An application of 1D convolution and deep learning to remote sensing modelling of Secchi depth in the northern Adriatic Sea

ABSTRACT

This paper presents a novel approach for predicting the water quality indicator – Secchi disk depth (Z_SD). Z_SD indirectly reflects water clarity and serves as a proxy for other quality parameters. This study utilizes Deep Neural Network (DNN) trained on satellite remote sensing and measured data from three sources: two datasets obtained from official agencies in Croatia and Slovenia, and one citizen science data source, all covering the northern coastal region of the Adriatic Sea. The proposed model uses 1D Convolutional Neural Network (CNN) in the spectral dimension to predict Z_SD. The model’s performance indicates a strong fit to the observed data, proving capability of 1D-CNN to capture changes in water transparency. On the test dataset, the model achieved a high R-squared value of 0.890, a low root mean squared error (RMSE) of 0.023 and mean absolute error (MAE) of 0.014. These results demonstrate that employing a 1D-CNN in the spectral dimension of Sentinel-3 OLCI data is an effective approach for predicting water quality. These findings have significant implications for monitoring Z_SD in coastal areas. By integrating diverse data sources and leveraging advanced machine learning algorithms, a more accurate and comprehensive assessment of water quality can be achieved.

KEYWORDS:

• Secchi
• Sentinel-3
• OLCI
• 1D-CNN
• Adriatic sea

1. Introduction

The Secchi disk depth (Z_SD) is a quantitative measure used to indicate the “transparency” or “clarity” of water in a body of water such as a lake or sea. The Secchi depth is the depth at which a circular disk, called a Secchi disk, is no longer visible when it is lowered into the water (Lee et al., 2015). It serves as an important indicator of water quality, reflecting the amount of suspended particulate matter (SPM) present, which includes materials such as algae, clay, silt, and others. In general, the clearer the water, the deeper the Secchi depth will be (Chapman, 1996). The relationship between Z_SD and SPM is complex, as SPM is influenced by various factors, including Z_SD, chlorophyll-a (Chl-a), and colored dissolved organic matter (CDOM). While Z_SD can indicate potential water quality problems, it cannot serve as a direct proxy for measuring SPM. For a comprehensive assessment of water quality, it is necessary to analyze additional parameters such as Chl-a, CDOM, and SPM (Harvey et al., 2019). However, obtaining measurements for these parameters requires specific instruments and additional laboratory analysis, making the process time-consuming and costly. Nonetheless, when used in combination with Secchi depth, these water quality parameters provide a more detailed understanding of the water quality and can help identify specific sources of pollution or other water quality issues. Moreover, Secchi depth is widely used in research studies focusing on aquatic ecology and the functioning of aquatic ecosystems. It enables the study of the impact of human activities on water bodies, such as pollution, nutrient loading, and land-use changes. For instance, in agricultural areas, excessive nutrient runoff from fertilizers can lead to high levels of algae growth and a decrease in water clarity. Additionally, Secchi depth is valuable for evaluating the effectiveness of water management strategies and identifying areas where water quality improvements are needed (Teubner et al., 2020). Overall, the combination of Secchi depth and other water quality parameters contributes to a more comprehensive and informed understanding of water quality conditions, facilitating better water quality management and conservation efforts.

Water quality assessment traditionally involves analyzing physical, chemical, and biological properties of field samples in a laboratory. Water bodies are often categorized as Case-1 or Case-2 based on their optical properties. Case-1 waters are mainly found in open oceans and stratified shelf seas, while Case-2 waters encompass coastal areas and estuaries, influenced by suspended matter and colored dissolved organic matter (He et al., 2021; Lee & Tang, 2022; Morel & Prieur, 1977). It is worth noting that the classification boundaries between Case-1 and Case-2 are not always clear (Mobley et al., 2004).

Earth observation has proven to be a valuable tool (Andres et al., 2018) to overcome challenges of water management. The improvement in computing technology and applications have enabled remote sensing techniques to monitor and detect changes on a large scale, which cannot be accomplished through traditional in situ measurements. Sensors mounted on satellites, aircraft, and drones assess water quality by evaluating spectral reflectance – the proportion of electromagnetic energy reflected by a surface to the incident energy in a specific wavelength (Gholizadeh et al., 2016). This enables the monitoring and assessment of water quality indicators such as Chl-a (Ivanda et al., 2021; Katlane et al., 2020), turbidity (Dogliotti et al., 2015; Katlane et al., 2020), total suspended matter (TSM) (Mao et al., 2012), Secchi disk depth (Z_SD) (Arias-Rodriguez et al., 2023; Zhang et al., 2022; Zhao et al., 2022), CDOM (Slonecker et al., 2016), etc. Furthermore, it is possible to estimate certain parameters by measuring another related parameter. For instance, a correlation can be established between Secchi depth and turbidity (Baughman et al., 2015). In situ measurements of turbidity can be measured using instruments such as nephelometers or spectrophotometers (Anassontzis et al., 2010).

Morel and Gordon (1980) proposed three approaches for interpreting “water color”: empirical, semi-empirical, and analytical methods. Empirical algorithms use statistical relationships and spectral properties to estimate parameters from remotely sensed data (Gholizadeh et al., 2016). For example, nonlinear models based on K_d(PAR) and 1/Z_SD have been developed (Ficek & Zapadka, 2010; Padial & Thomaz, 2008; Zhang et al., 2012). Semi-empirical methods are commonly utilized to study the optical properties of Case-2 waters and utilize physical and spectral information to create algorithms linked to measured water parameters. However, the complexity of Case-2 waters, especially for inland turbid lakes, can lead to algorithm failures (Lednicka & Kubacka, 2022). Analytical methods determine water constituents’ concentration from absorption and backscatter coefficients, using remotely sensed reflection (Budhiman et al., 2004). Attempts to connect Secchi depth to PAR or visible solar radiation (VSR) have been made (Lee et al., 2018, 2019; Paulson & Simpson, 1977; Stravisi et al., 1999; Umer & Malačič, 2022), but in situ measurements of these parameters are costly and time-consuming (Umer & Malačič, 2022). Machine learning and deep learning, which will be explained in detail, are considered empirical methods but not necessarily semi-empirical.

According to Sagan et al. (2020), machine learning methods show potential for estimating the optical properties of water bodies. For example, Maciel et al. (2021) assessed the clarity of Brazilian inland waters by evaluating the use of machine learning algorithms, such as Random Forest, Extreme Gradient Boosting, and Support Vector Machines, along with semi-analytical algorithms for Z_SD retrieval focused on Sentinel-2 imagery. Additionally, Shen et al. (2020) and Rubin et al. (2021) utilized random forest regression on Sentinel-3 OLCI and Landsat-4, -5, -7, and -8 imagery to estimate Z_SD.

Although machine learning algorithms have proven successful in solving various environmental problems, they often require a large amount of high-quality data to be effective. To address this challenge, there has been a growing trend towards citizen science, which involves engaging members of the public to collect data using simple and low-cost devices (Brewin et al., 2019). With this in mind, programs such as LAKEWATCH (Hoyer & Canfield, 2021) and Secchi disk project (Secchi Disk Project, 2013) were launched. Citizen science has the potential to provide large amounts of data that can be used for more frequent observations in focused campaigns collection (Menon et al., 2021). Recent studies have shown that data collected by citizens is often as reliable as official data (Canfield et al., 2002; Hoyer & Canfield, 2021). However, remote sensing by satellite enables the observation of larger areas. Although there is agreement between existing products and measured data (Luis et al., 2019), there is still a need to calibrate existing products or develop new ones using a variety of data. Deutsch et al. (2021) provided a validation of Landsat-8 Z_SD products using two data sources-one official and one based on citizen science – and reports on the need for the availability of large datasets to enable more accurate estimation of Z_SD. Thus, collecting more data through citizen science initiatives can provide valuable information for calibrating remote sensing products, leading to better environmental monitoring and management.

Deep learning, a part of machine learning, is widely used in geosciences due to its excellent performance in analyzing large amounts of remote sensing data (Zhang et al., 2016). The current progress of deep learning in predicting Z_SD (Secchi depth) is evident from recent studies that have shown promising results in utilizing deep learning architectures to estimate water quality parameters, including Z_SD. These studies have demonstrated that deep learning, particularly convolutional neural networks (CNNs) and recurrent models, can effectively capture complex correlations between remote sensing reflectance (R_rs) data, optically active constituents (OACs), and non-OACs to retrieve accurate water quality information (Ahmed et al., 2022; Cui et al., 2022; Guo et al., 2023; He et al., 2022; Kulshreshtha & Shanmugam, 2017). CNNs are a type of deep learning architecture that can process raw data and extract relevant features for tasks like classification or regression. CNNs are categorized based on their input dimensions, such as 1D, 2D, 3D, or 4D, depending on the data dimensionality they accept (Li et al., 2018). Satellite imagery provides both spectral and spatial information simultaneously, with the spectral resolution being relatively higher (i.e. consisting of multiple spectral bands for one pixel) than the spatial resolution. For point parameters, such as water quality indicators (e.g. Chl-a, Z_SD), it is reasonable to use the spectral vector of an individual spatial pixel to identify a specific parameter. One effective method for achieving this is by using 1D-CNN, which takes raw spectral vectors as inputs and outputs deep spectral features that can be used for classification (Li et al., 2018).

In remote sensing, 1D-CNN has been successfully used to detect water quality parameters such as Chl-a concentration in inland water bodies (Maier et al., 2021; Pyo et al., 2022), classify points (sea-land) using bispectral bathymetric echo (Hu et al., 2019), and classify land use and land cover in hyperspectral imagery using spectral signatures (Hu et al., 2015). For accurate estimation of Secchi disk depth from Sentinel-3 OLCI multispectral images, we adopted a 1D-CNN due to its effectiveness in processing high-dimensional spectral vectors, capturing non-linear relationships, and performing pointwise estimation. The feature extraction capability of 1D-CNN reduces the need for manual engineering, allowing it to adapt to the dataset’s spectral characteristics. Moreover, its capacity for learning diverse spectral patterns enhances generalization to unseen data, making it a suitable choice for our specific water quality estimation task. In our study, this is the first time that a 1D-CNN has been used specifically for this purpose. We believe that our unique approach has the potential to improve the accuracy and efficiency of Secchi disk depth estimation from satellite imagery.

The contribution of this paper is the use of a dataset created from three different sources covering a larger area of the northern Adriatic coast of Croatia and Slovenia: two official measurement sources (one from Croatia and one from Slovenia) and a citizen science project. The dataset covers 6 years of measurements and is rich in relevant information that can be used to effectively train a deep learning algorithm. In addition, the dataset contains a large number of examples that can be used to improve the generalisation capability of a deep learning algorithm.

Another contribution of this work is the use of a 1D Convolutional Neural Network that applies convolutional operations and feature extraction in the spectral dimension of a multispectral image. This network is able to automatically extract high-level features from the spectral response of a pixel and find complex patterns and relationships between the most valuable features and the measured value. The results show that our algorithm outperforms the current state of the art in estimating Secchi disk depth from satellite remote sensing.

2. Dataset

2.1. Study area

The study area is located in the northern Adriatic Sea, close to coasts of Croatia and Slovenia, as illustrated in Figure 1. The Adriatic Sea is a northern arm of the Mediterranean Sea, and water exchange with the Mediterranean Sea occurs through the 800 m deep Otranto Sill (Zavatarelli et al., 1998). The Adriatic Sea has a maximum depth of 1233 m, with an average depth of 259.5 m. The sea’s depth increases from the northwestern basin, which is only 15 m deep, to the southeastern basin, where the depth reaches 780 m (Blake & Topalović, 1996).

Figure 1. Adriatic Sea and position of the Secchi disk depth measurements used in this study.

The Adriatic Sea is known for its natural beauty and rich biodiversity. It is home to many species and provides food for the population living near the coast and is a source for numerous industries. Although it is traditionally considered to be quite clean and unpolluted, it is important to continuously monitor the status and trends of water quality in this water body. Timely detection of water quality degradation can save the health of food and people living in coastal areas, protect biodiversity and prevent degradation of the beauty of the sea.

2.2. Secchi depth

The Secchi disk is a widely used tool for measuring water transparency by determining the depth at which the disk is no longer visible. It is a simple and efficient method of immersing a white disk into the water column and measuring the depth at which it is no longer visible. The visibility of the Secchi disk visibility is given in metres (m).

In this study, in situ Secchi disk measurements were obtained from three different sources. Measurements in the Gulf of Trieste were provided by the National Institute of Biology, Marine Biology Station in Piran. Measurements related to the Croatian coastline were obtained from Hrvatske vode (a legal entity for water management) and the Secchi Disk Project website (Secchi Disk Project, 2013), which contains data provided by volunteers. The measurements from the National Institute of Biology and Hrvatske vode were collected following standard measurement protocols for official monitoring, ensuring their reliability and accuracy. However, it is important to note that the Secchi disk measurements from the Secchi Disk Project are volunteer-contributed data, and specific measurement conditions for these data points were not available. However, the volunteer dataset shows similar range and distribution as official measurements, so we take it as it is. Not all measurements were used directly in the study. To ensure the quality and integrity of our dataset by associating correct values with correct data, we employed satellite data processing techniques. If clouds were observed passing over the locations of the in situ measurements, we preprocessed the data points based on satellite data to mitigate any influence from cloud interference. This step was necessary as we could not directly control the measurement conditions for the in situ data. The spatial distribution of all in situ measurements, comprising a total dataset of 589 measurements collected between May 2016 and September 2021, is presented in Figure 1. Figure 1 depicts the locations of measurement sites, while on some sites multiple measurements were made during the observed time period. The Croatian dataset comprises 452 measurements, while the Slovenian dataset contains 118 measurements, and the dataset related to the Secchi Disk Project includes 19 measurements. In Figure 2, the probability distribution of the measured Z_SD values from the Croatian, Slovenian, and Secchi Disk Project datasets is shown. This distribution provides insights into the likelihood of different Z_SD values occurring within each dataset, allowing us to understand the range, concentration, and variability of the measurements in each dataset. Moreover, Table 1 presents the statistical characteristics of in situ measurements for each year, including the number of samples (count), the minimum value of Z_SD measurements (min), the maximum value of Z_SD measurements (max), the standard deviation (std) which measures the variability or spread of Z_SD values around the mean, and the mean value which represents the average Z_SD value across the dataset.

Figure 2. Probability distribution of measured Z_SD values in the Croatian, Slovenian, and Secchi disk Project datasets.

Table 1. Statistical characteristics of in situ Z_SD (m) through years.

Year	count	min	max	std	mean
2016	117	2	28	5	10
2017	115	3	19	3	8
2018	20	1	28	7	8
2019	153	4	28	6	10
2020	136	5	26	5	14
2021	48	5	30	6	17

2.3. Sentinel-3 OLCI data

The Sentinel-3 mission is jointly operated by European Space Agency (ESA) and European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) to provide operational ocean and land observation services. Mission is a constellation of Sentinel-3A satellite launched on 16 February 2016 and Sentinel-3B satellite launched on 25 April 2018. The key instruments on board Sentinel-3 are Ocean and Land Colour Instrument (OLCI), Sea and Land Surface Temperature Radiometer (SLSTR) and Synthetic Aperture Radar Altimeter (SRAL). OLCI is an imaging spectrometer operating in 21 spectral bands within the spectral range of 390 nm to 1040 nm, with a spatial resolution of 300 m and revisit time of one day, which is applicable to our study region, the Adriatic Sea. OLCI is commonly used for studying the open ocean and inland/coastal waters to measure sea surface topography, temperature and colour (Rodrigues et al., 2022).

In this study, we employed 185 different scenes of Sentinel-3 OLCI Level-1B TOA (Top of Atmosphere) satellite imagery, captured between 25^th April 2016 and 8^th December 2021. These scenes were retrieved via the Sentinel Hub API (Sentinel-3 OLCI L1B, n.d..) through a Python script. The selection of these scenes was specifically based on the dates of our in situ Secchi disk depth measurements. Nevertheless, only the data from locations of measurements on the date of the scene were extracted for further use. Subsequently, we applied cloud-based data filtering to ensure the quality of the imagery data used for our comprehensive Secchi disk depth estimation.

3. Methodology

The methodology includes several stages to develop an empirical remote sensing model for monitoring spectral variations of Secchi disk depth for the study area. Dataset construction based on in situ and satellite data is described in Section 3.1. The architecture of the one-dimensional convolutional neural network (1D-CNN) model was proposed in Section 3.2. Finally, the impact of hyperparameters on the model’s accuracy was described in Section 3.3.

3.1. Dataset construction

Sentinel-3 OLCI Level-1B TOA (Top of Atmosphere) satellite imagery was downloaded by using API and Python programming language from the Sentinel Hub (credit: Modified Copernicus Sentinel data 2016–2021/Sentinel Hub) (EO Browser,Sinergise Ltd, n.d..). Images were downloaded for the period May 2016 to September 2021, for dates where in situ Secchi measurements were available. The Sentinel Hub EO Browser makes use of atmospheric correction algorithms to convert Sentinel-3 OLCI Level 1 TOA radiance measurements into Sentinel-3 OLCI Level 1 TOA reflectance values. These algorithms take into account atmospheric effects such as Rayleigh scattering, absorption and emission by atmospheric gases, and the effects of aerosols to estimate the true surface reflectance. The EO Browser provides users with TOA reflectance values for Sentinel-3 OLCI Level 1 data based on these estimates. The TOA normalised reflectance can be calculated using the formula (1), as described in the Copernicus Sentinel-3 OLCI Land User Handbook (Sentinel-3 OLCI Land User Handbook, n.d..):

(1) $R_{\mathit{TOA}}=\mathit{\pi }\ast \left(L_{\mathit{TOA}}/\mathit{E}/\mathit{cos}\left(\mathit{\theta }\right)\right)$(1)

where R_TOA is TOA reflectance, L_TOA is TOA radiance, E is solar irradiance and θ is solar zenith angle. For this study, 21 TOA Sentinel-3 OLCI band reflectance values were read for each in situ measurement. Instead of applying atmospheric correction algorithms, such as POLYMER (Steinmetz et al., 2011), SeaDAS (Gordon & Wang, 1994), and C2RCC (Brockmann et al., 2016), to each of 185 different scenes (each scene containing 21.tiff images of Sentinel-3 OLCI bands), we opted to utilize the raw reflectance values directly from the Sentinel-3 OLCI satellite data. Performing atmospheric correction on this dataset would affect the automatic execution of the methodology. Moreover, the dynamic and variable atmospheric conditions in coastal areas like the Adriatic Sea pose unique challenges, making it difficult to effectively apply standard atmosphere correction methods. The performance of various atmospheric correction processors in coastal areas is studied by many researchers and (Vanhellemont & Ruddick, 2021) shows that none of studied AC algorithms have superior performance. Thus, we decided to use L1 satellite data and let CNN compensate for the atmospheric conditions. Machine learning algorithms can be adapted to work with satellite data that has not undergone atmospheric correction, allowing for the use of raw reflectance values without pre-processing for atmospheric correction (Shah et al., 2022). In this way, the model can provide accurate results without requiring explicit atmospheric correction in the preprocessing stage.

Secchi measurement requires sufficient light to penetrate the water column and reflects back to the instrument. As the measurement is performed in the vicinity of the surface, it would be beneficial to know bottom of atmosphere (BOA) reflectance to determine the Secchi depth. The sun light passes through the atmosphere on its way to the surface. After reaching the Earth’s surface, the light is reflected and passes through the atmosphere once again before reaching the instrument. The first pass may have an effect on the Secchi depth observations. L1 data includes reflectance values that have undergone both passes, and the first pass of the sunlight may have been absorbed or scattered by atmospheric constituents, affecting the reflectance measured by the instrument.

The use of 1D convolutional neural networks (CNNs) for atmospheric correction may hold promise in compensating for atmospheric absorption and extracting only the features associated with the observed Secchi depth. However, additional research is needed to provide evidence to support this claim. The CNN algorithm transforms the reflectance values into weighted sums and differences and performs increasingly complex transformations by adding more layers to the deep neural network. While it is possible that these transformations may be correct for atmospheric absorption, the lack of explanation of the feature transformation by deep neural networks impedes understanding of the process and the algorithm’s validity. Therefore, further research is necessary to explore the potential of CNNs for atmospheric correction in remote sensing. However, this falls outside the scope of the presented study.

3.2. Sentinel-3 OLCI data preprocessing

To ensure the quality of the satellite dataset, we performed preprocessing on the Sentinel-3 OLCI images. We removed effects of clouds in our dataset by using band Oa17. Band Oa17 has a wavelength of 865 nm in the near-infrared spectra, and can be used for atmospheric correction, aerosol correction, clouds, and pixel co-registration (Radiometric Resolution–21 bands in VIS/SWIR, n.d.; Sentinel-3 OLCI Land User Handbook, n.d.). The typical range of Sentinel-3 OLCI reflectance values for a given band is 0–0.4; however, highly reflective pixels, such as clouds, can have reflectance values above 1 (Sentinel-3 OLCI L1B, n.d.). Based on this, we studied the several satellite scenes of our study area in the QGIS tool and found out that band Oa17 has values higher than 0.17 for land and clouds pixels. Figure 3 depicts the mask created by applying a threshold value of 0.17 over the satellite image of Oa17 band for the area of Kaštela Bay and the Brač Channel in Croatia. Yellow color indicates pixels that have a value greater than 0.17, i.e. pixels related to land and clouds. The blue color indicates pixels that have a value equal to or less than 0.17, i.e. pixels related to the sea. It can be noticed that some land pixels are recognized as sea pixels. To maintain data diversity in the final dataset, we retained rows with Oa17 band values greater than 0.17. Instead of removing them, we assigned a Secchi depth value of zero, indicating that the depth of the Secchi disk cannot be estimated below the cloud.

Figure 3. Cloud and land mask based on band Oa17 values for the area of the Kaštela Bay and Brač Channel (Croatian coast) on August 2, 2020.

During our analysis, we observed that cloud shadows, passing over land, caused some land pixels to be incorrectly classified as sea pixels. Cloud shadows appear darker due to a higher proportion of diffuse solar radiation and can be challenging to distinguish from dark surfaces with similar spectral signatures (e.g. water) (Fernandez-Moran et al., 2021). This problem, as well as the atmospheric correction, at this stage of the research will be left to the proposed model to learn on its own how to achieve reliable Secchi prediction with these constraints.

Finally, each row of constructed dataset for training and testing is determined as:

Table

Oa1	Oa2	Oa3	…	Oa21	Secchi
0.185	0.171	0.141	…	0.025	16

where Oa1 to Oa21 present band values for each location of in situ measurement labelled as Secchi. To establish match-ups between concurrent satellite and field measurements, the satellite and field data were aligned based on the same sampling date and the latitude/longitude coordinates of the sampling locations. Although the exact time of the in situ measurements was not available, match-ups are made based on the date of measurement. This approach allowed the integration of satellite band values (Oa1 to Oa21) and the corresponding Secchi depth measurements for each data point in the constructed dataset for training and testing purposes.

Figure 4 presents the spectral values of the Sentinel-3 OLCI TOA reflectance for different in situ measurements of Secchi depth. The plot distinguishes the spectral reflectances between the maximum (30 m) and minimum (2 m) Secchi depth values when the sampling site was cloud-free and the minimum (1 m) Secchi depth value when cloud cover was present. The spectral curves of the maximum and minimum Secchi depth values under clear skies show similar trends but different magnitudes, especially in the visible part of the electromagnetic spectrum. However, the curve corresponding to the minimum Secchi depth value in cloudy conditions shows significantly higher spectral responses, especially in the infrared part of the spectrum where the Oa17 band is located, which is commonly used as a reference for the presence of clouds.

Figure 4. One dimensional data example—Sentinel-3 OLCI TOA reflectances corresponding to in situ Secchi values.

3.3. One dimensional convolutional neural network

Convolution is a mathematical operation used in image processing to extract features from images by applying specific filters. Traditionally, 2D convolution is applied to image patches. However, in our approach, we utilize 1D convolution on one dimensional data, like time series, represented by 21 values corresponding to surface reflections of 21 bands. This allows us to focus on the spectral response of surface pixels. Our hypothesis is that the relationship between different band reflections, captured using convolution, encodes the clearness of the water body, measured as Secchi depth.

A Convolutional Neural Network (CNN) is a type of deep neural network comprising convolutional layers, pooling layers, and fully connected layers. Convolutional layers apply filters to the input data, while pooling layers perform pooling and striding operations to extract features. During training, the CNN optimizes the filter weights to identify relevant patterns in the input data. Finally, the fully connected layers classify or regress the output values based on the learned features.

One dimensional convolutional neural network (1D-CNN) is specifically developed to deal with one-dimensional data. A 1D-CNN model can have one-dimensional convolutional layers, pooling layers, dropout layers and linear or non-linear activation functions to determine the output of nodes in a layer of the network. The convolutional operation is a linear operation that involves application of the filter w of length L known as the kernel, to an input vector x of length K. This operation gives unique values, creating a feature map that summarises the presence of detected features in the input. After creating the feature map, each value from the feature map together with the bias term b can be passed through a nonlinear function f such as Rectified Linear Unit (ReLU) (Lateef & Abbas, 2022). The result is a one-dimensional output layer y of length K−L + 1 with no zero padding, as shown in (2).

(2) $\mathit{y}\left(\mathit{j}\right)=\mathit{f}\left(\sum _{\mathit{i}=0}^{\mathit{L}-1}\mathit{w}\left(\mathit{i}\right)\mathit{x}\left(\mathit{j}-1\right)+\mathit{b}\right),\mathit{j}=0,1,\dots ,\mathit{K}-1$(2)

Figure 5 presents a state-of-the-art 1D-CNN architecture used for predicting Secchi disk depth values. The proposed architecture has three convolutional layers, the dropout layer, the maxpooling layer and two dense layers. The convolution layer is often followed by a pooling layer that operates on the feature map to produce the mapped pooled features. The pooled features may vary depending on the size of the pooling filter applied, stride and the type of pooling (max or average pooling).

Figure 5. Proposed 1D-CNN architecture for the Secchi disk depth prediction.

To tackle overfitting, a dropout layer is included, which randomly disables nodes during training (Qazi et al., 2022). The activation function used in the hidden layers is Rectified Linear Unit (ReLU) commonly used in deep learning. Unlike the Sigmoid and Tanh functions, which squash input values into a specific range, ReLU is a piecewise linear function that outputs the input directly if it is positive and zero if it is negative. This non-linearity helps the model learn complex relationships and mitigates the vanishing gradient problem, making training faster and more stable (Bandyopadhyay, 2021).

The proposed 1D-CNN model was implemented using the Python programming language version 3.8.16 (Van Rossum & Drake, 1995) and its libraries Keras (version 2.9.0) (Chollet et al., 2015) and Tensorflow (version 2.9.2) (Abadi et al., 2016).

3.4. Hyperparameters tuning

The model architecture is defined with hyperparameters that can be tuned during model training. The hyperparameters define the structure of the model. This includes defining the number of convolution layers, the kernel size (size of a convolution filter being used to perform the convolution) and the number of feature maps called filters (Zebin et al., 2016). Additionally, the training network parameters such as the number of epochs, batch size and learning rate can also be selected to improve and find the optimal model. Building a model also requires specifying a loss function and an optimizer. The loss function is a measure of the prediction error during the model training phase, defined here as mean squared error (MSE). An optimizer is an algorithm used to improve finding the best learnable parameters to minimize a loss function, and here we used the optimizer Adam (Diez et al., 2020).

Hyperparameter tuning or optimization is a crucial step in maximizing the performance of our model, as it allows us to identify the optimal combination of hyperparameters. In this paper, for hyperparameters tuning, we used the set of hyperparameters proposed in (Lateef & Abbas, 2022). Figure 6 illustrates the combination of hyperparameters that led to the best performance for our 1D-CNN model. Fine-tuning these hyperparameters is often an empirical process, as their optimal values can vary depending on the dataset and problem. Even small changes in hyperparameters, such as learning rate or batch size, can impact the model’s convergence and final performance. The selected hyperparameters were instrumental in achieving remarkable results in predicting Secchi disk depth based on satellite spectral data. The proposed 1D-CNN model is composed of three hidden Conv1D layers, expertly designed to capture relevant spectral features and dependencies. These Conv1D layers effectively detect patterns within the spectral data, allowing the model to extract important information for accurate predictions. To further process and learn non-linear relationships between the extracted features and the target output, we incorporated two hidden Dense layers in the model. The number of hidden layers in a neural network plays a crucial role in modeling complex relationships within the data. Adding more hidden layers can increase the model’s capacity to capture intricate patterns. However, the impact of varying the number of hidden layers is problem-dependent. In some cases, adding more layers may improve accuracy, while in others, it can lead to overfitting. Striking the right balance between model complexity and generalization is essential for achieving optimal results. In total, the combination of Conv1D and Dense layers results in a sophisticated 1D-CNN architecture, encompassing 17,009 learnable parameters.

Figure 6. Applied hyperparameters to 1D-CNN model.

To perform the modeling of the 1D-CNN, the data was stochastically split, ensuring that the samples were randomly assigned to the training, validation, and test sets. This stochastic approach allows for a random distribution of samples among the sets. While the exact number of samples from each in situ dataset may vary across partitions, the overall distribution maintains the desired percentages: 60% for training (355 samples), 20% for validation (117 samples), and 20% for testing (117 samples).

3.5. Accuracy assessment

According to Stehman and Czaplewski (1998), accuracy assessment quantifies data quality, which can help map users to evaluate the utility of a thematic map for their intended applications. Furthermore, the accuracy assessment can be described through three basic components:

• The sampling design – the protocol of selecting the reference sample units. In this paper, the Secchi disk value presents the point sampling unit as ground truth data for classifying remotely sensed imagery.

• The response design – the protocol for determining the reference land-cover classification of a sampling unit. It refers to the process of determining the measurement or observation that will be made at each point sampling unit. In this study, the response design for a point sampling unit of Secchi is a single pixel of Sentinel-3 OLCI with spatial resolution of 300 × 300 m. In this case, the point sampling unit is a specific location on the ground represented by the center of the pixel, and the measurement made at that point is the Secchi value assigned to the pixel based on the remotely sensed imagery.

• The analysis and estimation protocol – the protocol involves comparing the estimated continuous data to the ground truth data (analysis) and using the results of the analysis to make inferences about the population from which the sample was drawn (estimation).

In this paper, in order to assess the performance accuracy of our 1D-CNN model to predict continuous variable Secchi we used the following analysis techniques and measures (Knudby, 2021):

• Mean Absolute Error (MAE) – measures the absolute differences between the predicted values (y_i) and the measured values (x_i) and takes the average of these differences where N is the total number of data points. The smaller the MAE, the better the model is at predicting the target variable (Yue et al., 2018):

  (3) $\mathit{MAE}=\frac{1}{N}\sum _{\mathit{i}=1}^N\left|y_i-x_i\right|$(3)

• Relative Mean Absolute Error (RMAE) – unit/scale independent measure which is calculated as MAE/mean (i.e. mean of the validation dataset ($\bar{x}$)) (Li & Heap, 2011):

  (4) $\mathit{RMAE}=\frac{\mathit{MAE}}{\bar{x}}$(4)

• Root Mean Squared Error (RMSE) – measure of the square root of the mean of the squared differences between the predicted (y_i) and measured values (x_i), where N is the total number of data points. The smaller the RMSE value, the better the model is at predicting the measured values (Qin et al., 2017; Sara et al., 2019):

  (5) $\mathit{RMSE}=\sqrt{\frac{1}{N}\sum _{\mathit{i}=1}^N{\left(y_i-x_i\right)}^2}$(5)

• Relative Root Mean Squared Error (RRMSE) – unit/scale independent measure which is calculated as RMSE/mean (i.e. mean of the validation dataset ($\bar{x}$)) (Li & Heap, 2011):

  (6) $\mathit{RRMSE}=\frac{\mathit{RMSE}}{\bar{x}}$(6)

• Coefficient of determination R² is a statistical measure that presents the proportion of the variance in the dependent variable that is predictable from the independent variables in a linear regression model (Mansouri et al., 2018). R² represents how well the model fits the data and the value ranges between 0 and 1, so the higher the value of R² the better the model fits the data. The value of R² can be calculated using the following formula:

  (7) $R^2=\frac{\sum _{\mathit{i}=1}^n{\left(\widehat{y_i}-\bar{y}\right)}^2}{\sum _{\mathit{i}=1}^n{\left(y_i-\bar{y}\right)}^2}=1-\frac{\sum _{\mathit{i}=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{\sum _{\mathit{i}=1}^n{\left(y_i-\bar{y}\right)}^2}$(7)

where y_i is the value of the i-th sample, $\bar{y}$ represents the mean of variable y and ŷ_i is the estimated value of the i-th sample.

• Pearson’s correlation coefficient (r) – measures the strength and direction of the linear relationship between two variables. The value of r should be −1 < r < 1. The correlation between parameters x and y is quantified by the correlation coefficient calculated as Agarwal and Saxena (2011):

(8) $\mathit{r}=\frac{\sum _{\mathit{i}=1}^N\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{\sum _{\mathit{i}=1}^N{\left(x_i-\bar{x}\right)}^2}\sqrt{\sum _{\mathit{i}=1}^N{\left(y_i-\bar{y}\right)}^2}}$(8)

where y_i represents predicted and x_i measured values, while $\bar{x}$ and $\bar{y}$ represent mean values.

3.6. Comparison of 1D-CNN with other regression algorithms

Another way to demonstrate and evaluate the good performance and effectiveness of a proposed model 1D-CNN is by comparing it to other commonly used regression algorithms in GIS and remote sensing (Upreti, 2022) such as:

• Linear regression is a simple algorithm that models the relationship between a dependent variable and one or more independent variables as a linear function. The goal of linear regression is to find a line of best fit that minimizes the residual sum of squares between predicted and actual values (James et al., 2013a).

• Ridge regression is a type of linear regression that aims to prevent overfitting by adding a penalty term to the cost function. This penalty term restricts the values of the regression coefficients, thus reducing the model’s variance and improving its generalization performance (James et al., 2013b).

• Decision Tree regression is a non-parametric algorithm that recursively splits the data into subsets based on the values of the input variables. Each split corresponds to a node in a tree, and the goal is to find the sequence of splits that results in the lowest residual sum of squares (Loh, 2011).

• Random forest is an ensemble learning method that combines multiple decision trees where each decision tree in the forest is trained on a random subset of the data and features. The final prediction is based on the average or majority vote of the individual predictions (Breiman, 2001).

• Naive Bayes is a probabilistic algorithm that calculates the probability of each class given input features by applying Bayes’ theorem. It assumes that the input features are conditionally independent given the output variable, and then predicts the class with the highest probability based on these calculated probabilities (Prabhat & Khullar, 2017).

• Support Vector Machine regression is a kernel-based algorithm that finds a hyperplane in a high-dimensional space and contains a maximized margin that separates data points into different classes with a minimal penalty term (Smola & Schölkopf, 2004).

These regression algorithms were implemented by using the scikit-learn library version 1.0.2 for Python (Pedregosa et al., 2011). This powerful library provides a wide range of tools for machine learning and data analysis including a variety of regression methods. All implemented regression algorithms were applied to a dataset of 21 features and one observation (Secchi disk depth) and used default parameters defined in the scikit-learn library. The results of the analysis are presented in Section 4.2.

4. Results

In this section, we present the results of the proposed 1D-CNN model for predicting Secchi disk depth in the eastern Adriatic Sea. We also compare it with conventional machine learning methods for regression. Furthermore, based on the current model, we have produced a map showing state of art model that shows the distribution of Secchi disk depth values throughout the study area and observed spatial patterns or trends. As part of our comprehensive evaluation, we have included Figure 7, a chart illustrating the complete development and evaluation process of the proposed 1D-CNN model.

Figure 7. Flowchart of the 1D-CNN model development and evaluation process.

4.1. Quantitative algorithm performance

A quantitative evaluation of the performance of a 1D-CNN model for predicting the value of Secchi disk depth is presented first. Table 2 displays the performance of the 1D-CNN model on two datasets related to Slovenian and Croatian measurements. The Slovenian dataset includes in situ data acquired from the National Institute of Biology, Marine Biology Station in Piran, while the Croatian dataset contains data provided by the Croatian water management authority Hrvatske vode. It is worth noting that the model based solely on volunteer data collected through the Secchi Disk Project is not included in Table 2, because it contains too few data points for training and testing the 1D-CNN model (<20). The Final dataset in the table includes all the listed datasets together.

Table 2. Comparison 1D-CNN performance for different datasets.

Dataset		MAE	RMAE	RMSE	RRMSE	R^2	r
Slovenian measurement dataset	Train	0.012	0.241	0.019	0.361	0.815	0.904
	Test	0.012	0.239	0.022	0.499	0.666	0.844
Croatian measurement dataset	Train	0.015	0.187	0.020	0.305	0.915	0.929
	Test	0.021	0.193	0.028	0.325	0.830	0.850
The final dataset	Train	0.014	0.167	0.024	0.288	0.894	0.949
	Test	0.014	0.167	0.023	0.276	0.890	0.944

It is important to note that the metrics included in the performance evaluation Table 2 are calculated for train and test, but not on the validation portion of the dataset. The validation set was employed for hyperparameter tuning and model selection to optimize the model’s performance during the training of the CNN model. The final evaluation of the model’s performance was conducted on a separate test dataset, which was entirely independent and not used during the model training process. The detailed metrics for accuracy assessment of the proposed model, such as mean absolute error (MAE), relative MAE (RMAE), root mean squared error (RMSE), relative RMSE (RRMSE), coefficient of determination (R²) and Pearson’s correlation coefficient (r) are listed in Table 2 for the Slovenian, Croatian, and Final datasets. Metrics were calculated for the training and test datasets, where the test dataset provides an unbiased assessment of the model’s generalization to new, unseen data. The results shown in this table show how including more data from different sources, even by including volunteer data, without quality control, yields a model that better generalizes and predicts Secchi value more accurately.

Additionally, Table 2 presents a comprehensive comparison of the 1D-CNN model’s performance across different datasets. The coefficient of determination (R²) for both the Slovenian and Croatian datasets ranges from 66% to 83% on the test set, indicating the model’s ability to explain a significant portion of the variance in Secchi depth predictions. However, it is worth noting that the root mean squared error (RMSE) on the test set exceeds 2 m, revealing some level of prediction error. Additionally, the relative root mean squared error (RRMSE) demonstrates that, on average, the model’s predictions deviate by approximately 30% from the mean of the actual Secchi depth values in the Slovenian and Croatian test datasets. The observed discrepancy between the training and test performance metrics suggests potential overfitting of the 1D-CNN model for the Slovenian and Croatian datasets. While the model achieves high accuracy during training (as seen in the low RMSE and RRMSE), its generalization to new, unseen data (test dataset) is slightly compromised, leading to higher errors. Overall, the 1D-CNN model demonstrates promise in predicting Secchi depth, as evidenced by the favorable R² values (train: 0.894, test: 0.890) and relatively low MAE (train: 0.014, test: 0.014), RMSE (train: 0.024, test: 0.023), RMAE (train: 0.167, test: 0.167), and RRMSE (train: 0.288, test: 0.276) in the final dataset. These results highlight the model’s ability to explain a substantial proportion of the variance and achieve accurate predictions on unseen data. To gain a visual understanding of the model’s predictions, Figure 8 presents a prediction error plot for the final test dataset. The graph displays the difference between the predicted values and the measured values of Secchi depth in meters (m). Analyzing Figure 8, it can be seen a strong linear relationship between the predicted values and measured values on the final test dataset, as indicated by the plotted line. The line of best fit closely follows the data points, suggesting a correlation between the model’s predictions and the actual Secchi depth values and indicating a high degree of accuracy in the predictions. However, to quantify the accuracy of these predictions, additional statistical metrics listed in Table 2 such as mean absolute error (MAE) or root mean squared error (RMSE) should be considered.

Figure 8. A prediction error plot shows the difference between the predicted values and the measured values of Secchi depth in meters (m) on the final test dataset.

Figure 9 presents an error histogram that provides a visual representation of the distribution of errors between the predictions of the 1D-CNN model and the measured values of Secchi disk depth. The histogram reveals a Gaussian distribution of errors, indicating a central tendency around the mean value which is close to zero. This distribution suggests that the model’s predictions are generally accurate, with most errors clustered closely around the true values of Secchi disk depth. Such a well-formed Gaussian distribution further reinforces the model’s effectiveness in providing precise and consistent predictions for the given dataset.

Figure 9. Histogram of errors of 1D-CNN model on the final test dataset.

As can be seen in the graphs shown in Figures 8 and 9, the 1D-CNN model achieves quite good results in predicting the Secchi disk depth on the final test dataset. The results of the proposed model showed that it was able to make accurate predictions with small errors when we consider a dataset containing both Slovenian and Croatian measurements. The Root Mean Squared Error (RMSE) was 0.024 for the training data and 0.023 for the test data, indicating that the model fitted well to the training data but also generalized to new unseen data. In addition, the model achieved a low Mean Absolute Error (MAE) for both the training and test data, with values of 0.014 and 0.014 respectively, indicating that the model makes predictions that are, on average, very close to the true values. The low RMSE and MAE values indicate that the model makes accurate predictions. Furthermore, the 1D-CNN model shows a good fit to the training dataset with a R² value of 0.894 and also generalizes well to the test dataset with a R² value of 0.890. It is also noted that the 1D-CNN model has similar R-squared values for the training and test datasets. Furthermore, the model has a strong correlation between the predicted and measured values, as shown by the high Pearson correlation coefficient of 0.949 for the training dataset and 0.944 for the test dataset.

Overall, the model performed well in terms of accurate predictions with low error and was able to generalize well to new data. The fact that the values of the individual metrics are similar for the training and test datasets suggests that the model does not over-fit the training data and is able to generalize well to unseen data.

4.2. Performance analysis of 1D-CNN and commonly used regression algorithms

The results of the analysis are presented in Table 3, which includes a comparison of the accuracy assessment metrics of each algorithm. It can be noted that the utilization of regression algorithms was found to be less efficacious in comparison to the proposed 1D-CNN model for predicting Secchi disk depth, as evidenced by the results presented in Table 2.

Table 3. Comparison of regression algorithms metrics.

Model	Dataset	MAE	RMAE	RMSE	RRMSE	R^2	r
Linear	Train	0.029	0.334	0.039	0.448	0.727	0.853
	Test	0.030	0.372	0.041	0.500	0.638	0.809
RidgeCV	Train	0.041	0.462	0.052	0.593	0.514	0.718
	Test	0.038	0.472	0.049	0.615	0.476	0.698
Decision Tree	Train	0.000	0.002	0.002	0.023	0.999	0.999
	Test	0.022	0.327	0.043	0.635	0.597	0.795
Random Forest	Train	0.029	0.315	0.044	0.482	0.643	0.802
	Test	0.029	0.417	0.044	0.673	0.584	0.769
Bayesian Ridge	Train	0.029	0.342	0.039	0.451	0.724	0.851
	Test	0.029	0.350	0.039	0.474	0.665	0.819
Support Vector Regression	Train	0.064	0.730	0.073	0.827	0.039	0.754
	Test	0.063	0.760	0.071	0.865	−0.106	0.745

Linear, RidgeCV and Bayesian Ridge linear regression models, while relatively straightforward, struggled to capture the complex relationships within the data. Their MAE, RMSE, and R² values indicated that they couldn’t effectively model the Secchi disk depth predictions. The Decision Tree model displayed overfitting, where it fit the training data exceedingly well but performed poorly on the test data. This suggests that the model became overly complex during training, failing to generalize to new, unseen data. While Random Forest is an ensemble method that typically improves prediction accuracy, it still couldn’t outperform the 1D-CNN model. This could be due to limitations in capturing the nuanced patterns in the data. Support Vector Regression displayed relatively poor performance, with a negative R² on the test dataset. This suggests that the model struggled to fit the data or may not have been the best choice for this specific problem. In summary, the superior performance of the 1D-CNN model can be attributed to its ability to extract informative features and build a complex function that accurately captures the input-output relationship, particularly in dealing with the complexities of the Secchi disk depth prediction problem. The regression algorithms, while simpler, were less effective at modeling these intricate relationships. This analysis underscores the importance of feature extraction and the ability of deep learning models to handle complex data patterns effectively.

None of the regression models, including Linear, RidgeCV, Bayesian Ridge, Decision Tree, Random Forest, and Support Vector Regression, were able to attain a coefficient of determination (R²) that exceeded 0.8, with the exception of Decision Tree regression on the training dataset. However, performance of the algorithm on the test set significantly dropped, which exhibited evidence of overfitting. Additionally, the RMSE metric for both the training and testing sets was found to be greater than 3 m for the regression algorithms, whereas the 1D-CNN model demonstrated a lower error rate of less than 2.5 m on both sets of data. Furthermore, the RRMSE values of approximately 50% obtained for different regression models indicate that, on average, the models’ predictions deviate by around 50% or more from the mean of the actual Secchi disk depth values.

4.3. The spatial distribution of Secchi disk depth

While in situ measurement is performed on measurement locations and provide value of Z_SD on discrete locations, the 1D-CNN model has capability of predicting the Z_SD for the whole scene of study area. The aim of this study was to investigate the spatial distribution of Secchi disk depth in an Adriatic water body using a 1D-CNN model on remote sensing imagery. A map of the selected scene was created using a 1D-CNN model in Python and then visualized using the free and open source QGIS 3.10.10-A Coruña (QGIS Development Team, n.d.), as shown in Figure 10. The results of the model indicate that the Secchi disk depth is highest in areas farther from the mainland and lowest in the northern region and near the coastline. The northern Adriatic Sea has an average depth of 35 m, which is relatively shallow. The Po, Adige and Isonzo/Soča rivers are contributing factors to the low water transparency in this region, as they affect the concentrations of dissolved nutrients, biological productivity, salinity, and stratification in the northwestern part of the Adriatic Sea (Eker-Develi et al., 2022). Also, the map in Figure 10 illustrates that, besides the northern region, the coastal areas enclosed by particular islands, as well as sheltered areas such as coves and bays, exhibit lower sea transparency. These are the areas where water quality is of particular concern, especially near mariculture and in bathing waters. Several numerical models use Secchi depth in the equations for pathogenic microorganism die-off (De Marchis et al., 2013; Huang et al., 2017; Lešek & Žagar, 2018; Mancini, 1978). Moreover, a sensitivity analysis (Lešek et al., 2020) showed that Secchi depth is the most important environmental parameter for determining the decay of Escherichia coli in the coastal sea. The spatial and temporal resolution of the new 1D-CNN model will facilitate more accurate water quality modelling.

Figure 10. The map illustrates the distribution of Secchi disk depth in the study area on September 3, 2021.

To overcome the limitations of sparse and expensive in situ measurements, we opted to compare the efficacy of our model with the Case-2 Regional CoastColour (C2RCC) algorithm (Brockmann et al., 2016). Using the C2RCC processor v1.0 within the SentiNel Application Platform (SNAP) software, we generated a map of the kd_z90max product (Figure 11), i.e. the depth of the water column from which 90% of the water-leaving irradiance is derived. The kd_z90max product is an indicator of water clarity and is often used as a proxy for the Secchi disk depth, which is a traditional measurement used to assess water transparency. This product corresponds to 1/K_d_min, where K_d_min presents mean irradiance attenuation coefficient at the three bands with minimum K_d. The unit of kd_z90max product is meter (m) (Kyryliuk & Kratzer, 2019; Soriano-González et al., 2022). In addition to kd_z90max, the C2RCC processor can retrieve other important parameters related to the oceanic ecosystem, such as the chlorophyll concentration (conc_chl), total suspended matter (conc_tsm), the absorption of organic detritus and Gelbstoff at 443 nm wavelength (iop_adg) and the Gelbstoff absorption coefficient at 443 nm wavelength (iop_agelb). These parameters provide valuable information about the ocean’s composition and behavior (Kyryliuk & Kratzer, 2019).

Figure 11. The map illustrates the distribution of kd_z90max in the study region on September 3, 2021, created using the C2RCC processor in SNAP.

Furthermore, the comparison of maps of the spatial distribution of Secchi disk depth obtained by applying the 1D-CNN model (Figure 10) and kd_z90 max by applying the C2RCC processor (Figure 11) reveals that both maps show similar patterns of variation. This similarity can be observed in regions such as the northern Adriatic Sea, the Zadar Archipelago, and the Kaštela Bay. While the absolute values of the parameters in these areas may differ, the maps exhibit a consistent spatial change in Secchi disk depth and kd_z90max for both the 1D-CNN model and the C2RCC processor.

Due to the limited availability of measured data on September 3, 2021, we selected the closest data points to evaluate the predictive performance of 1D-CNN and C2RCC models for Secchi disk depth and kd_z90max values. The selected data points were representative of a variety of environmental conditions, including varying water turbidity levels, depths and distances from the coast. The results of this evaluation for four data points, including sampling date, geolocation, in situ measurements, and corresponding predictions by the C2RCC processor of kd_z90max and 1D-CNN model, are presented in Table 4. The 1D-CNN model outperformed the C2RCC processor parameter kd_z90max in predicting Secchi depth, with a maximum error of 4 m compared to the kd_z90max error of over 10 m. To further illustrate the differences in prediction performance between the 1D-CNN model and the C2RCC processor, we plotted the Secchi depth prediction values for each dataset using the two models, along with the in situ measurements, in Figure 12. The figure shows that the curve of the 1D-CNN model closely follows the curve of the in situ measurements, indicating high accuracy of the model predictions. In contrast, the curve representing the predictions of the C2RCC processor for kd_z90max deviates significantly from the curve of the in situ measurements, indicating lower accuracy of the algorithm’s predictions. Overall, these results indicate that the 1D-CNN model is more reliable than the C2RCC processor’s parameter kd_z90max in predicting Secchi disk depth.

Figure 12. Comparison of Secchi disk depth predictions using in situ measurements, 1D-CNN model, and C2RCC processor based on data from Table 4.

Table 4. Comparison of in situ Secchi depth measurements with kd_z90max predicted values from C2RCC processor and Secchi disk depth from 1D-CNN model.

#	Date	Lat	Lon	C2RCC [m]	1D-CNN [m]	In situ [m]
1	2021-09-01	45.173	14.657	11	18	22
2	2021-09-02	45.247	14.417	14	24	26
3	2021-09-03	44.787	14.157	15	21	23
4	2021-09-06	45.435	13.397	11	15	18

5. Discussion

In this section, we discuss the accuracy, limitations and applicability of the proposed model for predicting Secchi disk depth using Sentinel-3 OLCI data. We also explore potential future implications for monitoring long-term changes in Z_SD.

5.1. Accuracy of the 1D-CNN model

The proposed model’s performance has been thoroughly evaluated using various metrics, including R², RMSE, RRMSE, MAE and RMAE. The model demonstrates satisfactory accuracy, particularly when leveraging multi-spectral data. However, it is essential to acknowledge its limitations when applied to specific datasets. While the R² values indicate strong correlations between the predicted and measured Z_SD values, other metrics such as RMSE, RRMSE, MAE and RMAE suggest some variability and deviations from the true values. The observed variability can be attributed to complex interactions between water quality parameters, environmental conditions, and the inherent limitations of the modelling approach (Hafeez et al., 2019). Moreover, the model’s performance was compared quantitatively with regression algorithms, showing superior results. Additionally, a comparison was made with C2RCC processor’s parameter kd_z90max both quantitatively and qualitatively. These comparisons further support the model’s effectiveness in predicting Z_SD and highlight its potential advantages over other methods.

5.2. Limitations of the 1D-CNN model

Despite the promising performance, proposed model has certain limitations that should be considered. Firstly, the accuracy of predictions may be influenced by the quality and availability of ground truth data used for training and validation. Despite the performed, statistical analysis shows no deviation of the measurements performed by citizens in comparison to the official measurements, the Secchi depth is still considered subjective measure and cannot be absolutely independently validated. Additionally, the model’s performance could vary in different aquatic environments due to the diversity of water types and optical properties. The model’s sensitivity to outliers and noise in the data, especially during atmosphere correction, may impact its predictive capabilities. As with any machine learning model, there is a risk of overfitting to the training dataset (Chen et al., 2022). Therefore, it is essential to carefully manage hyperparameters and implement effective strategies to avoid overfitting. Considering these limitations and adopting appropriate measures to address them will enhance the model’s robustness and reliability in predicting Z_SD accurately across various scenarios and locations.

5.3. Applicability to other regions

The model’s applicability extends beyond the specific datasets from the Croatian and Slovenian coastal sea, making it suitable for other regions with similar water quality characteristics and spectral properties. Leveraging the Sentinel-3 OLCI data allows for the extension of the model to different geographic areas, benefiting from the instrument’s global coverage and frequent revisit times. However, it is important to note that applying the model to significantly different water bodies may necessitate retraining and adaptation to accommodate regional variations (Nasir et al., 2023). Nevertheless, the methodology described in this paper and demonstrated the process of model construction for the study area of northern Adriatic Sea can be reused in any other study area and region and yield significant results.

5.4. Future implications for long-term monitoring

The ability to predict Z_SD using remote sensing data opens possibilities for long-term monitoring of water quality and environmental changes. Continuous monitoring of Z_SD can provide valuable insights into the health of aquatic ecosystems, detect trends in water clarity and identify potential environmental factors or conditions that can cause disturbances. By integrating long-term Z_SD data with other environmental indicators, such as Chl-a concentration and water temperature, comprehensive assessments of water quality can be achieved. Moreover, the ability to monitor Z_SD over time allows for the identification of long-term changes in water transparency, which can be vital for understanding the impacts of climate change, retraining and adaptation to accommodate regional variations the biogeochemical processes, evolutions of aquatic ecosystems or human activities on aquatic environments (Li et al., 2020).

6. Conclusion

In this paper, we proposed a novel method to overcome the major challenges in satellite remote sensing for water quality monitoring. We developed an algorithm to estimate Secchi disk depth (Z_SD), which is a proxy for many water quality parameters obtained from satellite remote sensing imagery. To refine the algorithm, we created a larger dataset by combining two official data sources and a dataset from citizen scientists.

To achieve efficient feature extraction, we used 1D-CNN. This approach helped us to build a deep neural network for estimating the Z_SD value. Our results have shown that this approach achieves high accuracy compared to in situ measurement, and it does not overfit as other Machine Learning (ML) models on the same dataset. Our proposed method has the potential to improve the accuracy and efficiency of satellite remote sensing for water quality monitoring.

Furthermore, applying the new algorithm to a time series of satellite images will provide valuable datasets of Z_SD at high spatial and temporal resolution. Such datasets can improve the accuracy of ecological models for the transport of suspended sediment-bound pollutants and the decay of microorganisms in coastal waters with spatially varying conditions, where conventional measurements cannot provide a sufficient amount of data. In addition, high temporal resolution can increase our knowledge of biological processes and seawater quality throughout the coastal area along the Eastern Adriatic coast and facilitate water quality modelling over longer time periods.

In future work, we aim to further improve the accuracy and efficiency of monitoring and modeling Secchi disk depth by exploring additional data sources and processing levels. Specifically, we plan to incorporate additional data sources, such as high-resolution satellite imagery, to further improve the accuracy of our models for estimating Secchi disk depth. Additionally, we will investigate the use of L2 imagery, which can avoid the need for atmospheric correction, and compare its performance to that of our model which uses Sentinel-3 OLCI L1 imagery for Secchi depth estimation. By combining these approaches, we believe we can develop even more accurate and efficient methods for monitoring and modeling Secchi disk depth, with potential applications in a wide range of environmental monitoring and management contexts. We hope that our work will inspire future research in this area and contribute to the development of more accurate and efficient methods for monitoring and modeling Secchi disk depth.

Acknowledgements

The authors would like to express their deepest gratitude to the Croatian Legal entity for water management – Hrvatske Vode and the National Institute of Biology – Marine Biology Station Piran for sharing the valuable data used in this study. The authors thank the Secchi Disk project www.Secchidisk.org for the seafarer Secchi Depth data.

Disclosure statement

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

Data availability statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Additional information

Funding

This research was supported through project CAAT (Coastal Auto-purification Assessment Technology), funded by the European Union from European Structural and Investment Funds 2014–2020, Contract Number: KK.01.1.1.04.0064. The authors acknowledge the financial support from the Slovenian Research Agency (research core funding P2-0406 and P2-0180, and projects J2-3055 and J1-3033).

Notes on contributors

Antonia Ivanda

Antonia Ivanda is a current PhD student of Electrical Engineering and Information Technology at the University of Split. In 2019, she completed her MSc from the Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture in Split, with her thesis focused on developing a web system for managing student practices. Her research lies in the field of computer science, with a primary focus on artificial intelligence for data analysis and prediction of bathing water quality, as well as assessment of autopurification capabilities using a remote sensing data-driven approach. Additionally, Antonia is an expert in using qGIS software for spatial visualization of vector and raster data obtained via satellites.

Ljiljana Šerić

Ljiljana Šerić is associate professor at Department of Electronics and Computer Science at Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture, University of Split, Croatia. She is a member of Department for Modelling and Intelligent Systems. She participates in the activities of Laboratory for Intelligent Systems and Laboratory for Advanced Internet Technologies. She is a collaborator of Centre for wildfire research. Ljiljana Šerić received her PhD. in Computer Science in 2010 at University of Split. She has worked on scientific, specialistic and technical projects in the domain of environmental disasters protection and environmental hazards prevention. She participated in the projects dealing with wildfires, high winds, and coastal pollutions. Her research interests are artificial intelligence, web technologies and distributed systems.

Dušan Žagar

Dušan Žagar received his PhD Civil Engineering from the University of Ljubljana’s Faculty of Civil and Geodetic Engineering in 1999. He currently serves as a Professor at the University of Ljubljana’s Faculty of Civil and Geodetic Engineering in Ljubljana, Slovenia, where he has been a dedicated member of the faculty since December 1995. Throughout his academic journey, Žagar has held various positions within the university, starting as a Junior Researcher from 1995 to 1999, progressing to Researcher and Teaching Assistant from 1999 to 2004, and finally assuming the role of Assistant Professor from 2004 to 2014. In addition to his work at the University of Ljubljana, Žagar had the privilege of being affiliated with the Università della Calabria in Italy as a Professor from September 2017 to December 2017, contributing his expertise to the DIATIC department. His areas of expertise encompass a wide range of subjects, including environment, water quality, fluid mechanics, simulation, numerical modeling, modeling and simulation, numerical simulation, water engineering, modeling, and marine environment.

Krištof Oštir

Krištof Oštir received his PhD in remote sensing from the University of Ljubljana. His main research areas are optical remote sensing and image processing. He conducted research in land use and land cover classification, change detection, object-based classification, and laser scanning. Applications of remote sensing range from hazard monitoring, vegetation mapping, forestry, and agriculture to archaeology. He is actively involved in the development of small satellites for Earth observation. He is the author of the first Slovenian remote sensing monograph and of a number of papers on remote sensing, geographical information systems and computer engineering. He is employed at the Faculty of Civil and Geodetic Engineering, University of Ljubljana, as a professor of several courses on remote sensing and satellite image processing.