Verification of modeling of dynamic processes in the port structures area

. For problems involving the interaction of structures with sediments, physical models cannot be used for quantification because of the non-modellable nature of sediment dynamics. Mathematical modeling of sediment dynamics is used. The basis for verifying modeling results for such problems is in situ studies of coastal dynamics over a multi-year period, which are often not available. It is therefore possible to use the analysis of space images for a multi-year period together with a mathematical description of the dynamics of the coast under study. The subject of this paper is the coast of the Gelendjik Bay, Black Sea. An assessment of the coastline dynamics in the conditions of 5 extreme wave storms of 30-year period is made using mathematical modeling. To verify the results, the analysis of space images of the coastal zone for the period 2003-2022 is applied. The effectiveness of the proposed approach for predicting the intensity of sediment accumulation and erosion is shown and the mathematical model used is verified.


Introduction
The following methods are used to analyze the intensity of lithodynamic processes on seacoasts: 1. Data from direct instrumental measurements of seabed and shoreline changes over several years.
2. Aerial photographs of shoreline changes over several years.3. Remote sensing data -satellite images for several years, with the most detailed information available when processing commercial imagery with a resolution of 1 meter or less.
4. Beach particle size distribution data, characterizing the amount of different sediment fractions in different areas of the coast.5. Indirect (lithodynamic) data on the distribution of characteristics of hydrodynamic processes in the study area -distribution of wave and current fields [1].
To illustrate the possible use of remotely sensed data for modeling sediment movement, the conditions of Gelendjik Bay, located in the Russian north-western part of the Black Sea, are considered.
The area of Gelendjik Bay has been seriously studied, but the prediction of lithodynamic processes is necessary to support the development of the coastal zone of the region and has been undertaken by various authors and organizations.
Modeling of longshore sediment transport is a key component of many coastal engineering studies.There are at least four regimes of coastal sediment transport [2]: two for bottom sediment (the onset mode and the shear mode), the suspended sediment mode, and the riffle mode.
To date, many different formulas exist to describe this process of sediment movement, based on two approaches related to the initial and shear modes of motion, respectively.The first is the energetic approach developed by Bagnold and the second is the probabilistic approach introduced by Einstein [3].
A comparative analysis of the various semi-empirical formulas for sediment transport [3,4] has revealed the areas of application of each of them in river flows and in the coastal zone of the sea.In the Russian Federation, research on coastal sediment transport has traditionally been carried out at the Institute of Oceanology of the Russian Academy of Sciences.Recent papers [5,6] present a hybrid model of the theory of coastal slope equilibrium and the modeling of the process of slope change, based on the mechanism of advection of suspended sediment by waves crashing towards the shore.In this case, the swath is created and maintained by the subsequent deposition of sand particles.The modified volume flow rates in the transformation and collapse zones are determined based on the Bagnold-Baylard energy concept.An additional term is introduced to account for sediment suspension due to turbulation during wave collapse, as well as wave asymmetry.
In recent years, the Swedish-American model Lund-CIRP [7] has been developed for numerical modeling of the reshaping of coasts composed of sediments of different coarseness, which is successfully used in the numerical model of hydrodynamics and morphodynamics of the coastal zone CMS-M2D [8].
In preparing this paper, previous works on this topic were analyzed.The work of Hadla et al [9] contains materials on the use of composite modeling, which is based on the combined use of numerical and physical modeling.Information on the application of satellite bathymetry (SDB) for navigation, research, monitoring and design tasks can be found in the paper by Caballero [10].The work of Misra [11], which demonstrates the feasibility of using satellite bathymetry (SDB) to understand geomorphologic changes in coastal areas, is also reviewed.
The main objective of this paper is to verify the results of sediment transport modeling using satellite images for the period 2003 to 2022.The satellite images were acquired using Google Earth Pro program.

Materials and Methods
The COASTOX-MORPHO software package was used for calculations of lithodynamic coastal processes.A brief description of the program is given below.
The COASTOX-MORPHO model is based on the two-dimensional equation of bottom material mass balance in the coastal zone numerically realized on the same computational grid as COASTOX-CUR and COASTOX-SED models.The model was tested using standard laboratory tests for coastal scour models (e.g., the dynamics of the tombolo between the shore and the breakwater built parallel to the shore) and long-term coastal dynamics data using satellite imagery analysis.
Further, the data of numerical modeling of the fields of waves, currents, suspension propagation and sediment deposition, carried out in NIU MGSU in 2013-2017 on the project of construction of the new port of Gelendjik [12] are used (Figure 1).The comparison of these data with in-situ data obtained using satellite images was performed.
The composition of bottom sediments in the Gelendjik Bay is heterogeneous.In the deep parts of the bay sandy bottom sediments and loams prevail; in the coastal zone, depending on the specific hydrodynamic regime of the shore area, natural sandy bottom (beach "Sandy bottom"), areas of beaches composed of fine, medium, and coarse pebbles are observed [13,14].Then three zones of the Gelendjik Bay are considered: the eastern part; the northern part; the western part, where the port was planned and built according to the project described above.The southern part of the bay is not considered, as it has already been considered earlier [15].

Results
Further, the changes in the shoreline in some parts of the Gelendjik Bay are analyzed.

Eastern part of the bay
The results of calculations of the eastern zone of the Gelendjik Bay along the entire line show wave erosion of the shores -washing out of sand fractions of the coastal zone.This is clearly observed on space images for 19 years from 2003 to 2022 (Figure 2).
In the southern part of the considered area south of the beach "Red Talka", according to the modeling results, the erosion zone is observed.The same results are obtained when analyzing the images.However, when looking at the area of Red Talka beach itself, the satellite images clearly show that over the 19 years there has been accumulation and advancement of about 50 m, i.e., 2.6 m/year, although according to the modeling results, the area in question is in a sediment scour zone.This is one example of inaccurate prediction by mathematical modeling.Considering the beach area of the "Kavkaz" boarding house, a gradual retreat of the shore is noted.Mathematical modeling comes to the same conclusions.
Also interesting for review is the northern part of the study area -the beach "Sunny Beach" (Figure 2).
The southern zone of Sunny Beach is in the erosion zone according to the modeling results.However, based on space images it can be concluded that the beach zone is in the neutral zone, showing advance and retreat of the beach up to 0.8 m/year.The presented results of the modeling of the sand sediment recharge-erosion fields show that the northern part of the beach is mainly in the erosion zone and in the zone neutral to erosion under the influence of strong storms over a multi-year period.These results do not coincide with the analysis of satellite imagery, which shows that the northern part of the beach shows a gradual advancement of the shoreline by about 5 m/year.

Northern part of the bay
When looking at the northern part of the Gelendjik Bay (Figure 3), one can see both scour and accumulation zones, as well as zones neutral to scour and sediment accumulation.In the zone of the beach "Azure Coast", analyzing space images, in its eastern part there is a coastal retreat of 1.36 m/year, when the western part remains relatively neutral to scouring.The results of modeling coincide partially, because according to the calculation results the western part is in the neutral zone, but the eastern part is in the zone of accumulation, although insignificant.
Analyzing the zone between the beaches "Azure Coast" and "Sunny Beach" according to the modeling results, we note that the sediments are in the erosion zone.This is confirmed by the analysis of space images.Especially large erosion is observed in the middle of this zone, where the shore retreat is 2.2 m/year, which is clearly visible on satellite images.
In the north-western part of the considered zone of the Gelendjik Bay (Figure 3), according to the modeling results, a scour zone is observed, which is confirmed by space images.The average shore retreat in this area is 1.1 m/year.The eastern part of the considered area of the Gelendjik Bay remains stable during the considered period, showing shore advancement -retreat with intensity up to 1 m/year.The modeling results lead to the same conclusions.

Western part of the bay
The western zone of Geledzhik Bay (Figure 4) is of interest for consideration, since the port was built there, for the project of which the MGSU report mentioned earlier [12] was carried out, including numerical modeling of sediment deposition fields used in this work.
According to the results of the mathematical modeling, the Thin Cape beach area is in the scour zone before the port construction and in the scour-neutral zone under the influence of strong storms for the multi-year period after the port construction.Between 2003 and 2016, the area near the beach showed gradual shoreline advancement of 1.6 m/year.After the construction of the port, the beach shoreline remains stable, no significant scour -reclamation of this beach has been observed in the last 2 years after the construction of the port.The results of modeling in this area give twofold results.On the one hand, the modeling results before construction are erroneous because they predict scour, although accumulation has occurred.On the other hand, the results of modeling after construction coincide with the analysis of space images, although the period of 2 years is insignificant enough to form final conclusions.
The coastal zone south of the port is in the erosion zone according to the calculation results.The same picture is observed when analyzing space images.Part of the coastal sediment is washed away, settling at the base of the harbor fencing structure.
Layouts of protective structures constructed (upper Figure 4) and accepted in mathematical modeling of lithodynamic processes (lower Figure 4) differ.However, it is not essential from the point of view of analyzing lithodynamic processes and corresponding morphometric changes.

Discussion
The use of space images is an important tool for verification of mathematical modeling results.To verify mathematical modeling, in-situ studies are used first of all, but often it is not possible to apply them due to lack of availability.
The analysis has shown that the mathematical model used generally correctly predicts the dynamics of scour and sediment loading in Gelendjik Bay.However, in some cases the mathematical model incorrectly predicted the dynamics of the shoreline and gave incorrect data, predicting scour when there was accumulation and vice versa.In such cases, the results of space images allow to verify the results obtained during modeling and further correct the model.
In this study, satellite images were used for model verification, but this is not their only application.In [16] satellite imagery was used to evaluate proposed engineering solutions for approach channel protection and sediment flow management.
The objective of our study was not a detailed forecast of erosion and accumulation at individual shoreline sections, which would require as input data a map of sediment composition distribution over the bay water area and shores, but a comparative analysis of the results of mathematical modeling with the results obtained using space images for the period from 2003 to 2022 and verification of the model based on these results.The images were selected in 6-year increments, showing changes in the shoreline over a long period.For a more detailed study, a shorter spacing can be used.
One of the main disadvantages of space monitoring is the lack of data: data for a short period including recent years are available.Most of the images were taken after 2010 and earlier images are either in poor quality or not available.Also, the availability of imagery depends on the study area.A well-studied area may have images in 1-2-month increments, while a less well-studied area may have images in 2-3-year increments.All these factors impose limitations on more detailed studies using space images.
2. In general, the selected mathematical model correctly predicts the sediment dynamics of the considered parts of the coast of the Gelendjik Bay, but there are prediction errors on the modeling side, which can be seen from the analysis of space images.
3. In the eastern part of the Gelendjik Bay in the considered beaches, according to the results of the analysis of space images, both scour zones and accumulation zones are observed.While according to the results of mathematical modeling only scour zone is observed at the beaches under consideration.
4. In the northern part of the Gelendjik Bay around the beach "Azure Coast" there is a discrepancy between the results predicted by the mathematical model and space images.The rest of the northern area corresponds to the modeling results.
5. The modeling results of the western section of Gelendjik Bay coincide with the data obtained by space images analysis.However, the beach "Thin Cape" according to the modeling results before the port construction is in the erosion zone, when the results of space images analysis for the same period show a clear shore advancement.

Fig. 1 .
Fig. 1.Overview satellite images of the Gelendjik Bay Google Earth Pro: 2003 (left), 2022 (right) in comparison with the total field of change of bottom sand sediments in the bay for 5 extreme wave storms of 30-year period (bottom, numerical modeling)

Fig. 2 .
Fig. 2. Change of the shoreline of the Eastern section of the Gelendjik Bay from the Central Beach to the Sunny Beach, Google Earth Pro images from 2003 to 2022 in comparison with the total field of change of bottom sand sediments in the bay for 5 extreme wave storms of the 30-year period.

Fig 3 .
Fig 3. Change of the shoreline of the Northern section of the Gelendjik Bay from the beach "Sunny Beach" to the beach "Thin Cape", Google Earth Pro images from 2003 to 2022 in comparison with the total field of change of bottom sand sediments in the bay for 5 extreme wave storms of the 30-year period.

Fig. 4 .
Fig. 4. Shoreline change of the Western section of the Gelendjik Bay in the constructed port, Google Earth Pro images from 2003 to 2022 in comparison with the total field of change of bottom sand sediments in the bay for 5 extreme wave storms of 30-year period.