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.

中文翻译：

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卫星测高数据预测的测深法不确定度建模及其在海啸危险性评估中的应用

从卫星雷达测高仪得出的测深模型对于许多海洋过程的建模至关重要。它们受到需要量化的不确定性的影响。我们提出了一个不确定性模型，该模型假定错误是由于测高数据中缺少高波数内容引起的。然后将该模型应用于海啸危害评估。我们为智利北部建立了测深不确定度模型。使用多波束数据可以获得测高测深误差的统计特性。我们发现，冯卡曼相关函数和拉普拉斯边际分布可用于定义基于随机场的不确定性模型。我们还提出了一种以船上测量为条件生成合成测深样品的方法。该方法被进一步扩展以解决插值不确定性，〜10公里 我们通过量化测深法引起的海啸危害估计值的不确定性来说明该方法的有效性。我们证明了智利中/近场潮汐计和浮标的海啸前波预报对测深的不确定性不敏感。结果表明，海啸预警方法可以在数值模拟中充分利用测高预测的测深法。最后，我们通过评估15个全球分布区域的测深误差统计数据来评估在没有多波束数据的区域中对不确定性进行建模的可行性。我们发现一般的冯·卡曼相关性和拉普拉斯边际分布可以作为一阶近似。不确定性随机场模型的标准偏差在区域范围内变化，并根据拟议的缩放定律进行估算。