Comparative Analysis of Selected Geostatistical Methods for Bottom Surface Modeling

Digital bottom models are commonly used in many fields of human activity, such as navigation, harbor and offshore technologies, or environmental studies. In many cases, they are the basis for further analysis. They are prepared based on bathymetric measurements, which in many cases have the form of large datasets. Therefore, various interpolation methods are used for calculating these models. In this paper, we present the analysis in which we compared selected methods for bottom surface modeling with a particular focus on geostatistical methods. The aim was to compare five variants of Kriging and three deterministic methods. The research was performed with real data acquired with the use of an autonomous surface vehicle. The collected bathymetric data were reduced (from about 5 million points to about 500 points) and analyzed. A ranking approach was proposed to perform a complex and comprehensive analysis integrating typically used error statistics—mean absolute error, standard deviation and root mean square error. This approach allowed the inclusion of various views on methods of assessment while integrating various metrics and factors. The results show that geostatistical methods perform very well. The best results were achieved with the modifications of classical Kriging methods, which are disjunctive Kriging and empirical Bayesian Kriging. For these two methods, good statistics were calculated compared to other methods (for example, the mean absolute error for disjunctive Kriging was 0.23 m, while for universal Kriging and simple Kriging, it was 0.26 m and 0.25 m, respectively). However, it is worth mentioning that interpolation based on radial basis function in some cases is comparable to Kriging in its performance. The proposed ranking approach was proven to be useful and can be utilized in the future for choosing and comparing DBMs, mostly in mapping and analyzing seabed changes, for example in dredging operations. The research will be used during the implementation of the new multidimensional and multitemporal coastal zone monitoring system using autonomous, unmanned floating platforms. The prototype of this system is at the design stage and is expected to be implemented.