Forward and adjoint coupled ocean-ice sheet modelling

南极冰盖是一块巨大的冰川冰块，大小相当于欧洲，有几公里厚。它位于海平面以下的基岩上，所以在冰较薄的边缘，它自由漂浮在海床上，形成漂浮的冰架(图1)。在过去的几十年里，很明显，在冰架下的洞穴中循环的海水正在以越来越快的速度融化南极冰盖。这影响了冰川流向海洋的速度，因此是预测海平面上升的关键因素。西南极洲是21世纪海平面预测中最大的不确定性来源，斯韦茨冰川(Tg)比任何其他冰川对海平面的影响都更大。这一总体主题的重要性，特别是这一地理位置，导致了最近关于Thwaites Glacier(https://nerc.ukri.org/press/releases/2018/14-glacier/).的2000万GB国家科学研究中心和国家科学基金会的联合计划由皮戈特教授领导的伦敦帝国理工学院的一个团队正在通过对关键接地线区域进行详细的数值模拟，为其中一个项目((https://www.bas.ac.uk/project/melting-at-thwaites-grounding-zone-and-its-control-on-sea-level/)做出贡献。在过去的几年里，在使用灵活的网格方法模拟复杂冰架洞穴中的海洋方面取得了进展(Jordan等人，2014；Yeager 2018)，以及在冰盖建模中使用灵活的网格方法和伴随灵敏度技术(Kirke-Smith等人，2017；Https://github.com/gahansen/Albany/wiki/PAALS-Tutorial-2016)，和完全耦合的海洋-冰盖模型现在已经成为可能(Asay-Davis等人，2016年)。近年来，在几个冰盖模型的开发中，已经采用了自动代码生成的能力，以提供对共轭的方便访问(Kirke-Smith等人，2017年；https://icepack.github.io/index.html).促进这一发展的底层技术(https://www.firedrakeproject.org/)起源于伦敦帝国理工学院，我们最近使用它生成了一个伴随启用海洋模型(https://thetisproject.org/).因此，帝国理工学院有机会将这些前沿研究课题结合到一个单一的建模框架中：对海洋和冰盖进行灵活的网格建模，并使用伴随项进行敏感性分析和数据同化。最终目标是一个具有伴随能力的完全耦合的模型，允许敏感性在海洋和冰盖之间传播。这种能力可用于数据同化、不确定性量化以及模型校准和初始化。特别是，该模型将是第一个能够解决初始化冲击这一关键问题的模型。当海洋和冰模型耦合在一起时，冰花了几个世纪的时间来适应海洋模型的状态，而这种人工信号会覆盖任何真实的海平面变化。通过使用耦合伴随项完美地初始化冰/海洋模型，从而隔离由海洋融化变化驱动的真实冰盖变化，可以避免这种冲击。这项工作将有助于帝国科学研究院团队的更广泛的活动，特别是能够利用上述NERC-NSF Thwaites冰川项目下计划的数据和模拟活动。作为项目期间海洋学研究的一部分，学生很有可能有机会亲身体验南极的实地考察。

The Antarctic Ice Sheet is a giant slab of glacial ice that is the size of Europe and a few kilometres thick. It rests on bedrock that is below sea level, so around the margins where the ice is thinner it floats free of the seabed to form floating ice shelves (Fig. 1). Over the last few decades it has become clear that the seawater circulating in the cavities beneath ice shelves is melting the Antarctic Ice Sheet at an increasing rate. This impacts on the speed with which glaciers flow towards the ocean and thus is a critical factor in predictions of sea-level rise. West Antarctica represents the largest source of uncertainty in projections of sea level over the 21st Century, with Thwaites Glacier (TG) having greater potential to influence sea level than any other. The importance of this overall topic and this geographical location in particular led to a recent £20M joint NERC-NSF programme on Thwaites Glacier (https://nerc.ukri.org/press/releases/2018/14-glacier/). A team at Imperial College London, led by Prof. Piggott, is contributing to one of these projects (https://www.bas.ac.uk/project/melting-at-thwaites-grounding-zone-and-its-control-on-sea-level/ led by BAS) through detailed numerical modelling of the critical grounding line region. Over the past few years there has been progress in the use of flexible mesh methods to simulate the ocean in complex ice shelf cavities (Jordan et al., 2014; Yeager 2018), as well as the use of flexible mesh methods along with the use of adjoint sensitivity techniques in ice sheet modelling (Kyrke-Smith et al., 2017; https://github.com/gahansen/Albany/wiki/PAALS-Tutorial-2016), and fully coupled ocean-ice sheet modelling is now possible (Asay-Davis et al., 2016).In recent years the ability for automatic code generation to provide easy access to adjoints has been taken up in the development of several ice sheet models (Kyrke-Smith et al., 2017; https://icepack.github.io/index.html). The underlying technology which has facilitated this development (https://www.firedrakeproject.org/) originates from Imperial College London and we have recently used it to generate an adjoint enabled ocean model (https://thetisproject.org/). There is therefore an opportunity here at Imperial to combine these cutting-edge research topics within a single modelling framework: flexible mesh modelling of the coupled ocean and ice sheet, and the use of adjoints for sensitivity analyses and data assimilation. The ultimate goal is a fully coupled model with an adjoint capability that allows for sensitivities to be propagated between the ocean and ice sheet. This capability can be used for data assimilation, uncertainty quantification, and model calibration and initialisation. In particular, this model will be the first capable of solving the crucial problem of initialisation shock. When ocean and ice models are coupled together, the ice spends centuries adjusting to the ocean model state, and this artificial signal over-rides any real sea-level change. This shock can be avoided by using the coupled adjoint to initialise the ice/ocean model perfectly, thus isolating the real ice sheet change driven by changes in ocean melting.This work would contribute to the wider activities of the Imperial-BAS team, and in particular would be able to take advantage of the data and modelling activities planned under the above-mentioned NERC-NSF Thwaites glacier project. It is highly likely that the student will get the chance to experience Antarctic fieldwork first-hand, as part of an oceanographic cruse during the project.