ANALYSIS OF THE ACCURACY OF INTERPOLATION METHODS IN THE PROCESS OF BATHYMETRIC MAPPING OF INLAND WATERWAYS

The accuracy of various interpolation methods, used by specialists when working manually or technically implemented in software when plotting bottom relief on navigation maps of inland waterways, namely nearest neighbor interpolation, triangle based interpolation, bilinear interpolation and biquadratic spline interpolation, is analyzed in the paper. The study was conducted during the process of creating an electronic navigational chart of the Northern Dvina River. The aim of the study is to determine the interpolation method that guarantees the minimum deviation of the calculated values from the original values and the rendering of the least number of artefacts. In existing cartographic and geoinformation software, only interpolation methods based on regular grid calculations are used. In this study interpolation is performed on an irregular grid since depth sounding is carried out using a single beam echo sounder, and the depth grids obtained using this type of equipment are always irregular. This makes it possible to ensure the highest possible accuracy of the initial measurement during interpolation. The accuracy of the performed interpolation is verified by dividing all depths into two parts (longitudinal and transverse tacks) and calculating the depth values at longitudinal tacks using interpolation. The maximum discrepancies of up to 50 cm are detected when performing nearest neighbor interpolation. The minimum discrepancies of less than 10 cm are detected during biquadratic spline interpolation. According to the results of the study, biquadratic spline interpolation is the best method for building digital models of the bottom relief that can then be used to plot bathymetry on navigational charts.

electronic navigational chart, inland waterways, accuracy of interpolation, interpolation, spline interpolation, bathymetry, depth contour charting

1. Афонин А. Б. Исследование влияния подробности гидрографической съемки на оценку проходных глубин / А. Б. Афонин, И. Ю. Королев, А. Л. Тезиков // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. - 2017. - Т. 9 - № 5. - С. 1007-1016. DOI: 10.21821/2309-5180-2017-9-5-1007-1016.

2. Ратнер Е. А. Сплайн-интерполяция для построения трехмерных батиметрических моделей при картографировании внутренних водных путей / Е. А. Ратнер, А. И. Зайцев, М. А. Квасной // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. - 2020. - Т. 12. - № 5. - С. 894-905. DOI: 10.21821/2309-5180-2020-12-5-894-905.

3. Amante C. J. Accuracy of interpolated bathymetry in digital elevation models / C. J. Amante, B. W. Eakins // Journal of Coastal Research. - 2016. - Is. 76 (10076). - Pp. 123-133. DOI: 10.2112/SI76-011.

4. Amante C. J. Estimating coastal digital elevation model uncertainty / C. J. Amante // Journal of Coastal Research. - 2018. - Vol. 34. - Is. 6. - Pp. 1382-1397. DOI: 10.2112/JCOASTRES-D-17-00211.1.

5. Parente C. Interpolation of Single Beam Echo Sounder Data for 3D Bathymetric Model / C. Parente, A. Vallario // International Journal of Advanced Trends in Computer Science and Engineering. - 2019. - Vol. 10. - No. 10. - Pp. 6-13.

6. Wu C.-Y. Comparison of different spatial interpolation methods for historical hydrographic data of the lowermost Mississippi River / C.-Y. Wu, J. Mossa, L. Mao, M. Almulla // Annals of GIS. - 2019. - Vol. 25. - Is. 2. - Pp. 133-151. DOI: 10.1080/19475683.2019.1588781.

7. Alcaras E. Interpolation single beam data for sea bottom GIS modelling / E. Alcaras, L. Carnevale, C. Parente // International Journal of Emerging Trends in Engineering Research. - 2020. - Vol. 8. - No. 2. - Pp. 591- 597. DOI: 10.30534/ijeter/2020/50822020.

8. Павлова А. И. Анализ методов интерполирования высот точек для создания цифровых моделей рельефа / А. И. Павлова // Автометрия. - 2017. - Т. 53. - № 2. - С. 86-94. DOI: 10.15372/AUT20170210.

9. Ююкин И. В. Применение метода сплайн-функций при компьютерной визуализации подводного рельефа / И. В. Ююкин // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. - 2021. - Т. 13. - № 1. - С. 64-79. DOI: 10.21821/2309-5180-2021-13-1-64-79.

10. Ююкин И. В. Оптимизация моделирования навигационной изоповерхности методами базисных финитных сплайнов/ И. В. Ююкин // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. - 2019. - Т. 11. - № 2. - С. 266-274. DOI: 10.21821/2309-5180-2019-11-2-266-274.

11. Шикин Е. В. Кривые и поверхности на экране компьютера: руководство по сплайнам для пользователей / Е. В. Шикин, Л. И. Плис. - М.: ДИАЛОГ-МИФИ, 1996. - 242 с.