Open Access
Add to BibSonomy
Abstract
The particulate backscattering coefficient (bbp) plays an important role in the growth of coral reefs by influencing the light field conditions. Small-scale optically shallow waters are commonly found in coastal fringing reefs, making it challenging to monitor the spatial and temporal patterns accurately using Aqua satellites with a low spatial resolution. In this study, six existing optimization-based algorithms for deriving bbp at 400 nm (bbp(400)) were evaluated with three simulated Landsat-8 (spatial resolution = 30 m) data sets and in situ data from the Luhuitou Peninsula, Sanya. The comparison results indicated that the HOPE (hyperspectral optimization process exemplar) (Fix-H-error or Fix-H-error-free) algorithm which sets an input value of the water depth alone outperformed other algorithms. However, the estimated bbp(400) from all the algorithms tended to be either overestimated and underestimated due to the improper the spectral shape value of the backscattering coefficient. The HOPE (Fix-H-error) algorithm estimated-bbp(400) from in situ reflectance also had a good correlation with the in situ total suspended particle concentrations data derived-bbp(400), with a correlation coefficient of 0.83. Therefore, the HOPE (Fix-H-error) algorithm was selected to estimate the bbp(400) from satellite-based Landsat-8 data of the Luhuitou Peninsula, Sanya. Time-series (2014-2021) results from these Landsat-8 images reveal the seasonal variation of bbp(400). The bbp(400) was low from May to September every year. From October to December or January, bbp(400) had an increasing trend, and then it decreased until May. Spatial analysis indicated that bbp(400) decreased with increasing water depth. The spatial and temporal patterns of bbp(400) were consistent with in situ observations reported in the literature. This study preliminarily showed the efficiency of an optimization-based algorithm in deriving bbp(400) in small-scale optically shallow water region using Landsat-8 data.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The growth of corals largely depends on photosynthesis, which requires a sufficient light supply [1–3]. The water optical properties influence underwater light by absorbing or scattering radiation [4,5]. The particulate backscattering coefficient (${b_{bp}}$) is a water optical property that can indicate the light exposure of coral reefs. In addition, ${b_{bp}}$ is related to the total suspended matter (TSM) and particulate organic carbon (POC) [6]. Deriving ${b_{bp}}$ by remote sensing technology can reduce the costs and cover shortages of in situ observations.
Coastal coral reefs contain both optically deep and shallow waters. At present, significant effort has been devoted to ${b_{bp}}$ inversion for optically deep waters, and a series of inversion models for ${b_{bp}}$ have been developed for different satellite data [7–9]. Research on optically shallow waters is still undergoing development [10].
Currently, deriving particulate backscattering coefficient from optically shallow waters is limited due to the influence of the substrate. As a result, only the inversion algorithms which consider the influence of the substrate can be utilized for this purpose. McKinna, et al. [11] developed a model named the shallow water inversion model (SWIM) to simultaneously estimate the non-water backscattering coefficient, non-water absorption coefficient, and diffuse attenuation coefficient from MODIS data. The SWIM model requires input values of both water depth and bottom reflectance. Barnes, et al. [12] found that solely using the known value of water depth can enhance the inversion accuracy of the water properties. They subsequently developed the shallow water optimization with resolved depth (SWORD) approach to derive ${b_{bp}}$ at 440 nm. Due to the strong correlation between ${b_{bp}}$ and total suspended matter, Volpe, et al. [13] developed an optimization-based method that relates the ${b_{bp}}$ at 443 nm to the concentration of suspended matter. Then, the suspended matter concentration was estimated from a single band of several multispectral satellite sensors (such as Landsat, Aster, and Alos-Avnir), while keeping other parameters constant. However, X. Zhou, et al. [14] discovered that estimating the suspended matter concentration using only one band introduced significant uncertainty.
Efforts have been concentrated on utilizing low spatial resolution Aqua satellite multispectral data to simultaneously estimate ${b_{bp}}$ and other inherent optical properties (IOPs). Due to the presence of small-scale optically shallow waters in coastal fringing reefs, monitoring the spatial and temporal patterns of water optical properties using Aqua satellites with low spatial resolution becomes challenging. While optimization-based algorithms have been applied to high or medium-spatial-resolution imagery data, such as Landsat data, previous research concentrated on only a single parameter by by keeping other parameters constant. In terms of practicality, it is not feasible to set other parameters (except water depth) as constant values for complex optically shallow waters, especially when conducting time series analysis. Optimization-based algorithms that have the capability to simultaneously estimate several parameters are better suited for high or medium-spatial-resolution imagery data. Nevertheless, high or medium-spatial-resolution imagery data typically have fewer bands compared to Aqua satellite multispectral data. In order to fully utilize the potential of high or medium-spatial-resolution imagery data, it is essential to assess the effectiveness of current optimization-based algorithms in accurately estimating multiple parameters from high or medium-spatial-resolution imagery data. Among the existing high or medium-spatial-resolution imagery data with a spatial resolution $\le $ 30 m, Landsat-8 has four visible bands and three infrared bands for atmospheric correction [15]. For the optimization-based algorithm, Landsat-8 is suitable for deriving ${b_{bp}}$ and performing time series analysis. However, the performance of the existing optimization-based algorithms on Landsat-8 data is unclear and requires further investigation.
In this study, we had two objectives: 1) six optimization-based algorithms for deriving ${b_{bp}}$ at 400 nm (${b_{bp}}({400} )$) were chosen to evaluate with simulated and in situ data of optically shallow water using the Landsat-8 band set; 2) based on the performance, an optimization-based algorithm was chosen for the application to Landsat-8 images in order to uncover the spatial and temporal patterns of ${b_{bp}}({400} )$ in the Luhuitou Peninsula, Sanya.
2. Methods and data
2.1 Optimization-based shallow water optical properties approach
2.1.1 Semi-analytical model of optically shallow waters
The semi-analytical model of optically shallow waters developed by Lee, et al. [16] was the foundation for developing optimization-based algorithms. For optically shallow waters, the subsurface reflectance (${r_{rs}}$) can be simplified to a function of the water depth ($H$), particle backscattering coefficient (${b_{bp}}$), absorption coefficient of phytoplankton (${a_{ph}}$), absorption coefficient of gelbstoff and CDOM (${a_{dg}}$), and bottom reflectance ($\rho $) [16] (for brevity, wavelength $(\lambda )$ is omitted):
where ${b_{bp}}$, ${a_{ph}}$, ${a_{dg}}$ and $\rho $ can be expressed as functions of limited parameters:2.1.2 Six optimization-based algorithms
In this study, six existing optimization-based algorithms were selected and evaluated from a practicability perspective. The hyperspectral optimization process exemplar (HOPE) algorithm was selected as the first evaluation algorithm, serving as the foundation for the development of the other five existing algorithms [16](Table 1).
Table 1. Parameterization details for the six optimization-based algorithms
The HOPE algorithm works on water-leaving reflectance (${R_{rs}}$). Therefore, ${R_{rs}}$ is translated from ${r_{rs}}$ as follows [16]:
To match the satellite data or simulated Landsat-8 data, the simulated ${R_{rs}}$ of Landsat-8 bands was modeled by using the spectral response function ($F_{Ban{d_i}}^{Landsat - 8}$) as follows:
In the original HOPE algorithm, five unknowns, namely ${b_{bp}}({400\; nm} )$, ${a_{ph}}({440\; nm} )$, ${a_{dg}}({440\; nm} )$, H and B, were estimated using an optimization algorithm. Spectral matching was used to formulate the following cost function:
Barnes, et al. [12] found that setting H as a known value can improve the accuracy of IOPs estimated with simulated MERIS bands (413, 443, 490, 510, 560, 620, 665, 681 and 709 nm). Even though Landsat-8 only has four visible bands, it is still possible to derive H using a bathymetry approach. It is necessary to validate the efficiency of the SWORD approach for Landsat-8 data. In practice, the H input contains error. Thus, random relative errors within 20% were added to the input water depth. For the purposes of comparison, the H input without error was also fixed in HOPE algorithm. Hence, HOPE (Fix-H-error-free) and HOPE (Fix-H-error) were selected as the second and third evaluation algorithms, respectively.
The backscattering coefficient was determined not only by the reference wavelength but also the spectral shape value (Y) (Eq. (2)). Generally, Y is assumed to be a known value. However, obtaining or determining the preset value of Y can be challenging or may include errors. Thus, HOPE (Inverse-Y) treats Y as an unknown value. Furthermore, HOPE (Fix-H-error-Inverse-Y) treats Y as an unknown value and H as a known value.
To address the mixing phenomenon in multispectral remote sensing images, the Unmixing-based multispectral optimization process exemplar (UMOPE) algorithm was selected as the sixth evaluation algorithm [18]. The mixed substrate is expressed as follows:
Finally, six algorithms were selected, namely, HOPE, HOPE (Fix-H-error-free), HOPE (Fix-H-error), HOPE (Fix-H-error-inverse-Y), HOPE (Inverse-Y) and UMOPE. Table 1 provides the parameterization details for these six algorithms, while Table 2 displays the initial values and optimization ranges for the unknown variables. When the value of Y was fixed, the value of Y was set as 0.20 and 0.68, respectively. This was done to explore the influence of fixed spectral shape value of ${b_{bp}}$ on deriving ${b_{bp}}({400\,nm} )$.
Table 2. Initial values and optimization ranges of unknown variables for the six optimization-based algorithms
2.2 Simulated data
The semi-analytical model in Eqs. (1–7) was used to simulate ${R_{rs}}$ values of optically shallow waters for a given set of $IOPs$, H and $\rho $ values. The IOP values were obtained from the report 5 of the International Ocean-Colour Coordinating Group (IOCCG) [7]. The IOCCG report 5 generated 500 data sets, which are assumed to encompass a wide range of ocean conditions. The first 450 IOPs were selected and divided into three portions (Table 3). Subsequently, three simulated environments were constructed in different combinations. The input H varied from 1 m to 20 m, with intervals of 0.5 m. Two types of $\rho $ were used, namely sand and coral (shown in Appendix A, Fig. 10). Finally, a total of 12000 simulated reflectance values were generated for each simulated environment.
Table 3. Parameters’ ranges used for 3 simulated Data sets
2.3 In situ data
In situ data were collected from the Luhuitou Peninsula, Sanya on December 25, 2020. The location of the study site and field stations are shown in Fig. 1. The collected in situ data included ${R_{rs}}$ (Fig. 2), total suspended particle concentrations (TSPC), and water depth.
Fig. 1. Location of Luhuitou Peninsula in Sanya. Green triangles in (C) represent the locations of field stations.
During the field survey, a MAYA 2000Pro ocean optics single-channel spectrometer was used to measure the spectrum. The measured spectral range of this spectrometer is 198-1120 nm, and the spectral resolution was 3 nm. In order to ensure that the water-leaving signal would be unaffected by sun-glint, ship hulls, and human shadows, the water-leaving signal was measured multiple times with care to avoid shadows from the ships or people. The lowest value in the visible light range from the water-leaving signal was selected as the most accurate measurement value. The spectral measurement method was detailed in previous research [20]. Additionally, the water depth of each station was measured with a lead-line.
To obtain the TSPC, 1-8 L of seawater sample was filtered onto a preweighed 47 mm glass fiber filter (Whatman GF/F, 0.7 µm pore size) under low pressure until the filter was clogged. The filtrate was rinsed with 25-50 ml of Milli-Q water to eliminate as much salt as possible. This was done to prevent osmotic dysregulation, which could potentially lead to cell lysis [21]. The filter membranes and filtrates for suspended particulate matter determination were stored with aluminum foil at -20°C and weighed under dry conditions within 2 months. In the laboratory, the filters were dried (4 hours at 60°C) and reweighed under low humidity conditions. The TSPC was obtained by correcting the difference in the weight of the filter membrane before and after the filtration of seawater. Meanwhile, the weight of the blank sample was set as a reference. It is known that TSPC often has a good relationship with the backscattering coefficient. Therefore, an empirical model was applied to derive backscattering coefficients at 532 nm from the TSPC [22]:
Although the empirical model was not developed with the data from the Luhuitou Peninsula, the calibration parameters were reasonable when compared with other studies [22]. Thus, the indirectly obtained ${b_{bp}}({532} )$ values had a reasonable order of magnitude. For comparison, ${b_{bp}}({532} )$ was first transformed to ${b_{bp}}({470} )$ based on Eq. (2) where the reference band was changed to 470 nm. Then, the ${b_{bp}}({400} )$ was further obtained based on Eq. (2).The value of Y was set based on a study of the backscattering coefficient in the literature [23]. Overall, 23 stations from which TSPC was collected were used to estimate ${b_{bp}}({400} )$ in this study.
2.4 Atmospheric correction of satellite-acquired Landsat-8 data
In order to evaluate the selected algorithms with satellite data, 50 level-1 Landsat-8 images of the Luhuitou Peninsula were downloaded from Earth Explorer on the United States Geological Survey (USGS) website (https://earthexplorer.usgs.gov/). Before applying the selected algorithms to the Landsat-8 images, the path reflectance was corrected using ACOLITE.
ACOLITE is a free-access software for atmospheric correction for several kinds of satellite-based data. In the software, two algorithms are included [24]. Based on a previous study [25], the “dark spectrum fitting” algorithm was used. The “dark spectrum fitting” algorithm assumes that a specific region exists, over which the atmosphere state is homogeneous, and that there is at least one band containing pixels with zero reflectance. Then, the second simulation of the satellite signal in the solar spectrum-vector (6SV) radiative transfer model was used to construct a look-up table to correct the path reflectance of the Landsat-8 data [24]. More information on ACOLITE can be found at http://odnature.naturalsciences.be/remsem/software-and-data/acolite/. To remove the influence of sun-glint, the values in the visible bands were subtracted from the value in the near-infrared band [26].
2.5 Accuracy assessment
The correlation coefficient (R2), median absolute percentage difference (MAPD), root mean squared error (RMSE), and relative error were used to quantify the accuracy of the inversion approach. The MAPD, RMSE, and relative error were calculated as follows:
3. Results
3.1 Inversion results of simulated data
The six selected optimization-based algorithms were applied to simulated data sets 1, 2 and 3. Figure 3 shows the relative error of ${b_{bp}}({400} )$ at each water depth. The value of Y was set as 0.68 when the value of Y was fixed. In general, when the water depth is shallow, the accuracy of the estimated ${b_{bp}}({400} )$ is low and the values of the estimated ${b_{bp}}({400} )$ tend to be overestimated. However, as the water depth increases, the accuracy of all algorithm-estimated ${b_{bp}}({400} )$ values increases. Eventually, the accuracy of the estimated ${b_{bp}}({400} )$ reaches a stable value.
Fig. 3. Relative error of ${b_{bp}}({400} )$ at each water depth. The solid red line represents the middle value of relative error at each water depth. Y was set as 0.68.
In data set 1, all the estimated ${b_{bp}}({400} )$ values tend to be either overestimated or underestimated. Among the six algorithms, HOPE (Fix-H-error-free) algorithm demonstrates the best performance, exhibiting the most compact scatter and the least biased middle value of relative error at each water depth. On the other hand, HOPE (Fix-H-error-inverse-Y) algorithm shows the poorest performance in comparison. HOPE (Fix-H-error) and HOPE algorithms yield nearly identical accuracy in estimating ${b_{bp}}({400} )$. This suggests that fixing the water depth value with a biased value has no practical significance in data set 1. UMOPE algorithm has the same performance as HOPE and HOPE (Fix-H-error) algorithms in the deep region (water depth >16 m). However, when the water depth is shallower than approximately 16 m, HOPE and HOPE (Fix-H-error) algorithms outperform UMOPE algorithm. HOPE (Inverse-Y) algorithm outperforms HOPE (Fix-H-error-inverse-Y) algorithm. In short, HOPE (Fix-H-error-inverse-Y) algorithm performs the worst. HOPE (Fix-H-error-free), HOPE (Fix-H-error) and HOPE algorithms are more suitable for data set 1.
In data set 2, it appears that both HOPE (Fix-H-error-free) and HOPE (Fix-H-error) algorithms outperform the other algorithms. This can be attributed to the more concentrated scattering pattern observed in the results of these two algorithms, as compared to the scatters produced by the remaining algorithms. However, when examining the middle value of the relative error at each water depth, it becomes evident that HOPE, UMOPE and HOPE (Inverse-Y) algorithms outperform the other algorithms. This is reflected in the fact that the middle value of the relative error at each water depth closer to the y = 0 line. Among the above three algorithms, the scatter of the HOPE algorithm demonstrates a more compact distribution around the y = 0 line compared to other two algorithms. HOPE (Fix-H-error-inverse-Y) algorithm continues to exhibit the poorest performance in data set 2, just as it did in data set 1. Hence, with the exception of the HOPE (Fix-H-error-inverse-Y) algorithm, the remaining algorithms can be considered as alternatives for data set 2.
In data set 3, the middle value of the relative error at each water depth suggests that the estimated ${b_{bp}}({400} )$ is overestimated when the water depth is fixed. When the water depth is unknown, the estimated ${b_{bp}}({400} )$ tends to be underestimated. However, when the water depth is fixed, the scatter is tightly clustered. This phenomenon indicates that HOPE (Fix-H-error-free), HOPE (Fix-H-error) and HOPE (Fix-H-error-inverse-Y) algorithms outperform other algorithms for data set 3.
As a whole, the comparison results from the three data sets in Fig. 3 indicate that all the selected algorithms tend to either overestimate or underestimate ${b_{bp}}({400} )$. To explore the influence of the spectral shape on deriving ${b_{bp}}({400} )$, the value of Y was set as 0.20. Figure 4 shows the accuracy of the corresponding estimated ${b_{bp}}({400} )$. The accuracy of the estimated ${b_{bp}}({400} )$ was significantly improved by HOPE (Fix-H-error) and HOPE (Fix-H-error-free) algorithms, which means that Y has a significant influence on estimating ${b_{bp}}({400} )$. However, when the water depth was set as unknown, the influence of Y on the estimated ${b_{bp}}({400} )$ is not significant. Therefore, HOPE (fix-H-error-free) and HOPE (fix-H-error) algorithms can serve as alternatives for deriving ${\textrm{b}_{\textrm{bp}}}({400} )$ from Landsat-8 data. Due to the presence of errors in the input water depth, HOPE (Fix-H-error) algorithms may be more suitable for the Luhuitou Peninsula. The selection of HOPE (Fix-H-error) algorithm can be further confirmed through additional comparison with in situ data from the Luhuitou Peninsula. It should be noted that HOPE (Fix-H-error) algorithm is the SWORD algorithm which is developed by Barnes, et al. [12]. In other words, SWORD algorithm outperforms the other selected algorithms at estimating ${b_{bp}}({400} )$ from simulated Landsat-8 data.
Fig. 4. Relative error of ${b_{bp}}({400} )$ at each water depth. The solid line represents the middle value of relative error at each water depth. Y was set as 0.20.
3.2 Application of HOPE (Fix-H-error) algorithm in the Luhuitou Peninsula
HOPE (Fix-H-error) or SWORD algorithm is further applied to the Luhuitou Peninsula data to highlight the advantage of using the HOPE (Fix-H-error) algorithm. HOPE (Fix-H-error-free) algorithm is not included because as it is not practical to set an H input without any errors. However, the other four algorithms are also applied to the in situ data.
3.2.1 Results of in situ data
In the original results, it is observed that the estimated ${\textrm{b}_{\textrm{bp}}}({400} )$ have local optimal solutions that coincide with the upper and lower limits. In theory, these local optimal solutions indicate a potential failure in the inversion process. As a result, the samples corresponding to these points are eliminated to ensure the reliability. Figure 5 shows the scatterplots between the estimated ${\textrm{b}_{\textrm{bp}}}({400} )$ and in situ data-derived ${\textrm{b}_{\textrm{bp}}}({400} )$, and Table 4 shows the accuracy metric of the estimated ${\textrm{b}_{\textrm{bp}}}({400} )$.
Fig. 5. Scatterplots between estimated ${b_{bp}}({400} )$ and in situ data derived-${b_{bp}}({400} )$.
Table 4. Accuracy metrics of in situ data-derived bbp(400).
Among the selected algorithms, the R2 is the largest between the HOPE (Fix-H-error) algorithm-estimated ${\textrm{b}_{\textrm{bp}}}({400} )$ and the in situ data-derived ${\textrm{b}_{\textrm{bp}}}({400} )$, with a value of 0.81. The RMSE and MAPD of the HOPE (Fix-H-error) algorithm-estimated ${\textrm{b}_{\textrm{bp}}}({400} )$ are 0.039 m-1 and 0.44, respectively. As mentioned earlier, the optimization-based algorithm is capable of determining the relative value of ${\textrm{b}_{\textrm{bp}}}({400} )$ if the spectral shape is inappropriate. Without an in situ value for Y, the MAPD and RMSE values can only be used as references. Therefore, R2 is the most suitable metric for selecting the appropriate algorithm. Finally, HOPE (Fix-H-error) algorithm is selected as the appropriate algorithm for the Luhuitou Peninsula.
3.2.2 Results of Landsat-8 images
HOPE (Fix-H-error) or SWORD was applied to the Landsat-8 images of the Luhuitou Peninsula. The input H data was acquired from our previous study [25]. Before utilizing the bathymetry map, the tide influence was corrected. The spatial and temporal patterns of estimated ${\textrm{b}_{\textrm{bp}}}({400} )$ are shown in the subsequent section.
1) Spatial pattern of ${\textrm{b}_{\textrm{bp}}}({400} )$
The spatial patterns of estimated ${\textrm{b}_{\textrm{bp}}}({400} )$ is shown in Fig. 6. Figure 6(A) shows the ${\textrm{b}_{\textrm{bp}}}({400} )$ results in a Landsat-8 data scene which was acquired on January 1, 2021. In terms of spatial distribution, the inversion map reveals a trend where the ${\textrm{b}_{\textrm{bp}}}({400} )$ values in the southern region exhibit higher values compared to the northern region. To validate the observed trend, we conducted kriging interpolation on the in situ measured TSPC. The interpolation result is presented in Fig. 6(B). The interpolation result confirms that the TSPC in the south side is higher than that in the north side. The comparison between the estimated map and interpolated map suggests a reasonable consistency in the spatial distribution pattern.
Fig. 6. Comparison between estimated ${b_{bp}}({400} )$ map (left, image was acquired on January 1, 2021) and interpolated total suspended particles concentration map (right).
The estimated ${b_{bp}}({400} )$ of the optical shallow water area exhibited higher values compared to the adjacent optically deep area. To validate the observed trend, we present the TSPC values from five stations along a section line in Fig. 7. As the water depth increases, both the TSPC and ${a_{dg}}({440} )$ values exhibit a decreasing trend. In particular, There is a notable 4-fold maximum difference in the TSPC values between deep and shallow waters. Although the imaging time of the Landsat-8 data did not coincide with the in situ observation time, the phenomenon observed in Fig. 7 demonstrates a similarity to the pattern observed in the inversion map presented in Fig. 6(A).
Fig. 7. Total suspended particle concentrations along a section line in Luhuitou Peninsula. LHT is short for Luhuitou here.
2) Temporal pattern of ${b_{bp}}({400} )$
The temporal patterns of estimated ${b_{bp}}({400} )$ are shown in Fig. 8. In Fig. 8, the gray, green, and red shaded areas represent the values of ${b_{bp}}({400} )$ from October to April or May of the following year. The red arrow highlights an increasing trend, while the green arrow indicates a decreasing trend.
Fig. 8. Time series of ${\textrm{b}_{\textrm{bp}}}({400} )$ in Luhuitou Peninsula (2014-2021).The red arrow indicates an increasing trend, and the green arrow indicates a decreasing trend. The red number represents the month.
As a whole, from 2014 to 2021, there is a noticeable regular cycle of seasonal variation. The values of ${b_{bp}}({400} )$ in June, July, August, and September are typically low, while the values in December, January, and February are the highest. Within the green shaded areas, ${b_{bp}}({400} )$ displays an increasing trend from October to December or January of the following year. From December of the previous year or January of the current year to April or May of the current year, ${b_{bp}}({400} )$ decreases. However, within the gray and red shaded areas, the change in trend is not significant.
The seasonal variation observed from the Landsat-8 estimated ${b_{bp}}({400} )$ is consistent with previous research to some extent. Chen, et al. [27] collected the TSPC in the Sanya River, which is the upstream of the Luhuitou Peninsula, from November 2013 to March 2014. Their results also indicated that the TSPC value was highest in December and January compared with other months. Therefore, with the utilization of Landsat-8 data, our initial results demonstrate the effectiveness of monitoring the temporal pattern of ${b_{bp}}({400} )$ for the small-scale optically shallow waters of the Luhuitou Peninsula.
4. Discussion
4.1 Influence of spectral shape on deriving ${b_{bp}}({400} )$
The optimization-based algorithm is developed using a semi-analytical forward model, which is a function of IOPs. For the convenience of inversion, the IOPs are simplified and expressed as functions of a single unknown. However, the spectral shape of IOPs is not entirely determined by a parameter. Figure 9 illustrates a comparison of three simulated spectral shapes of ${\textrm{b}_{\textrm{bp}}}$. It is evident that the value of Y in Eq. (2) has profound impact on simulating ${b_{bp}}$. Optimization-based algorithms use all the visible bands of Landsat-8. In order to balance the contribution of the four visible bands to the residual of the cost function, ${b_{bp}}({400} )$ will be either overestimated or underestimated when the value of Y is fixed.
Fig. 9. Comparison of three simulated ${b_{bp}}$. Gray shaded areas represent the spectral response function of Landsat-8.
Developing an empirical algorithm for deriving ${b_{bp}}({400} )$ from optically shallow waters based on reflectance alone is challenging due to the influence of the substrate. The optimization-based algorithm has the advantage of considering substrate effects, but this advantage cannot guarantee the accuracy of the estimated ${b_{bp}}({400} )$. Since the inversion problem involves a similar number of unknowns as the number of bands, the inversion problem is ill-posed. To ensure the highly accurate estimation of ${b_{bp}}({400} )$, an alternative approach is to use in situ data to calibrate the estimated ${b_{bp}}({400} )$ values. As shown in Figs. 3, 4 and 5, the SWORD-estimated ${b_{bp}}({400} )$ has a good relationship with the TSPC or TSPC-derived ${b_{bp}}({400} )$. It is feasible to construct an empirical model on the basis of estimated ${b_{bp}}({400} )$. However, to develop a reliable and accurate empirical model, a substantial amount of in situ data is required.
4.2 Driving factors of ${\boldsymbol{b}_{\boldsymbol{bp}}}({400} )$ variation in the Luhuitou Peninsula
The application results of HOPE (Fix-H-error) or SWORD reveal the temporal pattern of ${b_{bp}}({400} )$ on the Luhuitou Peninsula, Sanya. Based on previous research, it has been found that the northeast monsoon in Sanya strengthens during the autumn and winter seasons. This intensified northeast monsoon is associated with increased disturbance, resulting in a decrease in the depth of the euphotic zone [28]. Consequently, this reduction in depth leads to an increase in the concentration of suspended matter. Therefore, it is highly likely that the monsoon plays a significant role in influencing the temporal changes in ${b_{bp}}({400} )$ or TSPC.
Additionally, human activities can be considered as an important factor influencing temporal variation in ${b_{bp}}({400} )$ or TSPC. The Luhuitou Peninsula, located in Sanya, acts as the southernmost touristic attraction in China. After October of each year, Sanya experiences a significant influx of tourists from the northern regions who are attracted by its warm climate. Especially during the week-long Chinese Spring Festival during January or February, many tourists visit Sanya [29]. Therefore, the time series of ${b_{bp}}({400} )$ is affected by human activities to some extent. An example of the influence of human activities can be observed in Fig. 8. The red shaded area in Fig. 8 marks the time period of the COVID-19 outbreak in 2020. The time-series results reveal that the ${b_{bp}}({400} )$ values from January to March 2020 were notably lower compared to the same months of other years. During this time period, there was a significant decrease in the number of tourists visiting Sanya, leading to a noticeable reduction in human activities. As a result, it is likely that human activities played a crucial role in the temporal variation of ${b_{bp}}({400} )$ or TSPC.
5. Conclusions
In this study, six optimization-based algorithms were employed to estimate ${b_{bp}}({400} )$ from three simulated Landsat-8 data sets. The results indicated that all the selected algorithms exhibited a tendency to either overestimate or underestimate ${b_{bp}}({400} )$. This discrepancy could possibly be attributed to an improper value assigned to Y (spectral shape of the backscattering coefficient). In general, HOPE (Fix-H-error) or SWORD algorithm outperformed other algorithms. Application of the selected algorithms to in situ data from the Luhuitou Peninsula further shows the advantage of the HOPE (Fix-H-error) or SWORD algorithm, with the highest R2 between the estimated and in situ TSPC-derived ${b_{bp}}({400} )$. The time-series analysis of Landsat-8 images indicates that there is a temporal pattern of ${b_{bp}}({400} )$ observed on the Luhuitou Peninsula. Nevertheless, accurately deriving ${b_{bp}}({400} )$ from small-scale optically shallow regions remains a challenging study. Further efforts are required to address issues related to the overestimation or underestimation of by optimization-based algorithms.
Appendix
Reflectance of substrate for simulated data.
Funding
National Natural Science Foundation of China (41876207, 42076190, 42206182); Hainan Province Science and Technology Special Fund (ZDYF2020174); Guangzhou Science and Technology Plan Project (2023A04J0204).
Acknowledgment
The authors express their sincere gratitude to the USGS for the distribution of Landsat-8 Level-1 data products.
Disclosures
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. P. G. Falkowski, Z. Dubinsky, L. Muscatine, and J. W. Porter, “Light and the Bioenergetics of a Symbiotic Coral,” BioScience 34(11), 705–709 (1984). [CrossRef]
2. W. C. Dennison, “Effects of light on seagrass photosynthesis, growth and depth distribution,” Aquat. Bot. 27(1), 15–26 (1987). [CrossRef]
3. L. Yong, L. Huang, X. Lei, X. Yu, C. Liu, L. Jiang, B. Y. Sun, M. Cheng, J. Gan, Y. Zhang, G. Zhou, S. Liu, J. Lian, and H. Huang, “Light availability regulated by particulate organic matter affects coral assemblages on a turbid fringing reef,” Mar. Environ. Res. 177, 105613 (2022). [CrossRef]
4. R. P. Dunne and B. E. Brown, “Penetration of solar UVB radiation in shallow tropical waters and its potential biological effects on coral reefs; results from the central Indian Ocean and Andaman Sea,” Mar. Ecol.: Prog. Ser. 144, 109–118 (1996). [CrossRef]
5. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic Press, 1994).
6. W. Zhou, W. Cao, J. Zhao, G. Wang, W. Zheng, L. Deng, and C. Li, “Variability of scattering and backscattering of marine particles in relation to particle concentration, size distribution, and composition off the eastern hainan coast in the south China sea,” Cont. Shelf Res. 232, 104615 (2022). [CrossRef]
7. IOCCG, Remote Sensing of Inherent Optical Properties: Fundamentals, Tests of Algorithms, and Applications, (Dartmouth, Canada, 2006).
8. P. J. Werdell, B. A. Franz, S. W. Bailey, G. C. Feldman, E. Boss, V. E. Brando, M. Dowell, T. Hirata, S. J. Lavender, and Z. Lee, “Generalized ocean color inversion model for retrieving marine inherent optical properties,” Appl. Opt. 52(10), 2019–2037 (2013). [CrossRef]
9. R. J. W. Brewin, S. Sathyendranath, D. Müller, C. Brockmann, P. Y. Deschamps, E. Devred, R. Doerffer, N. Fomferra, B. Franz, and M. Grant, “The Ocean Colour Climate Change Initiative: III. A round-robin comparison on in-water bio-optical algorithms,” Remote Sens. Environ. 162, 271–294 (2015). [CrossRef]
10. P. J. Werdell, L. I. W. McKinna, E. Boss, S. G. Ackleson, S. E. Craig, W. W. Gregg, Z. Lee, S. Maritorena, C. S. Roesler, C. S. Rousseaux, D. Stramski, J. M. Sullivan, M. S. Twardowski, Maria Tzortziou, and X. Zhang, “An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing,” Prog. Oceanogr. 160, 186–212 (2018). [CrossRef]
11. L. I. W. McKinna, P. R. C. Fearns, S. J. Weeks, P. J. Werdell, M. Reichstetter, B. A. Franz, D. M. Shea, and G. C. Feldman, “A semianalytical ocean color inversion algorithm with explicit water column depth and substrate reflectance parameterization,” J. Geophys. Res. Oceans 120(3), 1741–1770 (2015). [CrossRef]
12. B. B. Barnes, R. Garcia, C. Hu, and Z. Lee, “Multi-band spectral matching inversion algorithm to derive water column properties in optically shallow waters: An optimization of parameterization,” Remote Sens. Environ. 204, 424–438 (2018). [CrossRef]
13. V. Volpe, S. Silvestri, and M. Marani, “Remote sensing retrieval of suspended sediment concentration in shallow waters,” Remote Sens. Environ. 115(1), 44–54 (2011). [CrossRef]
14. X. Zhou, M. Marco, A. John, and S. Sonia, “Hyperspectral and Multispectral Retrieval of Suspended Sediment in Shallow Coastal Waters Using Semi-Analytical and Empirical Methods,” Remote Sens. 9(4), 393 (2017). [CrossRef]
15. D. P. Roy, M. A. Wulder, T. R. Loveland, C. E. Woodcock, R. G. Allen, M. C. Anderson, D. Helder, J. R. Irons, D. M. Johnson, and R. Kennedy, “Landsat-8: Science and product vision for terrestrial global change research,” Remote Sens. Environ. 145, 154–172 (2014). [CrossRef]
16. Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization,” Appl. Opt. 38(18), 3831–3843 (1999). [CrossRef]
17. Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt. 37(27), 6329–6338 (1998). [CrossRef]
18. Y. Liu, R. Deng, J. Li, Y. Qin, L. Xiong, Q. Chen, and X. Liu, “Multispectral bathymetry via linear unmixing of the benthic reflectance,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 11(11), 4349–4363 (2018). [CrossRef]
19. T. Petit, T. Bajjouk, P. Mouquet, S. Rochette, B. Vozel, and C. Delacourt, “Hyperspectral remote sensing of coral reefs by semi-analytical model inversion – Comparison of different inversion setups,” Remote Sens. Environ. 190, 348–365 (2017). [CrossRef]
20. J. Tang, G. Tian, X. Wang, X. Wang, and Q. Song, “The methods of water spectra measurement and analysis 1 : above-water method,” J. Remote Sens. 8, 37–44 (2004).
21. S. Woźniak, J. Meler, B. Lednicka, A. Zdun, and J. Stoń-Egiert, “Inherent optical properties of suspended particulate matter in the southern Baltic Sea,” Oceanologia 53(3), 691–729 (2011). [CrossRef]
22. Q. Song and J. Tang, “The study on the scattering properties in the Huanghai Sea and East China Sea,” ACTA OCE ANOLOGICA SINICA4, (2006).
23. H. Wang and D. Liu, “Spatio-temporal distribution and variation analysis of backscattering coefficient in Beibu Gulf,” Journal of ocean technology 39, (2020).
24. Q. Vanhellemont, “Adaptation of the dark spectrum fitting atmospheric correction for aquatic applications of the Landsat and Sentinel-2 archives,” Remote Sens. Environ. 225, 175–192 (2019). [CrossRef]
25. Y. Liu, J. Zhao, R. Deng, Y. Liang, Y. Gao, Q. Chen, L. Xiong, Y. Liu, Y. Tang, and D. Tang, “A downscaled bathymetric mapping approach combining multitemporal Landsat-8 and high spatial resolution imagery: Demonstrations from clear to turbid waters,” ISPRS J. Photogramm. Remote Sens. 180, 65–81 (2021). [CrossRef]
26. B.-C. Gao and R.-R. Li, “Correction of sunglint effects in high spatial resolution hyperspectral imagery using SWIR or NIR bands and taking account of spectral variation of refractive index of water,” Advances in Environmental Engineering Research 02, 1–16 (2021). [CrossRef]
27. P. Chen, X. Li, M. Wang, H. Li, W. Chen, and Y. Li, “Analysis of organic matter content in Sanya River during tourist season,” Journal of Qiongzhou University21, (2014).
28. X. Song, L. Huang, Y. Tan, J. Dong, C. Cai, J. Zhang, W. Zhou, and T. Li, “Distribution characteristics of primary production and its influence factors in Sanya Bay, Hainan Island during Northeast Monsoon Period,” Marine Science Bulletin 28, 34–40 (2009).
29. J. Zhang and L. Wu, “Modulation of the urban heat island by the tourism during the Chinese New Year holiday: a case study in Sanya City, Hainan Province of China,” Sci. Bull. 60(17), 1543–1546 (2015). [CrossRef]
