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

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 (Lee 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 coefficient 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.

The QAA algorithm has shown the advantages in reversion of inherent optical properties of water bodies; however, it requires specific bands, such as 413, 443, 490, 555, 640, 667, and 670 nm wavelengths, 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 do not include the 413 nm wavelength for the atmosphere's strong absorbance of sunlight as being a weak receiving signal for the sensors. Thus, due to its requirement for specific wavelengths, the QAA algorithm is mainly applied to hyperspectral data measured on a 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 et al. 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. (2014a, 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. 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) studied the effect of Raman scattering on QAA retrievals. Pitarch & 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 a blue wave segment and red band respectively, with a very prominent reflection peak in the near-infrared band which is obviously different from other components of water bodies. Previous studies on chlorophyll-a concentration have been carried out by using multi-source 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, such as the double-band model (Pulliainen et al. 2001), three-band model (Bi et al. 2018), and 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), and 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 Sentinel-3 OLCI satellite data, the Chl-a concentration spatial distribution for August 10, 2017, was derived. The technical route of research is shown in Figure 1.

There are many parameters and symbols used in the study. In order to facilitate the understanding of the model method, the abbreviations of relevant parameters are explained in Table 1.

Daihai Lake is located at 112°37′–112°46′E, 40°32′–40°37′N (Figure 2). It is a typical inland lake in a semi-arid area of Liangcheng County, Ulancha City, Inner Mongolia Autonomous Region, North China. The depth of the lake ranges from 4 to 16m, with an average depth of 7m. It is characterized as a light saltwater lake. The surface altitude is about 1,223m 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 (427mm) and high annual evaporation (1,938 mm).

Daihai Lake belongs to the 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 vigorous evaporation, have made the 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, have 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 being enriched, which can lead to serious eutrophication (Zeng & Wu 2010). In the last 20 years, the water pollution in Daihai Lake have been serious, and the concentrations of COD_Mn, BOD₅ and TP have exceeded the standard to 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).

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 10, 2017, from 10:00 am to 12:00 pm. 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 the water surface at the water sample points was collected by ASD Field Handheld 2 spectrometer, and the water about 10cm 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 is shown in Figure 2.

The 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. 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, and 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 −20 °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.

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 300m 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://sentinel.esa.int/web/sentinel/missions/sentinel-3. To reduce the inversion error caused by remote sensing data, the data were preprocessed for geometric positioning, calibration, and atmospheric corrections using the Fast Line-of-sight Atmospheric Analysis of Hypercubes (FLAASH) model and a resampled spatial resolution of 30m.

The QAA algorithm was proposed based on the radiation transmission model of a water body and it is applied to the optical deep-water area with several improvements and modifications. The basic idea of this algorithm is to establish the quantitative relationship between the remote sensing reflectivity and inherent optical quantity of the 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 the 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 empirical 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 obtained.

The basic steps of the QAA algorithm are divided into 12 steps, consisting of the three-step half-analysis relationship, four-step analysis relationship and five-step empirical relationship, which can be applied to the measured hyperspectral water surface and spectral data in multiple categories on board.

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 were 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 as shown in Figure 8 and were in the range 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 were in the range 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).

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 at 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 of wavelengths in the range 400–500 nm was low due to the water composition absorption (Sun et al. 2012).

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, R², 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 was in the range 0.026–0.167, with an R² 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, R² was above 0.98, and the ARE varied in the range 4%–20% (Table 5). With regard to the a_ph (Figure 16), the inversion performed well with an RMSE below 0.14, R² above 0.90, and ARE in the range 4%–16% (Table 6), providing support for the Chl-a concentration estimation. The result showed the inversion accuracy satisfied the research requirement.

The measured Chl-a concentration showed a linear relationship with the measured phytoplankton absorption coefficient at a wavelength of 674 nm, an R² of 0.88 (Figure 17), and with the inversed a_ph(674), an R² of 0.87 (Figure 18).

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 is shown in Figure 19 with an R² 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).

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.

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 wavelength in close proximity to band 11 on the Sentinel-3 OLCI was suitable as the reference wavelength, where the absorption coefficient was dominated by 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 R² of 0.76.

• (3)

  The exponential slopes were obtained after fitting a_CDM and performing the linear fitting relationship with the ratio of r_rs(440) and r_rs(560) with an R² of 0.92.

• (4)

  After comparing the inversed and measured absorption coefficients at the five characteristic wavelengths of 400 nm, 410 nm, 440 nm, 560 nm, 674 nm, respectively, the range for the three statistical indices, RMSE, R², 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 R² 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 a 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.

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.

This work was supported by Military Research Project: Research on the Key Technology for Water Source Detection System Based on Remote Sensing Information and Development Program of China: Groundwater Exploration Technology in the Water Shortage Region (863 Program: 2012AA062601).

All relevant data are included in the paper or its Supplementary Information.