Cross-Water-Body Validation of Chlorophyll-a Retrieval Using Synergistic UAV Hyperspectral and Satellite Multispectral Data in Eutrophic Inland Waters

Abstract

Eutrophication driven by algal blooms underscores the need for reliable chlorophyll-a (Chl-a) monitoring. Multi-source remote sensing, integrating Sentinel-2 multispectral and UAV hyperspectral data, provides complementary information but its applicability across optically diverse inland waters remains limited. This study evaluates the cross-water-body transferability of Chl-a inversion models using a “single training area with three validation areas” experimental design. Multiple empirical and machine learning models were constructed, and several hyperparameter optimization strategies were tested. Among all modes, the Extreme Gradient Boosting (XGB) model optimized using the Genetic Algorithm (GA) achieved the best performance for UAV data (R² = 0.98, MAPE = 18.59%, RMSE = 2.15 μg/L). The Sentinel-2 counterpart also performed well (R² = 0.86, MAPE = 50.03%, RMSE = 7.89 μg/L). While cross-water-body validation caused moderate performance declines, all models maintained R² > 0.71. Overall, integrating multi-source remote sensing with cross-water-body validation enhances the robustness and transferability of Chl-a inversion models for eutrophic inland waters.

1. Introduction

The rapid development of human activities, such as industry and agriculture, has led to massive pollutant discharge into water bodies, causing continuous water quality deterioration [1]. Eutrophication refers to the process by which water bodies receive excessive inputs of nutrients, particularly nitrogen and phosphorus, leading to enhanced primary productivity and subsequent degradation of water quality. The trophic status of a water body describes its nutrient condition and biological productivity and is commonly classified as oligotrophic, mesotrophic, eutrophic, or hypereutrophic. Poor trophic status generally corresponds to eutrophic and hypereutrophic conditions, which are characterized by high nutrient availability, excessive phytoplankton growth, and degraded water quality. Under such conditions, nutrient enrichment stimulates rapid phytoplankton proliferation, disrupts ecological balance, reduces biodiversity, degrades water usability, and poses risks to drinking water safety, thereby threatening aquatic ecosystem health and human water security [2,3,4,5]. Phytoplankton growth represents the primary biological response of aquatic ecosystems to nutrient enrichment and plays a central role in determining trophic status and overall water quality. Chlorophyll-a, as the main photosynthetic pigment in phytoplankton, is widely used as a proxy for phytoplankton biomass and a key indicator of eutrophication [6]. Variations in Chl-a concentration reflect both the magnitude and spatial distribution of algal growth and provide essential information for assessing trophic conditions and water quality dynamics. Effective monitoring of Chl-a therefore supports timely evaluation of eutrophication processes and provides a scientific basis for water quality management and the prevention of further environmental degradation [7].

Remote sensing technology has become an essential tool for Chl-a inversion and dynamic water quality monitoring due to its wide spatial coverage, low cost, rapid data acquisition, and ability to capture large-area synchronous observations [8,9]. Over the past five decades, research has focused on developing inversion models for biological, chemical, and physical properties of optically complex waters [10,11]. These models establish correlations between remotely sensed spectral information and in situ water quality parameters to achieve conversion between the two [12]. The core principle involves acquiring water-surface spectral reflectance and converting it into parameter estimates using physical or statistical approaches. Different water quality parameters influence the absorption, scattering, and reflection of solar radiation, producing distinct spectral signatures in remote sensing imagery. For example, chlorophyll-a, as the primary photosynthetic pigment and a major optically active substance, strongly absorbs blue–green wavelengths while enhancing reflectance in the green and near-infrared regions. This optical behavior creates a measurable correlation between Chl-a concentration and water-surface spectral reflectance, enabling water quality assessment through spectral analysis.

The spectral properties of water bodies refer to their characteristics of absorbing, scattering, and transmitting solar radiation, which are primarily determined by the composition of substances in the water (e.g., Chl-a, Total Suspended Solids (TSS)) and the state of the water body (e.g., turbidity and water depth), Water depth influences the optical path length of light propagation in the water and thus affects the degree of absorption and scattering, which in turn alters the apparent spectral response of the water body [13,14]. As the foundation of remote sensing monitoring, these properties reflect comprehensive information about the water body itself and the sub-stances it contains. The study of spectral features aims to screen sensitive bands for water quality monitoring to obtain optimal spectral information [15]. The spectral characteristics of water bodies are mainly characterized by high reflectance in the blue-green band and strong absorption in the near-infrared and short-wave infrared bands. Chl-a exhibits strong absorption in the blue and red spectral regions, while its absorption is relatively weak in the green region, as a result, water bodies with higher Chl-a concentrations typically show higher apparent reflectance in the green band [16,17]. Based on this property, researchers have developed various spectral models to estimate Chl-a concentration. For instance, Yu [18] identified two linear models for Chl-a at the peaks of 700 nm and 810 nm, which are the optimal estimation models for static and disturbed states, respectively; Cao [19] developed an algorithm for estimating Chl-a in turbid lakes using machine learning models; and Song [20] established a relationship between Chl-a concentration and reflectance in the blue and red bands using a two-band model. These studies provide a scientific basis for large-scale inversion of Chl-a concentration using remote sensing data.

The complex optical properties of water bodies pose challenges to remote sensing observations of inland and coastal waters. In addition to the inherent optical properties of water bodies themselves, limitations in sensor performance also affect inversion accuracy. For example, multi-spectral broadband satellites of the Landsat series have spectral resolution, band centers, and signal-to-noise ratios that are insufficient to meet the requirements of complex water areas. Satellites such as MODIS, SeaWiFS, and MERIS offer higher spectral resolution and shorter revisit cycles but lack sufficient spatial resolution, making them unable to accurately retrieve Chl-a in narrow inland water bodies.

In addition to sensor characteristics and water optical complexity, atmospheric effects represent a critical source of uncertainty in remote sensing–based water quality inversion. Scattering and absorption by atmospheric constituents can mask or distort the true water-leaving radiance received by the sensor, particularly over water bodies where surface reflectance is inherently low. Inaccurate atmospheric correction may therefore distort spectral signals and lead to significant errors in Chl-a inversion. Consequently, the selection and implementation of appropriate atmospheric correction methods are essential for obtaining reliable surface reflectance and achieving optimal inversion performance, especially for inland and eutrophic waters [21,22].

Sentinel-2 satellite data, with rich spectral bands and high spatial resolution, has advantages in water quality monitoring of inland and coastal waters. UAV remote sensing, by contrast, is suitable for small-scale, high-precision water quality monitoring, as it can acquire higher-resolution spectral and image data, effectively avoid the problem of mixed pixels, and improve inversion accuracy. The application of high-resolution remote sensing satellites (e.g., Sentinel-2) and UAV provide high-quality data sources for refined water quality monitoring [23]. For instance, Li [24] developed a ground-based remote sensing system based on a Micro-hyperspectral sensor for high-frequency real-time water quality monitoring, and retrieved water quality parameters such as Chl-a, TP, and TN using empirical methods and machine learning models. Zhang [25] integrated meteorological observation parameters as auxiliary variables with Sentinel-2 satellite image data to construct a machine learning model for monitored low Chl-a concentrations in Hulun Lake. To fully leverage the advantages of different remote sensing data sources, improve the spatiotemporal resolution and accuracy of water quality monitoring, the fusion of multi-source remote sensing data has become an important direction in remote sensing research on water quality.

In addition to data sources, inversion model construction is also critical. From early empirical models to semi-analytical models, bio-optical models, and recently emerging machine learning models, theories and methods of remote sensing inversion for water quality have been continuously enriched and improved [26,27]. However, significant differences in applicability exist across different types of water bodies, water quality parameters, remote sensing data sources, and inversion models. The applicability of an inversion model is a key indicator for evaluating its comprehensive performance [28]. Many existing models are developed for specific sites or datasets, limiting their transferability across eutrophic inland waters. For example, Pan et al. [29] and Assaf et al. [30] developed and evaluated Sentinel-2 based machine learning approaches, providing a transferable framework for inland waters Chl-a inversion, but reliable transferability remains challenging.

To address these limitations, this study integrates Sentinel-2 and UAV data to develop multi-source Chl-a inversion models. Sensitive bands were selected, and model parameters optimized to construct an inversion framework with high cross-water-body transferability. The optimal model was validated across multiple lakes and reservoirs to evaluate its generalization ability. The proposed multi-source Chl-a inversion framework can quickly and accurately assess eutrophication status, overcome accuracy limitations of traditional methods, shorten response time for water quality monitoring, This study aims to improve the applicability of chlorophyll-a remote sensing inversion models by enhancing their cross-water-body transferability and generalization across different eutrophic inland waters using multi-source (Sentinel-2 and UAV) data.

2. Materials and Methods

2.1. Study Area Overview

Shanzai Reservoir (Figure 1) is located at the former site of Shanzai Village, Xiaocang She Ethnic Township, Lianjiang County, Fuzhou City, Fujian Province, with geographical coordinates ranging from 119°16′ E to 119°20′ E and from 26°20′ N to 26°24′ N. It is a valley-type reservoir formed by damming, covering a total area of 3.5 km².

The Lianjiang Shanzai Water Conservancy Project is the third-stage project in the cascade development plan for the main-stream of the Aojiang River, the 6th largest river in Fujian Province. The dam site is situated in a canyon 1 km upstream of Tangban Longchou Natural Village, Pandu Township, Lianjiang County, 50 km away from Fuzhou City and 47 km away from Lianjiang County Seat. The controlled drainage area above the dam site is 1646 km². Also known as She Ethnic Group Lake, Shanzai Reservoir has a total storage capacity of 172.3 million m³ and a regulating storage capacity of 106.4 million m³, classifying it as a seasonal regulating reservoir. It serves multiple functions, including water supply, flood control, power generation, and irrigation. With an average daily water supply of 0.8 million m³, it is the second water source for Fuzhou City, and its average annual power generation over the years reaches 176 million kW·h.

The validation areas include the following water bodies of different types: (1) Baiyang Reservoir (a river-channel reservoir), Located in Xiapu County, Ningde City, Fujian Province, it is a small-scale reservoir with a storage capacity of 0.51 million m³ and serves dual purposes: domestic water supply and irrigation. (2) Lingxi Reservoir (a lake-type reservoir), Lingxi Reservoir Situated in Quangang District, Quanzhou City, Fujian Province, it has a water storage capacity of 18.75 million m³. Its primary functions are flood control and irrigation, supplemented by power generation. (3) Qishan Lake (a park-type lake), Located in Minhou County, Fuzhou City, Fujian Province, the water area of the lake covers 0.78 million m³. It is an ecological lake that integrates water conservancy functions and landscape value.

2.2. Data Collection

2.2.1. Field Water Sample Data

Field water samples were collected from Shanzai Reservoir, Baiyang Reservoir, Lingxi Reservoir, and Qishan Lake between July 2024 and January 2025 (Figure 2). Among these samples, 88 were used for model simulation (Shanzai Reservoir), and 58 were used for model validation (

Table 1. Number of sampling points, field sampling time, and satellite image acquisition time in the sampling area.

Watershed	Field Sampling Time	Sentinel-2 Satellite Image Time	Sampling Point Count
Shanzai Reservoir	10 July 2024, 8:30–16:00	11 July 2024	28
	21 July 2024, 8:30–16:30	21 July 2024	30
	14 October 2024, 9:00–16:30	14 October 2024	30
Baiyang Reservoir	25 August 2024, 9:00–17:00	25 August 2024	36
Lingxi Reservoir	10 September 2024, 15:00–15:30	9 September 2024	4
Qishan Lake	12 January 2025, 10:00–11:30	12 January 2025	18

).

To meet the requirements of surface feature spectroscopy and UAV images for solar radiation, sampling was conducted under sunny weather conditions with gentle wind and few clouds. At each sampling site, an organic glass water sampler was used to collect samples at 0.5 m below the water surface. The samples were stored in black sampling bottles, and 1 mL of 1% magnesium carbonate suspension was immediately added to fix Chl-a, prevent acidification and dissolution of pigments. Subsequently, the samples were preserved at 0–4 °C in a refrigerator and analyzed within 24 h.

In this study, Chl-a concentration was determined using a 721G visible Spectrophotometer, following the National Standard Method Water Quality—Determination of Chlorophyll by Spectrophotometry (HJ 897-2017) [31].

2.2.2. Sentinel-2 Images

Sentinel-2 is a high-resolution optical satellite developed by the European Space Agency. In this study, Sentinel-2 Level-2A products were used, which provide bottom-of-atmosphere surface reflectance after atmospheric correction. All Sentinel-2 images were processed using the ESA SNAP software. Specifically, all spectral bands were resampled to a common spatial resolution of 10 m, after which band stacking was performed to generate multi-band composite images. The study area was then extracted using the Subset Data from ROIs tool, and only water pixels within the reservoir boundaries were retained for subsequent analysis to ensure reliable spectral information for Chl-a inversion.

To ensure temporal consistency between satellite observations and field measurements, in situ sampling was conducted within ±1 day of the Sentinel-2 overpass. Previous studies have shown that when the time difference is within ±2 days, Sentinel-2 imagery can effectively support Chl-a inversion [29]. In addition, based on the spectral response functions of Sentinel-2, UAV hyperspectral reflectance was spectrally resampled to generate Sentinel-2 equivalent reflectance. The pre-equivalent and post-equivalent reflectance of the three Sentinel-2 image sets for Shanzai Reservoir are shown in Figure 3.

2.2.3. UAV Images

The UAV platform used in this study was a DJI Matrice 350 RTK (DJI, Shenzhen, China). It was equipped with a hyperspectral imaging sensor covering a spectral range of 400–1000 nm, with a spectral resolution of 2.5 nm, a pixel size of 5.86 μm, and a full-band imaging speed of 128 Hz. Hyperspectral images were acquired using a push-broom imaging mode during UAV flights.

After data acquisition, the UAV hyperspectral images were preprocessed using FigSpec Studio software, including image cropping, mosaicking, and radiometric correction. Reflectance calibration was then performed to convert the raw digital numbers into surface reflectance. Based on the geographic coordinates of the selected sampling points, the corresponding spectral reflectance values were extracted from the calibrated UAV hyperspectral images. UAV flights were conducted synchronously with field water sample collection, and the processed hyperspectral data are shown in Figure 3.

2.3. Spectral Band Combination Models for Chlorophyll-a Inversion

The expression of the single band is shown in Equation (1) [32]:

$$C\propto R\left(\lambda \right),$$

(1)

The expression of the band difference is shown in Equation (2) [33]:

$$\mathit{C}\propto \mathit{R}\left({\mathit{\lambda }}_{\mathbf{1}}\right)-\mathit{R}\left({\mathit{\lambda }}_{\mathbf{2}}\right),$$

(2)

The expression of the band ratio combination is shown in Equation (3) [32]:

$$\mathit{C}\propto {\displaystyle \frac{\mathit{R}\left({\mathit{\lambda }}_{\mathbf{1}}\right)}{\mathit{R}\left({\mathit{\lambda }}_{\mathbf{2}}\right)}},$$

(3)

The expression of the three-band combination is shown in Equation (4) [34]:

$$\mathit{C}\propto \mathit{k}({\displaystyle \frac{\mathbf{1}}{\mathit{R}\left({\mathit{\lambda }}_{\mathbf{1}}\right)}}-\mathit{R}{\displaystyle \frac{\mathbf{1}}{\mathit{R}\left({\mathit{\lambda }}_{\mathbf{2}}\right)}})\times \mathit{R}({\mathit{\lambda }}_{\mathbf{3}}),$$

(4)

In these equations, C represents the concentration of water quality parameters, R(λ₁), R(λ₂) and R(λ₃) denote the reflectance of different bands.

Commonly used sensitive band combinations for UAV images include three-band combinations, normalized indices, band difference combinations, and band ratio combinations. The Normalized Chlorophyll Index is a new chlorophyll estimation index proposed by Mishra [35].

2.4. Chlorophyll-a Inversion Models

The empirical models used in this study include simple linear regression, simple quadratic regression, simple cubic regression, and the exponential function model. The machine learning models used include the Random Forest (RF), Back Propagation Neural Network (BPNN), Support Vector Regression (SVR), and XGB. The key parameters of the machine learning models are shown in

Table 2. 4 Machine Learning Models and Their Key Parameters.

Model Category	Key Parameter
RF	Number of decision trees (n_estimators)
	Maximum tree depth (max_depth)
	Minimum number of samples per leaf node (min_samples_leaf)
	Number of decision trees (n_estimators)
BPNN	Learning rate (learning_rate)
	Weight decay
SVR	Internal penalty parameter (C)
	Kernel coefficient (gamma)
XGB	Epsilon-insensitive loss coefficient (epsilon)
	Maximum tree depth (max_depth)
	Number of decision trees (n_estimators)

.

2.5. Model Hyper-Parameter Tuning

Parameter tuning aims to find the optimal parameter combinations of a model to improve its practical application performance. The parameters include those automatically learned during model training and manually set hyper-parameters. The parameter tuning methods adopted in this study are Bayesian Optimization (BO), GA, Particle Swarm Optimization (PSO) and Simulated Annealing (SA).

Evaluation Indicators for Parameter Tuning and Model Accuracy

(1)

Evaluation Indicators for Parameter Tuning

The Loss Function (LOSS) is a commonly used indicator for parameter tuning, which is used to measure the difference between the model’s predicted values and true values. The loss function mainly used in this study is Mean Squared Error (MSE). The calculation formula [36] is:

$$Loss={{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n(y_i-{\overline{y}}_i)}^2,$$

(5)

$y_i$ represents the true value, ${\overline{y}}_i$represents the predicted value.

(2)

Model Accuracy Evaluation Indicators

This study used the coefficient of determination (R²), root mean square error (RMSE)and mean absolute percentage error (MAPE) to evaluate the model. The calculation formula [37] is:

$$R^2=1-{\displaystyle \frac{SSR}{SST}},$$

(6)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_n^1{(y_i-\widehat{y_i})}^2},$$

(7)

$$MAPE={\displaystyle \frac{1}{m}}{\sum }_{t=1}^m\left|{\displaystyle \frac{A_t-F_t}{A_t}}\right|\times 100\%,$$

(8)

SSR represents the sum of squared residuals; SST represents the total sum of squares; n is the number of data point; $y_i$is the true value of the i-th observation; $\widehat{y_i}$is the predicted value of the i-th observation; $A_t$represents the actual value; represents the predicted value; m is the number of observations.

2.6. Overall Technical Framework and Workflow

As illustrated in Appendix A Figure A1, an integrated workflow was developed to evaluate the applicability of remote sensing inversion models for water quality indicators in eutrophic water bodies. This study utilized multi-source data, including UAV hyperspectral imagery, Sentinel-2 satellite imagery, and synchronous in situ water quality measurements. In the data acquisition and preprocessing stage, UAV and Sentinel-2 images were independently subjected to radiometric correction and surface reflectance retrieval, and water pixels were extracted to obtain reliable spectral reflectance information. Field-measured water quality indicators and spectral data were used as ground truth for model development and validation.

Based on the processed multi-source reflectance data, sensitive band and band-combination analyses were conducted to identify spectral features strongly correlated with water quality parameters. Subsequently, both empirical models and multiple machine-learning models were constructed. Model hyperparameters were optimized using BO optimization, GA, and PSO to improve model performance. For each water quality indicator, the optimal inversion model was selected and further applied to different types of water bodies, including river-type reservoirs, lake-type reservoirs, and park lakes. This cross-water-body validation enabled a systematic assessment of model transferability and generalization capability, ultimately identifying the overall optimal inversion model for eutrophic inland waters.

3. Results

3.1. Selection of Inversion Bands

Sensitive bands refer to the bands that are highly correlated with changes in water quality parameters and can significantly reflect their dynamic changes. The selection of these bands is crucial for constructing an accurate Chl-a inversion model [38,39]. To enhance inversion performance and develop higher-precision models, we identified the bands or band combinations most strongly correlated with Chl-a concentrations via Pearson correlation analysis.

3.1.1. Inversion Band Selection Based on Sentinel-2

Python 3.9 was used to perform Pearson correlation analysis between the 10 bands (B1–B9) of the Sentinel-2 satellite and Chl-a data from 88 sampling points. In Figure 4a, among all single bands, B3 exhibited the highest correlation with Chl-a (R² = 0.3925). Overall, the correlation trend between single bands and Chl-a concentration was consistent with the satellite reflectance pattern (a large wave peak for B3 and a small wave peak for B5), indicating that the reflectance at the reflection peaks had a higher correlation with Chl-a concentration. In Figure 4b, the correlation between band difference combinations and Chl-a concentration was significantly higher than that of single bands. The highest correlation coefficient increased by approximately 0.34 compared with single bands, among which the correlation coefficient of B3 − B1 was close to 0.74, and that of B3 − BA8 was the lowest at 0.69. In Figure 4c, the band ratio combinations exhibited high overall correlation with Chl-a concentration: the highest correlation coefficient of 0.808 was observed for −B1/B4, and the lowest was 0.79 for −B2/B4. In Figure 4d, the three-band combination showed a maximum correlation coefficient of 0.7956 with Chl-a.

In summary, the correlation coefficients of band difference combinations, band ratio combinations, and three-band combinations with Chl-a were all significantly higher than those of the single-band method.

3.1.2. Inversion Band Selection Based on UAV

As shown in Figure 5a, the three-band combination (1/R(493) − 1/R(485)) × R(614) exhibited the highest correlation with Chl-a, with a correlation coefficient of 0.82; the top 10 three-band combinations in terms of correlation all had coefficients greater than 0.80. In Figure 5b, the normalized index combination (R(690) − R(606))/(R(690) + R(606)) had the highest correlation with Chl-a, at 0.78. In Figure 5c, the band difference combination R(407) − R(422) showed the highest correlation with Chl-a, with a coefficient of 0.69. In Figure 5d, the band ratio combination R(690)/R(606) exhibited the highest correlation with Chl-a, at 0.78.

3.2. Construction of Sentinel-2 Multispectral Inversion Models

Empirical Models for the Sentinel-2 multispectral inversion selected the bands/band combinations with the highest correlation with Chl-a concentration as sensitive bands and constructed models using four regression methods.

The four empirical models with the highest Chl-a inversion accuracy are shown in

Table 3. Fitting Results of Four Empirical Models for Chl-a Inversion.

Bands/Band Combinations	Regression Models	Fitting Equations	R2	RMSE (μg/L)	MAPE
−B1/B4	Simple Linear Regression	y = 55.2419x + 81.2462	0.65	12.37	84.28%
B3 + B1 × B9 + B3/B1	Simple Quadratic Regression	y = −2.8060x2 + 30.4717x − 29.0882	0.68	11.79	126.05%
	Simple Cubic Regression	y = 2.1027x3 − 24.2089x2 + 96.4744x − 88.7017	0.71	11.34	115.28%
	Exponential Function	y = 11.9905e0.3077x	0.63	12.76	137.40%

. The simple linear regression model achieved the highest accuracy when using the band ratio (−B1/B4) as the sensitive band; The other three models reached the highest accuracy when using the three-band combination (B3 + B1 × B9 + B3/B1) as the sensitive band. All four empirical models exhibited relatively high inversion accuracy, with R² values greater than 0.6. Among them, the simple cubic regression model achieved the best performance, with an R² of 0.71.

RF selected the bands/band combinations with the highest correlation with Chl-a concentration as sensitive bands. Parameter tuning for this RF model was conducted using two methods: BO and PSO. The optimized parameters for both BO and PSO included n_estimators, max_depth, and min_samples_leaf, with their respective search spaces set as 50–200, 10–30, and 1–5.

The fitting results of BO-RF and PSO-RF are shown in

Table 4. Fitting Results of BO-RF and PSO-RF Models on Sentinel-2 Satellite Multispectral Data.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-RF	B3	0.44	179.96	15.59
	B3 − B1	0.68	111.51	11.94
	−B1/B4	0.72	85.71	11.22
	B3 + B1 × B9 + B3/B1	0.76	91.03	10.34
PSO-RF	B3	0.62	142.27	13.19
	B3 − B1	0.69	110.14	11.65
	−B1/B4	0.79	76.53	9.73
	B3 + B1 × B9 + B3/B1	0.77	89.31	10.14

. In BO-RF: Single bands exhibited the weakest predictive ability for Chl-a and the largest error (R² = 0.44); multi-band combinations were significantly superior to single bands, with R² values of 0.68 (band difference combinations), 0.72 (band ratio combinations), and 0.76 (three-band combinations), respectively. In PSO-RF: The fitting performance of single bands was significantly improved compared to that in BO-RF (R² = 0.62); additionally, the performance of band difference combinations, band ratio combinations, and three-band combinations in PSO-RF was also better than that in BO-RF. For BO-RF, the highest accuracy was achieved when using three-band combinations as sensitive bands (R² = 0.76). For PSO-RF, the highest accuracy was obtained with band ratio combinations as sensitive bands (R² = 0.79). Overall, the fitting results of PSO-RF were better than those of BO-RF.

Parameter tuning for this BPNN was performed using two methods: BO and GA. The optimization ranges for the parameters of both BO and GA were set as follows: learning_rate: (10⁻⁵, 10⁻¹), weight_decay: (10⁻⁸, 10⁻³).

The fitting results of BO-BPNN and GA-BPNN are shown in

Table 5. Fitting Results of BO-BPNN and GA-BPNN Models on Sentinel-2 Satellite Multispectral Data.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-BPNN	B3	0.42	194.02	16.05
	B3 − B1	0.62	113.30	12.86
	−B1/B4	0.70	94.34	11.57
	B3 + B1 × B9 + B3/B1	0.73	113.29	10.92
GA-BPNN	B3	0.39	199.70	16.42
	B3 − B1	0.62	119.72	12.92
	−B1/B4	0.68	86.09	11.83
	B3 + B1 × B9 + B3/B1	0.86	81.05	11.31

. In BO-BPNN: Single bands exhibited the weakest predictive ability for Chl-a and the largest error (R² = 0.42); band difference combinations, band ratio combinations, and three-band combinations were significantly superior to single bands (all R² > 0.60), among which three-band combinations achieved the best performance (R² = 0.73). In GA-BPNN: Single bands also showed the weakest ability to predict Chl-a concentration (R² = 0.39); similarly, band difference combinations, band ratio combinations, and three-band combinations were significantly better than single bands (all R² > 0.60), with three-band combinations being the optimal (R² = 0.86).

Both BO-BPNN and GA-BPNN achieved the highest accuracy when using three-band combinations as sensitive bands. Compared with single bands, multi-band combinations significantly improved the predictive ability of the models.

Parameter tuning for this SVR was conducted using two methods: BO and SAPSO. The optimization ranges for the SVR parameters (applicable to both tuning methods) were set as follows: C: (0.01, 1000); gamma: (0.0001, 1); epsilon: (0.01, 1).

The fitting results of BO-SVR and SAPSO-SVR are shown in

Table 6. Fitting Results of BO-SVR and GA-SVR Models on Sentinel-2 Satellite Multispectral Data.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-SVR	B3	0.15	406.06	20.79
	B3 − B1	0.54	395.31	20.22
	−B1/B4	0.65	73.08	12.74
	B3 + B1 × B9 + B3/B1	0.69	87.01	11.91
GA-SVR	B3	0.37	161.86	16.56
	B3 − B1	0.62	99.86	12.93
	−B1/B4	0.70	85.81	11.58
	B3 + B1 × B9 + B3/B1	0.74	128.61	11.01

. In BO-SVR: Single bands exhibited the weakest ability to predict Chl-a concentration and the largest error (R² = 0.15); band difference combinations, band ratio combinations, and three-band combinations were significantly superior to single bands, with R² values of 0.54, 0.65, and 0.69, respectively. In SAPSO-SVR: Single bands also showed the weakest predictive ability for Chl-a concentration and the largest error (R² = 0.37); similarly, band difference combinations, band ratio combinations, and three-band combinations outperformed single bands significantly, with R² values of 0.62, 0.70, and 0.74, respectively. Except for single bands, the other three types of band combinations achieved relatively high fitting accuracy (all R² > 0.60). Both BO-SVR and SAPSO-SVR reached the highest accuracy when using three-band combinations as sensitive bands, with R² values of 0.69 and 0.74, respectively.

In general, the information from single bands is insufficient for accurate Chl-a prediction, while multi-band combinations can significantly improve the model’s predictive ability. Although the model errors are relatively large, except for single bands, the R² values of all other combinations are >0.50, indicating that the accuracy of Chl-a inversion using the SVR model is relatively high.

Parameter tuning for this XGB model was performed using two methods: BO and GA. The parameter optimization ranges were set separately as follows: For BO optimization: n_estimators: (20, 2000); max_depth: (1, 18); For GA optimization: n_estimators: (20, 500); max_depth: (1, 6).

The fitting results of BO-XGB and GA-XGB are shown in

Table 7. Fitting Results of BO-XGB and GA-XGB Models on Sentinel-2 Satellite Multispectral Data.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-XGB	B3	0.43	82.51	10.28
	B3 − B1	0.74	218.23	15.76
	−B1/B4	0.74	107.41	10.78
	B3 + B1 × B9 + B3/B1	0.65	103.51	10.18
GA-XGB	B3	0.64	144.79	12.90
	B3 − B1	0.86	50.03	7.89
	−B1/B4	0.84	56.45	8.36
	B3 + B1 × B9 + B3/B1	0.84	58.57	8.50

. In BO-XGB: Single bands exhibited the weakest ability to predict Chl-a concentration and the largest error (R² = 0.43); band difference combinations, band ratio combinations, and three-band combinations were significantly superior to single bands, with R² values of 0.74, 0.74, and 0.65, respectively. This indicates that the information from single bands is insufficient for accurate Chl-a prediction, while multi-band combinations can significantly improve the model’s predictive ability. In GA-XGB: Single bands also showed the weakest predictive ability for Chl-a concentration and the largest error (R² = 0.64); similarly, band difference combinations, band ratio combinations, and three-band combinations outperformed single bands significantly, with R² values of 0.86, 0.84, and 0.84, respectively.

Overall, the fitting results of the XGB models achieved relatively high accuracy. BO-XGB reached the highest accuracy when using band ratio combinations as sensitive bands (R² = 0.74), while GA-XGB achieved the highest accuracy with band difference combinations as sensitive bands (R² = 0.86).

3.3. Construction of UAV Hyperspectral Inversion Models

Empirical Models for the UAV hyperspectral Chl-a inversion selected the bands/band combinations with the highest correlation with Chl-a concentration as sensitive bands, constructed models using four regression methods. The four empirical models with the highest Chl-a inversion accuracy are shown in

Table 8. Fitting Results of Four Empirical Models for UAV Hyper-spectral Chl-a Inversion.

Bands/Band Combinations	Regression Models	Fitting Equations	R2	MAPE (%)	RMSE (μg/L)
(1/R(493) − 1/R(485)) × R(614)	Simple Linear Regression	y = 336.1873x + 41.3210	0.70	209.53%	11.78
	Simple Quadratic Regression	y = 1888.2116x2 + 503.0524x+ 40.3037	0.71	172.72%	11.39
	Simple Cubic Regression	y = −27,465.6926x3 − 2518.9323x2 + 410.8610x+ 43.1167	0.74	152.32%	10.78
	Exponential Function	y = 39.3885e12.6736x	0.69	191.09%	11.79

. The simple cubic regression model achieved the best performance (R² = 0.74). Although the R² values of the four empirical models are relatively high, their errors are also relatively large.

BO and PSO were adopted to optimize the model parameters of this RF. For this RF using three-band combinations as sensitive bands: The optimal parameters obtained via BO optimization were n_estimators = 50, max_depth = 10, min_samples_leaf = 2; The optimal parameters obtained via PSO optimization were n_estimators = 81, max_depth = 5, min_samples_leaf = 1.

The fitting results of BO-RF and PSO-RF are presented in

Table 9. Fitting Results of BO-RF and PSO-RF Models on UAV Hyperspectral Data.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-RF	(1/R(493) − 1/R(485)) × R(614)	0.91	132.66	6.25
	R(690) − R(606) × R(690) + R(606)	0.83	69.05	8.80
	R(407) − R(422)	0.84	68.26	8.42
	R(690)/R(606)	0.82	69.68	8.87
PSO-RF	(1/R(493) − 1/R(485)) × R(614)	0.96	82.51	4.37
	R(690) − R(606) × R(690) + R(606)	0.94	37.46	4.99
	R(407) − R(422)	0.80	82.12	9.46
	R(690)/R(606)	0.94	43.16	5.34

. For BO-RF: Band ratio combinations exhibited relatively the weakest ability to predict Chl-a concentration and the largest error (R² = 0.82); For PSO-RF: Band difference combinations showed relatively the weakest predictive ability for Chl-a concentration and the largest error (R² = 0.80); Three-band combinations, normalized indices, and band ratio combinations outperformed band difference combinations, with R² values of 0.96, 0.94, and 0.94, respectively. Both BO-RF and PSO-RF achieved the highest accuracy when three-band combinations were used as sensitive bands, with R² values reaching 0.91 and 0.96, respectively. Overall, the fitting results of the two models were of relatively high accuracy, with all R² values exceeding 0.80.

BO and GA were employed to optimize the parameters of this BPNN. Specifically, for the BPNN model using three-band combinations as sensitive bands: The optimal parameters obtained via BO optimization were learning_rate = −1.0, weight_decay = −8.0; The optimal parameters obtained via GA optimization were learning_rate = 0.0240, weight_decay = 2.4702.

The fitting results of BO-BPNN and GA-BPNN are presented in

Table 10. Fitting Results of BO-BPNN and GA-BPNN Models on UAV Hyperspectral Data.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-BPNN	(1/R(493) − 1/R(485)) × R(614)	0.91	132.66	6.25
	R(690) − R(606) × R(690) + R(606)	0.83	69.05	8.80
	R(407) − R(422)	0.84	68.26	8.42
	R(690)/R(606)	0.82	69.68	8.87
GA-BPNN	(1/R(493) − 1/R(485)) × R(614)	0.96	82.51	4.37
	R(690) − R(606) × R(690) + R(606)	0.94	37.46	4.99
	R(407) − R(422)	0.80	82.12	9.46
	R(690)/R(606)	0.94	43.16	5.34

. For BO-BPNN: Band difference combinations exhibited the weakest ability to predict Chl-a concentration and the largest error (R² = 0.58); three-band combinations, normalized indices, and band ratio combinations were significantly superior to band difference combinations, with R² values of 0.78, 0.60, and 0.70, respectively. For GA-BPNN: Band difference combinations also showed the weakest predictive ability for Chl-a concentration and the largest error (R² = 0.52); three-band combinations, normalized indices, and band ratio combinations were significantly better than band difference combinations, with R² values of 0.75, 0.68, and 0.67, respectively. The fitting results of normalized indices and band ratio combinations were relatively close.

Overall, the fitting accuracy of the two models was relatively high, with all R² values exceeding 0.50. Both BO-BPNN and GA-BPNN achieved the highest accuracy when three-band combinations were used as sensitive bands, with R² values of 0.78 and 0.75, respectively.

BO and SAPSO were employed to optimize the parameters of this SVR. Specifically, for the SVR model using three-band combinations as sensitive bands: The optimal parameters obtained via BO optimization were C = 101,743.0170, gamma = 10, and epsilon = 2.1315; The optimal parameters obtained via SAPSO optimization were C = 877.5624, gamma = 0.0458, and epsilon = 0.5905.

The fitting results of the BO-SVR and SAPSO-SVR are presented in

Table 11. Fitting Results of BO-SVR and SAPSO-SVR Models.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-SVR	(1/R(493) − 1/R(485)) × R(614)	0.75	108.66	10.83
	R(690) − R(606) × R(690) + R(606)	0.61	103.17	13.13
	R(407) − R(422)	0.56	148.62	14.95
	R(690)/R(606)	0.61	106.68	13.48
SAPSO-SVR	(1/R(493) − 1/R(485)) × R(614)	0.74	150.37	10.75
	R(690) − R(606) × R(690) + R(606)	0.61	96.60	13.88
	R(407) − R(422)	0.61	99.03	13.15
	R(690)/R(606)	0.61	97.51	13.09

. For BO-SVR: Band difference combinations exhibited the weakest ability to predict Chl-a concentration and the largest error (R² = 0.56); three-band combinations were significantly superior to band difference combinations (R² = 0.75). For SAPSO-SVR: Normalized indices, band difference combinations, and band ratio combinations showed relatively weak predictive ability for Chl-a concentration with larger errors, all having an R² of 0.61; three-band combinations were significantly superior to other combinations (R² = 0.74).

Overall, except for the BO-SVR model using band difference combinations as sensitive bands (which showed relatively low fitting performance), the overall fitting effect of the models was good. Both BO-SVR and SAPSO-SVR achieved the highest accuracy when three-band combinations were used as sensitive bands, with R² values of 0.75 and 0.74, respectively.

BO and GA were employed to optimize the parameters of this XGB. Specifically, for the XGB model using normalized indices as sensitive bands: The optimal parameters obtained via BO optimization were n_estimators = 1226 and max_depth = 11; The optimal parameters obtained via GA optimization were n_estimators = 107 and max_depth = 3.

The fitting results of BO-XGB and GA-XGB are presented in

Table 12. Fitting Results of BO-XGB and GA-XGB.

Inversion Models	Bands	R2	MAPE (%)	RMSE (μg/L)
BO-XGB	(1/R(493) − 1/R(485)) × R(614)	0.95	21.94	4.63
	R(690) − R(606) × R(690) + R(606)	0.96	8.79	4.18
	R(407) − R(422)	0.92	15.09	6.01
	R(690)/R(606)	0.96	15.67	4.17
GA-XGB	(1/R(493) − 1/R(485)) × R(614)	0.97	48.81	3.84
	R(690) − R(606) × R(690) + R(606)	0.98	18.59	2.15
	R(407) − R(422)	0.90	47.92	6.82
	R(690)/R(606)	0.98	19.70	2.17

. For BO-XGB: Band difference combinations exhibited relatively weaker predictive ability for Chl-a concentration with slightly larger errors (R² = 0.92); three-band combinations, normalized indices, and band ratio combinations were slightly superior to band difference combinations, with R² values of 0.95, 0.96, and 0.96, respectively. For GA-XGB: Band ratio combinations showed the weakest predictive ability for Chl-a concentration and the largest error (R² = 0.90); three-band combinations, normalized indices, and band difference combinations were slightly better than band ratio combinations, with R² values of 0.97, 0.98, and 0.98, respectively.

Overall, the fitting accuracy of the models was relatively high, with all R² values exceeding 0.90; however, this high training accuracy may be attributed to model overfitting. Both BO-XGB and GA-XGB achieved the highest accuracy when normalized indices were used as sensitive bands, with R² values of 0.96 and 0.98, respectively.

Optimal Chl-a Inversion Models for Different Data Sources as indicated in

Table 13. Optimal Chl-a Inversion Models for Different Data Sources.

Data Source	Sensitive Bands	Optimization Parameter	Model	R2	MAPE (%)	RMSE (μg/L)
Sentinel-2	Band difference	GA	XGB	0.86	50.03	7.89
UAV	Normalized Indices	GA	XGB	0.98	18.59	2.15

, under the Sentinel-2 satellite data source, the GA-optimized XGB (using three-band combinations as sensitive bands) achieved the optimal Chl-a inversion performance (R² = 0.86, MAPE = 50.03%, RMSE = 7.89 μg/L). Under the UAV data source, the GA-optimized XGB (using normalized indices as sensitive bands) exhibited the best inversion effect (R² = 0.98, MAPE = 18.59%, RMSE = 2.15 μg/L).

3.4. Applicability Validation of Optimal Chl-A Inversion Model

3.4.1. Applicability Validation of the Optimal Sentinel-2 Inversion Model

The Band difference-based GA-XGB model (which achieved the highest accuracy) was applied to Baiyang Reservoir, Lingxi Reservoir, and Qishan Lake to verify its applicability. As indicated in

Table 14. Applicability Validation Results of the Optimal Sentinel-2 and UAV Chl-a Inversion Models.

Data Source	Reservoir	R2	MAPE (%)	RMSE (μg/L)
Sentinel-2	Baiyang Reservoir	0.85	15.12	4.49
	Lingxi Reservoir	0.71	12.13	1.64
	Qishan Lake	0.89	256.17	7.11
UAV	Baiyang Reservoir	0.90	13.87	2.65
	Lingxi Reservoir	0.87	8.50	1.37
	Qishan Lake	0.91	75.17	6.10

, the accuracy of the optimal Chl-a inversion model for each water body is as follows: Baiyang Reservoir: R² = 0.85, MAPE = 15.12%, RMSE = 4.49 μg/L; Lingxi Reservoir: R² = 0.71, MAPE = 12.13%, RMSE = 1.64 μg/L; Qishan Lake: R² = 0.89, MAPE = 256.17%, RMSE = 7.11 μg/L. The verified model exhibited relatively high accuracy, indicating that this model has strong applicability. The inversion-predicted values and in situ measured values of Chl-a concentrations derived from Sentinel-2 multispectral data for each reservoir in the validation areas are provided in Figure A2.

3.4.2. Applicability Validation of the Optimal UAV Hyperspectral Inversion Model

The Normalized Indices-based GA-XGB model (which achieved the highest accuracy) was applied to Baiyang Reservoir, Lingxi Reservoir, and Qishan Lake to verify its applicability. As indicated in Table 14, the accuracy of the optimal Chl-a inversion model for each water body is as follows: Baiyang Reservoir: R² = 0.90, MAPE = 13.87%, RMSE = 2.65 μg/L; Lingxi Reservoir: R² = 0.87, MAPE = 8.50%, RMSE = 1.37 μg/L; Qishan Lake: R² = 0.91, MAPE = 75.17%, RMSE = 6.10 μg/L. All three models had R² values greater than 0.50, and the verified models exhibited relatively high accuracy, indicating that the models have strong applicability. The inversion-predicted values and in situ measured values of Chl-a concentrations derived from UAV hyperspectral data for each reservoir in the validation areas are provided in Figure A3.

4. Discussion

Model applicability, quantified by R², RMSE, and MAPE, is crucial for evaluating the performance of Chl-a inversion. In this study, models were validated for inland waters with chlorophyll-a concentrations ranging from approximately 0.273 to slightly over 70 μg/L, which is typical of the eutrophic conditions in the study area. The model’s performance outside of this range may require further investigation. We employed machine learning combined with BO, GA, and PSO hyperparameter optimization to minimize the deviation between predicted and in situ Chl-a values for eutrophic inland waters. Among all models, GA-XGB achieved the best balance between inversion accuracy and generalization capability, consistent with findings reported by Wang and Tian [40,41].

Moreover, the RMSE in our study was higher than that reported by Assaf et al. [30], who found an RMSE of 8.85 μg/L for their Random Forest model and 22.33 μg/L for the XGB model based on Sentinel-2 imagery. However, their RF model achieved a higher R² value of 0.93, which reflects a strong correlation between predicted and observed chlorophyll-a values. In comparison, our GA-XGB model, with a RMSE of 7.89 μg/L and an R² of 0.86, demonstrates slightly lower RMSE but with a more balanced generalization capability across different water bodies. Despite the differences in RMSE, our model still performs well in terms of accuracy, particularly in heterogeneous inland waters where spatial resolution and model calibration play significant roles.

Cross-validation across three distinct eutrophic water bodies showed a slight decrease in R² but notable reductions in RMSE and MAPE, indicating that the trained models maintained strong generalization across systems with different hydrological and optical characteristics. UAV-based GA-XGB further outperformed the Sentinel-2 counterpart, which can be attributed to UAVs’ higher spatial resolution and broad spectral range (400–1000 nm) compared with the limited band set (B1–B9) of Sentinel-2 used in this study. High-resolution UAV observations help reduce scale-related uncertainty in heterogeneous small water bodies [42]. However, converting hyperspectral DN values to physical reflectance requires calibration using diffuse reflection panels [43,44], and factors such as flight altitude and acquisition time may introduce additional uncertainties. UAV coverage constraints also limit long-term time-series monitoring [45], whereas Sentinel-2 enables regional-scale and continuous observations. Integrating both sources enables an air–space–ground workflow that addresses the accuracy–coverage trade-off in inland water monitoring.

A limitation of this study is the lack of analysis on how Chl-a interacts with other water-quality indicators such as total nitrogen, total phosphorus (TP), or chemical oxygen demand. As TP is often a dominant driver of Chl-a variation [46], incorporating multi-parameter datasets could help reveal synergistic or antagonistic effects and improve model stability. Future work should expand validation to diverse water types—including shallow lakes, rivers, and different climatic zones—to further enhance the universality and applicability of the inversion model for eutrophication assessment and bloom early-warning applications.

5. Conclusions

This study developed and calibrated Chl-a inversion models for eutrophic inland waters using Shanzai Reservoir as the training area and three additional eutrophic water bodies for validation. By analyzing sensitive bands and band combinations from both Sentinel-2 multi-spectral and UAV hyperspectral imagery data, empirical models and machine learning-based models were constructed with hyperparameter optimization tailored to improve inversion accuracy. The key conclusions are summarized as follows:

(1) Sensitive Band Analysis: The strongest correlation with Chl-a for Sentinel-2 was observed in the band ratio (−B1/B4), while UAV hyperspectral data showed the highest correlation with a specific three-band combination (1/R(493) − 1/R(485)) × R(614).

(2) Cross-Water Body Applicability of Inversion Models: The machine learning models, particularly GA-XGB, maintained strong generalization capability across different eutrophic water bodies, demonstrating their potential for large-scale, cross-site application.

These findings suggest that multi-source remote sensing combined with advanced machine learning techniques can offer robust solutions for Chl-a monitoring in eutrophic inland waters, ensuring accurate and transferable results for water quality management.