Automated spectral transfer learning strategy for semi-supervised regression on Chlorophyll-a retrievals with Sentinel-2 imagery

ABSTRACT

Multispectral images make it possible to retrieve water quality parameters over a wide range and long time series by remote sensing. The robustness of traditional supervised machine learning models, which have been widely used, is affected in various regions, and these models are developed by in-situ measurements and limited satellite images. This study combined a spectral transfer learning strategy with a semi-supervised regression model to conduct data augmentation and developed a robust model for two inland lakes in Jilin Province, Northeast China, based on Sentinel-2 Multispectral Instruments images. Specifically, this study integrated an automated module for Balance Distribution Adaptation and a spectral features transfer method, and then applied it to Co-training Regressors for Chlorophyll-a retrievals to achieve the highest accuracy, which solved the selection of parameters and models. The Automated model was developed and achieved the best performance (R² is 0.91, the root mean square error is 2.62 μg L⁻¹ and the mean absolute percentage error is 22.88%) compared with other models, and showed robustness in various lakes and months. Our results offer a reliable approach to provide an accurate Chlorophyll-a estimation of spatial–temporal variations.

KEYWORDS:

• Chlorophyll-a
• transfer learning
• semi-supervised regression
• machine learning
• Sentinel-2

1. Introduction

Lakes, one of the most important parts of the global hydrologic cycle, provide a favorable safeguard for human life and ecosystem integrity (Chen et al. 2021b). Different types of lakes are gradually beginning to experience eutrophication in water bodies due to their geographical location, human activities, natural winds, and waves, which has always been a prominent issue in lake management (Qin et al. 2023). Chlorophyll-a (Chl-a) is beneficial for describing phytoplankton biomass and affects many links during eutrophication (Brooks et al. 2016). Comprehensive and regular tracking of its spatial distribution characteristics and dynamic changes is of great significance for promoting the rational development of the water cycle (Yun-feng 2009; Chen et al. 2022).

The development of remote sensing technology has greatly simplified traditional Chl-a measurements using manual methods (Mamun, Ferdous, and An 2021). Simultaneously, remote sensing methods can address the limitations of monitoring temporal patterns and spatial changes (Hu, Feng, and Guan 2020). Moderate resolution imaging spectrometry (MODIS) has the advantage of long-term dynamic monitoring owing to its 1-day high time resolution (Gregg and Casey 2007). However, estimating Chl-a concentrations in lakes using terrestrial bands is challenging, mainly because of its limited spatial resolution of 250–1000 m and low sensitivity (Li et al. 2019). Sentinel-3 OLCI, with a spatial resolution of 300 m, also makes it difficult to achieve more precise monitoring of most inland lakes (Bramich, Bolch, and Fisher 2021). The Land Satellite Thematic Surveyor (TM) and Operational Land Imager (OLI) have been proven to provide parameter measurements over inland lakes (Franz et al. 2015; Vanhellemont and Ruddick 2015). However, considering the limited spectral bands and long revisit period, it is difficult to accurately retrieve Chl-a (Cao et al. 2020). The Sentinel-2 Multispectral Imager (MSI) captures bands with local spatial resolutions of 10, 20, and 60 m. In addition, the five-day revisit time of Sentinel-2 has better time coverage (Toming et al. 2016). The presence of the ‘red edge’ band centered at a wavelength of 705 nm can capture subtle Chl-a information (Beck et al. 2016). Thus, MSI is suitable for Chl-a retrievals in inland lakes.

Most existing algorithms for Chl-a retrievals have been developed using remote sensing data based on in-situ measured samples (Xu et al. 2021). Empirical algorithms, including the Band Ratio algorithm (Duan, Ma, and Hu 2012), the Three Bands algorithm (Gitelson et al. 2011), and the Enhanced Three index (Yang et al. 2010) have been widely used to estimate Chl-a concentrations. Machine Learning (ML) algorithms have also been applied as a branch of artificial intelligence. Several approaches, such as Support Vector Regression (SVR) (Li et al. 2021a), Random Forest (RF) (Hang et al. 2022), Mixing Density Network (MDN) (Cao et al. 2022), Convolutional Neural Networks (CNN) (Aptoula and Ariman 2021) and Genetic Algorithm-Artificial Neural Networks (GA-ANN) (Chen et al. 2021a) have achieved high model performance over a range of study areas. Based on CNN, WaterNet effectively retrieves Chl-a concentrations using spectral and spatial information from remote sensing images (Syariz et al. 2020). Multitask convolution neural network (MCNN) captures the seasonal sensitivity of Chl-a concentrations and develops a high-precision model that is insensitive to seasons (Van Nguyen et al. 2021). However, data from different environmental conditions always have an impact on ML models due to the characteristic of data learning. Therefore, when applied to different study areas, they have the same problem as empirical models, which is the phenomenon of reduced accuracy. With the rigorous validated algorithms, a standard procedure can be applied to verify the stability of ML models (Ruszczak, Wijata, and Nalepa 2022). In addition, most models are based on in-situ measurements (Liu, Xu, and Beck 2018). However, satellites often fly across lakes more than once, and data from satellites passing through the area without in-situ measurements are not involved in modeling. Thus, the differences among areas and the lack of suitable remote sensing data make the retrievals of Chl-a a challenging task.

Compared with other supervised ML methods, semi-supervised regression is not commonly applied, particularly for Chl-a retrievals (Niroumand-Jadidi, Bovolo, and Bruzzone 2019). Using collaborative training (co-training), semi-supervised regression methods such as Co-training Regressors (CoReg), have shown good performance (Zhou and Li 2005). Combining in-situ measurements with unlabeled samples, four water quality parameters, including the potassium permanganate index (CODmn), ammonia nitrogen (NH3-N), chemical oxygen demand (COD), and dissolved oxygen (DO), were retrieved (Wang, Ma, and Wang 2010). When the number of in-situ measurements is limited, the introduction of unlabeled samples is required to improve the model performance for temporal extents (Kostopoulos et al. 2018). On the other hand, traditional ML algorithms assume that the data being trained and tested are from the same distribution. Therefore, these methods are more suitable for small datasets (Hosna et al. 2022). Transfer learning can solve the problem of domain constraints by considering the similarity of data between regions and expanding the regional model at a lower cost (Pan et al. 2010). The transfer component analysis method (TCA) provides a new method for transferring in-situ water quality samples to the study area (Zhou et al. 2021). Joint probability distribution adaptation (JDA) simultaneously adapts both the marginal distribution and conditional distribution and then boils down to one optimization objective, iterating with weak classifiers to achieve good results (Long et al. 2013). Based on the Balance Distribution Adaptation (BDA) method, adjusting the weights of the conditional and marginal distributions can enhance the practical performance of the model in the recent study (Gao et al. 2022). A novel transfer learning method consisting of model pre-training, main training, and fine-tuning stages for Artificial Neural Network was proposed to solve the problems of insufficient in-situ samples and model overfitting (Syariz et al. 2021). The spectral signal changes significantly with various measuring instruments, and effective calibration transfer can improve the stability of the model (Zhang et al. 2022b). Thus, the transfer learning method not only helps to highlight the guiding effect of the measured points on the target area but also improves the accuracy of the model. Until now, few studies have focused on the combination of transfer learning methods and semi-supervised regression models for retrieving Chl-a concentrations using remote sensing images.

Considering the data learning and application difficulty of traditional supervised ML models, this study combines Sentinel-2 images with in-situ measurements to develop the ABDA-CoReg (Automated module for BDA and CoReg) model for Chl-a retrievals with good performance. Specifically, the contributions included (1) applying a spectral transfer strategy on the spectral features between in-situ and Sentinel-2 through an automated BDA module, which aims to utilize the advantages of guidance from in-situ measurements and perform domain adaptation. (2) Introducing unlabeled Sentinel-2 images that are unmatched with the in-situ measurements to augment the samples and perform an adaptive spectral transfer method to develop the ABDA-CoReg model. To develop a Chl-a retrieval model with high accuracy, this paper proposes an automated optimization method that can select the model with the best performance. (3) The model performance was higher than that of the state-of-the-art ML models for Chl-a retrievals based on Lake Chagan and Lake Yueliang Reservoir, which are two inland lakes from Northeast China. The spatiotemporal changes were also analyzed and mapped through the developed ABDA-CoReg model. The remainder of this paper is organized as follows. Datasets are described in Section 2, the ABDA-CoReg model is developed in Section 3. Results and spatiotemporal patterns are analyzed in Section 4. Section 5 presents the discussion of the experimental results, followed by the conclusion in Section 6.

2. Study area and materials

2.1. Study area

Lake Chagan (45° 09'−45° 30'N, 124° 03'−124° 34'E) is one of the largest freshwater lakes in Northeast China (Zhu et al. 2012). It is located in the hinterland of the Northeast Songnen Plain, most of which is in the former Golros Mongolian Autonomous County, northwest of Jilin Province, as shown in Figure 1 (L1). Lake Chagan is the National Natural Reserve, and lake and water networks provide protection for many large fish breeding bases. As a typical case 2 water sample, its eutrophication is required to be monitored. Lake Yueliang Reservoir (45° 39'−45° 47'N, 124° 02'−124° 46'E) is one of the freshwater fishery bases in Jilin Province. It is located at the junction of Da'an and Zhenlai in northwest Jilin Province, as shown in Figure 1 (L2). It is a large plain reservoir that is mainly used for flood regulation, irrigation, and fish farming.

Figure 1. The overview of the study area and the distribution of field measurements. The left part shows the geographical location and the right part shows the two lakes. L1 refers to Lake Chagan, and L2 refers to Lake Yueliang Reservoir.

2.2. In-situ data collection

In this study, five periodic in-situ measurements were conducted in Lake Chagan, and a total of 96 samples were collected between 2020 and 2021 with temporal coverage from spring to autumn (May to September) (Shi et al. 2022). Seven periodic in-situ measurements in Lake Yueliang Reservoir were conducted with a total of 114 samples collected in 2022 from summer to autumn (July to September). The in-situ hyperspectral data were measured using the Airborne Water Remote Sensing System (AWRMMS). An irradiance sensor and two radiance sensors were used, which can measure wavelengths ranging from 320 to 940 nm with a spectral sampling interval of 1 nm. The water surface spectrometer was placed approximately 1 m over the hull, and each point was measured 15 times. Considering the extent and water quality of the area, 20 sample points were evenly selected to cover the main area of the lake (Figure 1). One radiance sensor pointing to the sky was 40° from the normal direction of the surface to measure the sky radiance (L_sky), one radiance sensor pointing to the water surface was 40° from its normal direction to measure the total water leaving radiance (L_sw), and one irradiance sensor was pointed vertically to the sky to measure the total downwelling irradiance ($E_d(0^{+})$). The remote sensing reflectance ($R_{\mathrm{rs}}$) was then obtained using Equation (1) (Ansper and Alikas 2018): (1) $R_{\mathrm{rs}}=(L_{\mathrm{sw}}-r\times L_{\mathrm{sky}})/E_d(0^{+})$(1) where r refers to the air–water interface reflectance (Figure 2).

Figure 2. In-situ measured reflectance (R_rs) monthly averaged of the two lakes during the field experiments, where in-situ measurements were taken on Lake Chagan from 2020 to 2021 and on Lake Yueliang Reservoir in 2022.

Chl-a concentrations were measured using an EXO multiparameter water-quality meter. The algae sensor in the EXO is a dual-channel fluorescence sensor that can generate two independent sets of data. One set came from the fluorescence produced by Chl-a molecules in photosynthetic cells under blue light irradiation, which had a linear range of 0–400 µg L⁻¹ Chl-a equivalent concentrations with a linear correlation coefficient of R² > 0.9. At the same time, data from EXO also reflect very low interference from turbidity and dissolved organic matter, allowing for more accurate in-situ measurements. Sensor data were collected from the samples and their concentrations were measured by extracting chromosomes. The sky was clear and the Sentinel-2 images overpassed the study area around 2:35 UTC time on average, which fell in the range of 10:00 and 14:30 Beijing time during in-situ sampling. Each sampling point took an interval longer than 3 min, was measured twice, and then averaged. As shown in Table 1, the measured Chl-a concentrations show different ranges, indicating the importance of reducing the difference in data distributions for Chl-a retrievals. Finally, a total of 210 samples with matched in-situ points were collected.

Table 1. Summary for field measurements and Sentinel-2 datasets.

Lake	Samples	Chl-a (μg L^−1) Meanrange	Matched Sentinel-2	Unmatched Sentinel-2
Chagan	96	21.72 11.24–33.71	96	100
Yueliang Reservoir	114	10.26 2.85–28.54	114	160
Total	210	15.51 2.85–33.71	210	260

2.3. Sentinel-2 satellite data

The parameters for Sentinel-2 are listed in Table 2. Because Sentinel-2A and Sentinel-2B have the same sensor onboard, the revisit period of five days has advantages for long-term observation with the collaboration of the two satellites. Bands on MSI consist of visible light, near infrared (VNIR), and short-wave infrared (SWIR) bands, which can achieve a high level of monitoring. As shown in Table 3, 35 Sentinel-2 images were downloaded. Based on the date intervals between the in-situ measurements and the Sentinel-2 images, the 17 Sentinel-2 images with a mean time difference of 1.75 days from the in-situ measurements were selected as labeled images and consequently assigned to the matching Chl-a concentrations, whereas the other 18 Sentinel-2 images in Table 3 were selected as unlabeled images and were not assigned to the Chl-a concentrations. According to previous studies (Kutser 2012; Li et al, 2021a; Toming et al. 2016), the mean time difference in the matching dataset of this study is 1.75 days, which is also the allowed time interval for the good correlation between in-situ samples and Sentinel-2 images. Images with less than 10% cloud were selected to meet the requirements for further processing (Corbane et al. 2020) and all bands in the images were resampled to a spatial resolution of 10 m.

Table 2. Sentinel-2 parameters used in this study.

Sentinel-2 Bands	Central Wavelength (nm)	Resolutions (m)
Band 1 – Coastal aerosol	443	60
Band 2 – Blue	490	10
Band 3 – Green	560	10
Band 4 – Red	665	10
Band 5 – Vegatation Red Edge	705	20
Band 6 – Vegatation Red Edge	740	20
Band 7 – Vegatation Red Edge	783	20
Band 8 – NIR	842	10
Band 8A – Narrow NIR	865	20

Table 3. Dates of Sentinel-2 images.

Lake	Year	Field Measurements	Sentinel-2 Labeled unlabeled
Chagan	2020	07/22	07/22	05/28
	2020	08/21	08/21	06/17
	2020	09/26	09/30	06/22
	2021	05/26	05/18	08/31
	2021	07/18	07/22	09/05
Yueliang Reservoir	2022	07/21	07/20	07/12
	2022	07/22	07/22	08/09
	2022	08/06	08/06	08/19
	2022	08/12	08/11	09/03
	2022	08/16	08/16	09/05
	2022	09/01	08/31	09/10
	2022	09/26	09/28	09/13
	2022	–	–	09/18

3. Method

As shown in Figure 3, the automatic module includes two sections: one is the module for classification of Chl-a concentrations, and the other is the evaluation of model performances in different classification results. Twelve in-situ measured spectral features and the matched twelve spectral features from Sentinel-2 images were first transferred through ABDA, which is the M-ABDA module. Unmatched Sentinel-2 images were introduced as the new target domain and were transferred with the new spectral features after M-ABDA, including the twelve in-situ measured spectral features and Sentinel-2 spectral features after the first transfer, which is the U-ABDA model. Finally, the transferred matched and unmatched spectral features were input into the CoReg model as labeled and unlabeled data for model development. Moreover, the temporal and regional robustness of the model was tested and applied to observe the temporal patterns and spatial distributions during 2020–2021 in Lake Chagan and 2022 in Lake Yueliang Reservoir.

Figure 3. Diagram showing the process of ABDA-CoReg model developing. M-ABDA is the spectral features transfer between in-situ and Sentinel-2 in the process of M-ABDA, while U-ABDA is the spectral transfer for unmatched Sentinel-2. The new spectral features of labeled images and unlabeled images after transfer were input to the models for development.

3.1. Balance distribution adaptation

BDA is a transfer learning method used for distribution adaptation between data in different domains to reduce distribution differences (Wang et al. 2017). In domain adaptation, the data of the source and target domains are usually in different distributions. BDA aims to solve classic problems of the characteristic transfer learning method in which TCA and JDA have problems in the marginal probability distribution and conditional probability distribution when adapting the distribution between data from different domains. Therefore, BDA introduces a dynamic equilibrium factor to adjust the adaptation of the above two probability distributions dynamically, thereby improving the effect of distribution adaptation between different domains. In this study, BDA was first used for the transfer of spectral features between in-situ and matched Sentinel-2. During the process, Chl-a concentrations were clustered to fit the BDA method, and Chl-a labels were provided. $D_{\mathrm{sh}\mathrm{\_lable}}=\{(x_{\mathrm{sh}1},l_1),(x_{\mathrm{sh}2},l_2),\dots ,(x_{\mathrm{shn}},l_n)\}$ is the source domain with Chl-a labels of in-situ measured spectral features, where n denotes the number of samples, $x_{\mathrm{sh}}$ denotes the source hyperspectral and $l$ denotes their label. The matched Sentinel-2 features $D_{\mathrm{tm}=}\{x_{\mathrm{tm}1},x_{\mathrm{tm}2},\dots x_{\mathrm{tmn}}\}$were set as the target domain, where n denotes the number of samples and $x_{\mathrm{tm}}$ denotes the target MSI spectral from Sentinel-2. The Maximum Mean Difference (MMD) (Pan et al. 2010) was used to measure the distance between the hyperspectral data and the matched Sentinel-2 target MSI data according to Equation (2): (2) $\mathrm{MM}{D}^2(X_{s\mathrm{h}},X_{\mathrm{tm}})={\left|\left|{\displaystyle \frac{1}{n_{\mathrm{sh}}}\sum _{i=1}^{n_{\mathrm{sh}}}\varphi (x_{s{h}_i})-{\displaystyle \frac{1}{n_{\mathrm{tm}}}\sum _{i=1}^{n_{\mathrm{tm}}}\varphi (x_{t{m}_i})}}\right|\right|}_H^2$(2) where H is the reproducing kernel Hilbert space, φ is the mapping that minimizes the distance, X_sh denotes the source hyperspectral data, and X_tm denotes the target MSI data.

The optimization goal of BDA is to obtain a transformation matrix A by learning labeled samples in the source domain and unlabeled samples in the target domain to minimize the distribution difference between the source and target domains after mapping the transformation according to Equation (3): (3) $\begin{array}{rl}& min(\mathrm{\mu Y}(D_{\mathrm{sh}\mathrm{\_lable}},D_{\mathrm{tm}})+(1-\mu )Y_{\mathrm{Conditional}}(D_{\mathrm{sh}\mathrm{\_lable}},D_{\mathrm{tm}}){)}_H+\lambda ||A|{|}_F^2\\ & s.t.A^T\mathrm{XH}{X}^{T}A=I\end{array}$(3) where $H$ and $I$ are central and identity matrices, respectively.$\mu$ is the balance factor, adjusting the adaptation of the marginal probability distribution and conditional probability distribution of the in-situ and Sentinel-2 spectral features. $Y(D_{\mathrm{sh}\mathrm{\_lable}},D_{\mathrm{tm}})$ denotes the marginal probability distribution distance and $Y_{\mathrm{Conditional}}(D_{\mathrm{sh}\mathrm{\_lable}},D_{\mathrm{tm}})$ denotes the conditional probability distribution distance between the in-situ and Sentinel-2 spectral features, which can be constructed in $M_0$ and $M_c$ according to Equations (4) and (5), respectively (Pan et al. 2010): (4) $\begin{array}{r}(\end{array}{M}_0{)}_{\mathrm{ij}}=\{\begin{array}{cc}{\displaystyle \frac{1}{n^2},}& x_i,x_j\in D_{\mathrm{sh}\mathrm{\_lable}}\\ {\displaystyle \frac{1}{m^2},}& x_i,x_j\in D_{\mathrm{tm}}\\ -{\displaystyle \frac{1}{\mathrm{mn}},}& \mathrm{otherwise}\end{array}$(4)

(5) $\begin{array}{r}(\end{array}{M}_c{)}_{\mathrm{ij}}=\{\begin{array}{cc}{\displaystyle \frac{1}{n_c^2},}& x_i,x_j\in D_{\mathrm{sh}\mathrm{\_label}}\\ {\displaystyle \frac{1}{m_c^2}}& x_i,x_j\in D_{\mathrm{tm}}\\ -{\displaystyle \frac{1}{m_c{n}_c}}& \{\begin{array}{cc}{x}_i\in D_{\mathrm{sh}\mathrm{\_label}},& x_j\in D_{\mathrm{tm}}\\ x_i\in D_{\mathrm{tm}},& x_j\in D_{\mathrm{sh}\mathrm{\_label}}\end{array}\\ 0& \mathrm{otherwise}\end{array}$(5) After the mapping matrix A transformation, MMD is used to measure the distance, where $\lambda ||A|{|}_F^2$ is the canonical regularization term of Frobenius, and $\lambda$ is the tradeoff parameter. X denotes the matrix composed of X_sh and X_tm. The dimensions of X_sh and X_tm are both 210 × 12 because of the 210 matched points and 12 spectral features.

For the transfer method of unmatched Sentinel-2 spectral features from unlabeled Sentinel-2 images, the dimensions of the new target domain X_tu are 260 × 12 because of the 260 unmatched points and 12 spectral features. The new source domain X'_s, whose dimensions are 420 × 12, is composed of in-situ measured hyperspectral features X'_sh (210 × 12) and Sentinel-2 labeled MSI features X'_tm (210 × 12) after M-ABDA. This is also in accordance with the concept of feature mapping for new features in the transfer-learning method. The unlabeled data are numerically close to the labeled data, and there are no matched in-situ Chl-a values. Therefore, transferring unlabeled data are expected to be guided by in-situ measured spectral features and labeled Sentinel-2 spectral features simultaneously. Thus, more intersection areas between the two domains can reduce the difference, which is conducive to the semi-supervised CoReg model for training.

3.2. Coreg algorithm

This study introduces unlabeled Sentinel-2 data to develop CoReg, one of the semi-supervised models to retrieve Chl-a concentrations. A co-training method is applied to the regression task. Co-training is a method that uses two basic learners to cooperate and assist each other’s training. For an unlabeled sample with a relatively high degree of confidence in a learner, co-training passes the sample and its pseudo-label to another learner. The algorithm flow chart for the Chl-a retrievals by the CoReg model combined with Sentinel-2 images in this study is shown in Table 4. Sentinel-2 features after ABDA with Chl-a concentrations were considered as labeled samples, and the unlabeled data were the Sentinel-2 spectral features, which had no corresponding Chl-a concentrations according to the revisit period of Sentinel-2.

Table 4. Flow chart of CoReg algorithm.

Algorithm: CoReg

Input: L denotes the labeled MSI spectral features after M-ABDA and U denotes the unlabeled MSI features after U-ABDA. Output: Chl-a concentrations. Two K-Nearest Neighbor (KNN) models k1 and k2 are firstly set as the base learners, different orders are taken to calculate the 2nd-order Minkowski distance to develop the two base learners. Samples from L are randomly selected to form two datasets L1 and L2, respectively and samples from U are randomly selected to form two datasets U1 and U2, respectively. k1 trained by L1 is used to perform pseudo label yu1 on U1, and k2 trained by L2 is used to perform pseudo label yu2 on U2 Samples with the highest confidence in k1 are added to the L2 and samples with the highest confidence in k2 are added to the training set L1. The evaluation of confidence on samples are evaluated through Equation (6). (6) ${\delta }_{{\mathrm{x}}_{\mathrm{u}}}=\sum _{x_i\in {\Omega }_u}({(y_u-K(x_u))}^2-{(y_u-K^{\mathrm{\prime }}(x_u))}^2)$(6) where xu refers to the unlabeled samples in U1 and U2, Ωu refers to the set of neighboring samples in L1 and L2, K denotes to the basic learner and K’ denotes the new learner including k1 and k2 after adding several xu and their predicted values yu to the training set, respectively. Note that in each iteration the unlabeled example chosen by k1 can’t be chosen by k2. Iteration repeats for T rounds and ends until the MSE of L1 and L2 neither changes, the output regressor is the average of k1 and k2. Thus, the process of co-training and estimating Chl-a concentrations is completed.

3.3. ABDA-CoReg method

Considering that the BDA method is proposed for classification, it is of great importance to make some adaptations when applied to regression problems. Thus, this study aims to solve the regression problem using classification ideas, and the ABDA-CoReg model was developed to improve the performance on the datasets through an automated method. Technically, ABDA-CoReg consists of two processes, as shown in Figure 3. The first step was the introduction of the DBSCAN clustering method, which clusters Chl-a concentrations and is integrated into the BDA method. The DBSCAN method has been discussed in previous studies (Behara, Bhaskar, and Edward 2021), which can divide high-density areas into clusters for the discovery of arbitrarily shaped clusters in datasets. One advantage of DBSCAN is that there is no need to specify the number of clusters. Thus, the ABDA module adds the automated module to determine the Chl-a concentrations, and the second step is to combine the CoReg module to achieve the highest accuracy in various classification situations according to the cluster results. For each process, the clustering results were saved, and the corresponding labeled data were used for the U-ABDA module, which was used as input to the CoReg model along with the transferred unlabeled data for training. The highest accuracy on the test set was retained, and automation was completed. After the entire process, the high-accuracy Chl-a retrieval model was developed.

3.4. Model structure for Chl-a estimation

In this study, models were developed using 210 points including in-situ hyperspectral data, Chl-a concentrations, labeled and unlabeled Sentinel-2 images to estimate the Chl-a concentrations. The input variables included the first six bands of Sentinel-2 (443, 490, 560, 665, 705, and 740 nm) and six band combinations based on empirical algorithms that were applied to inland lakes (Table 5), where bands of the empirical algorithms were replaced by the value of the nearest Sentinel-2 bands. The twelve input features developed a relatively robust model for Lake Chagan (Shi et al. 2022) and the output was Chl-a concentrations.

Table 5. Six empirical models in input features.

Algorithm	Index	Reference
Band Ratio	Rrs(709)/Rrs(665)	Duan, Ma, and Hu (2012)
Three Bands	[Rrs(671)^−1 – Rrs(710)^−1]× Rrs(740)	Gitelson et al. (2011)
Enhanced Three Index	[Rrs (665)^−1 – Rrs(705)^−1]/ [Rrs (740)^−1 – Rrs(705)^−1]	Yang et al. (2010)
NIRRI	Rrs(865)/Rrs(655)	Duan et al. (2007)
NDCI	[Rrs (708) – Rrs(665)]/ [Rrs (708) + Rrs(665)]	Mishra and Mishra (2012)
BGI	Rrs(443)/Rrs(561)	Ha et al. (2017)

Traditional machine learning models, including eXtreme Gradient Boosting (XGBoost), RF, K-Nearest Neighbor (KNN), and support vector regression (SVR) models, which have been widely used in the retrievals of water quality parameters in inland lakes, were selected as candidate models to compare the effect of transfer learning and ABDA-CoReg model performance. These algorithms were discussed in previous studies (Han et al. 2018; Breiman 2001; Park et al. 2022; Ren et al. 2023; Shen, Xie, and Kong 2020). Considering the number of samples, the training set was evenly divided into 10 folds. Grid search strategy combined with a 10-fold cross validation was employed on the training samples to tune the hyper-parameters of each model for model training and evaluation (Table 6). Data were randomly selected at the ratio of 7:3. The training set (N = 147) was used to develop the model, and the test set (N = 63) was kept independent in the labeled dataset to test the model performance. The average Chl-a concentrations of each subset in the training set are 16.48 μg L⁻¹, and are 13.45 μg L⁻¹ in the test set, which is consistent with the idea of validation procedure (Ruszczak, Wijata, and Nalepa 2022). The unlabeled data were input into the CoReg model, in which the numbers of labeled and unlabeled data were 216 and 260, respectively.

Table 6. Hyperparameters of each ML model tuned in this study.

Model	Hyperparameters
XGBoost	'gbtree’, learning_rate = 0.1, max_depth = 5
RF	n_estimators = 171
KNN	p = 1, weights = 'distance'
SVR	C = 8, degree = 7, kernel = 'poly'

3.5. Statistical metrics

The root mean square error (RMSE), mean absolute percentage error (MAPE) and coefficient of determination (R²) were used to evaluate model performance. (7) $\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}\sum _{i=1}^n{((\mathrm{Chl}-a{)}_E^i-(\mathrm{Chl}-a{)}_M^i)}^2}}$(7) (8) $\mathrm{MAPE}=100\times {\displaystyle \frac{1}{n}\sum _{i=1}^n{\displaystyle \frac{|(\mathrm{Chl}-a{)}_M^i-(\mathrm{Chl}-a{)}_E^i|}{(\mathrm{Chl}-a{)}_M^i}}}$(8) (9) $R^2={\left({\displaystyle \frac{1}{n-1}\sum _{i=1}^n\left({\displaystyle \frac{(\mathrm{Chl}-a{)}_E^i-\overline{{(\mathrm{Chl}-a)}_E}}{{\sigma }_E}}\right)\left({\displaystyle \frac{(\mathrm{Chl}-a{)}_M^i-\overline{{(\mathrm{Chl}-a)}_M}}{{\sigma }_E}}\right)}\right)}^2$(9) where n is the number of points; $(\mathrm{Chl}-a{)}_E^i$ denotes the i-th model-estimated Chl-a concentrations; $(\mathrm{Chl}-a{)}_M^i$ denotes the i-th in-situ measured Chl-a concentrations; ${\sigma }_E$ and ${\sigma }_M$ are the standard deviations of the model-estimated Chl-a concentrations and in-situ measured Chl-a concentrations, respectively; $\overline{{(\mathrm{Chl}-a)}_E}$ and $\overline{{(\mathrm{Chl}-a)}_M}$ are the mean values of the model-estimated Chl-a concentrations and in-situ measured Chl-a concentrations, respectively.

4. Results

4.1. Performances of ABDA-CoReg

As shown in Figure 4, Tables 7 and 8, the ABDA-CoReg achieved the highest accuracy (R² = 0.91, RMSE = 2.62 µg L⁻¹, MAPE = 22.88%). The investigated algorithm ABDA-CoReg was very or extremely statistically significant compared with the other four ML models after ABDA according to the T-test method on the three indicators (Table 7). On the one hand, CoReg had better performance than other models before and after transfer learning. Before ABDA, CoReg has outperformed the other four traditional ML models (R²= 0.85, RMSE = 3.29 µg L⁻¹, MAPE = 29.86%), which indicates the importance of data augmentation through the introduction of Sentinel-2 unlabeled images. It should be noted that before ABDA, samples including labeled and unlabeled points trained in each model were not in the process of transfer learning. The samples trained in the models were transferred through the ABDA module, where the labeled points were transferred to the M-BDA module. The unlabeled points were transferred to the U-BDA module because the transferred labeled data were not in the same distribution as the unlabeled data, which was not suitable for data training in the CoReg. In contrast, the ABDA module significantly improved performance. It can be observed from Table 8 that there were significant differences in the accuracy of the models before and after transfer learning. Before transfer learning, except for the CoReg model with a higher accuracy, the SVR model had the lowest accuracy (R² = 0.60, RMSE = 5.43 µg L⁻¹, MAPE = 53.65%) among them, though XGBoost, RF, and KNN achieved relatively satisfactory Chl-a retrievals. However, R² of the ABDA-SVR model increased by 45% compared with SVR after the ABDA, with RMSE reduced by 42% and MAPE by 22.41%. In addition, all the models improved a lot including ABDA-KNN which achieved the second highest precision (R² = 0.90, RMSE = 2.69 µg L⁻¹, MAPE = 23.28%) after the ABDA-CoReg. Thus, although ML models have a certain data learning capability, the performance of the model can be greatly improved based on unlabeled data sample augments and domain adaptation processing from in-situ spectral features.

Figure 4. Performances of ABDA-CoReg, ABDA-XGBoost, ABDA-RF, ABDA-KNN and ABDA-SVR on the test set.

Table 7. The p-value after ABDA of each model compared to ABDA-CoReg.

Model	p on R^2	p on RMSE	p on MAPE
ABDA-XGBoost	0.0014	<0.0001	0.0008
ABDA-RF	0.0018	0.0006	0.004
ABDA-KNN	0.0001	<0.0001	0.0005
ABDA-SVR	<0.0001	<0.0001	<0.0001

Table 8. Accuracy of each model on three statistical metrics.

Model	R^2	RMSE (μg L^−1)	MAPE (%)
ABDA-CoReg	0.91	2.62	22.88
ABDA-XGBoost	0.89	2.90	27.59
ABDA-RF	0.89	2.93	26.94
ABDA-KNN	0.90	2.69	23.28
ABDA-SVR	0.87	3.15	31.24
CoReg	0.85	3.29	29.86
XGBoost	0.79	3.99	36.67
RF	0.80	3.87	38.68
KNN	0.81	3.80	32.12
SVR	0.60	5.43	53.65

The significant improvement in performance can also be partly explained by the changes in the data distribution during the transfer process. As shown in Figure 5, all the sample (N = 210) distributions of the first six input features before and after the ABDA method are revealed. Different from empirical algorithms, these features are more suitable to observe the effects of ABDA because they are not in the form of band math. It can be observed from the pair plots that both the scatter distribution and the density diagram show obvious differences between the spectral features of in-situ and Sentinel-2. After domain adaptation, the differences between the two groups were significantly reduced, which was more conducive to the learning by each ML model.

Figure 5. The data value distribution of the first six input spectral features between in-situ and Sentinel-2 before and after ABDA: (a) before ABDA (b) after ABDA, where the blue points denote all the in-situ measured spectral features and the orange points denote all the Sentinel-2 spectral features.

4.2. Robustness of ABDA-CoReg

To apply the model to the entire lake area and long-term research, it is necessary to examine the robustness of the developed ABDA-CoReg model for various areas and months. Regional robustness was tested for the two lakes. As shown in Figure 6(a), the ABDA-CoReg model achieved steady performances both in Lake Chagan with R²=0.87, RMSE = 1.85 µg L⁻¹, MAPE = 5.73% and in Lake Yueliang Reservoir with R²=0.90, RMSE = 2.16 µg L⁻¹, MAPE = 20.89%, respectively. The MAPE of the ABDA-CoReg model performance in Lake Yueliang Reservoir was relatively higher, possibly because the range of Chl-a concentrations in the lake during different periods of in-situ measurements was wider than that of Lake Chagan, resulting in more variation in the predicted values. In addition, because the measured data were from two different lakes and different periods, the performance of the ABDA-CoReg model should appear steady for the observation of dynamic changes. The temporal robustness was tested based on the measured data of July, August, and September. The three months were selected because they were commonly shared by the two lakes during the in-situ measurements. As shown in Figure 6(b). The ABDA-CoReg model shows relatively stable performance over the three months. The ABDA-CoReg model had the highest accuracy in July (R² = 0.96, RMSE = 1.97 µg L⁻¹, MAPE = 11.90%). And good performances were also achieved in August, which were R² = 0.92, RMSE = 1.70 µg L⁻¹, MAPE = 20.45% and in September, which were R² = 0.73, RMSE = 2.71 µg L⁻¹, MAPE = 9.40%, respectively. The reason for the relatively ordinary accuracy in R² in September may be the smaller number of points (N = 49), but the model accuracy is good in terms of RMSE and MAPE. Among the three months, the range of Chl-a concentrations in July was wider, with more points. In contrast, the data for August and September were moderate in terms of range and number of points.

Figure 6. Robustness of ABDA-CoReg model: (a) performances on different study areas, where the red points denote the samples from Lake Chagan and the blue points denote the samples from Lake Yueliang Reservoir (b) performances on different months, where the light red points denote samples from July, the light blue points denote samples from August and the light green points denote samples from September.

It can be observed that the performances of ABDA-CoReg show differences when it is applied to various regions and periods, which indicates the different characteristics of the two lakes. It is also suggested that the direct application of ML models for data from different distributions may have certain advantages in accuracy, but the dependence on data exists and the model performance may be affected by changing situations (Cao et al. 2020). The data distribution can be improved by transfer learning, and the accuracy can be maintained for different lakes to a certain extent, which is shown in Figure 5. In conclusion, the ABDA-CoReg model showed regional and temporal robustness and can be applied to Chl-a retrievals over a long time series between the two lakes.

4.3. Time series of Chl-a retrievals

Time series of Chl-a concentrations in the two lakes were mapped using Sentinel-2 images based on the developed ABDA-CoReg model. As shown in Figure 7, both lakes exhibited clear temporal changes. During the period of 2020–2021, the Chl-a concentrations in May were in a relatively low range, and the concentrations in 2021 were lower than those in 2020. The Chl-a concentrations in the summer, including June, July, and August, were the highest. The highest Chl-a concentration in 2020 was higher than that in 2021, whereas the lowest Chl-a concentration in 2021 was lower than that in 2020. September in the two years was within a moderate range, and the concentrations in September 2020 were higher. As for Lake Yueliang Reservoir, from July to September in 2022, the concentrations were the highest in August and the lowest in September. The highest Chl-a value of Lake Yueliang Reservoir was lower than that of Lake Chagan. In July, there were some areas with lower concentrations in Lake Yueliang Reservoir. In terms of spatial observation, the concentrations in the northeastern part of Lake Chagan were higher than those in the southwest. In Lake Yueliang Reservoir, the concentrations in the north of the center were higher in July and September, and it was more obvious in September because the concentrations in the southwest of Lake Yueliang Reservoir were also higher in July, which was in accordance with in-situ measurements.

Figure 7. Maps of Chl-a retrievals derived from the ABDA-CoReg model from 2020 to 2022 during in-situ measurements. (a) Lake Chagan in May 2020 (b) Lake Chagan from June to August in 2020 (c) Lake Chagan in September 2020 (d) Lake Chagan in May 2021 (e) Lake Chagan from June to August in 2021 (f) Lake Chagan in September 2021 (g) Lake Yueliang Reservoir in July 2022 (h) Lake Yueliang Reservoir in August 2022 (i) Lake Yueliang Reservoir in September 2022.

5. Discussion

5.1. Process of automation module

BDA method is a transfer learning method proposed for classification models, however, labels are required to be continuous Chl-a values when solving regression problems. Combined with the cluster method, the process of developing the model with the highest precision can be achieved on the data by the labeled Chl-a concentrations. One of the advantages of DBSCAN is that it involves a classification process. In the process of automated selection, the task of Chl-a concentration classification involves multiple cases. To demonstrate the performance of the models in other classification cases during the process, the spectral features with the highest silhouette coefficient during DBSCAN in each classification case were selected and input into each model for training. The training and testing sets of each model were the same as those of ABDA-CoReg because they are in the same process during the automation module.

As shown in Figure 8, the performances of the five models in different categories of Chl-a concentrations during the automated process were different. Among them, the ABDA-SVR model had the poorest performance for the three indicators in all classification cases. In contrast, the ABDA-KNN model showed good performance in some classification cases. ABDA-XGBoost and ABDA-RF are relatively balanced for each classification. However, it should be noted that during the process, the changing trend of the three indicators was basically in accordance with each model. In the case of the two categories, models generally showed better performances, which was consistent with the results shown in Figure 4. More importantly, compared to the developed ABDA-CoReg model (Table 8), it can be observed that the cluster results for classification and regression were able to improve the regression model accuracy.

Figure 8. Performances of models in each classification case during automated process of each model on the test set: (a) R² (b) RMSE (c) MAPE.

5.2. Implications for transfer learning

Owing to the different optical properties of water bodies, spectral data from satellites often exhibit different data distributions (Jackson, Sathyendranath, and Mélin 2017; Sun et al. 2014). Retrievals of Chl-a by first clustering in-situ hyperspectral data and then developing the model has good performance (Lee et al. 1996; Li et al. 2011). Data preprocessing methods, such as normalization and logarithmic transformation of Chl-a concentrations, have been applied to traditional ML models during the process of model learning, which contributes to model performance (Cao et al. 2022; Yu et al. 2020). However, it was unable to fundamentally change the data distribution. In this case, the data may not be suitable as direct input for model training. In addition, a high-accuracy ML model may be unavailable for the explanation of Chl-a retrievals owing to the lack of consideration of the bio-optical properties of Chl-a. Temporal and regional robustness can enhance the reliability of the model (Shi et al. 2022). Since the twelve input Sentinel-2 spectral features have developed a relatively robust model for Lake Chagan, spectral transfer between the two lakes was also applied in this study to explore the combination of the transfer learning method and remote sensing images for Chl-a retrievals. The first implication is the setting of source and target domains. In transfer learning, the source domain refers to the existing knowledge area, whereas the target domain refers to the area to be learned. The transfer method from the source domain to the target domain exhibits a better performance when there is a certain similarity between the source and target domains (Huang et al. 2023). The source domain often has a guiding effect on the target domain through established empirical knowledge (Li et al. 2021b), which requires a relatively robust model to be developed on the source domain before the transfer method. Therefore, before applying the spectral transfer strategy in this study, it is fundamental to verify the robustness of the field model before ABDA (Table 9). It can be seen that the in-situ spectral features had a good performance, which is suitable to be the source domain and is a good basis for the transfer of Sentinel-2 spectral features. Not only was a certain correction achieved from the field data (Hosna et al. 2022), but according to the principle of transfer learning, the output MSI data retained the characteristics of Sentinel-2.

Table 9. Performances of each ML on different transfer strategies.

Transfer strategies	Model	R^2	RMSE (μg L^−1)	MAPE (%)
ML performance using in-situ spectral features before spectral transfer	XGBoost	0.62	5.04	44.31
	RF	0.68	4.62	42.85
	KNN	0.62	5.03	42.26
	SVR	0.61	4.83	45.80
Apply twelve spectral features on Lake Yueliang Reservoir without transfer	XGBoost	0.44	4.67	62.81
	RF	0.56	4.13	53.84
	KNN	0.24	5.42	65.89
	SVR	0.22	5.50	65.92
Regional transfer	XGBoost	0.64	3.19	10.81
	RF	0.64	3.16	10.73
	KNN	0.71	2.88	10.33
	SVR	0.56	3.49	12.28

In addition, to explore the effect of transfer learning methods on the spectral features from different lakes, the twelve Sentinel-2 spectral features of Lake Chagan was taken as the source domain, and the twelve Sentinel-2 spectral features of Lake Yueliang Reservoir was the target domain, and the parameters were set according to the ABDA-CoReg model. It should be noted that in-situ spectral features are not involved in this attempt. It can be seen from Table 9 that if the twelve input features were directly applied to Lake Yueliang Reservoir, the performances greatly decreased owing to the various data distributions. However, when applying transfer learning methods, the accuracy of Lake Moon Reservoir has greatly improved. Although the effect is not as good as that of spectral transfer methods, it may be helpful for model developing when applied to different lakes. As shown in Figure 9, before the transfer method, there were clear differences in the numerical distribution of the Sentinel-2 spectral features between the two lakes, and the distribution of data after transfer learning was significantly improved. The performance of the ML model tends to be better for data training and prediction in the same distribution (González-Vidal et al. 2023). A transfer learning method based on features is conducive to this local characteristic (Li et al. 2022).

Figure 9. The data distribution of the first six input spectral features from Sentinel-2 between Lake Chagan and Lake Yueliang Reservoir before and after ABDA: (a) before ABDA (b) after ABDA, where the blue points denote the samples from Lake Chagan and the orange points denote samples from the Lake Yueliang Reservoir.

At the same time, if the Sentinel-2 spectral features were used as the source domain and the in-situ spectral features were used as the target domain, it should be noted that the result was unchanged. Swapping the two domains appears to have no influence on the results. Because the matrix dimensions of the two input domains are the same (210 × 12), and when retrievals are performed after transformation, the labels Y of Chl-a concentrations are also the same. Thus, regardless of whether it is the process of data transformation to improve data distribution or the process of model learning and training, the same transformation is performed after essentially swapping the domains. Thus, it is also important to verify the data dimensions and accuracy of the source domain model before transfer learning to avoid negative transfer (Zhang et al. 2022a).

5.3. Advantages and limitations of empirical algorithms

Traditional empirical algorithms have been widely used to retrieve Chl-a concentrations from remote sensing images (Le et al. 2011; Zhang et al. 2019). Empirical algorithms often have certain physical meanings, and regional empirical models have been developed based on data from in-situ regions. According to the optical properties of Chl-a in lakes, the retrievals of Chl-a is mainly based on two absorption peaks in the spectrum, which are usually located at 440 and 675 nm. The area near 440 nm was greatly affected by TSS and CDOM, while the area near 675 nm was less affected by other water factors. Therefore, empirical models have been applied as input features for ML models in recent years. To observe the retrievals of Chl-a by the empirical models in the two lakes of this study, three empirical algorithms in the input features, including Band Ratio, NIRRI and NDCI, were selected and verified according to the same training and testing sets as the ML models in this study. Among them, the Band Ratio is one of the most classical empirical methods (Kim et al. 2022), NIRRI has been applied to Lake Chagan (Duan et al. 2007) and NDCI is taken as a normalized form according to NDVI to retrieve Chl-a (Mishra and Mishra 2012). As shown in Figure 10(a), the best performance of the three empirical algorithms was R² = 0.29, RMSE = 7.78 μg L⁻¹, and MAPE = 87.63% from the Band Ratio method, thus it made an influenced when applying the models to the two lakes. Overall, the effects of the three empirical algorithms were relatively insignificant, which is insufficient for developing a model in various areas for Chl-a retrievals.

Figure 10. The performances and data value distribution of the empirical algorithms in two lakes:(a) performances of empirical algorithms, where the units of R² and MAPE are percentage (%), the unit of RMSE is μg L⁻¹ (b) data value distribution which the blue points denote the samples from Lake Chagan, and the orange points denote the samples from Lake Yueliang Reservoir.

However, if a model can be developed on multiple groups of data without transfer learning, this means that the model has a certain ability for data adaptation. In this study, the empirical algorithms also influenced model development. The ABDA-CoReg model proposed in this study combines empirical algorithms into the input features, and the data value distribution is shown in Figure 10(b). It should be noted that the features had a certain effect on reducing the data differences to some extent before transfer learning. The distribution of features achieved a few improvements in the data distribution, but not entirely. This also revealed the characteristics of the empirical algorithms in that they have basic adaptability for data from different distributions. When the data are based on several bands associated with water quality parameters in the form of ratios and other calculations, the problems of parameter retrievals in regional areas can be solved using empirical algorithms (Xu et al. 2021). Because the single band was much more easily affected by the changes in regions (Figure 9), differences in data distribution appeared when it was input to the model. The accuracy of the empirical algorithms decreased after the transfer method, partly because empirical algorithms already have the ability to adapt to the data distribution (Figure 10), and negative transfer may appear, leading to a decrease in model accuracy. Combining single bands as input features in ML models can achieve good results. The data distribution of the spectral features was further improved after transfer learning, which is also more conducive to ML model for training and predicting through multiple features (Shi et al. 2022).

5.4. Comparison with neural network models

With the development of deep learning, the strong computer power makes it easier to explore data and develop models with better accuracy from satellite images (Zhao et al. 2021). Based on the CNN model, WaterNet was developed which consists of band expansion, feature extraction and Chl-a estimation. The adoption of a 3D convolution kernel can utilize the spatial and spectral information of images in modeling (Syariz et al. 2020). In this study, ABDA-CoReg is further compared with WaterNet. Since WaterNet contains 4753 unknown parameters for training to reach global optimization, and the dimensions of input data are also different, this study used the WaterNet as the reference model and performed an Adaptive WaterNet (A-WaterNet) on the input data. As shown in Figure 11, firstly the input data were expanded to 3D. The main structure of the A-WaterNet was consistent with WaterNet, where the convolution size in the feature extraction layer was set to 1 × 1 × 30 and 1 × 1 × 10, while the other parameters were unchanged. In addition, an Attentioned A-WaterNet (AA-WaterNet) was also developed for comparison which added a Transformer module to the A-WaterNet as the attention mechanism on the feature extraction layer in order to extract features better. The encoder layer is one of the core components of the Transformer model. It is used to extract and encode features of the input sequence which includes three sub-layers. Multi-Head Self-Attention was used to calculate the input dependencies at different positions within the sequence, while Feed-Forward Neural Network was used to perform nonlinear transformation on the features of each position. Additionally, Residual Connection and Layer Normalization were used to enhance gradient flow and alleviate the vanishing gradient problem in training. It should be noted that for the fair comparisons, the A-WaterNet and AA-WaterNet were retrained by using the same data processing with the ABDA-CoReg.

Figure 11. Network structure of (a) A-WaterNet, (b) AA-WaterNet, which A-WaterNet is the adaptive model of WaterNet on the input data and AA-WaterNet adds a Transformer module to the A-WaterNet as the attention mechanism module.

It can be observed from Figure 12 and Table 10 that among these four deep learning models, the ABDA-A-WaterNet had the highest accuracy (R² = 0.87, RMSE = 3.12 µg L⁻¹, MAPE = 26.75%). At the same time, the A-WaterNet also had a good performance (R² = 0.82, RMSE = 3.68 µg L⁻¹, MAPE = 31.06%) though there were several points with excessively large or too small predictions. However, after the introduction of the Transformer module, the model performances were not improved. Compared to A-WaterNet, AA-WaterNet had a decrease in model accuracy (R² = 0.78, RMSE = 4.09 µg L⁻¹, MAPE = 26.57%). Similarly, although the performance of ABDA-AA-WaterNet (R² = 0.82, RMSE = 3.67 µg L⁻¹, MAPE = 34.63%) was improved compared to AA-WaterNet, there was no obvious improvement compared with A-WaterNet. Transformer-based model may be more suitable for the dealing of language or text information so the long-distance dependencies can be captured (Roshanzamir, Aghajan, and Soleymani Baghshah 2021). More representative samples with temporal characteristics are expected to capture the changes of Chl-a spatiotemporal information. In summary, ABDA-CoReg still shows stable performance compared with the deep learning model. On the one hand, the ABDA module has the ability to improve the accuracy of various models. On the other hand, CoReg takes advantage of utilizing more satellite data through natural sample expansion.

Figure 12. Performances of A-WaterNet, ABDA-A-WaterNet, AA-WaterNet and ABDA- AA-WaterNet on the test set.

Table 10. Accuracy of each deep learning model on three statistical metrics.

Model	R^2	RMSE (μg L^−1)	MAPE (%)
A-WaterNet	0.82	3.68	31.06
ABDA-A-WaterNet	0.87	3.12	26.75
AA-WaterNet	0.78	4.09	26.57
ABDA-AA-WaterNet	0.82	3.67	34.63

6. Conclusion

This study developed the ABDA-CoReg model based on in-situ measured data and Sentinel-2 images from two lakes in Jilin Province, Northeast China, from 2020 to 2022. First, ABDA was used to perform spectral feature transfer between the in-situ measured and Sentinel-2 to improve the data distribution. The unlabeled Sentinel-2 images unmatched with the in-situ measurements were used to conduct sample augmentation and transfer with spectral features after the M-ABDA. Then, the transferred labeled and unlabeled Sentinel-2 spectral features after U-ABDA were inputted to CoReg. Because the BDA was proposed for classification problems, the entire process was integrated to achieve the spectral transfer strategy and high-precision Chl-a retrievals. The developed ABDA-Coreg model outperformed the other four ML models (XGBoost, RF, KNN, and SVR), with R²= 0.91, RMSE = 2.68 μg L⁻¹ and MAPE = 22.60%. The proposed ABDA-CoReg model was also proven to be robust to regional changes and temporal variations between Lake Chagan and Lake Yueliang Reservoir. At the same time, the performances of XGBoost, RF, KNN, and SVR were all improved at various levels after transfer learning, indicating the availability of ML models for data learning. When this method is extended to other water bodies, more in-situ measured spectral data and different types of matched satellite images are required. Other transfer learning methods and semi-supervised or unsupervised regression models can also be considered based on this study to optimize the model. Overall, the results of this study demonstrate that it is feasible to introduce unlabeled satellite images to model development, which can not only take advantage of sample augmentation but is also beneficial for improving model performance owing to the limited number of in-situ measurements and matched satellite images. By combining the methods of transfer learning, data adaptation can be achieved. Thus, it can be applied to monitor Chl-a over a wide range and a long time series through satellites. In addition, our research provides a new method for improving the performance and robustness of ML models, which is of great significance for retrieving water parameters in remote sensing.

Acknowledgements

We would like to express our great appreciation to the editors and anonymous reviewers for the helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Sentinel-2 MSI were obtained from https://dataspace.copernicus.eu/, the in-situ measured data that support the findings of this study are available from the corresponding author [L. J.] upon reasonable request.

Additional information

Funding

The research is funded by the Technological Research and Development Projects of Jilin under Grant 20220201017GX and Land Observation Satellite Supporting Platform of National Civil Space Infrastructure Project [CASPLOS-CCSI].