Data artefact: Bathymetry reconstruction from experimental data with PDE-constrained optimisation

DOI: https://doi.org/10.15480/882.9601
URL: https://hdl.handle.net/11420/47625

Authors
=======

Judith Angel, Hamburg University of Technology (ORCID: 0009-0008-2098-4883)
Jörn Behrens, Universität Hamburg (ORCID: 0000-0001-9836-8716)
Sebastian Götschel, Hamburg University of Technology (ORCID: 0000-0003-0287-2120)
Marten Hollm, Hamburg University of Technology (ORCID: 0000-0001-5139-8918)
Daniel Ruprecht, Hamburg University of Technology (ORCID: 0000-0003-1904-2473)
Robert Seifried, Hamburg University of Technology (ORCID: 0000-0001-5795-7610)

Contact for inquiries: ruprecht@tuhh.de

Context
=======

The data set provides measurements of wave heights of waves generated in a water flume.
It contains two sets of measurements, one where the bottom of the flume is flat and one where we placed a Gaussian-shaped hill on the floor.
The hypothesis is, that it is possible to infer the shape of the hill from measurements of the height of the generated waves.
This is investigated in the accompanying paper (-> will add reference once the paper is published)


Data generation and processing
==============================

Please see the PDF provided with this data set for a detailed description of the experiment (in English).

Content
=======

This data set contains

 - this ReadMe file,
 - a ZIP archive file Data_Sensors.zip that contains the actual data as TXT files,
 - a video wave_flume_video.mp4 in MP4 format that shows the experimental setup,
 - a PDF file experiment.pdf in English language that describes the experiment in detail.

 Terms of use
 ============
 
 If you use any part of the material in this data set, please cite the dataset using
 
@misc{dataset,
        title = {Data artefact: Bathymetry reconstruction from experimental data with PDE-constrained optimisation},
        author = {Judith Angel and Jörn Behrens and Sebastial Götschel and Marten Hollm and Daniel Ruprecht and Robert Seifried},
        doi = {10.15480/882.9403},
        url = {https://hdl.handle.net/11420/46672},
        year = {2024}
        
}

 as well as the accompanying paper using
 
@article{AngelEtAl2024,
      title = {Bathymetry reconstruction from experimental data using PDE-constrained optimisation},
      journal = {Computers & Fluids},
      pages = {106321},
      year = {2024},
      issn = {0045-7930},
      url = {https://doi.org/10.1016/j.compfluid.2024.106321},
      doi = {10.1016/j.compfluid.2024.106321},
      volume = {278},
      author = {Judith Angel and Jörn Behrens and Sebastian Götschel and Marten Hollm and Daniel Ruprecht and Robert Seifried},
      keywords = {Bathymetry reconstruction, Shallow water equations, Wave flume experiment, PDE-constrained optimisation},
      abstract = {Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalized root mean square errors (NRMSE) are in line with other approaches.}
}

 Version history
 ===============
 v1.1: Update Bibtex entry in readme to final paper and added DOI of final paper under "Verknuepfungen"
 v1.0: Original dataset referenced in paper