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Abstract
Many chlorophyll-a (Chl-a) remote sensing estimation algorithms have been developed for inland water, and they are proposed always based on some ideal assumptions, which are difficult to meet in complex inland waters. Based on MIE scattering theory, this study calculated the optical properties of mineral particles under different size distribution and refractive index conditions, and the Hydrolight software was employed to simulate remote sensing reflectance in the presence of different mineral particles. The findings indicated that the reflectance is significantly influenced by the slope (j) of particle size distribution function and the imaginary part (n’) of the refractive index, with the real part (n) having a comparatively minor impact. Through both a simulated dataset containing 18,000 entries and an in situ measured dataset encompassing 2183 data from hundreds of lakes worldwide, the sensitivities of band ratio (BR), fluorescence baseline height (FLH), and three-band algorithms (TBA) to mineral particles were explored. It can be found that BR showed the best tolerance to mineral particles, followed by TBA. However, when the ISM concentration is less than 30 g m-3, the influence of CDOM cannot be ignored. Additionally, a dataset of over 400 entries is necessary for developing the BR algorithm to mitigate the incidental errors arising from differences in data magnitude. And if the amount of developing datasets is less than 400 but greater than 200, the TBA algorithm is more likely to obtain more stable accuracy.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Inorganic mineral particles usually play an important role in optical signals of Case 2 waters, which is the decisive factor of scattering and backscattering. [1–3]. The optical properties of inland water are complicated due to different combinations of the three components of water color (phytoplankton, suspended matter, and colored dissolved organic matter (CDOM)), and consequently, there are still great differences in the optical types of inland water in different locations and even in the same location at different times [4–7].
Chlorophyll-a (Chl-a), an indicator of phytoplankton, has been intensively studied. [4,8]. Correspondingly, several algorithms for remote sensing of Chl-a have been continuously evolving, progressing from the original blue-green band ratio established for marine environments to more advanced baseline-height and three-band algorithms specifically tailored for complex near-shore and inland water bodies [4,9–13]. Nonetheless, it has been evidenced that these algorithms do not consistently demonstrate optimal performance when water bio-optical characteristics exhibit considerable heterogeneity [14,15]. Earlier studies have classified inland waters into spectrally distinct clusters, and it has been observed that specific Chl-a retrieval algorithms exhibit varying performance for different water types [16,17]. Consequently, a common approach involves partitioning water bodies into different water types based on optical characteristics and employing specific Chl-a retrieval algorithms accordingly [18,19]. Although these strategies have somewhat enhanced the Chl-a estimation performance, the key factors influencing the accuracy of Chl-a estimation still remain elusive. Limited research has been conducted concerning the inherent optical properties (IOPs) of inorganic mineral particles within water bodies, and the varying features of these properties remain lacking. Generally, these constituents significantly contribute to the scattering and backscattering characteristics of inland water bodies and have a predominant influence on the performance of remote sensing estimation of Chl-a.
The optical properties of inorganic mineral particles are strongly influenced by their size distribution and composition (refractive index) [20–23]. Due to variations in particle size, structure, shape, refractive index real part (n) and imaginary part (n’), and concentration, these particles significantly influence the light scattering and radiative transfer processes within the water [20,24]. Therefore, it is not enough to simply regard mineral particles as a single type of bulk particle. Inland waters contain a complex mixture of inorganic and organic particles, and to date, there is still no precise in-situ technique to determine the size distribution and composition of these particles [25]. This has been one of the obstacles in improving the accuracy of remote sensing algorithms for water component retrieval. Fortunately, theoretical analysis has been employed to enhance the understanding of the variations in water reflectance caused by the presence of mineral particles. Peng and Effler [26] and Peng, et al. [25] analyzed the influence of mineral particles composition and particle size distribution on light scattering characteristics based on the measured data of Schoharie Reservoir. Neukermans, et al. [27] conducted an in-depth study of the mass-specific beam attenuation and backscattering of marine particles in relation to particle size, density, and composition based on the data collected in coastal waters of Europe and French Guiana. In terms of the impact of mineral particles on Chl-a estimation, Mckee, et al. [28] studied the effect of mineral particle concentration on the Sun-induced Chl-a fluorescence (SICF) signal using Hydrolight radiative transfer simulations and found that the presence of mineral particles concentration can reduce SICF by 50%. Woźniak and Stramski [29] used the MIE theory to simulate the impact of different size distributions and refractive index variations of mineral particles on the spectral reflectance of seawater and ocean Chl-a algorithms (OC2, OC4, and OCx) and concluded that the effect of particle size and the imaginary part (n’) of the refractive index on the ocean spectrum is significant. Algorithms based on blue-green band ratios produce severe Chl-a overestimations due to the presence of mineral particles. Although these studies have to some extent enhanced our understanding of the IOPs of mineral particles and have also simulated the impact of inorganic particles in marine environments on ocean Chl-a estimation algorithms, inland water are often dominated by inorganic suspended matter with more complex sources. Therefore, for inland waters with more complex inorganic mineral compositions and higher concentrations, are the results and the rules discovered by previous studies still applicable? How do mineral particles affect Chl-a estimation performance in inland water bodies? Therefore, this study aims to 1) simulate the inherent IOPs of a wider range of inorganic mineral particles in inland water environments using the MIE scattering theory, 2) combine Hydrolight radiative transfer simulations software to demonstrate how variations in particle size distribution, refractive index, and concentration of mineral particles affect the spectral reflectance characteristics of inland water bodies, 3) explore the sensitivity of several often used Chl-a estimation algorithms to mineral particles.
2. Data and methods
Our simulation methodology, as depicted in Fig. 1, can be divided into two main components. The first part involves simulating the IOPs of mineral particles in water using the MIE theory. This part supposes several characteristics of the mineral particles [26], typically including: (1) the particles are homogeneous and composed of spherical particles with the same refractive index, (2) the optical properties of the particles are the same in all directions, and (3) the scattering behavior between particles is independent, meaning the interaction between particles can be neglected. The second part involves utilizing the obtained IOPs characteristics of mineral particles from MIE theory as input data for simulating the radiative transfer process in water using the Hydrolight numerical simulation software. This allows us to obtain remote sensing reflectance of the water at different levels of mineral particles.
2.1 MIE simulation of inorganic mineral particles
The spectral mass-specific coefficients for absorption and scattering of mineral particles are influenced by four distinct characteristics of the particle assemblage: particle concentration, PSD, particle composition, and particle shape. In this study, the formula provided by Woźniak and Stramski [29] was used to calculate the inherent optical properties of mineral particles, and are only briefly reviewed here. Although several algorithms have been developed to model particle size distribution functions [26,30,31], the objective of this study is not to simulate an accurate representation of the real particle size distribution. Instead, the focus is on investigating the influence of particles with different sizes on optical properties. Therefore, this study assumes that the particle size distribution follows a widely adopted Junge-distribution model (power-law fitting) [31]($N(D )= K{D^j}$), whereas K determines the magnitude variations in PSD, parameter j dictates the shape of the PSD. And K is chosen to be 104 [29]. We choose three different slopes (j = -3.2, j = -4.0, j = -4.8) to simulate the particle size distribution of different sizes in water. A larger slope (j = -4.8) indicates a higher abundance of smaller particles. Three different real parts of refractive index were utilized in this study, n (relative to water): n = 1.10, n = 1.18, and n = 1.26, to represent the compositional variations of mineral particles in inland water [23,24,32,33] and two different imaginary parts of refractive index n’: a low n’ = 0.0005 and a high n’ = 0.005 [34]. It is important to note that these settings are based on the assumption that n and n’ are wavelength-independent and encompass the possible range of mineral particles and aggregates found in natural inland water, including most scenarios.
2.2 Radiative transfer simulation by Hydrolight
The Case 2 IOPs model of Hydrolight-Ecolight 6.0 was used to obtain remote sensing reflectance. This model comprises four constituents: water, phytoplankton, CDOM, and mineral suspension solids, enabling a more comprehensive simulation of optical radiation transfer processes in inland lake ecosystems. To enhance computational efficiency, all simulations are carried out within the wavelength range of 300-1000 nm, with a resolution of 5 nm. Subsequently, the results are resampled to a 1 nm interval. Surface wind speed is set at 3 m/s, assuming clear sky conditions, while the refractive index at the water-vapor interface is set to 1.34. The bottom boundary condition assumes an infinite optical water depth. The absorption and scattering coefficients of pure water are derived from Pope and Fry [35], and Smith and Baker [36], respectively. The mass-specific absorption and scattering coefficients of mineral particles are determined through MIE simulations as outlined in section 2.1. Four different mineral particles concentrations (0.1 g m-3, 1 g m-3, 10 g m-3, 100 g m-3) are employed to represent the wide range of mineral particles concentrations typically found in inland lakes. The Chl-a absorption and scattering coefficients are calculated using the following equations (Eqs. (1) and 2), implemented in the built-in algorithm of Hydrolight:
where $a_c^{{\ast} ^{\prime}}$ is the non-dimensional chlorophyll-specific absorption coefficient given in Prieur and Sathyendranath [37], C is the user-supplied Chl-a concentration and ${b_0} = 0.3$, ${\lambda _0} = 550$, $n = 0.62$, $m = 1$ [38,39].Six gradients of Chl-a concentration were set to represent the common range in inland waters: 0.5, 5, 10, 20, 50, and 100 mg m-3. Higher Chl-a concentrations are excluded from this study, such as those associated with algal blooms, algae typically accumulate at the water surface, exhibiting spectral characteristics similar to vegetation and traditional Chl-a algorithms are known to be ineffective in such water bodies [40,41]. Due to the focus of this study on investigating the impact of inorganic mineral particulate matter, the presence of CDOM (Chromophoric Dissolved Organic Matter) was not considered (i.e., CDOM = 0). However, inelastic scattering processes, Raman scattering, and Chl-a fluorescence scattering were simulated in this study, while CDOM fluorescence was not taken into account. Specifically, Chl-a fluorescence was modeled using a Gaussian distribution centered at 685 nm.
2.3 Simulated dataset
To simulate the diverse distribution of mineral particles found in natural water, a dataset of 18,000 samples was finally generated using the real and imaginary parts of refractive indices for mineral particles, along with different particle sizes and slopes (CDOM and CDOM fluorescence are considered here). This dataset encompasses Chl-a concentrations ranging from 0 to 100 mg m-3, ISM concentrations from 0 to 100 g m-3, and CDOM absorptions at 440 nm from 0 to 1 m-1, the CDOM absorption was modeled on an exponential function with an exponent of 0.014 and using absorption by CDOM at 440 nm as the reference wavelength. It's important to note that this range represents typical scenarios in most inland lakes, and extreme cases may not be fully covered.
2.4 In-situ measured data
The dataset used in this study consists of two main components. The first part includes a total of 1235 samplings from 44 field campaigns during the period from year 2008 to 2021, covering 18 lakes and reservoirs across China. The measured parameters include remote sensing reflectance (Rrs) and Chl-a concentration. Specific measurement methods for parameters such as Rrs and Chl-a are referred to previous research [42,43].
The second part of the dataset originates from The GLObal Reflectance community dataset for Imaging and optical sensing of Aquatic environments (GLORIA) [44]. This dataset is a collaboration among 59 institutions worldwide and encompasses 450 different water body types. It contains Rrs data along with co-located in situ measurements of at least one of Chl-a, total suspended matter, dissolved substance absorption, and Secchi disk depth. These in situ measurements were gathered to validate the conclusions obtained based on the simulated dataset in this study. To ensure consistency with the simulated dataset, only the portions of in situ measurements corresponding to Chl-a, ISM (Since some data lack ISM measurements, total suspended matter (TSM) was used as a substitute in this case.), and aCDOM(440) within the simulated data range were retained. This subset ultimately includes 948 data.
2.5 Algorithms for Chl-a remote sensing estimation
In order to avoid the influence of CDOM and inorganic suspended particles as much as possible, scientists have proposed numerous remote sensing algorithms to estimate the concentration of Chl-a in turbid Case-2 waters. These algorithms include the two-band ratio algorithm [10,45–47], the baseline height algorithm based on the Chl-a fluorescence peak [13,48], and the semi-analytic algorithm [11,49,50]. In this study, band ratio (BR), Fluorescence Line Height (FLH), and three-band algorithm (TBA) three representative algorithms were ultimately selected to explore the sensitivity of different algorithms to the presence of various mineral particles. It is worth noting that since the focus of this study is on investigating the relative influence of mineral particles on different algorithms rather than discussing the absolute accuracy of Chl-a estimation, the discussion does not delve into the optimal band combinations for each algorithm. The different forms of band combinations for the algorithms are as Eqs. (3)-(5).
2.6 Accuracy assessment
The algorithm's validation accuracy is assessed using Root Mean Square Error (RMSE) and Median Absolute Percentage Error (MdAPE). In comparison to the conventional Mean Absolute Percentage Error (MAPE), MdAPE demonstrates lower sensitivity to outliers and better captures the central tendency of errors. Furthermore, MdAPE avoids the issue of potentially yielding infinite values that can arise with MAPE when actual values are close to zero [51].
3. Result and discussion
3.1 Mass-specific absorption, scattering, and backscattering of mineral particles in inland water
The influence of variations in the real and imaginary parts of mineral particle refractive indices, particle size, and slope on the IOPs is illustrated in Fig. 2. It can be seen that the imaginary part n’ primarily affects the mass-specific absorption coefficient, while it has a relatively smaller impact on scattering and backscattering. On the other hand, the real part of refractive index n mainly influences the scattering and backscattering coefficients, with a more significant effect observed on backscattering ability. The variation in slope (j) significantly influences all IOPs (), but even greater effect can be observed on the $b_{b,m}^\ast (\lambda )$, as depicted in Fig. 2(b)(d)(f) and Table 1. Since the increase of j (from -3.2 to -4.8) is accompanied by the increase of the small particle content, it indicates that the increase in small particle sizes has a more pronounced impact on IOPs. The comparison results of $Dmax$ also verified this conclusion.
Fig. 2. The impact of PSD slope and variations in the real and imaginary parts of mineral particle refractive indices on IOPs, the dashed line represents high n’, while the solid line represents low n’. (a) Under the given PSD slope j = -4, the influence of the real part of refractive index (n) on the mass-specific absorption coefficient of mineral particles. (b) Under the given real part of refractive index n = 1.18, the influence of the PSD slope (j) on the mass-specific absorption coefficient of mineral particles. (c) and (d) as (a) and (b) but for mass-specific backscattering coefficient. (e) and (f) as (a) and (b) but for mass-specific scattering coefficient. The curves of Dmax = 50µm and Dmax = 10µm are intended to show the sensitivity of different Dmax to the result.
Table 1. The impact of changes in j on IOPs
3.2 Variations in remote sensing reflectance caused by mineral particles in inland waters
The variation pattern of Rrs in pure water with the addition of mineral particles with different types, concentrations, and particle sizes is illustrated in Fig. 3. It can be observed that the Rrs undergoes significant changes due to the presence of various mineral particles. Under the case of “low n'“, Rrs is generally higher than that of pure water, and with the increase in ISM concentration (C), two distinct shoulder peaks appear in Rrs after 400 nm, exhibiting a trend towards longer wavelengths. On the other hand, in the case of “high n’,” the shape of Rrs is pretty flatter, and overall, the reflectance magnitudes are lower compared to the “low n'“ scenario. As C increases, Rrs shows a decreasing trend at shorter wavelengths and a contrasting trend at longer wavelengths, intersecting near wavelength 500 nm. The intersection wavelength varies with the changes in mineral particle's refractive index (n) and slope (j). For instance, at j = -4 and n = 1.10, the intersection wavelength is approximately 510 nm, while at n = 1.26, it is around 480 nm. From Fig. 3(a)(b), it can be seen that the increase in n has a more significant impact on the magnitude of Rrs, while the shape remains almost unchanged. Although with the increase of C, Rrs showed a clear increasing trend at different n. Interestingly, at n = 1.10, Rrs at around 410 nm shows little variation as C changes, while significant increases are observed at shorter and longer wavelengths. Figure 3(c)(d) demonstrated the influence of changes in the j on Rrs at n = 1.18. The impact of j on Rrs is evident in both magnitude and shape. At j = -3.2 with a completely different result compared to previous cases, even under the condition of “low n’,” Rrs shows an opposite trend at short and long wavelengths with increasing C. This is primarily due to the low scattering and backscattering caused by j = -3.2 in the “low n'“ scenario (see Fig. 2(d)(f)). Hence, it is crucial to acknowledge that varying combinations of refractive index, particle size, and mineral particle concentration yield entirely distinct reflectance properties. These disparities must not be overlooked when developing the Chl-a estimation algorithm.
Fig. 3. The influence of different mineral particle concentrations with different real part, imaginary part, and slope on Rrs. The curve for pure water is represented by a thick solid black line. (a) (b) represents the Rrs of different n when j = -4; (c) (d) represents the Rrs of different j when n = 1.18.
The variation trends in remote sensing reflectance (Rrs) influenced by both Chl-a and mineral particles were drawn in Fig. 4 . The results showed that when only Chl-a is present, with an increasing Chl-a concentration, the blue light region shows a decreasing trend. However, there are continuously increasing peaks around 550 nm (due to weak absorption and cell scattering of Chl-a) and around 685 nm (Chl-a fluorescence). It can be seen that the influence of mineral particles on Rrs can be almost neglected when C = 0.1 g m-3. However, with an increase in C, it can be observed that the reflectance of low Chl-a concentrations is affected firstly. In the case of low n’, the increase in C significantly enhances the magnitude of Rrs but has a limited impact on the spectral shape. However, in the case of high n’, the situation becomes more complex due to the combined effects of mineral absorption and scattering. With the increase of C, the Rrs spectral shape tends to become flatter, and the characteristic peak of Chl-a is gradually covered by the signal of the mineral. Overall, the presence of both Chl-a and mineral particles results in diverse and intricate variations in remote sensing reflectance spectra. When the Chl-a concentration is less than 20 mg m-3, a mineral particle concentration of about 10 g m-3 can cause the optical characteristics of Chl-a to be seriously masked. This situation is more obvious in mineral particles with higher absorption properties, which may make most Chl-a algorithms invalid.
Fig. 4. The Rrs curves for various mineral particle concentrations (C) in the presence of Chl-a (n = 1.18, j = -4). The solid lines on the left two columns represent the scenario with low n’, while the dashed lines on the right two columns represent the case with high n’. The thick solid black line represents the Rrs curve when only Chl-a is present, without the presence of mineral particles.
3.3 Effect of mineral particles on Chl-a estimation algorithms’ performance
3.3.1 Effects of mineral particle concentration, composition, and size on the performance of Chl-a estimation algorithms
In order to assess the influence of mineral particles on Chl-a estimation, BR, FLH, and TBA algorithms were intensively evaluated. The Hydrolight software was employed to simulate a total of 200 synchronous data of only Chl-a exits and corresponding Rrs in the Chl-a concentration range of 0.5-100 mg m-3 with 0.5 mg m-3 as step length.
The relationship between Chl-a concentration and BR, FLH, and TBA is illustrated in Fig. 5, and it can be found that the three algorithms all have excellent performance when only Chl-a exists in the water body. Therefore, the ratio of Chl-a estimation values when both Chl-a and mineral substances coexist in the water to the estimation value when only Chl-a is present was used to evaluate the effect of mineral on Chl-a estimation. The closer the ratio is to 1, the less affected by mineral particles, and the value greater than 1 indicates that Chl-a is overestimated, otherwise it is underestimated.
Fig. 5. The empirical coefficients of the three algorithms determined by the simulated data when only Chl-a exists, where y represents the concentration of Chl-a, x represents the values of BR, FLH and TBA in (a) (b) (c) respectively, and the empirical coefficient is the fitting coefficient of the quadratic function.
The sensitivity analysis of mineral particles on Chl-a estimation was illustrated in Fig. 6-Fig. 8 (due to scaling issues, the curves “low n’ j = -4 n = 1.10” and “low n’ j = -4 n = 1.18” were obscured by other curves, Fig. 6 shows a partial magnification.). As Chl-a concentration increases, the effect of mineral particles gradually diminishes. At low Chl-a concentrations, an increase in the concentration of mineral particles leads to a significant overestimation of Chl-a by several tens to over a hundred times for all three algorithms. It is noteworthy that noticeable negative values appear in Fig. 6(a) and Fig. 8(a). This is attributed to the utilization of the models from Fig. 5, when the mineral particle concentration is zero, the Chl-a concentrations estimated by BR and TBA exhibit negative values. As the concentration of mineral particles increases, the increasing trend in remote sensing reflectance near 709/710 nm becomes significantly greater than that near 665/671 nm (Fig. 4(a)). Consequently, from the calculation formulas of BR and TBA, it can be observed that this will lead to an increase in both BR and TBA, resulting in a significant overestimation (positive values) in the estimation of Chl-a. However, this does not impact the computational outcomes of our study. Our primary objective is to investigate the differences in Chl-a estimation results with and without mineral particles and to quantify the influence of the presence of mineral particles on the three algorithms. However, the three algorithms perform differently when considering the type and size of mineral particles. Generally, The BR algorithm is more sensitive to highly absorbing mineral particles (the high n’ case), especially in cases of moderate to low Chl-a concentrations. In contrast, the impact of the real part is negligible, and most mineral particles in natural inland water bodies have low absorption, some studies even regard the imaginary part of mineral particles as zero [26]. Therefore, when using BR to estimate Chl-a concentration, minerals can be regarded as the same type of particle, and only concentration and particle size are considered. It is noteworthy that the influence of the parameter ‘j’ on BR does not always follow the same trend as changes in the slope. Instead, the highest overestimation occurs at j = -4.0, while the lowest overestimation is observed at j = -3.2.
Fig. 6. The ratio of Chl-a estimated by BR algorithm when mineral particles are present in water to Chl-a estimated when mineral particles are not present in water. (The dashed gray line represents a ratio of 1.), (a)-(f) represent different concentrations of Chl-a.
Figure 7 illustrates the impact of mineral particles on FLH, showcasing significant disparities compared to BR. The algorithm of FLH demonstrated distinct response patterns to mineral particles under low and high Chl-a conditions. When Chl-a < 10 mg m-3, the presence of mineral particles caused an overestimation of Chl-a, whereas as the concentration of Chl-a increased, the presence of mineral particles caused a severe underestimation of Chl-a. In addition, the real part has a significant influence on the FLH estimation results, and this influence will be amplified as the mineral particle concentration increases, especially at low n’. At a given C = 10 g m-3, Chl-a = 10 mg m-3, n = 1.10 yields about 5-fold overestimation, while n = 1.26 yields about 20-fold Chl-a overestimation. Therefore, when using FLH to calculate the concentration of Chl-a, not only the concentration of mineral particles, but the differences in particle types and particle size distribution must be considered.
Fig. 7. The ratio of Chl-a estimated by FLH algorithm when mineral particles are present in water to Chl-a estimated when mineral particles are not present in water. (The dashed gray line represents a ratio of 1.), (a)-(f) represent different concentrations of Chl-a.
Figure 8 shows the influence of mineral particles on TBA estimation performance, which is very similar to the BR algorithms. However, it seems that TBA exhibits somewhat lower sensitivity to mineral type when Chl-a > 20 mg m-3, as evidenced by the reduced influence of the imaginary part on TBA.
Fig. 8. The ratio of Chl-a estimated by TBA algorithm when mineral particles are present in water to Chl-a estimated when mineral particles are not present in water. (The dashed gray line represents a ratio of 1.), (a)-(f) represent different concentrations of Chl-a.
3.3.2 Effect of the proportion of mineral particle on Chl-a estimation
In natural environments, it is unlikely that particulate matter in natural water consists only of a single type of mineral particles. To address the effect of the proportion of mineral particle, a dataset comprising 18,000 simulated instances were employed to investigate how variations in the proportion of mineral particles, characterized by different types, sizes, and concentrations, affect the performance of three Chl-a estimation algorithms. The ISM/Chl-a ratio was chosen to represent the proportion of inorganic minerals in the water. Here, the Chl-a estimation accuracies were calculated based on the simulated dataset. Figure 9 illustrates the estimation accuracies of the three algorithms at different levels of ISM/Chl-a. For a given ISM/Chl-a ratio, both BR and TBA demonstrated favorable performance, far better than the FLH algorithm, which can be seen from their higher R2 and lower RMSE and MdAPE values. The FLH algorithm exhibits unsatisfactory results at ISM/Chl-a > 0.3, with R2 dropping below 0.4, and RMSE and MdAPE approaching 20 mg m-3 and 80%, respectively. From Fig. 9 it can be found that as the ISM/Chl-a value increases, estimation accuracy progressively decreases, with a turning point observed around ISM/Chl-a = 5 and 2 for BR and TBA respectively. As discussed in Section 3.2, the presence of inorganic matter enhances the scattering properties of water. When inorganic content is low, this scattering effect has a negligible impact on Chl-a estimation. However, as the proportion of inorganic particles increases, their scattering characteristics can influence or even mask Chl-a's optical features, which will result in poor estimation performance. BR and TBA have similar estimation performance at low ISM/Chl-a. With the increase of ISM/Chl-a, the performance of both algorithms showed a sharp decline, but the decline of the BR is more gentle. Overall, BR showed superior resistance to mineral particles, but even under the most turbid water conditions (maximum ISM/Chl-a), both BR and TBA exhibited satisfactory performance, with R2 above 0.6, and RMSE and MdAPE below 17 mg m-3 and 27%, respectively.
The simulated scenarios are based on simplified input parameters combined with theoretical deductions using numerical simulations. These simulations may not perfectly represent real inland complex water optical conditions. Therefore, a 2183 in-situ measured datasets was also employed to analyze the effect of the proportion of mineral particle on Chl-a estimation, and the result was depicted in Fig. 10. And it can be found there is a similar impact as the result obtained by using the simulated data, demonstrating a gradual decline in algorithm performance with increasing proportions of inorganic suspended matter. However, there were certain discrepancies compared to using the simulated data. When TSM/Chl-a is less than 0.4, TBA has a better estimation effect than BR, but as the proportion of mineral particles increases, the performance of TBA decreases more rapidly. As Section 3.3.1 discussed, it showed that when mineral particles account for a relatively small proportion, TBA is not sensitive to the mineral particle type than BR, but with the increase of mineral particles, the impact of concentration on TBA exceeds the impact of particle type differences. In the application of TBA to the in-situ data, the position of the turning point appears near TSM/Chl-a = 3, which is still smaller than the turning point of BR around 5, which shows that the BR algorithm is a better choice when the proportion of inorganic mineral particles is pretty higher.
3.4 Combined influence of CDOM and ISM on Chl-a estimation
As CDOM is generally considered to be a non-scattering substance, the impact must be attributed solely to its absorption effects. The impact of CDOM on the three algorithms is depicted in Fig. 11, it can be observed that when aCDOM(440) < 0.1 m-1, all three algorithms exhibit a certain degree of overestimation/underestimation by no more than 50%, except for TBA, for which the overestimation is about 4-fold when Chl-a = 0.5 mg m-3 and aCDOM(440) = 0.1 m-1. When Chl-a < 5 mg m-3, both BR and TBA have greater overestimation than FLH with the increasing CDOM concentration, however, as Chl-a concentration increases, the FLH algorithm is significantly more sensitive to CDOM compared to the other two algorithms. The influence of CDOM on the Chl-a estimation by using BR and TBA tends to decrease as a power function. It was also found that when Chl-a > 50 mg m-3, the influence of CDOM becomes negligible for both BR and TBA algorithms. Despite CDOM causing some alterations in the water's optical features and consequently leading to a degree of algorithm inefficiency, its impact is relatively smaller compared to ISM. This arises from the fact that CDOM absorption predominantly occurs in the ultraviolet and the blue portion of the visible light spectrum, exhibiting a power-law decrease with wavelength [16,52]. In contrast, Chl-a estimation in turbid water bodies relies on longer wavelengths within the red and near-infrared bands, thereby limiting the impact of CDOM on these estimations.
Fig. 11. The ratio of Chl-a estimated by different algorithms when CDOM is present in water to Chl-a estimated when there is only Chl-a in water, CDOM concentration is characterized using the value of aCDOM(440).
Although the influence of CDOM on Chl-a estimation is relatively minor, its significance remains notable when Chl-a concentrations are low. Additionally, in inland water bodies, both CDOM and ISM commonly play pivotal roles in shaping remote sensing reflectance. The simulated aCDOM(440) were categorized into low (0-0.2 m-1), middle (0.2-0.5 m-1), and high levels (0.5-1 m-1), ISM with different concentration gradients between 0 and 50 g m-3 was chosen to explore the coupled effect between CDOM and ISM on Chl-a estimation. As presented in Fig. 12, the performance of the three algorithms exhibited a consistent downward trend at varying levels of CDOM as the ISM increased, with the highest estimation accuracy observed at low CDOM concentrations. However, even at the lowest concentration of ISM, the estimation error caused by CDOM remains smaller than that caused by ISM. When ISM < 5 g m-3, differences in CDOM levels resulted in significant variations in estimation accuracy, and this discrepancy decreased with increasing ISM. When ISM is below 30 g m-3, both BR and TBA are still affected by the presence of CDOM to some extent. It is noteworthy that when ISM is less than 20 g m-3, the impact of middle and high CDOM concentrations on BR estimation performance reaches saturation, while for TBA it occurs when ISM is less than 10 g m-3. This further illustrates that BR is more robust to the presence of ISM, as evidenced by its need for higher ISM to mask the impact of CDOM. The performance of FLH is obviously influenced by CDOM when ISM falls below 15 g m-3. These conclusions indicate that among the three algorithms, FLH exhibits the greatest sensitivity to ISM. When aCDOM(440) < 0.5 m-1 in an aquatic system, both BR and TBA are affected by CDOM with varying degrees when the ISM is less than 30 g m-3. When aCDOM(440) > 0.5 m-1, BR is more susceptible to CDOM than TBA in scenarios with ISM less than 20 g m-3.
Fig. 12. Performance of three Chl-a estimation algorithms under different ISM and CDOM concentrations at Chl-a concentration less than 20 mg m-3. (a)(d)(g) represents R2, RMSE and MAPE of BR respectively, (b)(e)(h) and (c)(f)(i) are same as (a)(d)(g), but for the FLH and TBA respectively.
3.5 Sensitivity of three algorithms to the amount of developing dataset
In practical nature scenarios, the limitation of in-situ sampling often results in a relatively small dataset for Chl-a algorithm developing. Consequently, multiple Chl-a estimation algorithms may exist for the same region, and these algorithms heavily rely on the sampled data and sampling time. Therefore, based on our dataset of 18,000 simulations, a subset of data, ranging from 100 to 1000 samples respectively, was randomly selected. Within this chosen data subset, 3/5 were used for Chl-a algorithm developing, while the remaining 2/5 were utilized for algorithm evaluation. To mitigate potential discrepancies caused by a single choice, five random selections were repeated for each number of datasets, finally, the estimation accuracy of the five computations was averaged to represent the final accuracy, while the standard deviation indicated the stochastic variation inherent to the algorithms. The accuracy of the three algorithms varies with the amount of developing data as shown in Fig. 13. It can be observed that the amount of developing dataset has a remarkable influence on Chl-a estimation accuracy. The standard deviation of the three algorithms is very high when the amount of data is small and decreases with the increase of the number of algorithms. The standard deviation of FLH tends to be stable when the amount of dataset is greater than 600, but there are still relatively high RMSE and MdAPE. Among the three algorithms, although BR has the lowest RMSE and MdAPE, when the dataset is less than 400, it has a larger standard deviation, and the mean values of RMSE and MdAPE have larger fluctuations. In contrast, TBA has a relatively stable performance when the dataset is greater than 200, and its mean and standard deviation remain relatively unchanged. This indicates that BR has the best Chl-a estimation accuracy, but when the dataset is less than 400, the accuracy of BR is greatly affected by the difference of dataset. When the dataset is between 200 and 400, although the estimation accuracy of TBA is slightly lower than that of BR, it is less affected by the amount of dataset. To ensure the best Chl-a estimation accuracy in complex inland water environments, the BR algorithm should be considered firstly when the amount of dataset is greater than 400; TBA is the best choice when the amount of dataset is between 200 and 400, while when the amount is less than 200, BR and TBA have similar performance, and the algorithms are greatly affected by the amount of dataset. FLH had the worst performance in this simulation experiment and is therefore not recommended for applyed in inland water environment.
Fig. 13. The accuracy of the three algorithms varies with the amount of developing data. (a)(b) represents RMSE and MAPE of BR respectively, (c)(d) and (e)(f) are same as (a)(b), but for the FLH and TBA respectively.
3.6 Suggestions for the development of Chl-a estimation algorithm based on simulated results
Exploring the IOPs of organic components, rather than exclusively concentrating on Chl-a, has considerable value on the research about inland water optics. In this study, Hydrolight software was employed to simulate IOPs at various Chl-a concentrations as a surrogate indicator for organic components. Through this approach, the impact of mineral particles on Chl-a estimation was investigated. According to the findings from forward simulations results, the FLH algorithm may not be suitable for inland waters with higher inorganic mineral particles concentrations. This is because FLH is constructed using the fluorescence peak of Chl-a at 685 nm, as the concentration of inorganic substances in water gradually increases, the 685 nm peak is obscured due to strong backscattering of inorganic components in the red and near-infrared regions, causing the spectral peak to shift towards longer wavelengths (e.g., 709 nm). Therefore, according to our findings, it is recommended to integrate longer wavelengths into the baseline difference algorithm for inland waters, potentially improving its applicability. BR and TBA demonstrate notably robust performance in inland waters. However, our conclusions indicate a significant deterioration in the performance of TBA and BR algorithms when ISM/Chl-a exceeds 2 and 5, respectively. Therefore, in highly turbid waters (e.g., ISM/Chl-a > 5), accurate Chl-a estimation remains challenging due to the masking of Chl-a signals by mineral particle. The development of a new Chl-a algorithm was urgent necessary to consider extremely turbid conditions. According to simulation results, the type of inorganic substances has a considerably smaller impact on remote sensing reflectance than its concentration. The remote sensing reflectance at before 600 nm and in the 670-700 nm range are relatively less affected by the concentration of inorganic substances, whereas signals in wavelength beyond 720 nm predominantly originate from the contribution of inorganic particles, being heavily influenced by inorganic particles. Therefore, in the formulation of future Chl-a estimation algorithms, the exclusion of wavelength strongly influenced by inorganic particles was strongly recommended for improving algorithm estimation accuracy. It is worth noting that the accuracy of the algorithm is also related to the quantity of data involved in algorithm development. Therefore, the optimal estimation accuracy can be achieved by using a large amount of in situ data. According to the results of this study, the number of data involved in development was suggested to exceed 400.
4. Conclusion
Based on the MIE scattering simulation theory, this study simulated the effects of the refractive index real part (n), imaginary part (n’), and size distribution slope (j) of mineral particles on the optical properties of water. Combined with Hydrolight software, the remote sensing reflectance of waters with different mineral particles and Chl-a was simulated, and a simulation dataset containing 18,000 data pieces was established. The results showed that the slope j of particle size and the imaginary part n ‘of refractive index have significant effects on the reflectance, while the real part n has relatively little effect. Furthermore, the performance of three Chl-a estimation algorithms BR, FLH, and TBA was fully evaluated. When conducting Chl-a estimation in inland waters, it is necessary to consider not only the influence of mineral particle concentration but also the difference of mineral particle type and particle size. BR algorithms may yield more stable results when applied to inland water with complex mineral compositions. It was found when mineral particle concentration is less than 30 g m-3, the influence of CDOM cannot be ignored. To avoid BR algorithms specific to dataset and to minimize the incidental errors arising from data variations, the number of datasets used for algorithm development should not be less than 400. If the dataset used for developing algorithm is between 200 and 400, TBA is recommended for more stable accuracy.
Funding
National Natural Science Foundation of China (42201423, 42271341, U2102207).
Acknowledgements
The authors thanks to the graduate student of remote sensing application of Nanjing Normal University, China, for their help in laboratory analysis. We are grateful to all scientists and contributors who provided the GLORIA datasets data and the code for MIE calculations.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data and materials are available upon reasonable request.
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