Introduction. The task of promptly identifying the source of an emergency or discharge of pollutants into a water body arises when the consequences of an incident are eliminated and those responsible are brought to justice. Traditional monitoring, which relies on a network of stationary posts and sampling, records concentrations at individual points [1]. However, such data does not allow specialists to quickly restore a complete spatial and temporal picture of the spread of impurities. The processes of advection and turbulent diffusion quickly "blur" the trace of the source [2].

As the practice of implementing environmental control systems at industrial enterprises demonstrates, the gap between two classes of methods remains.

The first group includes computer vision (CV) and deep learning, which analyze satellite images [3]. Semantic segmentation distinguishes water areas [4]. Spectral indices (NDWI) record anomalies in water color [5]. However, CV only displays visible effects on the surface, leaving the dynamics of transport in the water column unexplained.

The second group consists of hydrodynamic modeling. Advection-diffusion equations predict impurity dispersion in a physically reasonable way [6]. However, the model needs prior knowledge of the coordinates and strength of the source, which are unknown in the classical formulation.

It would be beneficial to examine the limitations of current approaches in more detail.

Satellite monitoring and CV. Yusuf et al. [1] generalized effect-oriented methods for the aquatic environment, achieving high sensitivity to a wide range of substances. However, the authors did not propose any mechanisms for restoring source parameters. Chen et al. [2] performed a review of remote sensing data, demonstrating the high speed of obtaining spatial information. However, their study was limited to simply stating the fact of contamination without addressing the inverse problem. Wang et al. [5] analyzed surface water quality models, most of which operated in a direct predictive mode rather than being intended for retrospective source identification.

Water area selection tools. Program registration certificates [3] and [4] described automated tools for morphometric analysis and identification of water bodies. These tools solved the problem of identifying the water area, but they were not integrated with hydrodynamic transport models.

Digital twins and artificial intelligence. Maksoud and Mohamed [6] analyzed the use of digital twins in the water sector and concluded that the concept was promising, but required algorithms for automatic calibration based on observational data. Frincu [7] reviewed the use of AI to assess water quality. The main disadvantage of the review was the lack of physically sound transfer models. Only statistical methods were used.

Inverse identification of the source. Existing works [8] used hydrodynamic modeling and optimization algorithms [9]. However, the geometry of the water area was set manually or derived from static maps in these works, which prevented their operational use when new images were received.

The experience of processing more than a hundred Sentinel-2 images has shown that manually selecting the boundaries of a reservoir can take from 20 to 60 minutes per object in an emergency situation. This time is unacceptable.

Therefore, there is a need for a method that can:

− automatically extract the geometry of a water area from satellite data using CV;

− use this geometry in a hydrodynamic model to inverse identify the source;

− perform this in a time acceptable for rapid response (minutes, not hours).

The research aims to develop and validate an approach that combines computer vision (semantic segmentation of satellite imagery and cartographic data) with hydrodynamic modeling (two-dimensional advection-diffusion equation) to retrospectively identify the coordinates of an emergency discharge source using the observed concentration field.

Tasks:

− to implement the semantic segmentation module of water surface;

− to create a hydrodynamic model of passive impurity transfer;

− to develop a reverse identification algorithm by iterating through virtual sources and comparing the mean-square error (MSE);

− to validate the approach using synthetic data with a controlled error.

Materials and Methods. Methodological basis of the study was a sequential data processing algorithm (Fig. 1), in which information went from a raw image to a quantitative conclusion on the location of the source of pollution. The architecture of the solution included two fundamental interconnected modules operating in a single geographic information coordinate system.

A module for intelligent spatial data processing based on computer vision. This module was responsible for automated preparation of initial information for physical modeling and initial diagnostics. The system received an image of the water area under study, obtained from medium-resolution satellite platforms, such as Sentinel-2 and Landsat, using aerial photography from UAVs, or representing a digitized cartographic image. After the preprocessing stage, which included geometric and radiometric correction, as well as conversion to a single coordinate system, semantic segmentation of the water surface became a key task. To solve this problem, deep learning algorithms were used. These algorithms were specially adapted for analyzing images of the Earth and were often based on convolutional neural networks [10]. They were trained on mapped out sets of satellite images to accurately classify each pixel as “water” or “non-water”. The use of modern frameworks and libraries made it possible to achieve high segmentation accuracy even in difficult conditions such as cloud cover, glare on the water or a non-uniform coastline. The result of the module was a binary mask of the water area, which served as the basis for constructing the computational domain of the hydrodynamic model [11]. This stage completely eliminated subjective errors and significant time costs associated with manually selecting the contours of the reservoir [12].

After receiving the binary mask of the water area (the result of semantic segmentation), the contours of water bodies were highlighted. The cv2.findContours function from the OpenCV library (Python) was used for this. The cv2.RETR_EXTERNAL parameter ensured that only the outer contours were extracted, ignoring the inner cavities (for example, islands). The cv2.CHAIN_APPROX_SIMPLE parameter was used to compress the contour: redundant points lying on the same straight line were removed, which reduced the amount of data without losing the shape of the contour. Before selecting the contours, the mask was morphologically processed: closing operations (filling small gaps inside the water area) and opening operations (removing small noise fragments outside the reservoir) were performed sequentially. A 5×5 pixel core was used, with 2 iterations for closing and 2 iterations for opening.

Hydrodynamic modeling module and the inverse identification algorithm.

This module was the computing core of the system. A two-dimensional 2D model based on the advection-diffusion equation was used to describe the transport of pollutants in a reservoir [13]. This choice was determined by a compromise between computational efficiency, which was critical for multiple calculations when solving the inverse problem, and the adequacy of the description for most reservoirs [14], where horizontal scales significantly prevailed over vertical ones, and mixing could be considered quite intense. The transfer equation of the passive impurity concentration [15] C is as follows:

where κ and υ — components of the horizontal flow velocity vector (m/s); Dh — horizontal turbulent diffusion coefficient (m²/s); S(x, y ,t) — source function describing power, localization, and time mode of discharge. For the numerical solution, the finite volume method was used, which guaranteed the conservation of mass [15]. Flow velocity fields κ and υ could be set analytically for simple scenarios, read from the results files of a separate hydrodynamic model, or reconstructed from measurement data. It should be noted that, depending on the scale of the water area, the complexity of the currents, and the required accuracy, the system could use various numerical methods to solve equation (1). For most scenarios, especially when working with large bodies of water, the finite volume method was used to ensure mass conservation and stability of the solution. However, for problems with high dynamics or the need for increased accuracy in areas of intense concentration gradients, adaptive methods such as Runge-Kutta methods or finite-difference schemes of increased order could be used. This made it possible to optimize computational costs and increase the accuracy of source identification in various hydrodynamic conditions.

The algorithm of inverse identification of the source formalized the search problem solution. When the contamination zone was fixed (under the conditions of a synthetic experiment, simulated concentration field Cobs(x, y) in the area of possible location of sources (for example, along the entire perimeter of the reservoir specified by the computer vision module), a set of N virtual candidate points was generated. For each i-th point with coordinates (xiyi), a direct calculation was performed using equation (1), in which source function S (x, y, t) corresponded to the position of this candidate. The result was model field of concentrations (Cmod,i(x, y)). The similarity measure was calculated for quantitative comparison of each model with the observed field, for example, the mean square error (MSE):

where ω — water body area; A — its area. The source of contamination was the virtual candidate for which the proximity measure was minimal: (xs ys) = min (MSEi). Thus, the complex inverse problem was reduced to solving many direct problems and choosing the best match, which ensured the visibility and stability of the result.

Research Results. To objectively verify operability and evaluate accuracy of the proposed approach, a series of computational experiments were conducted using synthetic data. This allowed us to eliminate the influence of uncertainties inherent in real-world measurements and focus on testing the algorithm's performance. An oval-shaped water area with a stationary current field was modeled. Three independent scenarios were simulated, each representing the discharge of different types of pollutants. Each scenario had its own background value, runoff concentration, and maximum permissible concentration (MPC). The detailed parameters for each scenario are summarized in Table 1.

In each of the 300 tests, 100 for each parameter, the true source coordinate was randomly selected. The computer vision module accurately processed the input data, generating an accurate mask of the water area. The inverse identification algorithm, sorting candidates in 50-meter increments, demonstrated high efficiency consistently. Statistical analysis of the results revealed that in 285 cases (95%), the algorithm correctly identified the true source.

Despite the high efficiency of the proposed approach, there were several conditions that should be taken into account when considering the accuracy of the method. Firstly, the analysis of 15 cases with inaccurate results showed that most of the errors (12 out of 15) occurred when the source was located less than three meters from the water's edge. Near the shoreline, turbulent diffusion and boundary conditions became comparable to advection, leading to a “blurring” of the pollution trace and a decrease in the uniqueness of the inverse problem solution. Secondly, the method relied on a two-dimensional hydrodynamic model, which was justified for reservoirs with a well-mixed water column where horizontal scales dominated over vertical scales. However, in stratified bodies of water, for example, in deep lakes with a pronounced thermocline, or in areas with intense vertical currents, two-dimensional approximation could give significant errors. Thirdly, the developed algorithm required specifying a stationary or quasi-stationary field of flow velocities. With sharply unstable hydrodynamics, for example in tidal estuaries or during floods, the accuracy of identification could decrease without additional calibration of the model based on the hydrological data relevant to the time of the incident. The validation of the method was performed only on synthetic data, which allowed us to judge only its fundamental operability.

Visualization of the results clearly confirmed the high quality of the algorithm. Figures 2 and 3 show the final simulation maps for some of the parameters under research.

The color field shows the spatial distribution of the concentration (or deviation from the background), clearly highlighting the area affected by the discharge. It is important to note that the algorithm not only created a field, but also calculated a probable point of contamination. In all visualizations, the red marker accurately indicated the location calculated by the inverse analysis algorithm. In most tests, this location coincided with the coordinates of the source specified in the scenario. These graphs serve as convincing evidence that the system is able not only to detect contamination, but also accurately indicate its origin.

Discussion. Computational experiments showed that the accuracy of source identification was 95% (285 out of 300 tests). However, 5% of errors (15 cases) were not random. Twelve of them were related to the location of the source at a distance of less than 3 m from the water area boundary. Near the shore, diffusion and boundary conditions distorted the pollution trace, which reduced the uniqueness of the solution to the inverse problem.

As the practice of preparing computational domains showed, discretization at 50-meter intervals was a compromise between speed and accuracy. At 25-meter intervals, the computing time increased by 4 times, while the increase in accuracy did not exceed 2% (tested in test scenarios). Therefore, to ensure efficiency, it was decided to use 50-meter intervals. However, this was a potential source of error: a source shifted by 25–30 m could be attributed to a neighboring grid node.

Comparison with the literature data confirmed the competitiveness of the approach. Jiang et al. [8] reported an accuracy of above 90% for river spills, but their calculated area was created manually. Tao et al. [16] achieved high efficiency on distributed systems, but the geometry of the water area was set a priori. This method fully automated the selection of boundaries through semantic segmentation [4]. This reduced the pre-processing time from 20–60 minutes for manual work to 1–2 minutes.

Automation had its price. The quality of segmentation depended on the resolution of the image, clouds, and glare. Processing of more than a hundred Sentine l–2 scenes showed that when cloudiness was more than 30%, the accuracy of the binary mask dropped to 85–88%. Contour selection errors, expressed in a shift of 1–2 pixels, led to a displacement of the calculated area and, as a result, to an identification error of up to 50 m. In the current implementation, such distortions were not modeled. This is the task for the next stages.

The limits of the method's applicability were clearly defined by the assumptions made. (1) The two-dimensional model was only suitable for reservoirs with intense vertical mixing. For stratified lakes deeper than 10 meters with a thermocline, horizontal diffusion failed to describe the vertical concentration gradient, leading to errors exceeding 30%. (2) The passive impurity model ignored chemical transformations, which was incorrect for pH. Acid waste was neutralized by water's buffering properties, but in synthetic scenarios, pH was treated as a conservative tracer. This simplification reduced accuracy in real-world conditions. (3) The flow velocity field was assumed to be stationary. In practice, hydrodynamics change during floods and tides within a few hours. Without current data-based calibration, identification errors would increase.

In addition to the sources of error listed above, the choice of diffusion coefficient in all scenarios was also a source of error. In a real water body, this coefficient could vary depending on wind and turbulence. At the same time, a 2-fold increase in the diffusion coefficient shifted the source estimate by 30–50 m downstream. However, the coefficient used in the work was set as a constant, which was a weakness in the study. Adaptive assessment based on observational data was outside the scope of this research.

Another limitation was the synthetic nature of validation. The observed concentration field Cobs (x, y) in the experiments was free from measurement noise, data omissions, and ambiguity of spectral indices. In real conditions, the satellite image gives an integral concentration in the surface layer, rather than over the entire depth. This is acceptable for dissolved oxygen and chlorine, but not for pH. Thus, the stated accuracy of 95% is the top estimate. Based on real data, it is expected to decrease to 70–85%, depending on hydrological conditions.

The reliability of the conclusions lies in the fact that the proposed method has proven its fundamental operability. It is suitable for operational use in well-mixed water bodies, such as reservoirs, canals, and flat rivers, with a known or measured current field. For stratified or dynamic systems, a transition to a three-dimensional model and consideration of nonstationarity is required. The practical interpretation of the results is that the algorithm allows for the specification of a probable source area with an uncertainty radius of approximately 50 meters in 10–15 minutes. This timeframe is sufficient for on-site inspection and sampling.

The development prospects are related to the replacement of synthetic data with real satellite images with simultaneous field measurements. It is also necessary to calibrate the diffusion coefficient for the inverse problem. Without these steps, the method remains a prototype.

Conclusion. An algorithm for the inverse identification of the source of emergency pollution discharge into a water body has been developed and programmed. The algorithm consists of two modules: a computer vision module for semantic segmentation of satellite images and a two-dimensional hydrodynamic model of passive impurity transfer.

The computer vision module automatically identifies the water area and reduces the preprocessing time from 20–60 minutes (manually) to 1–2 minutes. This eliminates human errors. The hydrodynamic modeling module solves the advection-diffusion equation. The inverse identification algorithm iterates through virtual sources and selects the one with the minimum mean squared error (MSE) between the modeled and observed concentration fields.

Verification was conducted on synthetic data (300 tests for pH, dissolved O₂ and Cl⁻). The algorithm correctly determined the coordinates of the source in 285 cases. The accuracy was 95%.

The method is suitable for operational use in well-mixed water bodies (reservoirs, channels, flat rivers) with a known field of currents. The prospects: adaptation to real satellite data and calibration of the diffusion coefficient for the inverse problem.

1. Sanitary Rules and Regulations of (as amended on 17 March, 2025) SanPiN 1.2.3685-21 “Hygienic Standards and Requirements for Ensuring the Safety and (or) Harmlessness of Environmental Factors for Humans”. (In Russ.) URL: https://www.consultant.ru/document/cons_doc_LAW_375839/ (accessed: 20.01.2026).