## 2 Materials and Methods
### Data Processing  
The spatial data obtained in the measurement process had to be referenced to a single uniform coordinate system. This process, also known as harmonization, is an important element of geospatial analysis in the current state-of-the-art measuring techniques. The study used the Polish national plane coordinate system PL-2000. The PL-2000 system is a modification of the Gauss-Kruger projection, in which the mapping functions have the following form [33]:  
\[x=k_{0}N\Big{[}A+(1-T+C)A^{3}/6+\Big{(}5-18T+T^{2}+72C-58e^{\prime 2}\Big{)}A^{ 5}/120\Big{]} \tag{1}\]  
\[y=k_{0}\big{\{}M-M_{0}+N\tan\varphi\big{[}A^{2}/2+\big{(}5-T+9C+4C^{2}\big{)} \big{]}A^{4}/24\]  
\[+\Big{(}61-58T+T^{2}+600C-330e^{\prime 2}\Big{)}A^{6}/720\Big{\}} \tag{2}\]  
where:  
\[e^{\prime 2}=e^{2}/\Big{(}1-e^{2}\Big{)},\]  
\[N=a/\Big{(}1-e^{2}\sin^{2}\phi\Big{)}^{1/2},\]  
\[T=\tan^{2}\phi,\]  
\[C=e^{\prime 2}\cos^{2}\phi,\]  
\[A=(\lambda-\lambda_{0})\cos\phi,\]  
\[M=a[(1-e^{2}/4-3e^{4}/64-5e^{6}/256-\ldots)\phi-(3e^{2}/8+3e^{4}/32+45e^{6}/1 024+\ldots)\sin 2\phi\]  
\[+(15e^{4}/256+45e^{6}/1024+\ldots)\sin 4\phi-(35e^{6}/3072+\ldots)\sin 6\phi+\ldots]\]  
Modification of the original projection coordinates consists of changing the coefficient of scale change \(k_{0}\) from 1 to 0.999923 and the use of four meridional zones with a width of 3\({}^{\circ}\) and longitude of axial meridians \(\lambda\)0 of 15\({}^{\circ}\) E, 18\({}^{\circ}\) E, 21\({}^{\circ}\) E and 24\({}^{\circ}\) E, respectively. To distinguish the eastern coordinates in individual zones, the value of 500,000 m + (\(\lambda\)0/3\({}^{\circ}\)) \(\cdots\) 1,000,000 m is added to the coordinate values. The Gauss-Kruger projection is shown in \[y=k_{0}\big{\{}M-M_{0}+N\tan\varphi\big{[}A^{2}/2+\big{(}5-T+9C+4C^{2}\big{)} \big{]}A^{4}/24\]0  
The length and ellipsoidal width of the Geocentric curvilinear coordinates obtained by the GNSS RTK measurement were transformed into the PL-2000 system. Ellipsoidal heights were corrected for undulation of the PL-geoid-2011 geoid, which complements and refines the global geopotential model EGM2008 [34]. Selected characteristic points of the NCZ AWFiS marina were assigned coordinates, taking into account georeference (Figure 6) and coordinates in the local coordinate system of the point cloud (Figures 3 and 4). Based on the ICP method [35] and the SVD algorithm [36], the parameters of the transformation of the TLS point cloud coordinates were determined. The transformation matrix coefficients  
\[y=k_{0}\big{\{}M-M_{0}+N\tan\varphi\big{[}A^{2}/2+\big{(}5-T+9C+4C^{2}\big{)} \big{]}A^{4}/24\]1 Characteristic control points of the marina quay (**a**) measured by the GNSS RTK method with the Trimble R10 receiver (**b**) (source: www.geotronics.com.pl accessed on 4 May 2020). included the change in the scale of s, the translation vector T, and the rotation angle \(\theta\). The obtained parameter values were, respectively, s = 0.999998, TT = [6,550,742.821 m, 6,026,644.338 m, 1.878 m], \(\theta\) = 291.8782\({}^{\circ}\). The procedure of transformation of the TLS point cloud from the local coordinate system into the PL-2000 and normal height systems was carried out using the formula:  
\[y=k_{0}\big{\{}M-M_{0}+N\tan\varphi\big{[}A^{2}/2+\big{(}5-T+9C+4C^{2}\big{)} \big{]}A^{4}/24\]2  
where:  
\(\mathbf{P}^{\prime},\mathbf{P}^{\prime}\)--point coordinates vectors before and after transformation, respectively,  
\(\mathbf{R}_{\mathbf{Z}}(\mathbf{\theta})\)--rotation matrix by the angle \(\theta\) around the vertical axis OZ of the coordinate system,  
**T**--translation vector. Bathymetric data, in the form of depth measured with a single-beam echosounder, obtained positional data based on the coordinates determined by the Trimble R10 receiver. As in the case of determining the location of the characteristic points of the NSC marina quay, the receiver used the RTK GNSS differential measurement method.