Modeling Uncertainties of Bathymetry Predicted With Satellite Altimetry Data and Application to Tsunami Hazard Assessments

Models of bathymetry derived from satellite radar altimetry are essential for modeling many marine processes. They are affected by uncertainties which require quantification. We propose an uncertainty model that assumes errors are caused by the lack of high-wavenumber content within the altimetry data. The model is then applied to a tsunami hazard assessment. We build a bathymetry uncertainty model for northern Chile. Statistical properties of the altimetry-predicted bathymetry error are obtained using multibeam data. We find that a Von Karman correlation function and a Laplacian marginal distribution can be used to define an uncertainty model based on a random field. We also propose a method for generating synthetic bathymetry samples conditional to shipboard measurements. The method is further extended to account for interpolation uncertainties, when bathymetry data resolution is finer than ∼10 km. We illustrate the usefulness of the method by quantifying the bathymetry-induced uncertainty of a tsunami hazard estimate. We demonstrate that tsunami leading wave predictions at middle/near field tide gauges and buoys are insensitive to bathymetry uncertainties in Chile. This result implies that tsunami early warning approaches can take full advantage of altimetry-predicted bathymetry in numerical simulations. Finally, we evaluate the feasibility of modeling uncertainties in regions without multibeam data by assessing the bathymetry error statistics of 15 globally distributed regions. We find that a general Von Karman correlation and a Laplacian marginal distribution can serve as a first-order approximation. The standard deviation of the uncertainty random field model varies regionally and is estimated from a proposed scaling law.