An Improved QAA-Based Method for Monitoring Water Clarity of Honghu Lake Using Landsat TM, ETM+ and OLI Data

Abstract

Secchi disk depth (Z_SD) is used to quantify water clarity as an important water-quality parameter, and one of the most used mechanistic models for Z_SD is the quasi-analytical algorithm (QAA), of which the latest version is QAA_v6. There are two models in QAA for clear and turbid waters (referred to as QAA_clear and QAA_turbid). QAA_v6 switches between the two models by setting a threshold value for the remote sensing reflectance (R_rs, sr⁻¹) at the selected reference band of 656 nm. However, some researchers found that this reference band or the threshold value does not apply to many turbid inland lakes. In Honghu Lake, the R_rs (656) (R_rs at 656 nm) in the whole lake is less than 0.0015 sr⁻¹; therefore, only QAA_turbid can be applied. Moreover, we found that QAA_clear resulted in overestimation while QAA_turbid resulted in significant underestimations. The waters of inland lakes usually continuously vary between clear and turbid water. We proposed a hypothesis that QAA_turbid and QAA_clear transition evenly, rather than being distinguished by one threshold value, and we developed a model that combined QAA_clear and QAA_turbid according to our assumption. This model simulated the process of continuous change in water clarity. The results showed that our model had a better performance with an RMSE that reduced from 0.5 to 0.28, an MAE that reduced from 0.43 to 0.21, and bias that reduced from −0.4 to −0.05 m compared with QAA_v6. We applied QAA_Honghu to Landsat TM, ETM+, and OLI data and obtained 205 Z_SD maps with high spatial resolution in Honghu Lake. The results were consistent with the existing in situ measurements. From 1987–2020, the Z_SD results of Honghu Lake showed an overall downward trend and a distinct seasonal pattern.

1. Introduction

Water clarity is an important water-quality parameter that can affect the transmission of light in the water and thus the growth of aquatic vegetation. Secchi disk depth is an important indicator to quantify water clarity. It is closely related to phytoplankton concentration and water eutrophication [1]. The use of a Secchi disk is the simplest and lowest-cost water-quality measurement. Over the past 100 years, more than a million Z_SD measurements have been made in marine and inland waters [2].

Traditional studies have analyzed the variation characteristics of the Z_SD through many sampling data. Such studies require a large number of sites and are costly. Moreover, this analysis is not spatially continuous. Due to the low cost and high efficiency, there have been many studies on monitoring water clarity through remote sensing [3,4,5]. Most of this research uses two methods. The first one is to derive the Z_SD by empirical methods such as regression arithmetic [6] and machine learning [7]. This method is only applicable to waters that are similar to those for which the algorithm was developed, due to the nature of regression. In addition, the lack of measured data will cause greater error [8,9,10]. The second method is the semi-analytical algorithm based on solutions to the radiative transfer equation [11,12].

Lee proposed a new quasi-analytical algorithm based on underwater visibility theory [13]. QAA is a mechanistic model that derives the total absorption coefficient a (λ), total backscattering coefficient b_b (λ), and diffuse attenuation coefficient K_d (λ) from R_rs (λ). This algorithm has been applied in many waters around the world for various satellite sensors [14,15,16,17]. Yin et al. successfully applied QAA to Landsat TM and OLI data and observed the water clarity changes in Taihu Lake over 36 years [17]. However, this research did not change the QAA, so further improvements are significant for lakes with complex optical properties such as Honghu Lake.

QAA_v6 uses R_rs (656) to distinguish clear water from turbid water. If R_rs (656) < 0.0015 sr⁻¹, then the water is identified as clear water. Conversely, QAA_turbid is applied. These two models differ mainly in their choice of reference bands. The reference bands of QAA_clear and QAA_turbid are 560 and 656 nm respectively. However, many studies have shown that QAA_v6 or earlier versions often failed in some turbid waters [18,19,20,21,22,23]. QAA_v6 can underestimate the Z_SD of highly turbid inland waters [24,25,26]. The reason may be that the threshold value of R_rs (656) or the reference band may not be suitable for all waters, and this determination condition may cause discontinuity in the Z_SD estimation results near the threshold. Some studies have improved the performance of QAA by changing the reference band [14,22,27,28]. However, for inland lake waters, it is challenging to find an accurate threshold value. We found in our study that QAA_clear had a good performance when the Z_SD values were high. QAA_turbid performed better when the Z_SD values were low. Therefore, we assumed that the transition from QAA_clear to QAA_turbid should be a continuous process. A more applicable model can be developed through the combination of QAA_clear and QAA_turbid with gradual weight changes between them.

To validate the assumption and develop this new model, we selected Honghu Lake as the study area. Honghu Lake is a typical lake in the middle reaches of the Yangtze River, and it is the seventh-largest lake in China. For inland lakes such as Honghu Lake, where clear and turbid water spatio-temporal changes are frequent, the new model can reflect the process of clear–turbid water variation. Many of the current QAA applications use ocean color satellites such as MODIS, SeaWiFS, and CZCS [29,30]. However, most of the lakes and reservoirs in the world cannot be observed with the spatial resolution of existing ocean color sensors [31]. Some research has shown that the quality of remote sensing signals from land bands is comparable to that from ocean bands [14]. The Landsat series is considered highly promising for water-quality mapping in inland waters [31]. Lee et al. established an empirical relation to estimate the diffuse attenuation reflection coefficient K_d(λ) at 530 nm, filling the broad spectral gap of Landsat OLI in the visible domain [32]. Landsat series satellites have a spatial resolution of 30 m, which can be applied to inland shallow lakes. Since Landsat-5 was launched in 1984, Landsat-5–8 have delivered nearly 39 years of Earth imaging data, which can meet long-term water-clarity-monitoring needs.

Therefore, this study aims to: (1) develop a combined model (QAA_Honghu) using the original QAA_clear and QAA_turbid, which applies to inland waters with highly turbid water or frequent clear–turbid variation; (2) improve the QAA to be applied to Landsat TM, ETM+, OLI data, and derive 33 years of water clarity in Honghu Lake using Landsat series data from 1987 to 2020.

2. Study Region and Datasets

2.1. Study Region

Honghu Lake is the largest lake in Hubei Province and the seventh-largest lake in China. As a national wetland nature reserve, it has the most productive ecosystem in China. Honghu Lake is located in the subtropical monsoon climate region and the middle reaches of the Yangtze River (29°48′ N, 113°17′ E). Its total surface area is approximately 350 km². Honghu Lake is a representative of the shallow lakes in the Yangtze Plain. Its slopes gently descend from northwest to southeast, and the surface runoff in the lake area mainly flows into the lake through the main canal. Honghu Lake was listed as a wetland of international importance in 2008 and became a national nature reserve in 2014. It is a priority conservation area established by the World Wide Fund (WWF) to restore the dramatic loss of biodiversity.

The Honghu Lake wetland contributes great ecological value and performs important functions such as flood control, water supply, irrigation, and transportation. The area of enclosure aquaculture in Honghu Lake has increased since the 1950s. During this period, it experienced several catastrophic floods. These have led to the extreme deterioration of the water quality of Honghu Lake. Ecological and environmental issues in Honghu Lake include a sharp reduction in the lake surface area, eutrophication, and frequent floods. Therefore, monitoring water clarity variation is vital to the study of key drivers and lake-restoration management.

2.2. Datasets

From 2011 to 2020, we conducted field surveys on Honghu Lake and collected water-quality data. We selected the Z_SD of 24 sampling stations in this dataset (Figure 1). We used 116 pairs of match-ups to improve the algorithm and 44 match-ups to evaluate the performance.

Table 1. Image type and dates of image acquisition and in situ sampling.

Image Type	Image Date	Sampling Date
Landsat-8	12 May 2013	9 May 2013
Landsat-7	11 October 2013	9 October 2013
Landsat-8	6 October 2014	7 October 2014
Landsat-8	25 October 2015	21 October 2015
Landsat-7	13 April 2017	17 April 2017
Landsat-8	8 April 108	2 April 2018
Landsat-8	1 August 2019	26 July 2019
Landsat-8	5 November 2019	14 November 2019
Landsat-8	29 April 2020	29 April 2020

shows the time difference between the in situ-measured data and the remote sensing data.

Landsat Level-1 products were downloaded from the U.S. Geological Survey (USGS, https://www.usgs.gov/, accessed on 28 January 2021). A total of 205 images covering the study area without clouds from 1987 to 2020 were acquired, including 89 Landsat TM images, 78 Landsat ETM+ images, and 38 Landsat OLI images. Due to the Scan Line Corrector (SLC) failure in 2003, all Landsat-7 images collected after 31 May 2003, have data gaps. In addition, we used band-specific gap mask files to mask out the un-scanned pixels.

ACOLITE is a generic processor for aquatic applications of Landsat-5/7/8 and Sentinel-2, and it is especially suitable for processing turbid inland waters [33]. There are two atmospheric-correction algorithms in ACOLITE, and we used the Dark Spectrum Fitting (DSF) algorithm [34]. We processed these Landsat level-1 DN (Digital Number) data to generate R_rs data in ACOLITE.

3. Methods

3.1. The Original OLI Z_SD Algorithm

Lee et al. (2015) proposed a new underwater visibility theory and developed a model to derive the Z_SD from the visible spectrum. This model obtained an unbiased absolute percent difference of ~18% between in situ measurements and satellite estimates. This algorithm has strong robustness in nearshore clear water [13]. To obtain higher-spatial-resolution Z_SD maps, Lee et al. (2016) modified QAA to apply it to Landsat-8 data [32].

The main steps of the new model were based on Landsat-8 are similar to the original algorithm. There are three main steps to derive the Z_SD using QAA: a (λ) and b_b (λ) are retrieved from R_rs (λ), then K_d (λ) is calculated by the radiative transfer equation.

Then, according to the new underwater visibility theory, the relationship between the Z_SD and K_d (λ) is expressed as:

$$Z_{SD}=\frac{1}{2.5Min\left(K_d^{tr}\right)}ln\left(\frac{\left|0.14-R_{rs}^{PC}\right|}{0.013}\right)$$

(1)

where $Min\left(K_d^{tr}\right)$ is the minimum diffuse attenuation coefficient of the water body in the visible domain, and $R_{rs}^{PC}$ is the corresponding R_rs value of the wavelength with a minimum K_d. Compared to ocean color satellite sensors like MODIS and MERIS, Landsat-8 has fewer bands in the visible domain. To obtain a more accurate $Min\left(K_d^{tr}\right)$, Lee filled the wide spectral gap between 500–530 nm with an empirical relationship:

$$K_d\left(530\right)=0.20K_d\left(481\right)+0.75K_d\left(554\right)$$

Therefore, the bands involved in the $Min\left(K_d^{tr}\right)$ calculation are $K_d\left(443\right)$, $K_d\left(481\right)$, $K_d\left(530\right)$, $K_d\left(554\right)$, and $K_d\left(656\right)$. Equation (1) becomes:

$$Z_{SD}=\frac{1}{2.5Min\left(K_d\left(443,481,530,554,656\right)\right)}ln\left(\frac{\left|0.14-R_{rs}^{pc}\right|}{0.013}\right)$$

(2)

3.2. Developing a Combined Model for Honghu Lake

We found that QAA_v6 identified all of the water bodies in Honghu Lake as turbid water, which meant that only QAA_turbid could be applied. Then, we used QAA_turbid and QAA_clear separately, and the results showed that QAA_turbid severely underestimated the Z_SD, while QAA_clear overestimated it. Moreover, water bodies of inland lakes usually change continuously between the two states of clear and turbid water. This change is rapid and a burst of wind and waves can cause relatively clear water to become very turbid. We assumed that QAA_clear and QAA_turbid change uniformly with the two states, rather than being switched by a threshold value. We proposed a combined model that simulated the transition of QAA_turbid to QAA_clear according to the uniform change process of the Z_SD.

According to the characteristics of this process, we used logistic regression, a binary logistic model, to fit the model. The logistic model has been commonly used for binary regression, and it is frequently used in many areas, such as biology, economics, etc. [35]. There are three stages in our hypothesis: when the Z_SD is very low, the proportion of QAA_clear is 0; when the Z_SD is high enough, the coefficient of QAA_clear is 1; in another case, each of the two models has a certain proportion. The coefficient of QAA_clear and QAA_turbid varies continuously between 0 and 1. For this type of modeling, logistic regression is very suitable. We labeled the case where the water was turbid as 0, and the case where water was clear as 1. The regression was fitted with the lsqcurvefit function in MATLAB. The model (Figure 2) returned the weights of these two cases. We used the coefficient of QAA_clear to build a logistic function. It can be expressed as follows:

$$C_{clear}=1/\left(1+e^{-k\times \left(Z_{S{D}_{clear}}-x_0\right)}\right)$$

(3)

where $C_{clear}$ and $Z_{S{D}_{clear}}$ are the proportion and the Z_SD estimation of QAA_clear. k and x₀ are the steepness and the x value of the midpoint of the curve, and the sum of the proportion of QAA_turbid and QAA_clear should be 1.

Figure 2 illustrates the variation process of coefficients of the models. To fit this logistic curve, we chose the least-squares method. The basis of this method is to approximate the model and refine the parameters through successive iterations. There were 106 match-ups used for the fitting process. The values of QAA_clear and QAA_turbid are calculated for each sample point to obtain $Z_{S{D}_{clear}}$ and $Z_{S{D}_{turbid}}$. These two model values and the in situ-measured data were put into the logistic model to fit the model parameters of Equation (3). After fitting the coefficients of the two models, the Z_SD was therefore calculated as:

$$Z_{SD}=C_{clear}\times Z_{S{D}_{clear}}+C_{turbid}\times Z_{S{D}_{turbid}}$$

(4)

where $C_{clear}$ and $C_{clear}$ are the coefficients of QAA_clear and QAA_turbid. $Z_{S{D}_{clear}}$ and $Z_{S{D}_{turbid}}$ are the estimations of the two models.

After we fit the logistic model, we can derive the threshold R_rs (656) value from Equation (3) and

Table 2. Steps of QAA_v6 for Landsat OLI.

Step	Calculation
1	$r_{rs}\left(\lambda \right)=R_{rs}\left(\lambda \right)/\left(0.52+1.7R_{rs}\left(\lambda \right)\right)$
2	$u\left(\lambda \right)=\frac{-g_0+\sqrt{{\left(g_0\right)}^2+4g_1\times r_{rs}\left(\lambda \right)}}{2g_1}$, where $g_0$=0.089, $g_1$=0.1245
3	QAA_clear ($R_{rs}\left(656\right)<0.0015s{r}^{-1}$)	QAA_turbid (Else)
4	$\chi =log\left(\frac{r_{rs}\left(443\right)+r_{rs}\left(483\right)}{r_{rs}\left(554\right)+5\frac{r_{rs}\left(656\right)}{r_{rs}\left(483\right)}{r}_{rs}\left(665\right)}\right)$ $a\left({\lambda }_0\right)=a\left(554\right)=a_w\left(554\right)+{10}^{h_0+h_1\chi +h_2{\chi }^2}$$,\mathrm{where}{h}_0=-1.146$$,h_1=-1.366$$,\mathrm{and}{h}_2=-0.469$	$$\begin{gathered} a\left({\lambda }_0\right)=a\left(665\right)=a_w\left(665\right) \\ +0.39{\left(\frac{R_{rs}\left(656\right)}{R_{rs}\left(443\right)+R_{rs}\left(483\right)}\right)}^{1.14} \end{gathered}$$
5	$b_{bp}\left({\lambda }_0\right)=b_{bp}\left(554\right)=\frac{u\left(554\right)\times a\left(554\right)}{1-u\left(554\right)}-b_{bw}\left(554\right)$	$b_{bp}\left({\lambda }_0\right)=b_{bp}\left(656\right)=\frac{u\left(656\right)\times a\left(656\right)}{1-u\left(656\right)}-b_{bw}\left(656\right)$
6	$\eta =2.0\left(1-1.2exp\left(-0.9\frac{r_{rs}\left(443\right)}{r_{rs}\left(554\right)}\right)\right)$
7	$b_{bp}\left(\lambda \right)=b_{bp}\left({\lambda }_0\right){\left(\frac{{\lambda }_0}{\lambda }\right)}^{\eta }$
8	$a\left(\lambda \right)=\left(1-u\left(\lambda \right)\right)\left(b_{bw}\left(\lambda \right)+b_{bp}\left(\lambda \right)\right)/u\left(\lambda \right)$
9	$b_b\left(\lambda \right)=\frac{u\left(\lambda \right)\times a\left(\lambda \right)}{1-u\left(\lambda \right)}$
10	$K_d\left(\lambda \right)=\left(1+0.005\times {\theta }_s\right)a\left(\lambda \right)+\left(1-0.265\frac{b_{bw}\left(\lambda \right)}{b_b\left(\lambda \right)}\right)\times 4.26\times \left(1-0.52\times e^{-10.8\times a\left(\lambda \right)}\right)b_b\left(\lambda \right)$

Notes: $r_{rs}\left(\lambda \right)$: below-surface remote sensing reflectance; $R_{rs}\left(\lambda \right)$: above-surface remote sensing reflectance; $u\left(\lambda \right)$: ratio of backscattering coefficient to the sum of absorption and backscattering coefficients; ${\lambda }_0$: a reference wavelength; $a\left(\lambda \right)$: absorption coefficient of the total; $a_w\left(\lambda \right)$: absorption coefficient of pure water; $b_{bp}\left(\lambda \right)$: backscattering coefficient of suspended particles; $b_{bw}\left(\lambda \right)$: backscattering coefficient of pure seawater; $\eta$: spectral power for particle backscattering coefficient; $K_d\left(\lambda \right)$: diffuse attenuation coefficient; ${\theta }_s$: the solar zenith angle.

. In Figure 2, we can find the approximate position of the thresholds (the dotted line). If the Z_SD value is smaller than the first threshold, then QAA_turbid is used; if it is greater than the second threshold, then QAA_clear is applied; in the middle of the two threshold values, each of the two models has a certain proportion. In order to obtain the accurate threshold values, we used the change rate of the curve curvature. For the formula like Equation (3), its curvature is Equation (5):

$$K=\frac{\left|f^{″}\left(x\right)\right|}{{\left(1+f^{\prime 2}\left(x\right)\right)}^{3/2}}$$

(5)

f(x) is $C_{clear}$ in Equation (3) with model parameters, and $f^{\prime }\left(x\right)$ and $f^{″}\left(x\right)$ are the first- and second-order derivatives of f(x), respectively. The two threshold values correspond to the maxima and minima of the derivative formula for the rate of change K. The two threshold R_rs (656) can thus be derived by inversing the corresponding Z_SD values according to the equations in Table 2.

3.3. Applying QAA to Landsat TM and ETM+ Data

Landsat OLI/TIRS has acquired about 10,000 scenes since it was launched in 2013. To provide the long time-series water clarity monitoring, we used Landsat TM and ETM+ data. Landsat series satellites have a 30 m spatial resolution and are ideal for monitoring inland lakes. Landsat series data has been widely used in lake research [36,37,38], and some studies have validated the applicability of Landsat TM, ETM+ in QAA [16,17,39]. OLI has a narrower spectrum compared to TM and ETM+, and OLI adds a shorter-wavelength blue band (0.43–0.45 μm) [40]. Due to the similarity of band 1, we used band 2 to replace band 1 for the experiment when applying OLI data to QAA. Figure 3 shows very little difference before and after the replacement. This experiment inspired us to apply TM and ETM+ data to QAA. The flow of applying QAA to TM and ETM+ is roughly the same as OLI (Table 2). The difference is the band substitute and the representative wavelength.

Table 3. The representative wavelength of TM, ETM+ and OLI visible bands.

Band Wavelength (nm)	TM	ETM+	OLI
Band 1	486	479	443
Band 2	571	561	481
Band 3	668	661	554
Band 4			656

displays the representative wavelength of these sensors.

Normally, the direct substitute of 443 nm by 481 nm in QAA may lead to some changes in the results to a certain extent. It affects the empirical formula that determines $a\left({\lambda }_0\right)$ and $K_d\left(\lambda \right)$. To evaluate the error, we used Landsat-7 and Landsat-8 with overlapping acquisition dates to compare the results before and after the replacement. If this substitute works for Landsat-7, then it applies to Landsat-5 because of their similarity. Due to the satellite orbit settings, the time difference between the Landsat-7 and Landsat-8 satellite data is 8 days (

Table 4. Images acquisition dates of Landsat-7 and Landsat-8.

Landsat-7 Date	Landsat-8 Date
23 July 2013	31 July 2013
30 December 2013	22 December 2013
17 October 2015	25 October 2014
4 November 2016	12 November 2016
9 December 2017	17 December 2017
25 August 2019	17 August 2019
15 November 2020	7 November 2020

). The Z_SD is calculated through the K_d(λ) that is retrieved from QAA. We derived the minK_d(λ) (the minimum K_d(λ) in the visible domain) and the Z_SD from these satellite data using QAA_v6.

3.4. Error Metics and Statistical Indicators

To assess the performance of our algorithm, we used the following model-evaluation metrics: Pearson’s R (R), Mean Absolute Error (MAE), Root-Mean-Squared Error (RMSE) and bias. R represents how well the estimation fits the measurements; MSE shows how close the fitted line is to the data points; RMSE measures the distribution of the residuals and bias is a measure of the difference between the predicted values and the measured values. They are calculated as:

$$RMSE=\sqrt{\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(y_i-\widehat{y_i}\right)}^2}$$

(6)

$$MAE=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\left|y_i-\widehat{y_i}\right|$$

(7)

$$bias=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\left(y_i-\widehat{y_i}\right)$$

(8)

where N is number of samples, $\widehat{y_i}$ is the estimator and $y_i$ is the matched in situ measurement.

4. Results

4.1. Z_SD Estimation from Landsat Data by QAA_Honghu

Figure 4 shows the comparison of the two models using 125 pairs of match-ups. QAA_clear had a result with slope = 0.70, R = 0.70, RMSE = 0.50, MAE = 0.43 and bias = −0.40 m. QAA_turbid had a result with slope = 1.48, R = 0.61, RMSE = 0.31, MAE = 0.24 and bias = −0.04. The slope of these two models illustrated that QAA_clear had an overestimate and QAA_turbid had an underestimate. Although the R of QAA_clear was relatively low, the other metrics of QAA_clear were very high, and Figure 4a shows that basically, all of the Z_SD estimations of QAA_clear were higher than the in situ measurements. For QAA_turbid, on the other hand, most of its points were concentrated in the low-value region, and the higher the measured values, the more the Z_SD estimations were underestimated. Therefore, the combined model is required in order to adopt the advantages of QAA_clear and QAA_turbid to improve the algorithm.

To develop this model, we used 106 matching pairs of field measurements and spectra-estimated Z_SD in Honghu Lake from 2013 to 2020. We excluded sampling sites close to the lake shore because the bottom reflectance affects the water surface reflectance of shallow water areas [41,42,43]. The other parts of the match-ups were then used in the next section to validate QAA_Honghu. Then, we used these match-ups to fit the combined model coefficients according to Equation (4). It returned two model parameters: k = 11.84 and x₀ = 0.99 (Figure 5). k is the steepness of the S-curve, and it controls the rate of curve growth [44]. The logistic curve is steepest at the midpoint, x₀.

The parameters are applied to Equations (3) and (4). The Z_SD calculations were:

$$Z_{SD}=\frac{Z_{S{D}_{clear}}}{1+exp\left(-11.84\times \left(x-0.99\right)\right)}+\frac{Z_{S{D}_{turbid}}\times exp\left(-11.84\times \left(x-0.99\right)\right)}{1+exp\left(-11.84\times \left(x-0.99\right)\right)}$$

(9)

With certain model coefficients, we derived the $Z_{S{D}_{clear}}$ values of the threshold point, 0.67 m and 1.31 m. Next, we obtained the corresponding R_rs (656): if R_rs (656) < 0.010 sr⁻¹, then the water will be determined as clear water; if R_rs (656) > 0.020 sr⁻¹, then QAA_turbid will be applied. If R_rs (656) is between these two values, then both models will account for a certain proportion.

Figure 6 shows that QAA_Honghu had a significant improvement. Compared with QAA_clear and QAA_turbid, our model performed better with an RMSE that reduced from 0.5 to 0.28, an MAE that reduced from 0.43 to 0.21, and a bias that reduced from −0.4 to −0.05. Additionally, the trendline was closer to the 1:1 line. It improved the problem of too much deviation from the Z_SD measurements.

We applied QAA_Honghu to Landsat TM, ETM+, and OLI imagery and obtained 205 Z_SD maps with high spatial resolution. For these Landsat-7 data, we used the natural neighbor interpolation to fill the data gap. Figure 7 compared the trends between the measured Z_SD and estimated Z_SD from lake-centered sampling point Hu30 (29.829°N, 113.310°E). We used the average value within the 3 × 3 windows as the Z_SD estimation. The results showed an overall consistency and the feasibility of QAA_Honghu for monitoring the process of changing water clarity. Figure 8 displays the Z_SD of the Hu30 variation from 1987–2020, with an overall decreasing trend. Before 2000, the Z_SD fluctuated significantly but quickly returned to peak value. Since then, although the fluctuation range of the Z_SD was slight, the extreme values could not reach the previous level. There was a distinct downward trend from 2016–2020, and the peak values became smaller and smaller.

The Z_SD of Honghu Lake showed a distinct seasonal pattern. Figure 9 demonstrates the Z_SD variation from 1987–2020 by season; the Z_SD in summer had the most evident downward trend, while the other seasons have also declined, but not to a great extent. Figure 10 shows the spatial distribution of the seasonal Z_SD in 1991, 2016, and 2020. Overall, the Z_SD was the highest in summer and the lowest in winter.

4.2. Validation of QAA_Honghu Using in Situ Measurements

We used 44 pairs of match-ups of Honghu Lake from 2013–2020 to verify the stability of this model. Compared to QAA_v6, QAA_Honghu had a more stable and better result with R = 0.66, RMSE = 0.34 and a slope closer to 1. A comparison of the Z_SD estimations of QAA_v6 and QAA_Honghu (Figure 11) demonstrated the applicability of our model.

5. Discussion

5.1. The Performance of QAA_Honghu

Since the reference band and the threshold value set by the original algorithm (R_rs (656) = 0.0015 sr⁻¹) did not apply to Honghu Lake, it caused the original QAA to identify all water as turbid water and seriously underestimated the Z_SD. Instead of setting specific thresholds, our study fitted the respective percentage of QAA_clear and QAA_turbid by a logistic model. The critical values for QAA_clear and QAA_turbid corresponding to our fitted model were R_rs (656) = 0.010 sr⁻¹ and R_rs (656) = 0.020 sr⁻¹. When R_rs < 0.010 sr⁻¹, QAA_clear is used; when R_rs > 0.020 sr⁻¹, QAA_turbid is used; in addition to these two cases, each of the two models takes a certain percentage. We developed this combined model without a determination condition, which greatly improved the applicability of QAA in inland lakes. By fitting the coefficients of the two models, we obtained results with higher accuracy. Compared to the original algorithm, QAA_Honghu had a significant improvement in the validation dataset. QAA_Honghu had a higher R of 0.66, and the slope was closer to one. Moreover, this study improved the temporal resolution of the Z_SD products by using Landsat-5,7,8 satellite data and covered 33 years of available data.

5.2. Z_SD Trend of Honghu Lake

According to Figure 8, the Z_SD showed an overall decreasing trend from 1987–2020. Before 2000, the Z_SD fluctuated significantly, and the trendline was almost horizontal during this period. While some factors can significantly reduce the Z_SD, Honghu Lake can recover, and it does so very quickly. From 2000–2016, the Z_SD experienced a decline followed by an increase, and the peak values of the Z_SD had difficulty reaching the previous values. The changes in the Z_SD from 2000–2016 were primarily caused by human activities, especially enclosure aquaculture. Local fishermen used nets and bamboo poles to zone the open waters of Honghu Lake and then conducted aquaculture activities. Enclosure aquaculture remained an important factor in the ecological damage of Honghu Lake for a very long time [45,46,47]. After 2000, the area of enclosure aquaculture expanded rapidly. In 2004, the area reached 70% of the total lake area. During this period, the Z_SD decreased rapidly. In 2005, the Hubei provincial government required the removal of the purse seine from Honghu Lake; the two largest ones were in 2005–2006 and 2013–2014. Since these two large-scale seine removals, the Z_SD of Honghu Lake has increased. By 2017, the purse seine was completely removed.

In addition to human activities, extreme climatic events can also affect the water clarity of Honghu Lake. We found that the Z_SD of Honghu Lake decreased after floods. The Z_SD decreased to extreme values for some time immediately after the floods of 1996 and 1998 but quickly recovered to high levels. Then, after the catastrophic flood in 2016, the Z_SD continued declining until 2020. It was mentioned above that all of the purse seines were removed around 2017, yet the water clarity of Honghu Lake did not rise as expected.

Some studies showed that the catastrophic flood in 2016 led to the extensive death of aquatic vegetation in Honghu Lake, which decayed and deposited, further deteriorating the water quality of Honghu Lake [48]. Enclosure aquaculture can also lead to a reduction in the environmental carrying capacity, making it difficult to restore the ecological functions of Honghu Lake after flooding [49]. This flood has degraded the ecological system of Honghu Lake and made it difficult to restore water clarity to the previous level.

Overall, the Z_SD had a distinct seasonal variation from 1987–2020, with the highest in summer and the lowest in winter, and some early research had consistent results [15,50,51]. The drivers of this seasonal variation were also well-described by Feng et al. (2019), and it was caused by the rapid seasonal change in wind speed and precipitation in the Yangtze Plain [15,50,52].

5.3. Future Implication

In our study, we found that the error of QAA may originate from many factors. Firstly, the substitute of 443 nm by 481 nm had some impact. We used Landsat-7 and Landsat-8 data with overlapping acquisition dates (Table 4) to compare the satellite retrievals before and after the replacement. We generated 21 random points evenly over the study area and calculated the average value of minK_d(λ) and Z_SD from the satellite data. Average values can reduce the effect of the eight-day time window. Figure 12 shows the difference between the retrievals from Landsat-7 and Landsat-8. The minK_d(λ) values (Figure 12a) from Landsat-7 of most of these 21 points were smaller than the results from Landsat-8. The bias between minK_d(λ) from Landsat-7 and Landsat-8 was −0.018. Since the Z_SD is inversely proportional to K_d(λ), most of the Z_SD estimations (Figure 12b) from Landsat-7 were greater than Landsat-8 with bias = 0.009. The substitute of 443 nm by 481 nm resulted in a mild overestimation of Z_SD. As a result, the relationship between R_rs (443) and R_rs (481) may change with the water optical properties and thus inevitably impact the results. Therefore, the above substitute is a kind of stopgap. Many studies have used empirical formulas or virtual-band estimators to solve the problem of missing bands [17,32]. These methods require a large amount of in situ-measured R_rs (λ) data, and we are also collecting such measured data to improve our algorithm.

Other factors also cause errors, such as the atmospheric correction, lake bottom, and the time-matching of measurement data with satellite data. Atmospheric correction is vital for a remotely sensed observation of water color [53]. The effect of the atmosphere over water bodies on the radiance is significant because water is highly absorptive [54]. The atmosphere of inland waters is more optically heterogeneous, making atmospheric correction more difficult. We have tried several frequently used methods and found ACOLITE is the most effective. Atmospheric-correction methods specifically for inland lake waters are urgent for such research. We also found in our experiments that a main problem in applying QAA to inland lakes was that the lake bottom affected the reflectance of the water surface in places with shallow water depth, and it decreased the accuracy of the algorithm. There are some studies to attenuate or quantify the impact of bottom reflectance [55]. Another way to increase the accuracy of QAA could be eliminating the error of the lake bottom. Another source of error is that the previous measured data do not intentionally match the image acquisition dates. Waters tend to change rapidly in inland lakes compared to relatively stable offshore waters. A single gust of wind and waves can quickly disturb the sediment in the lake, causing a rapid change in water clarity. Therefore, more satellite transit matching data are vital for improvement.

In recent years, the government has proposed many conservation measures to restore the water quality of Honghu Lake and protect the ecosystem diversity of its wetlands. The measures include removing all the purse seines, returning the embankments to the lake, and controlling pollution sources. However, the results so far have failed to reach expectations. Due to the limitation of data acquisition, this study could not quantitatively analyze the influence of various factors on the water clarity of Honghu Lake. In future research, NDVI data, water-level data, various meteorological data, and other water-quality parameters could be used to reveal the degree of influence factors.

6. Conclusions

The original QAA switches between QAA_clear and QAA_turbid by R_rs (656) = 0.0015 sr⁻¹. It is unapplicable for inland lakes such as Honghu Lake. It caused the identification of all water bodies as turbid water. A new hypothesis in this research is that QAA_turbid and QAA_clear transition evenly. We developed a model for this change process. This model combines QAA_turbid and QAA_Honghu. After the modeling and validation, QAA_Honghu was applied to Landsat TM, Landsat ETM+, and Landsat OLI data for a total of 205 satellite imageries. The improved algorithm results reduced the RMSE from 0.5 to 0.28, the MAE from 0.43 to 0.21, and the bias from −0.4 to −0.05. The Z_SD products with a high spatial resolution of Honghu Lake for 1987–2020 were obtained. Overall, the water clarity of Honghu Lake trended downward and demonstrated distinct seasonality.