# Determining the Variability of the Territorial Sea Baseline on the Example of Waterbody Adjacent to the Municipal Beach in Gdynia

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Planning Measurement Work

- H
_{PL-KRON86-NH}—normal height of a point in the PL-KRON86-NH system [m], - H
_{PL-EVRF2007-NH}—normal height of a point in the PL-EVRF2007-NH system [m], - dH—difference of normal heights between the systems PL-EVRF2007-NH and PL-KRON86-NH, which depends on the geodetic latitude (ϕ) and longitude (λ) of a point [m].

#### 2.2. Measurements of the Territorial Sea Baseline

_{TSB}) from the following formula:

- H
_{CWL}—current water level in the adopted reference frame [m], - H
_{LWL}—the lowest water level in the adopted reference frame [m].

## 3. Results

- H
_{A}, H_{B}, H_{C}– normal heights of the triangle ABC, - S
_{A}, S_{B}, S_{C}– areas of the opposite triangles, formed by division of the triangle A’B’C’ with line segments connecting the triangle vertices with point P’.

_{A}, S

_{B}, S

_{C}). It is used to calculate a triangle area when the lengths of its sides are known. Since the vertex coordinates for the ABC triangle and the rectangular coordinates for point P are given, they can be used to calculate the areas of component triangles. Heron’s formula can be noted in the following manner:

- p – semi-perimeter of the A’B’C’ triangle,
- a, b, c – lengths of sides of the A’B’C’ triangle.

_{2018-2016}). In order to determine the spatial and temporal variability of seafloor relief of the waterbody, only those pairs of points were compared (with the same rectangular coordinates on both DTMs) for which normal heights could be calculated. There were 21322 such pairs of points in the area under study.

_{2000}, Y

_{2000}). The following formula was used to calculate ΔH

_{2018-2016}:

- H
_{2016}, H_{2018}– normal heights of a point on DTMs based on data acquired by the geodetic method in 2016 and 2018, respectively.

^{3}and decreased by 759.1 m

^{3}in the area of 21070.7 m

^{2}(the municipal beach in Gdynia has a sandy bottom) within the past two years. The landmass balance, i.e., the difference between the total erosion volume (V

_{TE}) and the total accretion volume (V

_{TA}) shows that the sand volume in the area increased by 936.1 m

^{3}. This amount is relatively small because if the excess sand was spread evenly across the entire area, the bottom of the waterbody adjacent to the municipal beach in Gdynia would increase by just 4 cm.

- X
_{C}, Y_{C}—rectangular coordinates PL-2000 of the points measured along the coastline in 2016 and 2018, - N
_{C}—the number of points measured along the coastline in 2016 and 2018, - ${\overline{\mathrm{X}}}_{\mathrm{C}}$—arithmetic average for the northing coordinates of points measured along the coastline in 2016 and 2018,
- ${\overline{\mathrm{Y}}}_{\mathrm{C}}$—arithmetic average for the easting coordinates of points measured along the coastline in 2016 and 2018.

- X
_{RL}, Y_{RL}—rectangular coordinates PL-2000 of the points that determine the reference line.

- X
_{PLi}, Y_{PLi}– rectangular coordinates PL-2000 of the points that determine the i-th line perpendicular to the reference line, - i – numbering of perpendicular lines, increasing southwards.

_{i}because it depends on the distance between successive perpendicular lines. It was assumed for this study that the distance will be 1 m.

_{i}) were calculated from the coordinates of these lines intersecting with the perpendicular line drawn to the reference line (Figure 7):

- X
_{RLi}, Y_{RLi}—rectangular coordinates PL-2000 of the reference line intersection points with the i-th line perpendicular to it, - X
_{TSBi}, Y_{TSBi}—rectangular coordinates PL-2000 of the baseline intersection points with the i-th line perpendicular to the reference line.

- j—number of the baseline intersection with the i-th line perpendicular to the reference line,
- k—the number of the baseline intersections with the i-th line perpendicular to the reference line,

_{2018-2016i}) using the following formula:

- d
_{2016i}—distance between the baseline measured in 2016 and the reference line calculated along the i-th line perpendicular to the reference line, - d
_{2018i}—distance between the baseline measured in 2018 and the reference line calculated along the i-th line perpendicular to the reference line.

- N—the number of lines perpendicular to the reference line.

## 4. Discussion

^{3}and decreased by 759.1 m

^{3}in the area of 21070.7 m

^{2}(the municipal beach in Gdynia has a sandy bottom) within the past two years. The landmass balance—i.e., the difference between the total erosion volume (V

_{TE}) and the total accretion volume (V

_{TA})—shows that the sand volume in the area increased by 936.1 m

^{3}. This amount is relatively small because if the excess sand was spread evenly across the entire area, the bottom of the waterbody adjacent to the municipal beach in Gdynia would increase by just 4 cm.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The effect of the baseline to the outer limits of maritime zones. Own study based on: [6].

**Figure 3.**Territorial sea baseline measurement (

**a**) and recorded measurement points (

**b**) by the geodetic method during the second measurement campaign.

**Figure 4.**Digital Terrain Models (DTM) of the waterbody adjacent to the municipal beach in Gdynia acquired by the geodetic method in 2016 (

**a**) and 2018 (

**b**).

**Figure 5.**Illustration of point height determination in a Triangulated Irregular Networks (TIN) model.

**Figure 6.**Height differences between DTMs created on the basis of data acquired by the geodetic method in 2016 and 2018.

**Figure 8.**A specific case, in which the line perpendicular to the reference line intersects the baseline at more than one point.

**Figure 9.**Distances between territorial sea baselines determined by the geodetic method in 2016 and 2018.

**Figure 10.**The course of the territorial sea baseline of the waterbody adjacent to the municipal beach in Gdynia determined by the geodetic method in 2016 (yellow) and in 2018 (red).

**Table 1.**Processing parameters during territorial sea baseline measurements in the waterbody adjacent to the municipal beach in Gdynia.

Parameter | Value |
---|---|

Country | Poland |

System/zone | 2000/18 |

Reference ellipsoid | WGS 84 |

Semi-major axis of ellipsoid | 6378137 |

Flattening of ellipsoid | 0.00335281067183 |

Projection | Gauss-Krüger |

Latitude of origin | 0 |

Central meridian | 18 |

False Northing | 0 |

False Easting | 6 500 000 |

Scale factor | 0.999923 |

Azimuth | North |

Grid orientation | Rising northeast |

Height transformation | Geoid |

Geoid model | PL-geoid-2011 |

Reference frame | Kronstadt |

**Table 2.**Division of the waterbody adjacent to the municipal beach in Gdynia with respect to height differences between 2016 and 2018 Digital Terrain Models (DTM).

Min. Elevation (m) | Max Elevation (m) | Real Area (m²) | Percentage of Total Area (%) |
---|---|---|---|

−0.605 | −0.600 | 2.3 | 0.01 |

−0.600 | −0.500 | 172.7 | 0.82 |

−0.500 | −0.400 | 709.6 | 3.37 |

−0.400 | −0.300 | 1227.9 | 5.83 |

−0.300 | −0.200 | 2317.9 | 11.00 |

−0.200 | −0.100 | 3182.2 | 15.10 |

−0.100 | 0.000 | 3587.1 | 17.02 |

0.000 | 0.100 | 4511.0 | 21.41 |

0.100 | 0.200 | 3964.3 | 18.81 |

0.200 | 0.300 | 1128.5 | 5.36 |

0.300 | 0.400 | 254.6 | 1.21 |

0.400 | 0.438 | 12.7 | 0.06 |

S_{T} = 21070.7 m^{2} |

**Table 3.**Volume changes of the waterbody adjacent to the municipal beach in Gdynia with respect to height differences between the DTMs.

Min. Elevation (m) | Max Elevation (m) | Erosion Volume (m^{3}) | Percentage of Total Erosion Volume (%) | Accretion Volume (m^{3}) | Percentage of Total Accretion Volume (%) |
---|---|---|---|---|---|

−0.605 | −0.600 | 0 | 0 | 0 | 0 |

−0.600 | −0.500 | 7.4 | 0.97 | 0 | 0 |

−0.500 | −0.400 | 47.7 | 6.28 | 0 | 0 |

−0.400 | −0.300 | 133.1 | 17.54 | 1.4 | 0.08 |

−0.300 | −0.200 | 211.4 | 27.85 | 39.7 | 2.34 |

−0.200 | −0.100 | 207.8 | 27.38 | 230.3 | 13.58 |

−0.100 | 0.000 | 117.1 | 15.43 | 467.4 | 27.57 |

0.000 | 0.100 | 34.4 | 4.53 | 578.5 | 34.12 |

0.100 | 0.200 | 0.1 | 0.01 | 293.9 | 17.34 |

0.200 | 0.300 | 0 | 0 | 75.7 | 4.47 |

0.300 | 0.400 | 0 | 0 | 8.2 | 0.48 |

0.400 | 0.438 | 0 | 0 | 0.2 | 0.01 |

V_{TE} = 759.1 m^{3} | V_{TA} = 1695.2 m^{3} |

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**MDPI and ACS Style**

Specht, M.; Specht, C.; Wąż, M.; Dąbrowski, P.; Skóra, M.; Marchel, Ł.
Determining the Variability of the Territorial Sea Baseline on the Example of Waterbody Adjacent to the Municipal Beach in Gdynia. *Appl. Sci.* **2019**, *9*, 3867.
https://doi.org/10.3390/app9183867

**AMA Style**

Specht M, Specht C, Wąż M, Dąbrowski P, Skóra M, Marchel Ł.
Determining the Variability of the Territorial Sea Baseline on the Example of Waterbody Adjacent to the Municipal Beach in Gdynia. *Applied Sciences*. 2019; 9(18):3867.
https://doi.org/10.3390/app9183867

**Chicago/Turabian Style**

Specht, Mariusz, Cezary Specht, Mariusz Wąż, Paweł Dąbrowski, Marcin Skóra, and Łukasz Marchel.
2019. "Determining the Variability of the Territorial Sea Baseline on the Example of Waterbody Adjacent to the Municipal Beach in Gdynia" *Applied Sciences* 9, no. 18: 3867.
https://doi.org/10.3390/app9183867