Formalization for Subsequent Computer Processing of Kara Sea Coastline Data

Abstract

This study aimed to develop a methodological framework for predicting shoreline dynamics using machine learning techniques, focusing on analyzing generalized data without distinguishing areas with higher or lower retreat rates. Three sites along the southwestern Kara Sea coast were selected for this investigation. The study analyzed key coastal features, including lithology, permafrost, and geomorphology, using a combination of field studies and remote sensing data. Essential datasets were compiled and formatted for computer-based analysis. These datasets included information on permafrost and the geomorphological characteristics of the coastal zone, climatic factors influencing the shoreline, and measurements of bluff top positions and retreat rates over defined time periods. The positions of the bluff tops were determined through a combination of imagery with varying resolutions and field measurements. A novel aspect of the study involved employing geostatistical methods to analyze erosion rates, providing new insights into the shoreline dynamics. The data analysis allowed us to identify coastal areas experiencing the most significant changes. By continually refining neural network models with these datasets, we can improve our understanding of the complex interactions between natural factors and shoreline evolution, ultimately aiding in developing effective coastal management strategies.

1. Introduction

The Arctic coasts are among the most dynamic in the world [1], and the coast of the Kara Sea is no exception [2]. Numerous parameters influence coastal erosion [3], particularly climate change [4]. Climatic factors affecting coastal dynamics include temperature and hydrodynamic regimes [5], storms [6] and wind effects, sea level rise, air temperature [7], and the duration of ice cover [8]. Additionally, factors related to the shore zone characteristics, such as morphology [9], permafrost composition and structure, and the mechanisms of coastal destruction (predominant geological processes) [10], also play a significant role.

These factors and processes can be divided into two groups. The first group includes those that can be observed in the present, such as the lithological composition or the prevalent permafrost features. The second group consists of unpredictable factors, such as the future strength of storms or the average annual temperature for the coming year. The abundance of influencing factors, many of which are inherently random, makes it challenging to develop models that can directly predict coastline changes.

Recently, research methods utilizing artificial intelligence (AI) have been increasingly employed to identify patterns in such complex systems. The use of artificial neural networks (ANNs) in permafrost science has been documented in various studies, such as detecting ice-wedge polygons [11], mapping thermokarst landforms [12], identifying the distribution of frozen rocks in Alaska [13], and segmenting the Alaskan coast [14]. ANNs have also been used in coastline studies, including simulations of coastal failure in the Costa da Caparica area [15] and the coast of Venice [16]. Intertidal mudflat dynamics were investigated using dense Sentinel-2 time series with deep learning [17]. Clustering based on the rate of retreat of various coastal segments has been explored in some studies [18], and the coastal retreat rates for all Arctic coasts have been predicted using Sentinel-1, deep learning, and change vectors [19].

As part of the Arctic Coastal Dynamics (ACD) project, a database on the coastal dynamics of the circumpolar region was compiled [20]. However, the data in this database are of limited use for further work because they were obtained by different researchers using various assessment methodologies. Additionally, specific shoreline sections (up to the first tens of kilometers) may be represented by a single retreat rate value due to the vast area covered. This article discusses the fundamental principles of compiling and formalizing data on the coastline, examines the temporal aspects of climatic factors influencing coastal destruction, and explores the spatial correlation of coastal retreat rates. This article takes a different approach to those focusing on specific coastal retreat locations and presenting data through erosion rate maps. Instead, it analyzes generalized data without specifically evaluating areas with higher or lower retreat rates. The aim is to develop approaches and methods for predicting coastal dynamics using machine learning techniques. However, before moving to modeling and forecasting, it is crucial to identify which parameters are necessary. Therefore, several important questions need to be addressed: how the data are described (what does the dataset contain?), whether the retreat rates exhibit linear or nonlinear changes, and what time horizon is appropriate for making predictions. Additionally, it is essential to determine if there is a spatial correlation in retreat rates and over what distance along the coastline this correlation manifests. Finally, it is important to understand if the coastal retreat rates follow any statistical patterns, which could improve the prediction accuracy and enhance the application of machine learning methods.

2. Materials and Methods

2.1. Study Area

Three areas were chosen (Figure 1) for investigation to characterize the spatial features of the coastal dynamics of the Kara Sea coasts. The Faculty of Geography at Lomonosov Moscow State University has been researching these three sites since the 1980s, resulting in a wealth of historical data for these territories. Previous studies in this region indicate that the average annual retreat rates over the long term (30–50 years) range from 0.3 to 1.7 m per year [18,21,22,23].

The selected areas are located in a zone of continuous permafrost. The lithological composition of the coastal bluff varies from loamy clays to sands, with sandy silts predominating [24,25]. There are several geomorphological levels in the study area.

The studied segment of the Ural coast is located along a 5 km stretch of coastline between the islands of Torasavey and Levdieva. The coastal plain’s elevations above sea level range from 4 to 6 m (low surface) in the eastern part of the study area to 12–14 m (high surface) in the western part. These areas are separated by a 1.3 km-long laida (tidal lowland surface) along the sea’s coast, with berms 1–2.5 m high. The high surface mainly consists of sands with a low ice content (20–30%). Ice-rich silts and clays with ice lenses dominate the western part of the low terrace [25].

The Yamal Coast is situated along an 8 km-long coastal segment northwest of the gas pipeline on the opposite side of Baydaratskaya Bay. The topography levels vary from layda in the southeast to an elevated surface of up to 12 m in the northwest part of the territory. The coastal mass is mainly composed of sands with a low ice content. Ice wedges also occur in the northwest part of the area [26].

The Kharasavey Coast is located along a 7 km-long coastal segment between Cape Kharasavey and the Kharasavey settlement on the western Yamal Peninsula, 105 km northwest of the Bovanenkovo field. The coastal plain is mainly situated on a high surface of 4–7 m with gullies and deltas of small streams. The central part of the coast is composed of saline clays with an ice content of more than 40%. Sandy sediments with an ice content of 20–30% compose the other part of the coast [18,26,27].

The tide height on the Ural coast is up to 1.1 m, and on the Yamal coast, it is up to 0.8 m [28], and the average tidal height on the Kharasavey coast is 0.6 m [29]. The sea level can rise by 1.4–1.5 m during autumn surges and storms [28,29].

2.2. Estimation of Coastal Retreat

Despite the apparent clarity of the term “coastal retreat rate”, different authors studying the dynamics of Arctic coasts interpret this parameter differently. In the mid-20th century, field measurements of retreat along profiles became widely adopted [7,27]. Shoreline position changes are commonly measured using remote sensing methods [19,22,30,31], etc., where the coastline offset is determined from transects obtained manually [32] or using the ArcGIS (10 version number of software) plugin DSAS (Digital Shoreline Analysis System) [18,30,33]. Some authors estimate the area of the eroded coast divided by the length of the section [23]. This distinction is crucial since the coastal retreat value can be either a vector or scalar quantity, depending on the chosen approach.

In this study, shoreline change was defined as the rate of bluff top retreat. The coastal retreat rates were estimated as a scalar quantity, following the approach described below. The method used to assess the coastal retreat considered the eroded area of the coastal segment.

In the first stage, the position of the coastal bluff was interpreted for various time slices. This interpretation was based on satellite images (

Table 1. Remote sensing data for the key sites.

Key Site	Data Source	Date	Spatial Resolution, m
Ural coast 1	Aerial images	June 1988	1.4
	QuickBird-2	August 2005	0.55
	WorldView-1	July 2012	0.5
	WorldView-2	July 2013	0.5
Yamal coast	Corona KH-4	August 1968	2.2
	Aerial images	July 1988	0.65
	QuickBird-2	August 2005	0.5
	WorldView-3	June 2016	0.3
Kharasavey coast 2	Aerial images	July 1972	0.75
	Aerial images	July 1977	2.5
	Aerial images	July 1988	0.5
	ALOS PRIZM	July 2006	2
	WorldView-2	June 2016	0.5

¹ Remote sensing data were supplemented with DGPS data from 2013–2015 and 2017. ² Remote sensing data were supplemented with drone survey data from August 2022

) from multiple years and field measurement data obtained by the authors using differential GPS surveys (Trimble R8 GPS Receiver, Trimble TSC2 Controller, Trimble HPB450 (Sunnyvale, CA, USA)) and unmanned aerial vehicle photography equipment (quadcopter Phantom 4 Pro (DJI, Shenzhen, Guangdong, China)).

The images and data were imported into ArcMap and referenced using the WGS 84 UTM42N coordinate system. The positions of the bluff tops were digitized sequentially from the oldest to the most recent for different years (Figure 2).

In the next step, the baseline (polyline) was chosen to represent the general direction of the coast (Figure 3a). A grid of transects, perpendicular to the baseline and spaced at a constant interval of 10 m, covered the study area (Figure 3b). The area (S1 in Figure 3c) formed by these two coastlines and two adjacent transects represented the destruction during the selected time interval for the chosen coastal segment. Since the direction of the coastline in a local segment may not be parallel to the baseline, estimating the retreat as the length of the transect segment is incorrect (false and true coastal retreats are shown in Figure 3c). The selected segment could be approximated as a quadrilateral with two parallel sides (Figure 3d). The true coastal retreat was calculated as the perpendicular distance from the “new” shoreline (L1) drawn from the midpoint of the “old” shoreline. The total area (m²) formed by the transects was calculated automatically in ArcMap and corresponds to the area of the figure ABCD (Figure 3d).

Also, the area is $S_{ABCD}=S_{ABC’D}-S_{BC’C},\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} S_{BC’C}=L_1·{\displaystyle \frac{h’}{2}};$ $\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}$ $S_{ABC’D}=L_1·h;$ consequently, $S_{ABCD}=L_1·h-L_1·{\displaystyle \frac{h’}{2}}=L_1\times \left(h-{\displaystyle \frac{h’}{2}}\right)$. This means that $Retreat={\displaystyle \frac{S_1}{L_1}}$ or the division of the area of the eroded coast on the straight line of the “new” coastline.

Calculations using areas (m²) make it possible to consider small coastal segments in local retreats that do not intersect with transects.

The development of a ravine during ice-wedge degradation can change direction in time; accordingly, the transect can become subparallel to the strike of the ravine. Thus, if the analyzed line is heavily indented, as is often the case in permafrost zones, then local sections of the coast appear at a large angle to the baseline, resulting in significantly overestimated values. To avoid this problem, we developed another approach to analyze the coastal retreat without excluding individual points. The data from the comparison between our proposed method and the DSAS (Digital Shoreline Analysis System) method is shown in Figure A1.

2.3. Data Compilation

Obtained coast retreat rates were compiled in tables (metadata in

Table 2. Metadata.

Column	Description
S_Area	Study area: 1—Ural coast; 2—Yamal coast; 3—Kharasavey
Morpho	Morphological level: 1—laida (up to 4m); 2—low surface from 4 to 9 m; 3—high surface from 9 to 15 m
Average cliff height	Cliff height, m: for Ural coast, based on DGPS survey; for Yamal coast, according to [33]; for Kharasavey coast, according to [27].
Permafrost processes	Predominant permafrost processes
Lithology	Lithology type
VT	Virtual transect number
No_WE	Transect’s numbers from west to east
Ret YEAR-YEAR	Coastal retreat during time slices (chosen YEAR), meter
Y YEAR	Longitude coordinate of bluff position in chosen YEAR
X YEAR	Latitude coordinate of bluff position in chosen YEAR
VR YEAR-YEAR	Coastal retreat rate during time slices, meter/year

).

The datasets were supplemented with the results of the field observations. For each transect, data on the retreat were augmented with categorical features characterizing the morphological and permafrost features of the coast. For example, we considered whether the coast segment at the intersection with the transect belonged to a high level, a low surface, or a laida. In a separate column, the average value of the height of the coastal cliff in absolute elevation (meters) relative to the beach was reflected. For each measurement point, data on the following lithology of the coastal bluff were recorded in the table: sands, loams, the interlayering of sands and loams, and peat. The complete scheme of augmented categorical features is shown in

Table 3. Categorical features of the dataset.

Categorical Feature	Code	Description
Morphological level	1	A laida (lowland surface flooded by tides) up 4 m above the sea
	2	A low surface from 4 to 9 m above the sea
	3	A high surface from 9.1 to 15 above the sea
Lithology	1	Sands
	2	Loams
	3	Sands and loams
	4	Peat
Permafrost processes	1	Thermodenudation is a destructive coastal process whose intensity depends on the thermal regime of the territory and provokes the thawing of sediments and their removal from the slope.
	2	Thermal abrasion is a coastal process of mechanical and thermal destruction that develops under the combined influence of waves and temperature.
	3	Thermoerosion is the liner process that actively evolves during ice-wedge thaw.
	4	Thermokarst is a process whereby ice-rich deposits or ground ice thaws, causing the ground surface to subside and form thaw depressions and lakes.

.

3. Results and Discussion

3.1. Datasets Description

As a result of this work, we obtained datasets for three coastal segments: the Ural coast, the Yamal coast, and the Kharasavey coast (available online: https://rus.arcticcoast.ru/project_bogatova_202320251/, (accessed on 14 August 2024)). The total number of transects and assessed retreats for all years are provided in

Table 4. Statistics of coastal retreat datasets.

1	Number of Considered Shoreline Segments	Number of Considered Periods	Number of Assessed Retreats for All Years
Ural coast	472	6	2110
Yamal coast	804	3	1425
Kharasevey coast	847	5	3115

. It should be noted that estimating the retreat volume (or erosion rate) was not possible for all coastline segments. In some cases, the lack of remote sensing data for certain segments or features of the coastline, such as river and stream mouths, prevented the assessment of the retreat magnitude. In these instances, the retreat magnitude was not assessed. An example from this database is shown in

Table 5. Example of database: table row for Yamal coast.

S_Area	Morpho	Av_height	PPP	Lithology	VT	No_WE	Y_1968	X_1968	Ret_1968-1988	Y_1988	X_1988	Ret_1988-2005	Y_2005	X_2005	Ret_2005-2016	Y_2016	X_2016	VR_1968-1988	VR_1988-2005	VR_2005-2016
2	1	0.7	2	1	117	688	7,686,309.093	463,170.55	1.9	7,686,309.2	463,171.02	7.6	7,686,310.52	463,179.361	19.4	7,686,313.74	463,199.284	0.1	0.4	1.8
2	1	0.7	2	1	118	687	7,686,319.068	463,169.59	2.4	7,686,319.5	463,172.30	4.7	7,686,320.51	463,178.480	20.4	7,686,323.41	463,196.429	0.1	0.3	1.9
2	1	0.7	2	1	119	686	7,686,329.167	463,169.40	2.8	7,686,329.5	463,171.71	4.9	7,686,330.18	463,175.639	15.7	7,686,332.91	463,192.532	0.1	0.3	1.4
2	1	0.7	2	1	120	685	7,686,339.040	463,167.81	2.9	7,686,339.6	463,171.13	5.1	7,686,340.46	463,176.591	15.5	7,686,342.87	463,191.484	0.1	0.3	1.4
2	1	0.8	2	1	121	684	7,686,348.917	463,166.25	1.6	7,686,349.3	463,168.46	4.5	7,686,350.00	463,172.924	17.5	7,686,352.75	463,189.924	0.1	0.3	1.6
2	1	0.8	2	1	122	683	7,686,358.789	463,164.65	1.8	7,686,359.0	463,165.73	6	7,686,359.82	463,171.034	17.2	7,686,362.93	463,190.247	0.1	0.4	1.6
2	1	0.7	2	1	123	682	7,686,368.179	463,160.08	4.7	7,686,368.7	463,163.01	5.8	7,686,369.56	463,168.640	28.2	7,686,373.75	463,194.506	0.2	0.3	2.6
2	1	0.7	2	1	124	681	7,686,377.400	463,154.46	6.2	7,686,378.3	463,160.10	7	7,686,379.32	463,166.320	26.5	7,686,383.77	463,193.846	0.3	0.4	2.4
2	1	0.7	2	1	125	680	7,686,386.850	463,150.26	7.7	7,686,388.0	463,157.10	4.8	7,686,388.97	463,163.345	25.7	7,686,393.55	463,191.664	0.4	0.3	2.3
2	1	0.7	2	1	126	679	7,686,396.422	463,146.81	8.9	7,686,397.7	463,154.94	4.3	7,686,398.49	463,159.605	24.9	7,686,403.09	463,188.018	0.4	0.3	2.3
2	1	0.8	2	1	127	678	7,686,406.240	463,144.88	9.8	7,686,407.9	463,155.01	3	7,686,408.36	463,158.006	25.2	7,686,412.87	463,185.853	0.5	0.2	2.3
2	1	0.8	2	1	128	677	7,686,416.719	463,147.04	6.5	7,686,418.2	463,155.94	3.7	7,686,418.71	463,159.337	22.6	7,686,423.22	463,187.200	0.3	0.2	2.1
2	1	0.8	2	1	129	676	7,686,427.540	463,151.31	6.7	7,686,429.1	463,161.19	0.1	7,686,429.42	463,162.900	18	7,686,433.98	463,191.119	0.3	0	1.6
2	1	0.7	2	1	130	675	7,686,454.655	463,256.28	12.5	7,686,442.9	463,183.89		7,686,440.60	463,169.445	4.5	7,686,444.77	463,195.197	0.6		0.4
2	1	0.8	3	1	131	674	7,686,462.789	463,243.94	2.6	7,686,456.5	463,205.30		7,686,451.72	463,175.519		7,686,456.45	463,204.769	0.1
2	1	0.8	3	1	132	673	7,686,472.057	463,238.61	0.5	7,686,470.0	463,226.00		7,686,463.87	463,188.045		7,686,466.76	463,205.886	0
2	1	0.8	3	1	133	672	7,686,481.730	463,235.79	6.1	7,686,482.5	463,240.31		7,686,476.97	463,206.356	0.1			0.3		0
2	1	0.8	3	1	134	671	7,686,492.016	463,236.75	11.4	7,686,494.3	463,250.89		7,686,489.47	463,220.988	3.5			0.6		0.3

.

The resulting datasets were made publicly available on the website of Geoecology of the Northern Territories Laboratory of the Faculty of Geography of Moscow State University https://rus.arcticcoast.ru/project_bogatova_202320251/, (accessed on 14 August 2024).

3.2. Nonlinear Changes in the Rates of Coastal Retreat in Time

While studying the rate of coastline displacement in the study areas, we observed nonlinear changes in the coastal retreat rate over time (Figure 4).

Some areas of the studied coastline retreated more rapidly during certain periods, but then their retreat rate slowed down in the next period. In other periods, however, other areas experienced a significant acceleration in the rate of coastal retreat. Additionally, these coastal areas showed reduced or, conversely, increased retreat rates relative to the coastline as a whole during the given time interval t1 (1972–1977), exhibiting peaks or troughs. However, in the subsequent time interval t2 (1977–1988), the trend shifted, causing the retreat rate to either sharply increase or decrease (individual low or high values at specific points, as shown in Figure 4A, are “inversion behavior” in specific segments). This behavior change was likely due to the heterogeneous structure of the coast, where erosion-resistant zones affect coastal erosion, thereby slowing down the process. However, as the shoreline crosses these zones and encounters changes in coastal properties, the erosion rate may increase dramatically, causing the shoreline to approach the average level more rapidly. Another reason could be processes occurring in the coastal waters, with the formation of and changes in local currents [9].

It is important to note that these changes in the retreat rates of local sections of the coast were time-nonlinear and, in terms of local values over time, significantly exceeded the general average trend of the coastline retreat.

3.3. Temporal Aspect of Coast Retreat Prediction

The coastline’s shape and spatial position results from the interaction of the coastal massif and the processes causing its destruction.

Among the factors influencing the stability of the coast, we can note the following factors that determine the resistance of the coast to destruction: lithological properties, the presence or absence of permafrost, the height of the coast relative to sea level, the presence and type of vegetation cover, etc.

Among the factors influencing the destruction of the coast (impact factors), we noted temperature conditions, the strength and direction of wind–wave effects, the presence or absence of local temporary or permanent coastal currents, etc.

The fundamental difference between the factors of coastal resistance to destruction and the impact factors is that we can observe the former here and now by studying the coastal massif and obtaining data on the lithological composition and the type of permafrost and receiving data on the geomorphology of the coastline. At the same time, the influencing factors are essentially random. Indeed, we cannot reliably predict whether the next summer will be warm or cold (the temperature regime that affects the thawing of frozen rocks), nor can we predict the number and severity of storms in the coming summer season. When forming a forecast for the coastline’s movement, we can consider the factors of the coast’s resistance to destruction. Still, the impact factors are essentially random for us over short periods.

However, as the time interval under consideration increases, fluctuations in the strength of the influencing factors average out and tend to be specific average values. Thus, the question arises about the time depth of the forecast, namely at what time intervals the random nature of the strength of the influencing factors becomes predictable.

Using data from earlier works [18,22] on the values of wind–wave energy obtained using the Popov–Sovershaev method [34], we tried to estimate the time interval at which the values of wind–wave energy tended to some average values (Figure 5a). The cumulative average was used to estimate such a time interval, which showed how the average value of the wind–wave energy data changed as new observations were added. The first year of observation (1979) was just the value of wind–wave energy itself. The second one was the average of the first two values (Figure 5b).

Figure 5b shows that only with an averaging period of 10–20 years or more do individual annual values of wind–wave energy cease to impact the average values significantly. This means that it is precisely at this time interval that we can talk about some average coastline movement, free from annual wind and wave action variations. But even with such a time interval, we see an upward trend in the cumulative average, which suggests that in the past we observed a slowing down in the coastline retreat due to a decreased wind and wave impact.

A similar assessment was carried out for the temperature factor. Figure 6 shows that the average annual temperature stabilized when averaged over ten years. Identically to the wind–wave climate, we observed a decrease in the cumulative yearly average temperature, indicating a reduction in temperature impact.

Thus, when modeling and forecasting coastlines, it should be considered that local annual changes in wind–wave energy can significantly impact obtained values. Since climate parameters cannot be predicted, forecasting must be probabilistic for periods of less than 20 years. Over 30 years or more, the annual variability of wind–wave energy results will tend to specific values and can be used for forecasting.

3.4. Geostatistical Aspect of Coast Retreat Prediction

A coastline can be perceived as a continuous and dynamic system wherein each shoreline point interacts with its surroundings. Through observations of an ensemble of points instead of a single point, discernible patterns and interdependencies between a coastline’s states across different time points can be identified, facilitating the use of empirical methods to predict the system’s future state.

When observing a natural variation in the retreat rates, velocities along neighboring transects changed systematically rather than randomly. For example, it can be seen that between the 103rd and 113th transects or 164th and 183rd transects (Figure 7), a linear relationship was observed between the points’ position and the coastal retreat, occurring systematically rather than randomly. This was observed along the entire coastline. The rate of shoreline retreat for a particular transect was determined by the structural features and evolution of the entire shore segment, and changes observed for nearby transects demonstrated interrelated behavior.

Experimental semi-variograms of the coastal retreat values were calculated to estimate the numerical characteristics of the length of a coastal section behaving as a single ensemble. A variogram is a graphical representation of variation. One of the key parameters of a variogram is the sill, which represents the level at which the variogram approaches large distances. The sill reflects the overall data variance. The range is the distance at which the variogram reaches the sill, and beyond this distance, points are considered independent, meaning spatial dependence disappears. Another important parameter is the nugget effect, which represents the variance at very small distances. This effect is often associated with measurement errors or small-scale variations not explained by spatial dependence. Together, these parameters help describe and understand the spatial structure of the data and predict values in unobserved locations [35]. The main property of a variogram is that it reflects relationships within one dataset with each other, depending on the distance between observation points.

The Gstools package [36] was used to create directional, experimental semi-variograms in a Python programming envelope. The variogram parameters given in

Table 6. Experimental semi-variogram parameters.

Key Sites	Azimuth, °	Bin Size, m	Angle Tolerance, Degrease	Bandwidth, m
Ural	104.6	100	17	8
Yamal	168	100	17	8
Kharasavey	24	100	17	8

were used.

On a typical variogram, as the distance between the compared points increases, the variance also grows, eventually reaching a point where it stops increasing and the graph flattens out, reaching its sill. The distance at which the variogram curve reaches this still marks the range within which all values are spatially correlated. The inflection point on graph 8a is further than 1.5 km; this means that the values of the coastal retreat in this coastal segment are related to each other by a common pattern. In Figure 8c,h–m, the inflection points are much closer and range from 200 to 1000 m. We observe another pattern when the variogram does not reach the sill as the distance increases (Figure 8b,d–g,n). In this case, this indicates that the scale of the phenomena influencing the rate of coastal retreat exceeds or is comparable to the extent of the studied areas. In the random, uncorrelated behavior of a variable in space, the variogram appears as a simple horizontal line, which we do not observe in obtained data. This indicates a spatial correlation between the coastal retreat rates for neighboring transects for all study areas (Figure 8).

Thus, the obtained experimental semi-variograms show the presence of spatial dependencies in the values of the coastal retreat at a distance of hundreds of meters from 200 to almost 1000 m for the studied sections of the coast (Figure 8). Entire sections of the coastline hundreds of meters long represent a single ensemble, and the coastline retreat’s values correlate with each other.

3.5. Basic Statistical Characteristics of Coastline Retreat Values by Sections and Time Slices

We calculated the main statistical characteristics of datasets obtained for sites at various time intervals. Histograms were also prepared. The results are shown in

Table 7. Main statistical parameters of coastal retreat rates.

Site	Time Interval	Number of Transects	Max. Value	Min. Value	Mean	Variance	Standard Deviation	Median
Ural coast	1988–2005	464	4.3	0	1.9	0.8	0.9	1.9
	2005–2012	451	14.4	0	2.7	8.8	3.0	1.6
	2012–2013	411	18.6	0	3.5	9.2	9.7	1.6
	2013–2014	261	17.0	0	1.1	4.1	2.0	0.4
	2014–2015	260	10.4	0	1.4	3.2	1.8	0.6
	2015–2017	264	4.5	0	0.6	0.6	0.8	0.3
Yamal coast	1968–1988	314	2.4	0	0.3	0.1	0.3	0.2
	1988–2005	477	1.6	0	0.4	0.1	0.3	0.3
	2005–2016	634	15.3	0	2.0	6.2	2.5	1.1
Kharasavey	1972–1977	751	9.0	0	1.5	2.2	1.5	1.1
	1977–1988	661	7.1	0	1.3	2.0	1.4	0.8
	1988–2006	672	6.0	0	1.1	0.5	0.7	1.0
	2006–2016	632	3.8	0	1.0	0.5	0.7	0.9
	2016–2022	421	6.3	0	1.9	1.7	1.3	1.7

and in Figure 8.

Analysis of the statistical characteristics suggested the presence of few types of populations based on the magnitude of shoreline retreat (Figure 9).

The log-normal distribution of the retreat values represents the first population and is present in all shoreline comparison pairs (Figure 9c–g,j,m). This type of distribution is typical for the short periods when the coast was either stable or the coastal retreat measurements were related to the determination error (Figure 9c–f). For the long periods (Figure 9g,j), it was most likely that this population was contaminated by data acquisition errors (e.g., inaccuracies in image alignment and limitations in measurement accuracy due to pixel size). In any case, for this population, it was impossible to distinguish which offset values along the transects were noise and which reflected the objective process of shoreline change. Unfortunately, errors were unlikely to be random with the methodology used since distortions when working with images can be a significant source of errors. Such errors could have led to incorrect estimates of erosion rates. This made the model unstable and reduced its ability to predict shoreline dynamics accurately.

The second population has a normal (or Gaussian) distribution (Figure 9a,m). This distribution describes a random variable that takes values around the mean [35]. With this distribution, the entire studied section of the coast was subject to one leading retreat process (mechanism), and the coastal dynamic behaved as a single ensemble.

• The third population has the Gaussian kernel (Figure 9b,h,i,k–m), similar to the normal distribution. The Gaussian kernel is a function that measures the “similarity” between two data points based on the distance between them in the feature space and is derived from the concept of the Gaussian (normal) distribution [37]. The Gauss kernel indicates that shoreline change processes are smooth and continuous, with small incremental changes being more probable than sudden shifts. This suggests that the shoreline dynamics exhibited a high degree of spatial correlation, meaning that changes at one location were strongly related to neighboring points (Section 3.4). Moreover, the Gaussian kernel’s ability to handle nonlinear relationships implies [38] that complex factors influenced the coastal retreat, such as thermal abrasion and ice-wedge thawing, making it a suitable approach for modeling these intricate interactions.

Thus, the last two distributions were manifested in pairs of data comparisons with a significant time difference of 15 and 7 years. This is quite natural since, during these periods, the total bluff retreat exceeded the error in data acquisition (noise), and we see the true process of coastal change, which behaves as a single ensemble.

4. Conclusions

The prepared datasets for the coastlines of the Ural and Yamal coasts of Baydaratskaya Bay in the Kara Sea and the Kharasavey coast provided a solid base for applying data analysis and using neural nets. These data include detailed assessments of coastal retreat rates, permafrost characteristics, and morphological features. The collected data and coastal features will be used to develop models for predicting shoreline changes. Future data analysis will allow the identification of more stable and dynamic areas of the coast. Using datasets will improve the investigation accuracy, leading to the more precise prediction of the Arctic shoreline’s dynamics.