## 2 Materials and Methods
### Estimation of Measurement Time Spent on Survey Lines  
Knowing the parameter of the distance \(L_{s}\) between the survey lines and the width of the survey area, the number of main survey lines \(N_{PP}\) is determined as follows:  
\[N_{PP}=\frac{W}{L_{s}}+1, \tag{8}\]  
where \(W\)--width of the survey area [m]. The next step is to calculate the total length of the main survey lines \(DL_{PP}\). Assuming that the average length of the main survey line is equal to the length of the research area, the total length of the main survey lines is calculated from the product:  
\[DL_{PP}=N_{PP}\cdot L_{PP}, \tag{9}\]  
where \(L_{PP}\)--length of a single main survey line [m]. Assuming that the length of a single cross lines is approximately equal to the width of the survey area \(W\), the total length of the cross lines \(DL_{PK}\) is obtained from the following relationship:  
\[DL_{PK}=N_{PK}\cdot L_{PK}, \tag{10}\]  
where \(N_{PK}\)--number of planned cross lines; \(L_{PK}\)--length of a single cross line [m]. Cross lines are used to assess the accuracy of measurements performed on the main scheme survey lines. They enable the detection of random and systematic errors. In good weather conditions, the direction of the cross lines should be perpendicular to the direction of the main lines and the measurements conducted at the beginning of the survey [35; 38; 39]. These measurements additionally increase the survey data density. The guidelines of the International Shipowners Association IMCA [3] recommend that when surveying with a multi-beam echosounder, depth measurements should be made on at least two cross lines. The more varied and irregular the bottom surface is, the greater the number of cross lines required. For large water bodies (e.g., 10 km by 30 km), the cross lines should be designed every 1-5 km. The Canadian standards for hydrographic measurements state that the distance between the cross lines should not be greater than fifteen times the distance between the basic profiles [40]. Ultimately, the number of cross lines will depend on the size of the survey water body, the shape of the bottom, and the requirements contained in the specification. The final decision is made by the hydrographic responsible for the entire survey project. The layout of the main and cross lines schemes and the basic survey parameters are presented in Figure 2.  
Figure 2: Layout of the main and cross survey lines. The decision regarding the line orientation and spacing for the methodical sounding of an area will be influenced by the equipment to be used. The total time spent conducting depth measurements following the main survey lines \(T_{PP}\) includes the time spent measuring the main tracks, the time necessary for vessel turns, and the time spent measuring the speed of sound in water column:  
\[T_{PP}=T_{bat1}+T_{cz1}+T_{sep}, \tag{11}\]  
where \(T_{bat1}\)--survey time on main lines [s]; \(T_{cz1}\)--time necessary to perform vessel turns [s]; and \(T_{sep}\)--time for measuring speed of sound in the water column [s]. Formula (11) is developed to the following form:  
\[T_{PP}=\frac{DL_{PP}}{V_{PP}}+T_{z1}\cdot(N_{PP}-1)+n_{sep}\cdot T_{sep1}, \tag{12}\]  
where \(V_{PP}\)--vessel speed on the main survey lines [m/s]; \(T_{z1}\)--time to perform vessel turn to the next main lines [s]; \(n_{sep}\)--number of SVP measurements; and \(T_{sep1}\)--time of a single measurement of SVP [s]. The time of survey measurements on cross lines \(T_{PK}\) is derived from:  
\[T_{PK}=T_{bat2}+T_{cz2}, \tag{13}\]  
where \(T_{bat2}\)--time of bathymetric measurement on cross lines [s]; \(T_{cz2}\)--time necessary to perform vessel turns [s]. The distance between the cross lines is usually much greater than the distance between the main line; thus, the survey vessel will probably move at maximum speed to the next cross line.