near-infrared wavelengths. Based on the measurement comparison, the reference wavelength was chosen as 710 nm, close to the band 11 wavelength on the Sentinel-3 OLCI, where the a n-w was approximate to zero ( Figure 6).
The power function index of the particle backscattering coefficient varies in water samples due to the different compositions and sizes of the particles and this influences the inversion result (Gallegos et al. 2005;Wang et al. 2017). Y can be estimated by empirical relation to the subsurface reflectance ratio of the blue and green bands (Aurin & Dierssen 2012) and varies depending on the reference wavelength (Yang et al. 2013). The particle backscattering coefficient was calculated with the measured spectral reflectance and the non-water absorption coefficient (Figure 7). After the power function fitting, the indices for the 40 samples were derived with one fitting example shown in Figure 8 and ranged from 0.99-2.65 (Figure 9). The linear model was built between Y and the subsurface reflectance ratio at wavelengths of 440 and 560 nm (Figure 10).
After fitting the absorption coefficient of the colored detrital materials for the 40 water samples with the one fitted example shown in Figure 11, the obtained exponential slopes ranged from 0.019-0.037 ( Figure 12) and elucidated the linear relationship with the ratio of the subsurface reflectance at the wavelengths of 440 and 560 nm (Figure 13).
Combining the QAA model and the above improvement, we obtained a concrete process for the MQAA model (Table 3).

Assessment of the retrieved result
The retrieved accuracy can be evaluated by statistical indices; and the root mean square error (RMSE), the average relative error (ARE), and the coefficient of determination (R 2 ) are as follows.  Uncorrected Proof where N is the number of the water samples, X est,i is the estimated value, and X mea,i is the measured value.

RESULTS AND DISCUSSION
Remote sensing spectra From the measured above water remote sensing reflectance curve, we found three main peaks in the ranges of 560-570, 690-700, and 800-810 nm and an obvious trough between 670-680 nm (Yang et al. 2013). The first and third peaks were mainly caused by the strong reflection of the particles, while the second was caused by the typical reflection characteristics of Chl-a. The typical absorption of the Chl-a produced the trough and the reflection in the wavelength from 400-500 nm was low due to the water composition absorption (Sun et al. 2012).    Uncorrected Proof

Comparison of the inversed and measured absorption coefficient
In order to analyze the inversion precision of the MQAA model, five characteristic wavelengths, 400, 410, 440, 560, and 674 nm, respectively, were chosen and the three statistical indices, RMSE, R 2 , and ARE were used to evaluate the inversion error for the absorption coefficients. Between the inversed and measured a n-w (Figure 14), the RMSE ranged from 0.026-0.167, with an R 2 value above 0.90, and an ARE of no more than 16% (Table 4). For the a CDM (Figure 15), the RMSE was below 0.20, the R 2 was above 0.98, and the ARE varied from 4-20% (Table 5). With regard to the a ph (Figure 16), the inversion performed well with an RMSE below 0.14, R 2 above 0.90, and the ARE from 4-16% (Table 6), providing support for the Chl-a concentration estimation. The result showed the inversion accuracy satisfied the research requirement.

Empirical
Step 5 b bp (l)

Empirical
Step 11 a ph (l) ¼ a(l) À a w (l) À a CDM (l) Analytical Figure 14 | The comparison of the inversed and measured a n-w in different wavelengths.

Chl-a concentration inversion by Sentinel-3 OLCI
The wavelengths in the MQAA model were replaced by the matched bands in the Sentinel-3 OLCI data. The MQAA model was applied to the preprocessed Sentinel-3 OLCI data to inverse the phytoplankton absorption coefficient and the linear regression model was shown in Figure 19 with an R 2 of 0.84 less than the inversion precision based on the measured a ph (674) for the estimation error. The space distribution of the Chl-a concentrations in Daihai Lake on August 10, 2017 were drawn after applying the MQAA model to the entire area ( Figure 20).

Uncorrected Proof
We observed an increasing trend in the Chl-a concentrations from south to north, and mid-eutrophication occurred in the north and outermost edge at an area proportion of 84% (Table 7). The main reasons for this feature of the distribution map are the human activity at the edge and tourism development in the north.

CONCLUSIONS
In this study, the MQAA model was put forward on the basis of the measured data including the in-situ remote sensing reflectance, the absorption coefficient of the non-water, colored dissolved material, phytoplankton, and the Chl-a concentration to inverse the IOPs and Chl-a concentrations in Daihai Lake. From these results, we can draw certain conclusions as follows.
(1) The 710 nm in close proximity to band 11 on the Sentinel-3 OLCI was suitable as the reference wavelength, where the absorption coefficient was dominated by the pure water absorption.
(2) Based on the measured a n-w and R rs values, the backscattering coefficients for the particles were derived and the power function index Y was fitted and elucidated the linear relationship between the subsurface reflectance ratio at wavelengths of 440 and 560 nm with an R 2 of 0.76.  (3) The exponential slopes were obtained after fitting a CDM and performed the linear fitting relationship with the ratio of r rs (440) and r rs (560) with an R 2 of 0.92. (4) After comparing the inversed and measured absorption coefficients at the 5 characteristic wavelengths of 400 nm, 410 nm, 440 nm, 560 nm, 674 nm, respectively, the range for the 3 statistical indices, RMSE, R 2 , and ARE were below 0.20, above 0.90, and no more than 20%, respectively. (5) The measured C Chl-a and a ph (674) showed a linear relationship with an R 2 of 0.88 and the MQAA model was applied to the preprocessed Sentinel-3 OLCI data for Daihai Lake. The delineated space distribution of the Chl-a concentrations revealed an increasing trend from south to north, and the mid-eutrophication occurred in the north and the outermost edge at an area proportion of 84%.
The results of this study filled the gap of using semi-analytical model to retrieve water quality in semi-arid lakes, improved the accuracy of remote sensing retrieval of inland lake water quality, and provided support for the detection of inland water characteristic changes. The model proposed in the study was suitable for Daihai Lake. In the follow-up study, the model can also be applied to the inversion of suspended solids, salinity and other water parameters, so as to master the water quality of Daihai Lake more comprehensively. It should be noted that, although the model has a good effect in water quality inversion in Daihai Lake, its applicability in other similar salt lakes is still worth studying. In addition, there may be differences in water quality in different periods. In order to understand the water quality in Daihai Lake more comprehensively, it is necessary to obtain more Sentinel -3 OLCI data to analyze its temporal and spatial variation characteristics. The low spatial resolution of Sentinel-3 OLCI data also limits the application potential of this model to some extent. In order to enhance the applicability of the model, it is necessary to explore the inversion effect of the model based on other multispectral remote sensing data with higher spatial resolution.

CONFLICTS OF INTEREST
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.