Next-Generation Modelling of Glacial Isostatic Adjustment

现代海平面的变化可以用潮汐计或卫星测高来测量，这些观测提供了关于人为气候变化影响的重要定量信息。同样，基于卫星的地球引力场测量也被用于监测格陵兰岛和南极冰盖的质量损失。然而，由于冰川均衡调整（GIA）的重大贡献，这种现代测量不能直接用现代过程来解释；这是固体地球的持续变形和伴随的海平面变化，这是由最后一次冰川消融引起的。因此，有必要在现代观测中对GIA进行建模和校正。同样，在确定海平面预测时，也需要GIA的贡献，从而评估和减轻特定沿海地区未来海平面上升的风险。目前，在这些不同的应用中，GIA修正中的误差构成了一个重要的，但难以量化的不确定性来源。的确，GIA修正的幅度有时可以与感兴趣的现代信号一样大，而这些修正的不确定性也是如此。获得GIA修正的过程涉及到所谓的GIA逆问题的解决。解决后一个问题的关键步骤是使用(i)假设的地球模型和（ii）追溯到最后一个冰川期的冰盖演变模型对GIA进行数值模拟。迄今为止，大多数这类研究都是基于地球结构（特别是地幔粘度）只随深度而变化的假设。鉴于这一假设，模拟GIA的计算成本很低，这使得简单的方法可以应用于解决基于运行具有不同输入参数的非常多模拟的能力的逆问题。然而，地幔内粘度的三维变化确实存在，尽管它们的具体形式尚不清楚。在过去20年左右的时间里，一系列的研究表明，这种粘度的变化可以对GIA产生重大影响。然而，在三维地球模型中模拟GIA的成本比早期的一维计算大大增加，这使得解决反问题的旧方法变得无用。在可预见的未来，考虑到3D粘度变化的GIA逆问题的唯一计算可行的方法是应用基于梯度的优化（GBO）。这种方法被广泛应用于其他领域，包括天气预报、海洋学和地震层析成像。这种方法的一个关键技术方面是应用所谓的伴随方法来计算迭代更新模型所需的导数，以便更好地拟合数据。最近，首次将GBO应用于GIA逆问题，初步结果显示出很大的前景。然而，这项研究清楚地表明，这种方法的未来大规模应用受到现有计算工具的阻碍。因此，本提案的目的是开发新的高效数值方法，以促进GBO在GIA逆问题中的应用。这种集中的方法工作对于未来的实际研究是必要的，这些研究旨在提高GIA校正的准确性，从而提高我们监测和了解地球气候变化的能力。

Modern-day changes to sea level can be measured using either tide-gauges or with satellite altimetry, and these observations provide vital quantitative information about the effects of anthropogenic climate change. Similarly, satellite-based measurements of the Earth's gravitational field are used to monitor mass-loss from the Greenland and Antarctic ice sheets. Such modern-day measurements cannot, however, be straightforwardly interpreted in terms of modern-day processes due to significant contributions from glacial isostatic adjustment (GIA); this being the on-going deformation of the solid Earth and concomitant sea level change caused by the last deglaciation. It is, therefore, necessary to model and correct for GIA within modern-day observations. Similarly, GIA contributions are also required when determining sea level projections, and hence for assessing and mitigating the risk of specific coastal locations to future sea level rise. At present, errors within GIA corrections constitute a significant, but poorly quantified, source of uncertainty within these various applications. Indeed, the magnitude of GIA corrections can sometimes be as large as the modern-day signals of interest, while the same can be true of the uncertainties on these corrections.The process by which GIA corrections are obtained involves solution of the so-called GIA inverse problem. An essential step in solving this latter problem is the numerical simulation of GIA using (i) an assumed earth model and (ii) a model of ice sheet evolution back to the last glacial period. To date, most such studies have been based on the assumption that Earth structure (and in particular, mantle viscosity) varies only with depth. Given this assumption, the computational cost of simulating GIA is low, and this allows for simple methods to be applied in solving the inverse problem predicated on the ability to run very many simulations with different input parameters. Substantial 3D variations of viscosity within the Earth's mantle certainly do exist, however, though their specific form remains poorly known. Within the past 20 years or so, a range of studies have shown that such viscosity variations can have a significant effect on GIA. The cost of simulating GIA in 3D earth models is, however, dramatically increased over earlier 1D calculations, and this has rendered useless older methods for solving the inverse problem.Within the foreseeable future, the only computationally viable approach to the GIA inverse problem that can take account of 3D viscosity variations is to apply gradient-based optimisation (GBO). This approach is widely used in other fields, including weather forecasting, oceanography, and seismic tomography. A key technical aspect of this approach is the application of the so-called adjoint method for calculating the derivatives required to iteratively update the model so as to better fit the data. Recently, the first application of GBO to the GIA inverse problem has been undertaken, and the initial results show great promise. This research has, however, made clear that future large-scale applications of this method are being held back by the computational tools available. The aim of this proposal is, therefore, the development of new and highly efficient numerical methods to facilitate the application of GBO to the GIA inverse problem. Such focused methodological work is necessary to enable future practical studies aimed at increasing the accuracy of GIA corrections, and hence improving our ability to monitor and understand the Earth's changing climate.