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。由于当前一代冰盖模型之间的巨大不一致，对未来世纪质量损失的预测受到阻碍。主要的挑战是缺乏合适的观测约束模型校准和准确的历史，过去的表面气候，可能作为表面强迫边界条件在冰盖模型模拟。该项目通过使用观测数据来应对这些挑战，观测数据的形式是由许多冰层穿透雷达测量成像的恒定年龄的地层层位，这些数据可以作为对过去冰盖模型流动和边界条件的数据约束。该方法的发展将提供一种新的方法，严格的冰盖校准和初始化。除了针对冰盖内部数据的过去气候重建的科学应用之外，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。将状态和参数估计问题作为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）开发与年龄层数据中封装的时间历史一致的随时间演化的GrIS状态;（ii）联合反演一组最佳模型参数（即，模型校准）和与底层冰盖演变一致的时变最佳表面强迫（即，重建一个一致的气候强迫历史）;和（iii）开发一个现实的瞬变模拟的冰盖在全新世时期，导致目前的状态，可以作为良好的平衡的初始条件进行预测，并为初始化冲击或人工模型漂移预计将是最小的，通过建设。一个关键的计算成分，使拟议的工作是一个时间依赖的伴随模型的冰盖模型，能够发展内部冰河时代的结构的发展。我们建议通过算法微分（AD）与开源工具OpenAD，应用于模拟代码的POLythermal冰盖（SICOPOLIS）模型来实现这一点。过去的冰流和格陵兰冰盖的边界条件的重建是必要的再现观测年龄（从冰芯），也使我们能够测试与更精细的时空细节的重要过去的气候事件，包括全新世气候最佳期和小冰期的开始。准确地说，这些事件可能是如何，何时，在哪里恢复这个国家的估计将揭示如何GrIS应对气候的快速变化，无论是在其整体和区域。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的知识价值和更广泛的影响审查标准的支持。

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.