Sensitivity Analysis and Optimization of a Radiative Transfer Numerical Model for Turbid Lake Water

Abstract

Remote sensing can detect and map algal blooms. The HydroLight (Sequoia Scientific Inc., Bellevue, Washington, DC, USA) model generates the reflectance profiles of various water bodies. However, the influence of model parameters has rarely been investigated for inland water. Moreover, the simulation time of the HydroLight model increases as the amount of input data increases, which limits the practicality of the HydroLight model. This study developed a graphical user interface (GUI) software for the sensitivity analysis of the HydroLight model through multiple executions. The GUI software stably performed parameter sensitivity analysis and substantially reduced the simulation time by up to 92%. The GUI software results for lake water show that the backscattering ratio was the most important parameter for estimating vertical reflectance profiles. Based on the sensitivity analysis results, parameter calibration of the HydroLight model was performed. The reflectance profiles obtained using the optimized parameters agreed with observed profiles, with R² values of over 0.98. Thus, a strong relationship between the backscattering coefficient and the observed cyanobacteria genera cells was identified.

1. Introduction

Recently, remote sensing has become a prevalent technique for detecting the dynamics of harmful algae magnitude and timing through the analysis of the optical features of water bodies [1,2,3]. The optical features of inland water have significant variables such as absorption, scattering, and fluorescence emission that are crucial in identifying the concentration and spatial distribution of algae [4,5]. Furthermore, vertical profiles of the optical information enable the identification of the algal profile at each water depth because harmful species, such as cyanobacteria, can vertically migrate using a buoyancy mechanism to ensure optimal nutrient and light availability [6]. Thus, the optical profile of the water bodies can provide insights on water quality issues, including the detection of harmful algae and water resource management.

The HydroLight model (referred to as HydroLight) is a radiative transfer numerical model that computes the radiance, irradiance, reflectance, and attenuation that are induced by water absorption and scattering [7]. In particular, HydroLight can generate the reflectance spectra as a function of water depth. Several studies have applied this model to estimate water surface reflectance [8,9] and vertical profiles [10,11].

These studies utilized the simulated reflectance to estimate chlorophyll-a concentration, which is an indicator of algal biomass [12]. HydroLight was developed for optical oceanography; therefore, its model parameters describe optical properties of oceans [13]. Furthermore, evidence from recent years has shown that the application of HydroLight can be extended to estuaries, deltaic water bodies, wetlands, rivers, and lakes [14,15,16,17]. By extension, further exploration of the model parameters for inland water optics is needed. The identification of the parameter sensitivity determines the importance of model parameters that are highly correlated with the model output and reduces the simulation uncertainty by excluding insignificant parameters.

Sensitivity analysis of the model parameters can provide the most influential parameters [18]. In addition, parameter sensitivity analysis delivers the prerequisite information for model calibration by narrowing the range of parameter selections [19]. The values of the parameters of HydroLight vary for seawater and fresh water because the model parameters are dependent on the absorption and scattering features of the constituents in each water type. The optimal parameters for ocean water may be insensitive to the optical features of inland water [13,20]. Thus, a sensitivity analysis of the parameters of HydroLight needs to be performed to investigate the parameters associated with inland water and to increase the efficiency of the model calibration process. Moreover, sensitivity analysis is carried out by generating an input parameter matrix using a random sampling method, conducting a model simulation, and evaluating the influence and significance of input and output relationships [21]. This process produces numerous model inputs. However, HydroLight implements the simulation based on each observation point; consequently, point-based HydroLight simulation for sensitivity analysis can be exceedingly time-consuming.

Therefore, this study was to develop a sensitivity analysis tool for HydroLight; the proposed tool can implement multi-point simulations. Parameter calibration was conducted to identify the optimal values of the parameters that are highly sensitive to the optical features of inland water. To achieve these objectives, this study (1) designed a MATLAB GUI structure, (2) built the GUI configuration for sensitivity analysis with multiple executions of HydroLight, (3) implemented the parameter sensitivity analysis for the vertical reflectance in the lake, and (4) optimized the HydroLight parameters for evaluating the reflectance spectra at the surface and beneath the surface of the lake water, in addition to depths of 0.5 m and 1.0 m.

2. Materials and Methods

2.1. Study Area

Figure 1 shows the study area, which is in Daecheong dam (36°28′40.7′′ N, 127°28′51.3′′ E). The water from the dam is mainly utilized for domestic water supply. The dam has a surface area of 72.8 km², a storage volume of 1490 × 10⁶ m³ and a length of 86 km. The average water depth is 20 m. In the Daecheong dam region, the Chuso (CS) and Huinam (HN) regions, denoted by the red boxes in Figure 1, were selected for the case study. In particular, CS has been reported as a region with severe cyanobacteria outbreaks because of a high nutrient load and prolonged water retention time [22]. HN has a deeper water depth (i.e., 25 m) and a shorter water retention time compared to CS, resulting in relatively fewer algal blooms. [23].

2.2. Observation Data and Model Setup

This study conducted field monitoring in the regions of HN and CS in 2018 and 2019.

Table A1. Observed Chl-a in HN and CS regions.

Chl-a	2018					2019
Region	Date	0+	0−	0.5 m	1.0 m	Date	0+	0−	0.5 m	1.0 m
HN (n = 23)	07/27	6.99 ± 0.81	6.98 ± 0.81	7.56 ± 0.33	8.03 ± 1.21	07/09	2.86 ± 0.18	3.03 ± 0.26	3.30 ± 0.43	3.75 ± 0.54
	-	-	-	-	-	07/24	5.42 ± 0.93	5.47 ± 0.99	6.03 ± 0.56	6.62 ± 0.55
	-	-	-	-	-	08/24	6.08 ± 0.43	6.08 ± 0.43	6.07 ± 0.44	6.05 ± 0.40
	-	-	-	-	-	09/18	2.48 ± 0.44	2.40 ± 0.56	3.58 ± 0.47	5.19 ± 0.67
CS (n = 104)	07/27	10.77 ± 3.52	11.78 ± 3.89	14.20 ± 3.66	17.20 ± 3.03	07/09	12.47 ± 1.42	12.93 ± 1.53	14.58 ± 2.22	15.71 ± 2.25
	08/16	7.95 ± 2.31	8.07 ± 2.31	8.50 ± 1.65	7.99 ± 1.17	07/24	15.51 ± 4.94	15.57 ± 4.90	11.65 ± 3.39	9.10 ± 3.15
	09/06	17.52 ± 12.81	16.07 ± 12.56	8.93 ± 7.83	5.13 ± 4.33	08/08	7.33 ± 1.56	7.33 ± 1.56	8.17 ± 1.93	7.70 ± 0.83
	09/17	4.59 ± 1.36	5.01 ± 1.21	10.06 ± 9.27	8.23 ± 3.50	08/23	7.69 ± 0.88	7.69 ± 0.88	7.63 ± 0.79	7.09 ± 0.85
	09/19	8.37 ± 3.82	8.86 ± 3.15	9.00 ± 2.08	6.92 ± 1.52	09/17	5.25 ± 1.26	6.24 ± 1.10	9.50 ± 3.35	12.51 ± 3.61
	10/11	10.17 ± 1.33	9.11 ± 1.61	7.69 ± 1.56	7.69 ± 1.56	-	-	-	-	-
	10/25	5.53 ± 2.44	5.57 ± 2.44	9.54 ± 2.89	12.00 ± 1.67	-	-	-	-	-

n is number of samples, and 0+ and 0- indicate the concentrations at the surface and beneath the surface of water, respectively.

and

Table A2. Observed TSS in HN and CS region.

TSS	2018					2019
Region	Date	0+	0−	0.5 m	1.0 m	Date	0+	0−	0.5 m	1.0 m
HN (n = 23)	07/27	5.43 ± 1.30	5.09 ± 0.77	4.90 ± 0.58	4.78 ± 0.55	07/09	4.31 ± 0.11	4.42 ± 0.17	4.59 ± 0.28	4.88 ± 0.35
	-	-	-	-	-	07/24	6.22 ± 0.33	6.22 ± 0.35	6.36 ± 0.36	6.75 ± 0.36
	-	-	-	-	-	08/24	6.34 ± 0.26	6.34 ± 0.26	6.39 ± 0.29	6.38 ± 0.26
	-	-	-	-	-	09/18	3.88 ± 0.22	4.01 ± 0.37	4.77 ± 0.31	5.82 ± 0.43
CS (n = 104)	07/27	9.16 ± 2.01	9.64 ± 1.89	9.39 ± 1.97	9.10 ± 1.80	07/09	11.05 ± 1.12	11.42 ± 1.21	12.72 ± 1.75	13.61 ± 1.78
	08/16	14.83 ± 6.34	14.56 ± 6.31	14.22 ± 6.10	13.66 ± 4.85	07/24	13.45 ± 3.90	13.50 ± 3.87	10.40 ± 2.68	8.39 ± 2.49
	09/06	12.90 ± 2.36	12.98 ± 2.30	12.57 ± 1.98	12.85 ± 2.30	08/08	7.00 ± 1.23	7.00 ± 1.23	7.65 ± 1.53	7.29 ± 0.66
	09/17	10.73 ± 1.77	10.92 ± 2.20	11.44 ± 3.59	11.33 ± 2.77	08/23	7.28 ± 0.75	7.28 ± 0.75	7.23 ± 0.68	6.81 ± 0.72
	09/19	13.24 ± 3.81	13.13 ± 3.81	13.57 ± 3.11	12.39 ± 3.11	09/17	5.35 ± 1.00	6.13 ± 0.87	8.71 ± 2.64	11.09 ± 2.85
	10/11	4.60 ± 1.39	4.60 ± 1.39	2.93 ± 0.48	2.97 ± 0.52	-	-	-	-	-
	10/25	5.29 ± 2.57	5.29 ± 2.57	9.84 ± 2.71	12.42 ± 1.60	-	-	-	-	-

n is the number of samples, and 0+ and 0- indicate the concentrations at the surface and beneath the surface of the water, respectively.

present the specific sampling periods and observed data points. The monitoring was conducted under clear sky conditions with a light wind speed of less than 5 m s⁻¹. At each point, the radiance from the water surface and irradiance from the sky were measured using an ASD hand-held VNIR spectroradiometer device with specific accessories, including bare fiber with the cosine irradiance collector (Malvern Panalytical Ltd., Malvern, UK). The measurement protocol maintained an azimuth angle between 130° and 135° and a viewing angle between 35° and 40° [7]. Based on the measured radiance and irradiance, the remote sensing reflectance of the water surface was calculated as

$$R_{\mathrm{rs}}\left(\lambda \right)=\frac{L_{\mathrm{w}}^t\left(\lambda \right)-c{L}_{\mathrm{sky}}\left(\lambda \right)}{E_{\mathrm{d}}\left(\lambda \right)}$$

(1)

where $\lambda$ is the spectral wavelength; R_rs($\lambda$) is the remote sensing reflectance at the water surface; L^t_w($\lambda$) the total radiance from the water including sky radiance reflected at the air-water interface (W m⁻² nm⁻¹ sr⁻¹); L_sky($\lambda$) is the radiance from the sky (W m⁻² nm⁻¹ sr⁻¹); c is defined as 0.025 implying a Fresnel reflectance ratio for the skylight; and E_d($\lambda$) is the downwelling irradiance at the water surface (W m⁻² nm⁻¹).

The radiance of water was vertically measured, at the subsurface and at depths of 0.5 m and 1.0 m, by using an attachable jumper optical fiber with a length of 1.5 m. The observed reflectance at each depth was calculated using Equation (6). In addition, an EXO-2 multiparameter water quality instrument (YSI Inc., Yellow Springs, Ohio, USA) was employed to measure the vertical profiles of the chlorophyll-a (Chl-a) and total suspended solids (TSS) concentrations. Water samples were also collected for the absorption analysis of Chl-a. The detailed experimental procedure is described in [24]. In addition, algal identification and cell counts were analyzed using an optical microscope, in accordance with the standard methods for examining water pollution [25].

The algal cells were used to investigate the relationship between cell characteristics and the optical scattering of water.

2.3. Radiative Transfer Numerical Model: HydroLight

This study simulated the reflectance profile of lake water using the radiative transfer numerical model HydroLight version 5.2 (Sequoia Scientific Inc., Bellevue, Washington, DC, USA) [26]. HydroLight is an algorithm for solving the radiative transfer equation. The simulation considers chlorophyll fluorescence and Raman scattering by water. Water surface condition was determined by the clear sky having a sun zenith angle of 30° and no waves. The water depth was set as infinite. The condition of inherent optical properties (IOPs) was used by the observed absorption coefficient of phytoplankton. In addition, HydroLight used the vertical chlorophyll-a (Chl-a) and total suspended solids (TSSs) profiles, which were observed using the EXO-2 sensor for calculating the absorption and scattering coefficients as a function of depth. The total absorption of the water constituents was modeled using the following equation:

$$a\left(z,\lambda \right)=a_{\mathrm{w}}\left(\lambda \right)+a_{\mathrm{chla}}\left(z,\lambda \right)+a_{\mathrm{p}}\left(z,\lambda \right)+a_{\mathrm{cdom}}\left(z,\lambda \right),$$

(2)

where a$\left(z, \lambda \right)$ is the total absorption coefficient of water constituents (m⁻¹) at depth z (m); a_w($\lambda$) is the absorption coefficient of pure water; a_chla(z,$\lambda$) is the absorption coefficient of chlorophyll-a; a_p($z, \lambda$) is the absorption coefficient of particulate matter except for the algal pigment (m⁻¹); and a_cdom($z, \lambda$) is the absorption coefficient of colored dissolved organic matter (CDOM) (m⁻¹). This study used the observed absorption coefficient for a_p($z, \lambda$) to calculate the total absorption coefficient [7]. However, CDOM absorption is calculated using an exponentially decaying function that covaries with Chl-a absorption as

$$a_{\mathrm{cdom}}\left(z,\lambda \right)=p_0{a}_{\mathrm{chl}}\left(z,440\right)\exp \left[-q_0\left(\lambda -440\right)\right],$$

(3)

where a_chl(z,440) is the absorption coefficient of Chl-a for the wavelength of 440 nm (m⁻¹) at depth z (m); 440 nm is the reference wavelength; p₀ is the empirical parameter; and q₀ is the decay constant.

In addition, the total scattering coefficient is modeled via the following equation:

$$b\left(z,\lambda \right)=b_{\mathrm{w}}\left(\lambda \right)+b_{\mathrm{p}}\left(z,\lambda \right)$$

(4)

Here, b($z,\lambda$) is the scattering coefficient of water constituents (m⁻¹) at depth z (m); b_w($\lambda$) is the scattering coefficient of lake water (m⁻¹); and b_p($z,\lambda$) is the scattering coefficient of the particulate matters (m⁻¹).

The scattering coefficient of the particulate matter follows a power law referred by [27] as

$$b_{\mathrm{p},\mathrm{x}}\left(z,\lambda \right)=b_0{\left(\frac{550}{\lambda }\right)}^m{\left[\mathrm{x}\left(z\right)\right]}^n,$$

(5)

where x indicates the particulate matter, including Chl-a and TSS; b_p,x($z,\lambda$) is the scattering coefficient of Chl-a and TSS (m⁻¹) at depth z (m); x(z) is the concentration of Chl-a and TSS (mg m⁻³) at depth z; 550 nm is the reference wavelength; and b₀, m, and n are model parameters. For the scattering phase function, the backscattering ratios (b_pb/b_p) of Chl-a and TSS were set to a constant at each depth.

Based on the IOPs, HydroLight solves the radiative transfer equation to generate the radiance at each depth [7]. The remote sensing reflectance is then calculated via the ratio of water radiance and downwelling irradiance as follows:

$$r_{\mathrm{rs}}\left(z,\lambda \right)=\frac{L_{\mathrm{u}}\left(z, \lambda \right)}{E_{\mathrm{d}}\left(z, \lambda \right)}$$

(6)

where r_rs($z,\lambda$) is the remote sensing reflectance (sr⁻¹) at depth z (m); L_u($z, \lambda$) is the upwelling radiance (W m⁻² nm⁻¹ sr⁻¹); and E_d($z,\lambda$) is the downwelling irradiance (W m⁻² nm⁻¹).

2.4. Sensitivity Analysis

For sensitivity analysis, the parameter set generation is performed using the Latin hypercube (LH) and one-factor-at-a-time (OAT) sampling methods. LH sampling is one of the most sophisticated random sampling methods; it is based on the Monte Carlo method [28]. The LH sampling method subdivides the distribution of each parameter into N ranges, after which one parameter value is randomly sampled.

Then, OAT sampling is carried out by changing one parameter value at a time while the other parameter values are fixed [29,30]. Thus, the LH-OAT method produces N × (P+1) number of input files, where P is the number of the selected parameters for sensitivity analysis [19,31,32].

After N × (P+1) model simulations, the elementary effect (EE) method is employed to implement the sensitivity analysis of each input parameter by ranking the parameters in order of importance [30,33]. The EE value is calculated by the differentiation of the model output with respect to the input parameter as

$${\mathrm{EE}}_i\left(p\right)= \frac{\mathrm{f}\left(p_1, \dots ,p_i+\mathsf{\Delta }, \dots ,p_k\right)-\mathrm{f}\left(p\right)}{\mathsf{\Delta }}$$

(7)

where p_i is the ith input parameter of the model; $\mathsf{\Delta }$ is the predetermined perturbation factor of p_i; f(p) is the model output for parameter p; and f(p₁,…,p_i+$\mathsf{\Delta }$,…,p_k) is the model output for the change $\mathsf{\Delta }$ in p_i.

The finite distribution of EE values can provide sensitivity indices using the mean and standard deviation of the EEs as follows:

$$\mu =\frac{{{\displaystyle \sum }}_{i=1}^N{\mathrm{EE}}_i}{N}$$

(8)

$$\sigma =\sqrt{\frac{1}{N} {\displaystyle \sum }_{i=1}^N({\mathrm{EE}}_i-\mu )}$$

(9)

where $\mu$ is the mean of EEs; $\sigma$ is the standard deviation of EEs and N is the number of parameters.

The mean of the EEs indicates the sensitivity strength with regard to parameter change and model output response [34]. A high EE means implies that the output has a high sensitivity to the parameter. Furthermore, the standard deviation of the EEs represents the strength of interaction of a particular parameter with other parameters [35]. In this study, the EE method for sensitivity analysis was implemented using the SAFE Toolbox of MATLAB software version 2019a (MathWorks Inc., Natick, MA, USA) [36].

In the CS region, a total of 104 monitoring and experimental data points were utilized as input data for HydroLight model simulation. This study selected 12 parameters for sensitivity analysis. The number of OAT sampling points was assigned as 10, thereby generating a total of 2,990 input files (i.e., (10 × (12+1)) × 23) for HN and a total of 13,520 inputs (i.e., (10 × (12+1)) × 104) for CS. In addition to the parameters in Equations (2)–(5), the backscattering ratio for Chl-a and TSS, Chl-a fluorescence quantum efficiency, and Raman scattering coefficient of water were chosen for analysis because the concentrations of the constituents of the lake water are relatively high compared to those of the constituents of ocean water. Before conducting sensitivity analysis, the ranges of the selected parameters were defined based on previous studies that mainly focused on investigating the optical properties of inland waters (

Table 1. Parameter information for sensitivity analysis.

Component	Parameter of HydroLight	Min	Max	Reference
Chlorophyll-a	Scattering coefficient (b0)	0.1	1.0
	Scattering coefficient (m)	0	1.0
	Scattering coefficient (n)	0	1.0	[39]
	Backscattering ratio	0.0005	0.021	[40]
	Chlorophyll-a fluorescence efficiency	0.003	0.02	[41]
CDOM	Empirical parameter (p0)	0.2	1.0	[42]
	Exponential decay constant (q0)	0.012	0.021
TSS	Scattering coefficient (b0)	0.1	1.0
	Scattering coefficient (m)	0	1.0
	Scattering coefficient (n)	0	1.0	[39]
	Backscattering ratio	0.0005	0.021	[43]
Water	Raman scattering coefficient	0.000232	0.00032	[44]

).

2.5. GUI Development for Sensitivity Analysis of HydroLight

In this study, the GUI structure for sensitivity analysis of HydroLight parameters was developed using MATLAB. The GUI performed input file generation based on LH–OAT sampling; furthermore, it carried out multi-point HydroLight simulation by establishing a multiple execution system. Figure 2 presents a schematic of the GUI-based HydroLight sensitivity analysis program. First, an input template and parameter information (including name and specific range of the selected parameters) are loaded on to the model (Figure 2a and Figure 3a). The formats of the input template and the parameter information are text and excel files, respectively. After loading the files, the number of parameters, P, is displayed on the GUI (Figure 3). Subsequently, LH–OAT sampling of the model parameters is carried out (Figure 2b and Figure 3b). The number of sampling points, N, is determined by the user, and then the sampling process generates N × (P+1) parameter sets that are displayed by GUI. Furthermore, a set of observation data is imported, after which N × (P+1) input files are generated, as shown in Figure 2c and Figure 3c.

All of the input files are prepared by multiplying the total number of observation points N × (P+1) by the number of input files (Figure 3). After input file generation is completed, the model is replicated based on the number of multi-executions, X (Figure 2d and Figure 3d). Then, multi-point simulations are simultaneously performed upon pressing the model simulation button (Figure 2e and Figure 3e). Furthermore, the simulation results are gathered for sensitivity analysis (Figure 2f and Figure 3f). The model error is determined based on the difference between the modeled reflectance profiles and observed profiles; the errors are then transferred to the sensitivity analysis toolbox (Figure 2g and Figure 3g). Finally, the sensitivity analysis results of each parameter are computed via the mean and standard deviation of the EEs, and the results are shown in the result window and as a scatter plot (Figure 2h and Figure 3h).

2.6. Parameter Optimization

Once the important parameters were identified, the selected parameters were calibrated to calculate the reflectance profiles of lake water. A pattern search algorithm was adopted to calibrate the model parameters. Pattern search is one of the numerical optimization methods without the gradient of the optimization equation [37]. Furthermore, this method is simple and efficient to optimize diverse objective functions because it is based on direct function evaluations without the derivatives. Thus, this method can be employed for parameter optimization of the HydroLight model. In addition, pattern search is capable of convergence to local minima by identifying the neighbor parameters of the current point and then investigating an optimal direction. If all neighboring points cannot find a decrease in the error, thereby reducing the search step. Thus, the search of minimizing the error stops when the step is substantially small that converges to the local minimum. In addition, manual calibration was also performed to improve the results of the pattern search implementation [38].

3. Results and Discussions

3.1. Vertical Profile of Chl-a and TSS

Table A1 and Table A2 show the Chl-a and TSS concentrations in HN and CS at the surface, subsurface, and at depths of 0.5 m and 1.0 m. These specific depths corresponded to the depths at which remote sensing can measure reflectance. The EXO-2 sensor can measure the vertical profiles of water constituents, including Chl-a and phycocyanin, and the turbidity; furthermore, the measured profiles show good agreement with experimentally analyzed concentrations of water quality variables [45,46,47,48]. In 2018 and 2019, CS showed higher Chl-a and TSS concentrations at each depth than the concentrations in HN. This was due to the river-bends in CS, where the water retention time is high. In particular, CS exhibited a high Chl-a concentration in July, August, and early September. A high water temperature and low flow velocity triggered the increase of algal growth. Furthermore, the variation of the solar radiation intensity may have resulted in the vertical variation in the concentration of Chl-a due to the algal buoyancy mechanism [49]. During the periods with high Chl-a concentrations, high TSS concentrations were also observed in CS. However, when TSS showed the highest concentration level, on 16 August 2018, the concentration of Chl-a was found to be relatively low. This may be because a high TSS concertation reduces the light availability for the phytoplankton owing to increased light attenuation [50].

In HN, the concertation of TSS was generally higher than that of Chl-a, at each depth. Thus, based on the observed concentrations of the constituents, the optical properties may differ for the water in CS and HN, resulting in different parameter sensitivities for the HydroLight model.

3.2. Sensitivity Analysis

A sensitivity analysis tool for the HydroLight model was implemented to determine the influential optical parameters for HN and CS. Figure 4 shows the sensitivity analysis results for HN. The major parameters were related to suspended solids. Notably, the backscattering ratio for suspended solids was the most sensitive parameter in the case of HN, whereas the scattering coefficient (n) was secondary. In

Table 2. Sensitivity parameter ranking.

		HN				CS
Component	Parameters	0(+)	0(−)	0.5m	1.0m	0(+)	0(−)	0.5m	1.0m
Chlorophyll-a	Scattering coefficient (b0)	5	5	5	6	4	4	5	5
	Scattering coefficient (m)	11	11	11	10	11	10	11	11
	Scattering coefficient (n)	6	6	6	5	3	3	3	3
	Backscattering ratio	3	3	3	2	1	1	1	1
	Chlorophyll-a fluorescence efficiency	9	9	10	11	9	9	9	9
CDOM	Empirical parameter (p0)	7	7	7	7	7	7	7	7
	Exponential decay constant (q0)	8	8	8	8	8	8	8	8
TSS	Scattering coefficient (b0)	4	4	4	4	2	2	2	2
	Scattering coefficient (m)	10	10	9	9	10	11	10	10
	Scattering coefficient (n)	2	2	2	3	6	6	6	6
	Backscattering ratio	1	1	1	1	5	5	4	4
Water	Raman scattering coefficient	12	12	12	12	12	12	12	12

, the parameters are ranked based on the sensitivity, with respect to the depth (surface level, subsurface level, 0.5 m, and 1.0 m). The parameter ranking at each depth was observed to possess a similar ranking because the reflectance profile was calculated as a function of depth [7]. Figure 5 presents the sensitivity analysis results for CS, showing that the highly sensitive parameters were associated with Chl-a. The backscattering ratio of Chl-a was the most sensitive parameter, and the specific scattering coefficient (b₀) of suspended solids was secondary in the case of CS. The sensitivity ranking of the parameters showed a similar trend with regard to the depth profiles (Table 2). The difference in the optical features of the HN and CS regions may induce different parameter sensitivity results. HN exhibited a low Chl-a concentration; thus, the effect of the parameters related to non-algal matter was strong for HN. However, CS primarily contained a high concentration of Chl-a and suspended solids, resulting in the most sensitive parameters being related to both Chl-a and TSS.

The most sensitive parameter, namely, the backscattering ratio, is considered a critical factor for addressing discrepancies between modeling-based and observed remote sensing data because this ratio is indicative of the particle composition in water bodies. [51]. In particular, this ratio is related to the level of suspended solids and dissolved matter in fresh water, which significantly influences the reflectance. In addition, the backscattering ratio was used to estimate the bulk refractive index with respect to the particle size distribution [52].

This indicates that the sensitivity of the ratio depended on the concentration of Chl-a or TSS due to their various refraction indexes [53]. Furthermore, this ratio was utilized as a proxy to determine the scattering phase function that was used to fit the light field of the water column [26]. In addition to the backscattering ratio, the scattering coefficients (i.e., n and b₀) showed secondary importance in estimating reflectance by calculating the backscattering coefficient because these parameters directly affected the concentrations of Chl-a and TSS, as seen in Equation (5) [54]. However, the scattering coefficient (m) was used to assign the wavelength, a parameter with minor sensitivity, for both Chl-a and TSS. The wavelength variation, with respect to the reference wavelength, insignificantly affected the reflectance profile. Prior studies normally used previously published values of this parameter.

CDOM affected the intrinsic properties of water, such as Chl-a absorption level, because the optical features of CDOM substantially affect the photo-processes and radiance in the upper water column. However, the parameters (p₀ and q₀) for CDOM showed low sensitivity to the reflectance profile in both HN and CS (Table 2). The CDOM exhibited relatively low absorption compared to the other constituents, and the optical feature corresponding to CDOM is negligible in the red spectral band because CDOM absorption exponentially decreases with an increase in wavelength [55]. Particularly, several studies have investigated the spectral slope, q₀, for fitting the CDOM absorption curve because the slope values were site-specific and varied with the water constituents [42,56,57,58].

Chl-a fluorescence quantum efficiency was the 11th (of 12) parameter in terms of sensitivity. This parameter affected specific Chl-a absorption and also improved the fit of the Chl-a reflectance estimates with the near-infrared spectral peaks [59,60]. However, the fluorescence quantum efficiency has been considered less variable than is commonly believed [61]. That is, the fluorescence efficiency value is generally constant across a wide range, although the variation of the fluorescence efficiency is certainly valuable for particular species or conditions [62].

The extent of the Raman scattering was the least sensitive parameter in this study. That is, the effect of the variability of Raman scattering of water was relatively insignificant when calculating the vertical reflectance of fresh water. This is in accordance with the authors of [63], who also found a lack of significant differences in Raman scattering between clear ocean water and pure water.

3.3. Parameter Calibration for Reflectance Profile

After implementing the sensitivity analysis tool for the HydroLight model, this study calibrated the selected parameters for sensitivity analysis in order to estimate the reflectance profile in terms of the six examples in Figure 6. The value of the downwelling diffuse attenuation coefficient indicated that the depth of penetration of sunlight into water varied from 0.69 m to 2.17 m, which was calculated by 1/Kd(490) [63]. The penetration depths were less than 1.0 m in July and August, but over 2.0 m in October, because the penetration depth of the turbid lake water was significantly affected by the absorption and scattering effect arising from suspended particulate matter [64].

Shen et al. [65] observed the effect of variation of the penetration depth from 0.09 m to 1.36 m in lake waters with high concentrations of chlorophyll-a and suspended particulate matters. The simulated vertical profiles of reflectance showed good agreement with the observed profiles. The simulated spectra at various depths (i.e., surface, subsurface, 0.5 m, and 1.0 m) had R² values > 0.93 and RMSE values < 0.0025 sr⁻¹. Lee at al. [66] showed that subsurface reflectance simulated using the HydroLight model had an error of 0.9%. In Nouchi et al. [67], the reflectance spectra were estimated at a depth of 1.0 m and measured within an acceptable level of uncertainty. However, the simulated spectra in the spectral range of 615 nm to 630 nm showed disagreements with the observed spectra, but the discrepancy was still within the range of the expected observation uncertainty (Figure 6). This may be because of the difficulty of accurately reflecting the characteristics of a cyanobacteria-dominant bloom due to the presence of phycocyanin, which leads to a spectral curvature at 620 nm [6]. Overall, the calibrated parameters of the HydroLight model provided reasonable simulation accuracy for the water reflectance of inland water with respect to the depth.

Table 3. Calibrated parameters for estimating reflectance profile.

Component	Parameters	Optimized Parameter Range
Chlorophyll-a	Scattering coefficient (b0)	0.4–0.8
	Scattering coefficient (m)	1.0
	Scattering coefficient (n)	0.5–0.9
	Backscattering ratio	0.0009–0.01
	Chlorophyll-a fluorescence efficiency	0.002–0.018
CDOM	Empirical parameter (p0)	0.6–0.7
	Exponential decay constant(q0)	0.020
TSS	Scattering coefficient (b0)	0.3–0.8
	Scattering coefficient (m)	1.0
	Scattering coefficient (n)	0.4–0.9
	Backscattering ratio	0.0008–0.01
Water	Raman scattering coefficient	0.00026

presents the calibrated parameter ranges. The most sensitive parameter, the backscattering ratio, had a wide range. Although the theoretical value of the backscattering ratio is 0.02, based on oceanography [52], a backscattering ratio lower than 0.02 was also assigned based on observation, reflecting the characteristics of water dominated by phytoplankton and organic detritus [54,68,69,70]. The increase in the backscattering ratio was induced by a decrease in the size of the suspended particles [71]. Specifically, very small organic and detrital matter, with a size between 1.0 μm and 10.0 μm, mainly contributed to the backscattering coefficient of the water [72,73]. Snyder et al. [69] and Whitmire et al. [54] showed that the backscattering ratio of coastal waters varied between 0.005 and 0.060. McKee and Cunningham [74] showed that the backscattering ratio for the ocean water varied between 0.005 and 0.050. Loisel et al. [68] found that the backscattering ratio of coastal water changed from 0.0024 to 0.0417. Boss et al. [75] showed that the backscattering ratio of seawater varied from 0.005 to 0.035. These backscattering values were relatively high compared to the calibrated backscattering ratio in this study (Table 3). The dynamic range of the backscattering ratio may imply the large variability of the particle composition of inland water with a high concentration of optical matters. Haltrin et al. [76] reported that the backscattering ratio in turbid water increased with the concentration of Chl-a. In our study, the calibrated scattering coefficients (b₀ and n) showed relatively high values compared to those for ocean water (Table 3). The high parameter values lead to the relatively high backscattering coefficients, which in turn corresponded to high Chl-a and TSS concentrations in fresh water [77]. The typical values of b₀ and n for ocean water were documented as 0.30 and 0.62, respectively [27,78]. In the case of turbid inland water, the parameters needed to be adjusted because the backscattering coefficient could not be elucidated using the parameters published based on oceanography [43]. Conversely, the scattering parameter (n) was corroborated with the value in the literature as 1.0 [27].

The calibrated p₀ for CDOM showed a higher value than 0.20, which is the typical value for coastal waters (Table 3). This may be due to the relatively high concentration of CDOM in inland water compared to that in ocean water. However, the calibrated decay constant, q₀ was found to have a similar value to that obtained in previous studies. Green and Blough [79] documented that the decay constant value for seawater ranged from 0.019 to 0.021. Stedmon and Markager [80] suggested a decay constant value of 0.0194 for coastal water. Schwarz et al. [57] showed that the decay constant was 0.0173 for global ocean water. Thus, this study found that there was no significant difference in the decay constant values between ocean water and inland water.

The Chl-a fluorescence quantum efficiency exhibited a wide range for the calibrated value, which was lower than the typical value of 0.02 (Table 3). Gilerson et al. [62] also reported that the Chl-a fluorescence efficiency varied from 0.005 to 0.01. The Chl-a fluorescence efficiency was directly influenced by the concentration of the water constituents. The value of the Chl-a fluorescence efficiency decreases as TSS concentrations increase because of decreasing light availability due to the strong light attenuation [61].

Regarding the least sensitive parameter, the Raman scattering coefficient of water, there was no significant difference between sea and fresh water. The calibrated Raman scattering coefficient of water showed the same value as that for coastal water [26] (Table 3).

3.4. Scattering Property for Cyanobacteria Genera Cells

After calculating the remote sensing reflectance, the inherent optical backscattering coefficient was utilized to deduce the optical properties of water quality constituents such as algal cells and particulate organic carbon matter [69]. In this study, the absorption coefficients of phytoplankton were measured experimentally, which were then used to simulate the reflectance spectra derived from the HydroLight model. As evidenced by the calculated reflectance, the reflectance simulation was accurate and provided reasonable values for the backscattering coefficients, thereby approximating the relationship between the coefficients and the dominant algal cells. Figure 7 presents the simulated backscattering spectra at the subsurface of water. These spectra decrease exponentially with an increase in the wavelength (Figure 7a,c). Furthermore, the values of these spectra varied substantially with respect to the sampling points and periods due to the different compositions of the optical matter [81]. In particular, this study focused on variations in the backscattering coefficient in response to a change in the number of cyanobacteria cells, because the study area experiences frequent cyanobacteria bloom. The value of the backscattering coefficient was found to increase when the number of cyanobacteria cells increased (Figure 7b,d). [82] reported a logarithmic relationship between the backscattering coefficient and the biomass of Microcystis. The high scattering was attributed to the volume, length, and diameter of the cyanobacteria cells [83,84]. In addition, the internal gas vacuoles in cyanobacteria also caused an increase in backscattering due to the increased scattering at backward angles exceeding 90° [85,86]. The specific genus of the cyanobacteria associated with the backscattering coefficient at 550 nm is presented in Figure 8 and Figure 9. The wavelength of 550 nm was chosen considering the strong reflectance peaks of phytoplankton [87]. The backscattering coefficient of 0.1781 m⁻¹, observed on 9 September 2018, was caused by the cyanobacteria cell concentration exceeding 1.9 × 10⁶ cells mL⁻¹ (Figure 8c). In particular, Oscillatoria limnosa was a dominant species with more than 1.6 × 10⁶ cells mL⁻¹. On the contrary, the backscattering coefficient of 0.0117 m⁻¹, observed on 25 October 2018, was driven by Microcystis aeruginosa with 3.6 × 10³ cells mL⁻¹ (Figure 8d). On 9 July 2019 and 24 July 2019, total cyanobacterial cell concentrations exceeding 2.8 × 10⁴ cells mL⁻¹ and 3.4 × 10⁵ cells mL⁻¹ induced backscattering coefficients of 0.0422 m⁻¹ and 0.1742 m⁻¹, respectively. During these periods, Aphanizomenon flosaquae and Microcystis aeruginosa were the dominant genera with concentrations exceeding 1.6 × 10⁴ cells mL⁻¹ and 1.7 × 10⁵ cells mL⁻¹, respectively (Figure 9a,b). The small size, gas vesicles, heterocyst, and akinetes of Microcystis and Aphanizomenon genera likely resulted in the high backscattering values [88]. Moore et al. [13] also reported backscattering values between 0.02 m⁻¹ and 0.15 m⁻¹ at 443 nm for cyanobacteria concentrations ranging from 1 × 10⁴ cells mL⁻¹ to 6 × 10⁵ cells mL⁻¹.

3.5. Implication of Developing Sensitivity Analysis Tool

The GUI software provided the sensitivity analysis results for the HydroLight model parameters for inland water. Based on the results, this study calibrated the parameters for calculating the reflectance profile and then interpreted the calibrated parameters for representing the optical properties of fresh water. The GUI software is very straightforward and has obvious advantages. First, the GUI software substantially reduced the HydroLight simulation time. Originally, it took approximately 50 h to simulate 2990 input files for the HN region (i.e., 1 min for each simulation), but with the GUI software, it only took 4 h to simulate the input files using 13 multiple executions. Moreover, the simulation of 13,520 input files for the CS region took approximately 225 h using the normal simulation; in contrast, the simulation time was reduced to approximately 17 h using the GUI software. Second, after the model simulations, the GUI software automatically gathered the simulation results in order to prepare for the sensitivity analysis. Third, the sensitivity results were then provided, and the mean and standard deviation values (Figure 3) and related scatter figures (Figure 4 and Figure 5) were displayed. Therefore, the GUI software developed in this study improves the effectiveness and range of applicability of the HydroLight software with regard to sensitivity analysis. In addition, the versatility of the GUI software allows additional sensitivity analyses to be conducted; furthermore, the software can be consistently employed as new datasets become available for various study areas. Several studies also proved these kinds of advantages in developing GUI software for various objects [89,90,91,92]. In the future, a more practical GUI software should be developed by extending the proposed software for studying and estimating water constituents that affect water quality. The software will optimize HydroLight model parameters and then calculate the Chl-a, TSS, CDOM, and phycocyanin concentrations by selecting proper bio-optical algorithms using the simulated reflectance profile.

4. Conclusions

This study developed GUI software to perform a sensitivity analysis of the parameters of the HydroLight model using multiple executions. The GUI model carried out the LH–OAT sampling of selected parameters, multi-point simulations, and sensitivity analysis; furthermore, it displayed the sensitivity analysis results. The Chl-a concentrations, TSS concentrations, and absorption coefficients for inland water in the HN and DC regions of the Daecheong dam area were measured to simulate the reflectance profiles using the model. The sensitivity analysis results showed that the scattering parameters correspond to Chl-a and TSS were more important than the other parameters. In particular, the backscattering ratios of TSS and Chl-a were the most sensitive parameters for the HN and CS regions, respectively, because TSS was a major constituent in the water in HN and Chl-a was a major constituent in that in CS. Moreover, this study calibrated the HydroLight parameters to estimate the reflectance profiles of inland water bodies. The simulated reflectance profiles showed good agreement with direct observations. In addition, the scattering property was strongly correlated with the cyanobacteria genera cells. The differences and similarities between the parameter values obtained in this study and those previously obtained based on oceanography were elucidated. It was found that the proposed GUI software extends the applicability of the HydroLight model and significantly reduces simulation time. With regard to related future work, the optical algorithm included in the GUI software can be practically applied to directly obtain information regarding the algal biomass in water bodies.