Optimal Hyperspectral Characteristic Parameters Construction and Concentration Retrieval for Inland Water Chlorophyll-a Under Different Motion States

Abstract

In recent decades, the rapid expansion of phytoplankton blooms caused by lake eutrophication has led to severe ecological destruction and impeded the sustainable economic development of local regions. Chlorophyll-a (Chl-a) is commonly used as a biological indicator to detect phytoplankton blooms due to its ease of detection. To improve the accuracy of Chl-a estimation in aquatic systems, an accurate understanding of its true spectral characteristics is imperative. In this study, a comprehensive and realistic experimental scheme was designed from the perspective of real algal strains and real water states. Both in situ and laboratory-based hyperspectral data were collected and analyzed. The results show that there are huge spectral differences not only between laboratory-cultured and real algae strains, but also between static and disturbed water surface conditions. A total of ten different categories of spectral characteristics were selected in both disturbed and static states. Then, six parameters with the best models to the Chl-a concentration were identified. Finally, two linear models of the Chl-a concentration at peaks of 810 nm and 700 nm were identified as the best estimation models for the static and disturbed states, respectively. The results provide a scientific reference for the large-scale retrieval of the Chl-a concentration using satellite remote sensing data. This advancement benefits inland water monitoring and management efforts.

1. Introduction

Inland lakes have historically played a vital role in providing drinking water and habitat for various organisms [1]. However, the increasing frequency of phytoplankton blooms in lakes, linked to global climate change and human activities, suggests a gradual deterioration in overall lake water quality [2,3,4,5]. Recent studies [6] show a significant increase in the global maximum bloom extent (MBE), reaching 312,723.99 km², nearly 11.7% of the total global lake area. Furthermore, compared to traditional chemical pollution, phytoplankton blooms are considered to be a greater threat to human health and ecosystems in inland lakes compared to conventional chemical pollution [7,8]. These blooms can hinder the sustainable development of society [9]. Therefore, the accurate identification and quantification of phytoplankton blooms are critical for managing the aquatic environment and maintaining a healthy aquatic ecological cycle [10,11].

The chlorophyll-a (Chl-a) concentration is a widely recognized indicator of phytoplankton biomass in freshwater and marine environments [12,13]. It serves as a valuable metric for assessing the trophic status of these environments [13]. Traditional approaches to Chl-a monitoring are predominantly manual, labor-intensive, and lacking spatial continuity, limiting their effectiveness [14]. However, the emergence of remote sensing technology offers a significant advantage by enabling the large-scale, spatially continuous monitoring of Chl-a concentrations in water bodies [15,16,17].

To accurately determine the concentration of Chl-a, it is essential to obtain more accurate spectral characteristics of Chl-a [18,19]. Extensive research has been conducted on the spectral characteristics of Chl-a with hyperspectral data processing. The resulting models are mainly categorized into empirical, semi-empirical, and analytical types [20]. Empirical models, which are widely used for Chl-a retrieval from remote sensing data, are mainly based on the statistical relationship between the Chl-a concentration and remote sensing parameters [21,22,23]. Semi-analytical models combine the theoretical analysis of radiative transfer with empirical statistics to delineate the retrieval process [24,25,26,27,28]. Analytical models, based on the radiative transfer principles, analyze the relationship between remote sensing reflectance and the absorption and backscatter coefficients of Chl-a in water. This is achieved through a bio-optical model and facilitates the retrieval of Chl-a concentrations in water [29,30,31]. However, current research in this area still faces several of the following limitations in experimental design:

• The impact of in situ collection. Chl-a spectral data are typically collected either in situ or in the laboratory. While in situ measurements can collect data quickly, data from phytoplankton bloom areas are difficult to collect from research vessels using the standard method [32] because ships and water collectors will disturb the distribution of phytoplankton during the collection process. Therefore, our experiments will be conducted in a laboratory environment, which can reduce the errors caused by collecting data.
• The impact of the water surface motion state. Based on the previous research, it was observed that the distribution of cyanobacteria differs depending on whether the water surface is disturbed (e.g., windy) or static [33]. These distribution differences lead to distinct spectral characteristics in both states [33]. In disturbed states, cyanobacteria are uniformly dispersed throughout the three-dimensional space, reducing their absorption and scattering effects [33,34]. Concurrently, the formation of numerous capillary waves on the water surface increases the water’s surface area, thereby enhancing absorption in the near-infrared band [35]. Conversely, in static states, the quantity of cyanobacteria below the surface rapidly decreases, and they distribute evenly across the water surface [36]. As light traverses the water surface, its intensity diminishes, reducing the water’s absorption and resulting in a significant increase in surface reflectance [37]. The Chl-a exhibit strong reflection and scattering in the near-infrared range [20]. Consequently, this study conducted experiments under both disturbed and static states.
• The impact of laboratory-cultured algal strains. Traditional studies often relied on cultured algal strains [38], which may not accurately represent the characteristics of natural algal populations, particularly cyanobacteria. This suggests laboratory-cultured algal strains might exhibit spectral properties that differ from those of wild cyanobacteria, thus potentially affecting the Chl-a concentration estimation. To address this, this study first conducted a comparative experiment to investigate the differences between cultured and wild cyanobacteria. Subsequently, Taihu Lake was selected as the site to collect wild cyanobacteria for further laboratory analyses.

In general, to enhance the accuracy of the Chl-a concentration retrieval in real-world conditions, a more comprehensive experiment was designed. The primary objectives of this study were as follows: (1) to indicate the existence of the spectral difference caused by algal strains and water surface states; (2) to obtain spectral characteristic parameters which have a high correlation with the Chl-a concentration in static and disturbed states, respectively; (3) to explore the different relationship between the Chl-a concentration and spectral characteristic parameters with varying water states; (4) to construct the best estimation models of the Chl-a concentration for different states. It is the first trial in Chl-a spectral characteristic analysis and Chl-a concentration estimation taking both the strains and distribution of cyanobacteria into account. The findings provide scientific-based reference for the large-scale retrieval of the Chl-a concentration using satellite remote sensing data. This advancement benefits the inland water monitoring and management efforts.

The rest of the paper is organized as follows: Section 2 describes the dataset and research methods used in this study. Section 3 illustrates the design and details of the experiments. Section 4 displays and analyzes the experimental results. Section 5 discussed the applicability of the model proposed in this paper and its shortcomings. Section 6 concludes this study, as well provides limitations.

2. Materials and Methods

2.1. Study Area

Taihu Lake is located on the border of Zhejiang and Jiangsu provinces in the southern part of the Yangtze River Delta [39]. It is the third largest freshwater lake in China. With an area of 2425 km², it serves as an important water source for the Shanghai, Suzhou, Wuxi, Changzhou, Hangzhou, and Jiaxing areas [40]. In 2007, the Wuxi section of Taihu Lake experienced a severe phytoplankton bloom crisis, posing a significant threat to agricultural and drinking water safety in the surrounding areas [41]. Due to the unique geographical location, Gonghu Bay became one of the areas with the most serious phytoplankton bloom outbreaks in this crisis [41]. Therefore, this study focused on Gonghu Bay for the in situ experiment (Figure 1).

2.2. Datasets

The analysis is based on the following two main data sources: hyperspectral data and water samples. Hyperspectral data were obtained in situ and under laboratory conditions using an ASD FieldSpecFR spectrometer. Water samples were collected with varying Chl-a concentrations. These data are detailed in

Table 1. Data utilized in this study.

	Data Type
	Hyperspectral Data		Water Samples
Scenario	Laboratory-based	In situ	Laboratory-based
Position	Roof of Liren Building, Fudan University	Gonghu bay of Taihu	Roof of Liren Building, Fudan University
Purpose	Spectral analysis	Spectral characteristic verification	Chl-a concentration measurement
Time	2 and 3 October 2014	8–10 August 2014	2 and 3 October 2014
Methods	ASD FieldSpecFR 350~1000 nm; 651 bands		SL 88-2012 [42]

.

3. Methodology

3.1. Examining Differences Between Cultured and Wild Cyanobacteria

In this study, we used wild algae collected directly from Taihu Lake for the laboratory-based experiment, which was dominated by Microcystis aeruginosa. A comparative experiment was conducted to investigate the morphological and spectral differences between cultured and wild cyanobacteria. For the morphological part, the following four key aspects were focused on: the micro-morphology, colony morphology, macro-morphology, and surface morphology. After 4 days of laboratory culture, the wild algae strain and laboratory-cultured Microcystis aeruginosa FACHB-905 were compared with microscope.

3.2. Designing Experiment of Chl-a Retrieval Models

To construct Chl-a concentration retrieval models applicable to a wide range of Chl-a concentrations and various water states, a series of controlled experiments were designed. As shown in Figure 2, the framework was divided into the following two parts: in situ experiment and laboratory-based experiment, mainly including the following three steps: hyperspectral data acquisition, spectral characteristics analysis, and Chl-a concentration modeling.

3.2.1. Laboratory-Based Experiment

• Step 1: Hyperspectral data acquisition and concentration measurement

This experiment was conducted on the roof of Liren Building, Fudan University, on 2 and 3 October 2014, respectively. To ensure a more realistic representation of natural populations, the large-grained Microcystis aeruginosa directly collected from Taihu Lake was utilized. To avoid the death of Microcystis, the samples were stored in a refrigerator at 4 °C before the experiment. Two water states (static and disturbed) were set to simulate the real water surface motion under various wind conditions. In each water state, both the hyperspectral data and Chl-a concentration were collected.

Hyperspectral data were collected under cloud-free conditions using natural light as the source. Black plastic-lined containers (0.45 m × 0.35 m × 0.3 m) covered with blackout cloth were used to ensure minimal reflectance from the interior surfaces (<1% within the 400–800 nm wavelength range). The fiber optic probe of the spectrometer was positioned vertically 0.3 m above the water surface, in the central normal direction of the container. The corresponding Chl-a concentration was determined by the spectrophotometry method [42]. Water samples were filtered using a fiber filter membrane. The filter membrane was stored in a refrigerator for 12 h. Then, the samples were extracted using hot ethanol at a constant temperature of 80 °C and broken down using a cell disruptor. The resulting extract was centrifuged to extract the supernatant, which was washed and centrifuged twice. Finally, 1% hydrochloric acid was added to acidify the supernatant before measuring the absorbance at 665 nm and 750 nm using a spectrophotometer. The data were then used to calculate the concentration of Chl-a.

For the experiment conducted on 2 October, a wide range of Chl-a concentrations from 0 to 1190.46 μg/L were established (

Table 2. Chl-a concentration data collected in this study.

Date	State	Chl-a Concentration (μg/L)
2 October 2014	Static	0	20.72	35.57	58.49	79.21	91.79	116.64	151.05
		167.08	188.99	228.85	294.49	418.23	570.83	841.23	1190.46
	Disturbed	0	20.72	35.57	58.49	79.21	91.79	116.64	151.05
		167.08	188.99	228.85	294.49	418.23	570.83	841.23	1190.46
3 October 2014	Static	85.89	184.76	324.49	444.04	577.67	727.61	983.64	995.18
		1134.60
	Disturbed	15.31	27.79	33.51	52.29	75.33	87.34	94.18	110.66
		149.40	175.05	199.62	450.90

). Initially, containers were filled with pure water. Then, varying volumes of cyanobacteria solution were added to each container and thoroughly mixed to ensure homogeneity (Figure 3). After each addition, three samples were collected for the Chl-a concentration measurement (using the average value). Following each Chl-a measurement, spectral data of the solution were continuously acquired multiple times while maintaining a disturbed state. Five minutes later, until the water surface was static and the cyanobacteria were evenly distributed on the water surface, the spectral data of the solution were continuously acquired multiple times (average value used). These datasets served as training samples for constructing retrieval models due to their covering the potential Chl-a concentrations found in various lake regions. On 3 October, to expand the dataset and further test the models, two sets of experiments were conducted under static and disturbed states, respectively. To maintain a decreasing concentration gradient, pure water was continuously added to both containers. Samples were collected in the same manner as on the first day, under both static and disturbed water surface conditions.

In the laboratory-based experiment on 2 October 2014, containers were filled with pure water firstly. Then, a known volume (50 mL, specified in the Figure 3 vertical axis) of cyanobacteria solution was gradually added into the container and stirred thoroughly to ensure a homogeneous mixture. After each addition, three samples were collected for the Chl-a concentration measurement (with the average value used). Following each Chl-a measurement, the spectral data of the solution were continuously acquired multiple times while maintaining a disturbed state. Five minutes later, until the water surface was calm and the cyanobacteria were evenly distributed on the water surface, the spectral data of the solution were continuously acquired multiple times (with the average value used). The Chl-a concentration in each sample was determined using the spectrophotometric method (SL 88-2012) [42].

On 3 October 2014, building on the experiment conducted on 2 October 2014, one set of experimental data was collected by diluting a sample with water into the container of last day, acting as the disturbed data. Simultaneously, another set of static experiments was conducted in another container. The data of the laboratory-based experiment are shown in Table 2.

• Step 2: Spectral characteristics analysis

Based on the hyperspectral data, the first-derivative spectra were calculated, which helps to effectively remove the influence of partially linear or nearly linear background noise and enhance the spectral characteristics of interest [43]. Then, the original first-derivative spectra were used to obtained the feature bands. For each selected band, various spectral characteristic parameters were calculated.

Spectral curves can be characterized by their peaks (representing reflectance) and valleys (representing absorption). In Figure 4, the left panel shows an absorption valley, where B, E, and F denote the start, peak, and end, respectively. The right panel shows the reflectance peak, with A, C, and F representing the starting point, peak, and end of the reflectance peak, respectively. In both panels, D represents the distance of the peak or valley; R_A and λ_A represent the reflectance value and corresponding wavelength at point A. This study focuses on inflection points, which are points where the curvature of the curve changes (marked by dashed lines in Figure 4). These inflection points are used to define the beginning and end of both peaks and valleys. The parameters that collectively describe spectral characteristics are referred to as “spectral characteristic parameters”. In this study, 10 parameters (

Table 3. Ten spectral characteristic parameters and corresponding formulae (in the formulae, R represents the reflectance, λ represents the wavelength, P represents the peak, V represents the valley, and A-F represent the spectral characteristics appearing in Figure 4).

Spectral Characteristic Parameters	Formula
Peak/valley wavelength	the wavelength corresponding to the first derivative equal to zero (or the extreme point of the reflectivity curve)
Peak height/valley depth	${\mathrm{D}}_{\mathrm{P}}={\mathrm{R}}_{\mathrm{C}}-{\mathrm{R}}_{\mathrm{F}}-({\mathrm{R}}_{\mathrm{A}}-{\mathrm{R}}_{\mathrm{B}})\times {\displaystyle \frac{{\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{C}}}{{\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{A}}}}$ ${\mathrm{D}}_{\mathrm{V}}={\mathrm{R}}_{\mathrm{F}}-{\mathrm{R}}_{\mathrm{E}}-{\displaystyle \frac{({\mathrm{R}}_{\mathrm{F}}-{\mathrm{R}}_{\mathrm{B}})\times ({\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{E}})}{{\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{B}}}}$
Peak/valley area AP and AV	${\mathrm{A}}_{\mathrm{P}}={\displaystyle {\int }_{\mathrm{i}={\lambda }_{\mathrm{A}}}^{{\lambda }_{\mathrm{F}}-1}\frac{{\mathrm{R}}_{\mathrm{i}}+{\mathrm{R}}_{\mathrm{i}+1}}{2}}\mathrm{d}\lambda -{\displaystyle \frac{({\mathrm{R}}_{\mathrm{F}}+{\mathrm{R}}_{\mathrm{A}})({\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{A}})}{2}}$ ${\mathrm{A}}_{\mathrm{V}}={\displaystyle \frac{({\mathrm{R}}_{\mathrm{F}}+{\mathrm{R}}_{\mathrm{B}})({\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{B}})}{2}}-{\displaystyle {\int }_{\mathrm{i}={\lambda }_{\mathrm{B}}}^{{\lambda }_{\mathrm{F}}-1}\frac{{\mathrm{R}}_{\mathrm{i}}+{\mathrm{R}}_{\mathrm{i}+1}}{2}}\mathrm{d}\lambda$
Peak/valley left half area APL and AVL	${\mathrm{A}}_{\mathrm{PL}}={\displaystyle {\int }_{\mathrm{i}={\lambda }_{\mathrm{A}}}^{{\lambda }_{\mathrm{C}}-1}\frac{{\mathrm{R}}_{\mathrm{i}}+{\mathrm{R}}_{\mathrm{i}+1}}{2}}\mathrm{d}\lambda -{\displaystyle \frac{({\mathrm{R}}_{\mathrm{D}}+{\mathrm{R}}_{\mathrm{A}})({\lambda }_{\mathrm{D}}-{\lambda }_{\mathrm{A}})}{2}}$ ${\mathrm{A}}_{\mathrm{V}\mathrm{L}}={\displaystyle \frac{({\mathrm{R}}_{\mathrm{E}}+{\mathrm{R}}_{\mathrm{B}})({\lambda }_{\mathrm{E}}-{\lambda }_{\mathrm{B}})}{2}}-{\displaystyle {\int }_{\mathrm{i}={\lambda }_{\mathrm{B}}}^{{\lambda }_{\mathrm{E}}-1}\frac{{\mathrm{R}}_{\mathrm{i}}+{\mathrm{R}}_{\mathrm{i}+1}}{2}}\mathrm{d}\lambda$
Peak/valley right half area APR and AVR	${\mathrm{A}}_{\mathrm{PR}}={\mathrm{A}}_{\mathrm{P}}-{\mathrm{A}}_{\mathrm{PL}}={\displaystyle {\int }_{\mathrm{i}={\lambda }_{\mathrm{A}}}^{{\lambda }_{\mathrm{C}}-1}\frac{{\mathrm{R}}_{\mathrm{i}}+{\mathrm{R}}_{\mathrm{i}+1}}{2}}\mathrm{d}\lambda -{\displaystyle \frac{({\mathrm{R}}_{\mathrm{F}}+{\mathrm{R}}_{\mathrm{D}})({\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{D}})}{2}}$ ${\mathrm{A}}_{\mathrm{VR}}={\mathrm{A}}_{\mathrm{V}}-{\mathrm{A}}_{\mathrm{V}\mathrm{L}}$
Peak/valley symmetry SP and SV	${\mathrm{S}}_{\mathrm{P}}={\displaystyle \frac{{\mathrm{A}}_{\mathrm{P}\mathrm{L}}}{{\mathrm{A}}_{\mathrm{P}}}}$${\mathrm{S}}_{\mathrm{V}}={\displaystyle \frac{{\mathrm{A}}_{\mathrm{V}\mathrm{L}}}{{\mathrm{A}}_{\mathrm{V}}}}$
Peak/valley baseline slope KP and KV	${\mathrm{K}}_{\mathrm{P}}=\tan \theta =\left|{\displaystyle \frac{{\mathrm{R}}_{\mathrm{A}}-{\mathrm{R}}_{\mathrm{F}}}{{\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{A}}}}\right|$${\mathrm{K}}_{\mathrm{V}}=\left|{\displaystyle \frac{{\mathrm{R}}_{\mathrm{F}}-{\mathrm{R}}_{\mathrm{B}}}{{\lambda }_{\mathrm{F}}-{\lambda }_{\mathrm{B}}}}\right|$
Peak–valley distance ΔD near 700 nm	$\Delta \mathrm{D}={\mathrm{R}}_{\max \mathrm{of}\mathrm{R}}-{\mathrm{R}}_{\min \mathrm{of}\mathrm{R}}$
Peak-to-valley depth ratio RDP/V near 700 nm	$\mathrm{R}{\mathrm{D}}_{\mathrm{P}/\mathrm{V}}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{P}}}{{\mathrm{D}}_{\mathrm{V}}}}$
Peak-to-valley area ratio RAP/V near 700 nm	$\mathrm{R}{\mathrm{A}}_{\mathrm{P}/\mathrm{V}}={\displaystyle \frac{{\mathrm{A}}_{\mathrm{P}}}{{\mathrm{A}}_{\mathrm{V}}}}$

) of different characteristic bands were selected in both disturbed and static states.

• Step 3: Chl-a concentration modeling

Based on the spectral characteristic parameters’ calculation of different feature bands, their correlation with the Chl-a concentration was investigated with the Pearson correlation coefficient (r). This analysis was helpful for explaining which spectral characteristics had a stronger response relationship with the changes in the Chl-a concentration. Parameters with the highest r were selected to be further applied to the Chl-a concentration modeling.

For each parameter, three models, including linear, exponential, and power models, were constructed and compared by R² to select the optimal model. In this study, separate models were constructed for disturbed and static water states. Data from laboratory-based experiment conducted on 2 October 2014 served as training samples to develop the models, while data from the separate laboratory-based experiment conducted on 3 October 2014 were employed as test samples. The model’s performance was assessed with the R² and RMSE.

3.2.2. In Situ Experiment

To verify the consistency of spectral characteristics between laboratory-based experiments and cyanobacteria in the natural environment, an in situ experiment was conducted at Gonghu Bay, Taihu Lake, from 8–10 August 2014. Hyperspectral measurements were collected in 10 positions (Figure 1) under both static (wind speed under 2 m·s⁻¹) and disturbed states. A total of 30 sets of in situ cyanobacterial spectral data were used for spectral characteristic validation. The comparison focused on both original spectra and their first-derivative spectra.

4. Results

4.1. Differences Between Cultured and Wild Cyanobacteria

As Figure 5a shows, wild cyanobacteria exhibit distinct morphological characteristics compared to laboratory-cultured strains. In terms of colony morphology, wild cyanobacteria tend to aggregate into clusters and form communities, which are not observed in the laboratory-cultured strains. In the macro-morphology, wild cyanobacteria are observed to be suspended in clusters in the water, in contrast to the uniform distribution of laboratory-cultured cyanobacteria in their containers. Surface morphology shows that, in a static state, wild cyanobacteria gradually rise to the surface of the container, forming a clumped state, while laboratory-cultured cyanobacteria do not exhibit this behavior. These observed differences verify the distinct characteristics of wild cyanobacteria compared to their laboratory-cultured counterparts. Additionally, their hyperspectral curves are illustrated in Figure 5b. A distinct red-edge feature was observed in the hyperspectral curve of wild Microcystis aeruginosa. While similar trends are evident, a more pronounced difference between adjacent peaks and valleys was found in the hyperspectral curve of wild Microcystis aeruginosa.

4.2. Analysis of Spectral Curve Characteristics of Cyanobacteria

The hyperspectral curves of cyanobacteria measured in laboratory-based experiment is shown in Figure 6. It highlights the following two key differences in spectral reflectance between disturbed and static states for the same Chl-a concentration:

(1)

Lower Reflectance in the Disturbed State: Overall, the spectral reflectance is lower in the disturbed state compared to the static state. This is evident in the maximum peaks around 550 nm and 700 nm, where reflectance values are significantly lower in the disturbed state (0.08 < 0.13 and 0.17 << 0.48, respectively).

(2)

Double Peak vs. Flat Peak in the 700–850 nm Range: In the range of 700 nm to 850 nm, the disturbed state exhibits a saddle-shaped double peak, while the static state shows a relatively flat peak. Under disturbed states, the left peak of the double peak is situated around 710 nm and shifts towards longer wavelengths as the concentration of cyanobacteria increases. The right peak is located at 810 nm, with a faint serrated sub-peak at 762 nm. In contrast, the static states have a single, broader peak that is shifted significantly to the right (around 90 nm) compared to the disturbed state, reaching approximately 900 nm.

Figure 6e shows the spectral reflectance of cyanobacteria on a lake surface disturbed by wind and waves, which closely resembles the reflectance patterns observed in the disturbed state of the laboratory-based experiment (Figure 6a–d). Similarly, Figure 6f shows the spectral reflectance of cyanobacteria on a calm lake surface, aligning well with the reflectance observed in the static state of the laboratory-based experiment. These findings confirm that the controlled laboratory-based experiments successfully replicated the key spectral characteristics of cyanobacteria under real-world conditions (disturbed and static water bodies). This validation strengthens the applicability of the experimental results for in situ monitoring of phytoplankton blooms.

Furthermore, the spectral reflectance data from both laboratory-based and in situ experiments exhibit many consistent characteristics. In the 400–500 nm range, the reflectance of pure water is around 0.02. It gradually decreases to less than 0.01 beyond 710 nm. After adding cyanobacteria to the water, the reflectance gradually increases, and the waveform changes significantly. Clear valleys are observed near 440 nm, 620 nm, and 675 nm. These valleys correspond to the absorption of Chl-a, phycocyanin (PC) [44,45], and Chl-a in the red light band [27,46], respectively. A strong peak around 550 nm is attributed to the combined effects of Chl-a and carotene scattering, along with weak absorption of cyanobacteria in the green light band [46,47]. This peak makes it a valuable marker for Chl-a detection. Then, a weak secondary peak at 650 nm is caused by the PC absorption [48] and the interaction between algae cell scattering, pigment absorption, and water absorption [49,50]. Additionally, a shoulder-shaped peak near 700 nm arises from the combined influence of Chl-a fluorescence and the weak absorption of water and Chl-a. It is generally believed that the presence or absence of Chl-a is the basis for determining whether the water contains it [51]. Figure 7 displays the first-derivative spectra from the original reflectance spectra of cyanobacteria in both laboratory-based and in situ experiments. Some interesting observations are revealed. Except for the peaks near 700 nm, the positions (wavelengths) of peaks and valleys in the first-derivative spectra remain relatively unchanged across different samples (varying Chl-a concentrations). Their magnitudes (peak heights and valley depths), however, do increase with an increasing cyanobacterial concentration. The peaks around 700 nm exhibit a unique behavior. Not only does their height increase with an increasing cyanobacterial concentration, but their corresponding wavelengths shift slightly towards longer wavelengths (red shift). However, the peak position in the first derivative spectra do show a significant shift. This suggests that the red edge shift effect observed in the original reflectance spectra might be relatively small.

The above experimental results indicate the following: (1) The spectral characteristics of disturbed and static states have similar wavelength positions. However, significant differences are observed in the magnitudes (amplitudes) and shapes of the spectral characteristics. (2) These differences closely resemble the spectral variations between wind-induced disturbed and static states observed in the in situ experiment data from Taihu Lake. This suggests that laboratory-based experiments can effectively simulate real-world scenarios in lakes with varying wind conditions.

4.3. Relationship Between Main Characteristic Parameters of Cyanobacteria and Chl-a Concentration

In this study, totally 28 spectral characteristic parameters of different feature bands were calculated.

Table 4. Correlation coefficient between spectral characteristics of cyanobacteria and Chl-a in the laboratory-based experiment.

Wavelength (nm)	Spectral Characteristic Parameters	Pearson Correlation Coefficient (r)
		Disturbed	Static
Peak 550	Maximum reflectance wavelength	−0.09	0.57
	Maximum reflectance	0.93	0.91
Valley 620	Minimum reflectance wavelength	—	—
	Minimum reflectance	0.52	0.89
Valley 680	Minimum reflectance wavelength	—	—
	Minimum reflectance	0.16	0.86
	Valley area	0.97	0.94
	Valley left area A1	0.78	0.92
	Valley right area A1	0.98	0.94
	Symmetry	−0.67	−0.61
	Baseline slope	0.99	0.99
	Depth	0.97	0.99
	End wavelength (red edge)	0.68	0.90
	End reflectance	0.95	0.96
Peak 700	Maximum reflectance wavelength	0.77	0.86
	Maximum reflectance	0.99	0.99
	Peak area	0.98	0.85
	Peak left area A3	0.99	0.52
	Peak right area A4	0.93	0.88
	Symmetry	0.75	−0.13
	Baseline slope	1.00	0.98
	Height	0.94	−0.91
Peak 810	Maximum reflectance wavelength	−0.33	0.43
	Maximum reflectance	0.99	1.00
Peak 700 vs. Valley 680	Distance	0.76	0.84
	Height/depth ratio	−0.48	−0.98
	Area ratio	−0.44	−0.35
	Left/right area ratio (A3/A2)	0.82	−0.13

displays the correlation coefficients between various spectral characteristic parameters and Chl-a concentration. From Table 4, the following patterns are identified:

(1)

Green Peak (550 nm): There is a strong correlation (r > 0.90) between the Chl-a concentration and the reflectance value at 550 nm (green peak). Weak correlation was observed between the peak wavelength and Chl-a concentration, indicating the “green peak” shifts with changes in the Chl-a concentration. However, this shift is not only influenced by Chl-a [46,47], which explains the weak correlation between the wavelength of the maximum reflectance value at 550 nm and Chl-a. The value of r is much higher in the static state compared to the disturbed state, indicating that the distribution of cyanobacteria may be the primary factor contributing to this difference. The correlation between peak wavelength and Chl-a is stronger in the static state, suggesting that cyanobacteria distribution might influence the peak shift under disturbed states.

(2)

Valley at 620 nm: Valley positions of around 620 and 680 nm remain relatively unchanged with Chl-a variations, which result to the blank in Table 3. Under disturbed states, the reflectance values at the valley show a weak correlation (a low r value) with Chl-a, with r values of 0.52. Under static states, the r values are higher, at 0.89, indicating a stronger correlation.

(3)

Valley at 680 nm: The total area, left/right half areas, baseline slope, and valley depth at 680 nm generally show high correlation with Chl-a (strongest with baseline slope and valley depth). Valley asymmetry shows a weak negative correlation with Chl-a.

(4)

Peak at Around 700 nm: Both the peak reflectance value and baseline slope exhibit strong correlation with Chl-a (r > 0.98) regardless of the disturbed or static state. For the remaining parameters, except for the peak wavelength, higher correlation exists in disturbed states compared to static states. Among these parameters, peak symmetry shows the weakest correlation. Peak height correlation with Chl-a is strong but flips direction (positive in disturbed states; negative in static states).

(5)

Peak at Around 810 nm: The correlation between the peak wavelength and Chl-a is weak with low r values. Peak reflectance, on the other hand, exhibits a very strong correlation (r > 0.99) with the Chl-a concentration.

(6)

Red Edge: The position of the “red edge” (valley at the 680 end of the wavelength) shows moderate correlation with Chl-a (r values around 0.6–0.9), while the reflectance values show a strong correlation with Chl-a (r values > 0.94). Generally, the correlation between red edge parameters and Chl-a is stronger in the static state compared to the disturbed state.

Generally, this analysis reveals several spectral characteristic parameters that exhibit strong correlations with the Chl-a concentration. These parameters can potentially be used to develop robust models for predicting Chl-a in phytoplankton blooms using spectral reflectance data under both disturbed and static water conditions.

Figure 8 depicts the distribution of correlation coefficient between 28 types of spectral characteristic parameters (listed in Table 4) and the Chl-a concentration. The analysis reveals the following key observations: (1) Most of the spectral characteristic parameters of cyanobacteria are positively correlated with the Chl-a concentration. (2) Four characteristic parameters (a peak 700 symmetry, peak 700 height, peak 810 peak wavelength, and left–right area ratio) show inconsistent correlation between disturbed and static states. Their R values can be positive in one state and negative in the other, (3) Regardless of the state (disturbed or static), a positive correlation coefficient is generally preferred for the Chl-a prediction model. Among the positively correlated parameters, the valley 680 end (red edge) reflectance, the valley 680 baseline slope, the valley 680 depth, the peak 700 reflectance, the peak 700 baseline slope, and the peak 810 reflectance stand out as having the strongest correlation with the Chl-a concentration.

4.4. Quantitative Estimation of Chl-a Concentration Based on Cyanobacteria Characteristic Parameters

Based on the above analysis, it is evident that, among the 28 spectral characteristic parameters, the reflectance at the end of valley 680, the baseline slope of valley 680, the depth of valley 680, the reflectance at peak 700, the baseline slope of peak 700, and the reflectance at peak 810 have the highest correlation with Chl-a. Therefore, these six spectral characteristic parameters are selected as independent variables to establish a prediction model for Chl-a, with the concentration of cyanobacterial Chl-a as the dependent variable. The prediction model includes the following three types of models: exponential, power, and linear. The modeling results are depicted in Figure 9 and Figure 10. In these figures, the exponential, power, and linear fitting models are represented by the dashed line, dotted line, and solid line, respectively.

Table 5. R² of different models with spectral characteristic parameters in disturbed and static states. The bold represent the best model selected for subsequent experiments.

	Model R2	Disturbed States			Static States
Parameters		Exponential Model	Power Model	Linear Model	Exponential Model	Power Model	Linear Model
Valley 680 end reflectance		0.84	0.98	0.98	0.63	0.91	0.93
Valley 680 baseline slope		0.76	0.77	0.98	0.59	0.97	0.91
Valley 680 depth		0.82	0.91	0.93	0.79	0.97	0.99
Peak 700 reflectance		0.76	0.91	0.98	0.77	0.96	0.99
Peak 700 baseline slope		0.70	0.85	0.99	0.75	0.91	0.94
Peak 810 reflectance		0.73	0.91	0.98	0.76	0.96	0.99

displays the R² for the different models (exponential, power, and linear) developed using each spectral characteristic parameter. In disturbed states, the valley 680 end-point reflectance performed best when modeled with a power function, while the remaining five parameters are best represented by linear models. All of the exponential models exhibited the weakest performance. In the static states, except for the power model of the valley 680 baseline slope, which achieved the best results, the linear models outperformed the power models for the other five characteristic parameters.

Based on the above results, the models with the highest R² for each parameter were chosen. Their performance was evaluated using data from the laboratory-based experiment on 3 October 2014. The accuracy evaluation is shown in

Table 6. Performance metrics of the model on test data across multiple states. The bold represent the best performing model in each state.

Models	Metrics	States
		Disturbed	Static
(a) Power model of the reflectance at the end of valley 680	R2	0.53	0.88
	RMSE	256.33	170.80
(b) Linear model of the baseline slope of valley 680	R2	0.77	0.52
	RMSE	164.02	563.70
(c) Linear model the depth of valley 680	R2	0.87	0.16
	RMSE	105.71	457.78
(d) Linear model the reflectance at peak 700	R2	0.87	0.99
	RMSE	115.01	40.55
(e) Linear model the baseline slope of peak 700	R2	0.99	0.87
	RMSE	28.87	184.85
(f) Linear model the reflectance at peak 810	R2	0.91	0.99
	RMSE	91.53	37.33

.

In disturbed states, the linear model for the peak 700 baseline slope provides the most accurate results for the Chl-a estimation, followed by the linear model for the peak 810 reflectance. In static states, the linear model of the peak 810 reflectance provides the most accurate results for quantitative estimation of Chl-a, followed by the linear model of the peak 700 reflectance.

Overall, the linear models for the peak 700 baseline slope and the peak 810 reflectance emerged as the most effective models for Chl-a prediction, regardless of whether in disturbed or static water states, based on the chosen spectral characteristic parameters.

To comprehensively assess the model’s performance on the entire dataset, linear regression analysis was conducted between the true and predicted Chl-a concentrations. This analysis included both the modeling samples (hollow dots) and the test samples (black dots), as illustrated in Figure 11 and Figure 12. The dashed line represents the regression line fitted to the entire dataset, while the solid line indicates perfect agreement between the true and predicted values (X = Y). The degree of overlap between the dash and the solid lines signifies the accuracy of the model fitting. Figure 11e and Figure 12f demonstrate excellent model performance, as evidenced by the close alignment between the dashed and solid lines. This indicates a high degree of agreement between the true and predicted concentrations, suggesting that the proposed models effectively capture the underlying relationships between the spectral characteristics and the concentration of Chl-a.

Table 7. The mean and standard deviation of the difference between the true Chl-a concentration and the predicted concentration on the whole dataset. The bold represent the best performing model in each state.

	Disturbed State		Static State
Models	Mean	Standard Deviation	Mean	Standard Deviation
(a) Power model of the reflectance at the end of valley 680	−156.57	225.07	88.74	146.22
(b) Linear model of the baseline slope of valley 680	−33.27	145.84	−176.72	531.97
(c) Linear model the depth of valley 680	−42.83	103.18	260.48	407.32
(d) Linear model the reflectance at peak 700	−20.50	100.88	−82.74	170.23
(e) Linear model the baseline slope of peak 700	6.03	26.11	−73.86	185.36
(f) Linear model the reflectance at peak 810	−24.18	83.46	13.41	36.98

evaluates the performance of each model on the entire dataset by the mean and standard deviation of the difference between the true value and the predicted value. Again, models (e) and (f) perform best in the disturbed state and static states, respectively.

5. Discussion

There are obvious differences in the spectral curves and reflectance values of the same concentration of Chl-a under disturbed and static states, mainly concentrated around 550 nm and between 700 and 850 nm (Figure 6). Additionally, previous studies have shown that, when the water temperature exceeded the threshold for cyanobacteria proliferation, wind conditions (direction and speed) are the primary determinants of phytoplankton blooms in lakes [34]. Wind conditions shape different hydrodynamic fields, leading to varying horizontal and vertical migration patterns of phytoplankton, which directly affects the spatial distribution [36,52]. However, remote sensing methods can only measure the surface Chl-a concentration. Therefore, considering different water motion states is crucial in remote sensing-based Chl-a concentration retrieval studies. Furthermore, studies have suggested that phytoplankton blooms often result from the upward movement, aggregation, and migration of phytoplankton to the water surface due to wind action rather than rapid in situ growth [53]. This implies that the Chl-a concentration in the water may not change significantly. Consequently, traditional retrieval models relying solely on spectral features may not be sufficient for accurate Chl-a concentration estimation due to their limited robustness [37]. Therefore, this study proposes separate retrieval models for Chl-a concentration in disturbed and static water states, offering greater scientific and practical value. The study showed that a wind speed below 2 m·s⁻¹ tended to homogenize the vertical distribution of phytoplankton [9]. Based on these findings, it is recommended to use the static model for wind speeds below 2 m·s⁻¹ and the disturbed model for higher wind speeds in practical applications. In addition, it is important to note that, while this study simulated the spectral characteristics of wild cyanobacteria Chl-a concentrations, these models may not be directly applicable for predicting Chl-a concentrations in real-world environments. This is because Chl-a in natural environments originates from various phytoplankton, not just cyanobacteria [9,34]. Compared to Chl-a, PC exhibits a stronger association with cyanobacteria [54]. This specificity arises from PC’s exclusive presence in cyanobacteria, while Chl-a is found in various phytoplankton and aquatic plants [54,55]. However, the high spectral requirements of PC have limited its widespread application [12]. Until now, numerous algorithms have been proposed to estimate Chl-a concentrations [32]. This preference is further supported by the fact that, in contrast to Chl-a, the remote sensing estimation of the PC concentration at larger scales is limited by the scarcity of data with high spatial and spectral resolution [56,57].

Compared to previous studies, this study established a wider range of Chl-a concentrations for data collection and modeling. Field observations revealed that, although the average Chl-a concentration in central areas of Taihu Lake was around 30 μg/L [58], cyanobacteria blooms gathering along the lake shore bring a high Chl-a concentration, with an average of 369 μg/L [59]. These high concentrations of cyanobacteria can form cyanobacteria scums, such as the sixth and eighth spots of Figure 1. Since 2007, the frequency of cyanobacterial scums in Taihu has intensified at a rate of 0.23% per year [58]. This is also common in other lakes [60]. Studies have confirmed that waters with and without cyanobacterial scums exhibit distinct optical characteristics [61,62]. Therefore, to simulate conditions with and without cyanobacterial scums, multiple groups with high Chl-a concentrations were set. As shown in Figure 3, under the same Chl-a concentration, cyanobacterial scums are more likely to appear in relatively static water than in disturbed water. When the Chl-a concentration reached 418 μg/L, cyanobacterial scums appeared on the water surface regardless of water disturbed or static, but it was more obvious on the static water surface. This suggests that the spectral differences between low and high Chl-a concentrations are more pronounced in static waters compared to disturbed waters. This finding also explains why the RMSE of the Chl-a retrieval model developed in this study is higher for static states than for disturbed states (Table 6).

In addition, the range of Chl-a concentrations in this study is wider than that reported in other studies [58], which leads to a higher RMSE metric. However, the retrieval model developed in this study can be applied to both water covered by cyanobacterial scums and water without scums, improving its universality.

6. Conclusions

This study investigated the spectral characteristics of cyanobacteria and their relationship to the Chl-a concentration using laboratory-based experiments and in situ measurements. Compared with existing studies on the spectral characteristics of Chl-a, the experiment was improved in the following three aspects: (1) Utilizing wild cyanobacteria: Recognizing the potential discrepancies between laboratory-cultured and wild cyanobacteria, this experiment utilized cyanobacteria directly collected from Taihu Lake, ensuring a more realistic representation. (2) Static vs. disturbed states: A comparative approach was employed, with two experimental groups exposed to static and disturbed states. This allowed for the differentiation of spectral characteristics based on the environmental state of the cyanobacteria. (3) Continuous concentration gradient: By continuously adding cyanobacterial solution to the water, the experiment generated spectral curves corresponding to a range of Chl-a concentrations. The identified spectral parameters and the model development approach provide a valuable basis for further research and optimization in real-world monitoring applications.

In the experiment, ten categories of spectral characteristics were selected, resulting in a total of twenty-eight spectral characteristic parameters. Correlation analysis revealed six parameters that had the strongest correlation with the Chl-a concentration, including the end reflectance of valley 680 (red edge), the baseline slope of valley 680, the depth of valley 680, the reflectance at peak 700, the baseline slope of peak 700, and the reflectance at peak 810. These six spectral characteristics parameters were selected to establish linear, exponential, and power prediction models for estimating Chl-a concentrations. The results showed that the model performance depended on both the spectral characteristic parameter and the water state (disturbed or static). In disturbed states, the power model performed best for the valley 680 end reflectance, while the linear model outperformed the others for the remaining five characteristic parameters. Similar to disturbed states, the linear model was generally superior for all parameters, except the valley 680 baseline slope, where the power model yielded the best results in static states. Notably, all of the exponential models exhibited the weakest performance across both disturbed and static states. Based on the analysis, the linear models for the peak 700 baseline slope and peak 810 reflectance emerged as the most effective for the Chl-a concentration prediction in both disturbed and static water states, with the other parameters showing less ideal performance.

While the well-designed experiments in this study enabled a focused analysis of spectral characteristics related to the Chl-a concentration in cyanobacteria, further research might be needed to refine the models for broader applicability. This could include incorporating data from a wider range of algal strains and environmental conditions. It should be noted that the experiment data in this paper are not strictly normally distributed. In future experiments, the selection of characteristic bands should probably use the Spearman coefficient instead of the Pearson coefficient. Simultaneously, this study only explores the application of single-band spectral characteristics in the estimation of the Chl-a concentration. Further research is needed to investigate the application of multi-band combination parameters. Additionally, in natural aquatic environments, Chl-a in water bodies is not only derived from cyanobacteria, but also from other aquatic plants and phytoplankton. Distinguishing the spectral characteristics of these organisms from those of cyanobacteria will also be a major challenge in the future research.