Physics-based satellite-derived bathymetry

Coastal and inland shallow-water environments are increasingly exposed to climate-change-related impacts such as sea-level rise, coastal erosion and ecosystem degradation. Reliable numerical hydrodynamic and morphological models are essential for assessing these impacts and supporting coastal adaptation strategies [1]. The performance of such models strongly depends on accurate bathymetric input data. Albeit providing a high accuracy, traditional shipborne acoustic surveys remain time-consuming, costly and operationally limited in shallow or hazardous environments, resulting in data gaps and infrequent recurring measurements [2,3].

Satellite-derived bathymetry (SDB) has therefore emerged as a cost-efficient and spatially continuous alternative for mapping optically shallow-waters [3]. Empirical and semi-empirical SDB approaches rely on statistical relationships between reflectance and depth, offering computational simplicity but limited transferability due to their dependence on site-specific calibration. In contrast, physics-based inversion models explicitly describe radiative transfer within the water column, accounting for wavelength-dependent light attenuation controlled by inherent optical properties of the water column. These approaches provide physically interpretable bathymetric retrievals that remain applicable across a range of optical water conditions, with to-be expected accuracies ranging from approximately 0.5 to 1.0 m RMSE for water depth up to 30 m [2,4].

This study implements and extends the physics-based inversion model described in [4] within an open-source Python framework for transparent and reproducible SDB and optical water quality retrieval from multispectral satellite data. The framework enables the simultaneous estimation of the physical water depth and potentially biologic parameters such as suspended matter concentration, chlorophyll-a concentration and colored dissolved organic matter absorption. Beyond the current state-of-the art, this study scrutinizes different implementation parameters to assess and improve computational stability and adaptability across varying optical environments, while maintaining a physically consistent radiative transfer formulation. The approach was validated at two optically contrasting sites: the semi-turbid Lake Constance (Untersee) in southern Germany and the clear-water One Tree Reef (Great Barrier Reef) in eastern Australia. Overall, this study demonstrates that the open-source development of a physics-based SDB approach can achieve competitive accuracy while remaining reproducible and adaptable, making a transferable, cost-efficient bathymetric mapping retrieval in operational shallow water monitoring available to a broader (scientific) audience.

[1] Pacheco, A., Horta, J., Loureiro, C., and Ferreira, (2015). Retrieval of nearshore bathymetry from landsat 8 images: A tool for coastal monitoring in shallow waters. Remote Sensing of Environment, 159:102–116. http://dx.doi.org/10.1016/j.rse.2014.12.004.

[2] Ashphaq, M., Srivastava, P. K., and Mitra, D. (2021). Review of near-shore satellite derived bathymetry: Classification and account of five decades of coastal bathymetry research. Journal of Ocean Engineering and Science, 6(4):340–359. https://doi.org/10.1016/j.joes.2021.02.006.

[3] Liu, Z., Liu, H., Ma, Y., Ma, X., Yang, J., Jiang, Y., and Li, S. (2024). Exploring the most efective information for satellite-derived bathymetry models in diferent water qualities. Remote Sensing, 16(13):2371. http://dx.doi.org/10.3390/rs16132371.

[4] Albert, A. (2004). Inversion technique for optical remote sensing in shallow water. PhD thesis, University of Hamburg. Retrieved from https://ediss.sub.uni-hamburg.de/handle/ediss/812.