Introduction. This study is devoted to mathematical modeling of accidental oil spill scenarios in the Red Sea in the vicinity of the floating storage and offloading unit FSO Safer off the coast of Yemen. Predictive trajectories of oil-slick drift were constructed under the combined effects of advection, diffusion, evaporation, dissolution, and biodegradation. The modelling results made it possible to identify spatiotemporal patterns of slick transformation, determine the areas of greatest environmental risk along the Yemeni coast, and assess potential damage to marine ecosystems and the region’s socioeconomic infrastructure. Materials and Methods. A three-dimensional numerical oil-spill model was developed to predict oil transport and weathering during the first 72 h, which are most critical for mounting an emergency response. The numerical model uses surface currents and temperature from the HYCOM GOFS 3.1 global analysis and winds from the ERA5 reanalysis. Oil dynamics were simulated accounting for the multifraction composition of the oil, the mesoscale character of the currents, physicochemical weathering processes (evaporation and dissolution), and biodegradation kinetics coupled with microbial population dynamics. Results. The results show a slow northeastward displacement of the slick at a velocity of approximately 0.03 m/s (6.5 km over 72 h), with landfall near Ras Isa during the first day. Mass loss over 72 h is 23.4%, of which 96.7% is due to evaporation and 3.3% is due to dissolution, whereas the contribution of biodegradation at realistic microbial biomass levels does not exceed 0.1% over this time horizon. In addition, a regime of persistent northward transport was considered, selected from a threeyear series of current and wind data for 2023–2025. From January 29 to February 1, 2023, the slick travels approximately 100 km northward along the Yemeni coast to the Kamaran Islands in three days, while mass loss increases to 32%. Discussion. Accurate drift forecasting requires up-to-date hydrometeorological data for the scenario date because the trajectory and displacement distance are determined by the current and wind fields. Satellite radar monitoring data are used as initial conditions. Conclusion. A reproducible predictive oil-spill model based on open data was developed for operational monitoring and environmental risk assessment in the southern Red Sea. The results provide a scientific basis for the urgent implementation of protective measures and for planning regional emergency-response scenarios.

Introduction. The problem of determining the principal directions of a point set in the plane or in space is solved numerically. The task is to determine the orientation of an extremal line passing through the centroid of the set and minimizing or maximizing the functional defined as the sum of the squared distances from all points of the set to the line. This problem is relevant as an auxiliary component of many tasks involving intelligent systems. Materials and Methods. For a point set in the plane, the principal-direction problem is solved explicitly for two polar angles specifying the directions of the extremal lines corresponding to the maximum and minimum of the error functional. If the denominator in the resulting formula degenerates because the points are arranged symmetrically, changing one coordinate of a single point by 10⁻¹⁴ is sufficient to break the symmetry, make the formula applicable, and obtain a doubleprecision result. For a point set in three-dimensional space, the problem is reduced to a numerical iterative algorithm based on gradient descent with respect to the orientation angles of a line passing through the centroid of the set. A minimal compact C++ implementation for determining the principal directions in the three-dimensional case is proposed. Results. For a spatial point set, an explicit expression is obtained for the error functional and for the components of its gradient in the azimuthal and polar directions of a spherical coordinate system. An empirical formula for the gradient step is obtained as a function of the number of iterations, enabling a double-precision numerical solution with a relatively small number of iterations. It is shown that 100 iterations are sufficient to determine the extremal angles even when the initial orientation differs from the final orientation by π/2 for each angle. Discussion. The principal-direction problems for point sets in the plane and in space are solved numerically with double precision. Two test examples confirm double-precision accuracy for cases with the largest deviation between the initial and final line orientations. Both the explicit formulas for the two-dimensional problem and the formulas of the threedimensional iterative algorithm involve only coefficients represented by homogeneous second-order sums that depend on the point coordinates. There are three such coefficients in the two-dimensional case and six in the three-dimensional case. Conclusions. Despite its algorithmic simplicity, the gradient descent method yields well-defined iterative formulas for any initial and intermediate orientation of a line passing through the centroid of a point set in space. The explicit formulas obtained for the principal directions of a point set in the plane and the gradient-descent formulas for the three-dimensional case can be used in analysis problems involving intelligent systems and neural networks.

Introduction. The PSPNet, SMD-Net, and YOLO26-Seg semantic segmentation architectures are considered for the task of detecting oil spills in satellite imagery. Particular attention is paid to comparing segmentation accuracy under identical training conditions. Materials and Methods. PSPNet uses a ResNet101 backbone with a pyramid pooling module for semantic segmentation. SMD-Net is a lightweight shared-backbone architecture with two decoders and CTGM, CoordAtt, and ASPP modules. YOLO26-Seg combines a YOLO26 encoder backbone with fixed weights and a lightweight decoder. The following metrics are compared: IoU (Intersection over Union), defined as the ratio of the intersection of the predicted and ground-truth regions to their union; Dice (Dice coefficient), a measure of segment overlap based on the intersection area; accuracy, the proportion of correct predictions among all predictions; inference time, the time required by the model to process one input; and the number of trainable parameters. Results. After 50 epochs of training on the existing dataset masks without manual annotation, PSPNet significantly outperformed SMD-Net in binary oil-spill segmentation (IoU = 0.704, Dice = 0.770, Acc = 0.896 versus IoU = 0.467, Dice = 0.575, Acc = 0.671 for SMD-Net). The additionally fine-tuned YOLO26l-seg model demonstrated moderate pixellevel metrics (IoU = 0.320) at a reduced detection threshold, which limits its applicability to this task. Discussion. The choice of architecture for oil-spill segmentation is governed by a trade-off between accuracy and speed: PSPNet provides the highest segmentation quality, SMD-Net performs worse across all metrics, and YOLO26-SemSeg cannot reliably detect oil spills without task-specific training. Conclusion. PSPNet significantly outperforms SMD-Net and YOLO26-Seg in binary oil-spill segmentation under identical training conditions (IoU = 0.704 versus 0.467 for SMD-Net), confirming the effectiveness of the ResNet101 backbone combined with pyramid pooling.

Introduction. The coastline of a reservoir is a complex natural object, which geometry has irregularity and signs of selfsimilarity, and the length depends on the scale of measurement. Despite the widespread study of its fractal properties, the transition to a digital representation of the coastline is a complex procedure and is a current topic of research. The purpose of the article is to develop a mathematical-algorithmic scheme for analyzing the coastline, including geometry validation, geodetic measurement, scale dependence analysis, fractal dimension assessment and selection of an adaptive quadrilateral grid using the example of the Black Sea. Materials and Methods. Normalization and validation procedures are applied to the coastline represented as a finite sequence of geographic points to obtain an intermediate, geometrically plausible contour. The contour length is calculated on a sphere using the haversine formula. The “box-counting” method is used to address the coastline՚s multi-scale nature and fractal characteristics. To transition from the line to a 2D representation of the water area, the Lambert azimuthal equal-area (LAEA) projection is used, followed by the construction of a grid with the required cell size. Subsequently, detailed and coarse full-quadrilateral grids are generated using the Delaunay, Frontal-Delaunay for Quads, and Packing of Parallelograms algorithms. A comparison of the grid generators is then conducted. Results. A computational experiment was conducted using Black Sea coastline data. A comparison of two sets of grids demonstrated that Delaunay is the superior generator based on the specified multi-criteria metric. The Delaunay method with a range of 125–250 m should be used to preserve significant coastal features across the entire water area. A highresolution Delaunay configuration with a range of 50–250 m should be selected when accurate reconstruction of the seabed topography is the priority. Discussion. The practical significance lies in the ability to prepare verified contours and grids for seabed topography modelling, geoinformation analysis, and subsequent hydrodynamic calculations. Conclusions. Future research prospects involve expanding the range of coastal systems analyzed, comparing various methods for estimating fractal dimension, investigating the impact of source geodata spatial resolution on the stability of calculated metrics, and adapting the approach for multi-scale monitoring of coastal dynamics.

Introduction. The paper presents the development and testing of an index-based algorithm for detecting indicators of soil erosion by water from Sentinel-2 remote sensing data, considered as the first practical stage in constructing a hybrid physics-based mass-transport model with neural-network parameter identification. Materials and Methods. The algorithm relies on joint analysis of time series of the Normalized Difference Vegetation Index (NDVI) and the Bare Soil Index (BSI), followed by spatial change detection (ΔBSI) with threshold filtering at the 90th percentile. The algorithm was first validated on synthetic data and then applied to real Sentinel-2 imagery for two test sites – the Kamensky District of Rostov Oblast and the vicinity of Moldovanskoye village, Krymsky District, Krasnodar Krai – covering 10 dates within 2024. Results. The algorithm is shown to consistently identify spatially localised zones of increasing bare-soil exposure. Discussion. A key limitation – the inability to distinguish erosion-related exposure from ordinary agrotechnical bare soil — is discussed, along with directions for resolving it (digital elevation model overlay, multi-year analysis). Conclusion. An index-based algorithm for detecting indicators of water-induced soil erosion from Sentinel-2 multispectral time series was developed and validated. Verification on synthetic data and application to two real test areas in southern Russia confirmed its operability while demonstrating the need to separate erosion-related changes from agricultural soil exposure in subsequent model development.