Paleochronometry as a control problem for recovering holocene climate variations over the Greenland Ice Sheet

格陵兰冰盖（GrIS）已成为当今乃至未来全球海平面上升的重要因素。由于当前各代冰盖模型之间存在巨大分歧，对未来一个世纪冰盖质量损失的预测受到了阻碍。主要的挑战是缺乏适合模式校准的观测约束和过去地表气候的准确历史，这些历史可以作为冰盖模式模拟中的地表强迫边界条件。该项目通过使用以恒定年龄地层层位形式的观测数据来解决这些挑战，这些观测数据是由许多穿冰雷达调查成像的，可作为冰盖模型过去流动和边界条件的数据约束。所开发的方法将为严格的冰盖校准和初始化提供一种新的方法。除了针对从冰盖内部数据重建过去气候的科学应用之外，实现这一目标的基础设施将基于开源冰盖模型向社区公开。该项目将支持女性早期职业科学家向独立研究职业的过渡。将状态和参数估计问题作为一个终端约束控制问题来解决，使我们能够取得几个关键的科学进展：(i)开发一个与年龄层数据中封装的时间历史相一致的随时间变化的GrIS状态；（ii）联合反演一组最佳模式参数（即模式校准）和与下伏冰盖演变相一致的时变最佳地表强迫（即重建一致的气候强迫历史）；（iii）对全新世时期的冰盖进行真实的瞬态模拟，从而得出当前状态，该状态可以作为预测的良好平衡初始条件，并且通过构建，预计初始冲击或人工模式漂移将最小。使所提出的工作成为可能的一个关键计算要素是开发一个能够演变内部冰期结构的冰盖模型的随时间伴随模型。我们建议通过使用开源工具OpenAD的算法微分（AD）来实现这一目标，并将其应用于多热冰盖（SICOPOLIS）模型的模拟代码。这种对过去冰流和格陵兰冰盖边界条件的重建对于再现（从冰芯）观测到的年龄是必要的，也使我们能够以更精细的时空细节测试过去重要气候事件的开始，包括全新世气候最佳期和小冰期。这些事件究竟如何、何时以及在何处得以恢复，这将揭示GrIS是如何对整体和区域气候的快速变化做出反应的。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The Greenland ice sheet (GrIS) has emerged as a significant contributor to present-day, and possibly future global sea level rise. Predictions of mass loss over the coming century have been hampered by large discord between current-generation ice sheet models. Major challenges are the lack of suitable observational constraints for model calibration and accurate histories of past surface climates that may serve as surface forcing boundary conditions in ice sheet model simulations. This project addresses these challenges through the use of observational data in the form of stratigraphic horizons of constant age that have been imaged by numerous ice-penetrating radar surveys, which serve as a data-constraints on the past flow and boundary conditions of an ice sheet model. The method developed will provide a novel approach for rigorous ice sheet calibration and initialization. Beyond the scientific application that is targeted at past climate reconstruction from ice sheet internal data, the infrastructure to enable this will be publicly available to the community, being based on the open-source ice sheet model. The project will support the transition of a female early-career scientist into an independent research career.Solving the state and parameter estimation problem as a terminal constraint control problem enables us to make several key scientific advances: (i) develop a time-evolving GrIS state that is consistent with the time history encapsulated in the age layer data; (ii) jointly invert for a set of optimal model parameters (i.e., model calibration) and time-varying optimal surface forcings that are consistent with the underlying ice sheet evolution (i.e., reconstruction of a consistent climate forcing history); and (iii) develop a realistic transient simulation of the ice sheet over the Holocene period, leading into a present state that may serve as well-balanced initial condition for prediction, and for which initialization shocks or artificial model drift are expected to be minimal, by construction. A key computational ingredient that enables the proposed work is the development of a time-dependent adjoint model of an ice sheet model that is able to evolve internal ice age structures. We propose to accomplish this by means of algorithmic differentiation (AD) with the open-source tool OpenAD, applied to the SImulation COde for POLythermal Ice Sheets (SICOPOLIS) model. This reconstruction of past ice flow and the boundary conditions of the Greenland Ice Sheet is necessary to reproduce the observed ages (from ice cores) and also enables us to test with finer spatio-temporal detail the onset of important past climatic events, including the Holocene Climatic Optimum and the Little Ice Age. Exactly how, when, and where these events may be recovered by this state estimate will shed light on how the GrIS responds to rapid changes in climate, both in its entirety and regionally.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.