Accurate estimations of ice thickness and volume are indispensable for ice flow modelling, hydrological forecasts and sea-level rise projections. We present a new ice thickness estimation model based on a mass-conserving forward model and a Bayesian inversion scheme. The forward model calculates flux in an elevation-band flow-line model, and translates this into ice thickness and surface ice speed using a shallow ice formulation. Both ice thickness and speed are then extrapolated to the map plane. The model assimilates observations of ice thickness and speed using a Bayesian scheme implemented with a Markov chain Monte Carlo method, which calculates estimates of ice thickness and their error. We illustrate the model's capabilities by applying it to a mountain glacier, validate the model using 733 glaciers from four regions with ice thickness measurements, and demonstrate that the model can be used for large-scale studies by fitting it to over 30 000 glaciers from five regions. The results show that the model performs best when a few thickness observations are available; that the proposed scheme by which parameter-knowledge from a set of glaciers is transferred to others works but has room for improvements; and that the inferred regional ice volumes are consistent with recent estimates.

中文翻译：

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用于大规模应用的贝叶斯冰厚度估计模型

对于冰流建模、水文预报和海平面上升预测，准确估计冰的厚度和体积是必不可少的。我们提出了一种基于质量守恒正演模型和贝叶斯反演方案的新冰厚度估计模型。正演模型计算高程带流线模型中的通量，并使用浅冰公式将其转换为冰厚度和表面冰速。然后将冰的厚度和速度都外推到地图平面。该模型使用通过马尔可夫链蒙特卡罗方法实施的贝叶斯方案来吸收对冰厚度和速度的观测，该方法计算冰厚度及其误差的估计值。我们通过将模型应用于高山冰川来说明模型的功能，使用来自四个地区的 733 条冰川测量冰厚度来验证该模型，并证明该模型可用于大规模研究，方法是将其拟合到来自五个地区的 30 000 多个冰川。结果表明，当有几个厚度观测值可用时，该模型表现最佳；将一组冰川的参数知识转移到其他冰川的提议方案可行，但仍有改进空间；并且推断的区域冰量与最近的估计一致。将一组冰川的参数知识转移到其他冰川的提议方案可行，但仍有改进空间；并且推断的区域冰量与最近的估计一致。将一组冰川的参数知识转移到其他冰川的提议方案可行，但仍有改进空间；并且推断的区域冰量与最近的估计一致。