Development of a Viscoelastic Ice-flow Model for Process-based Prediction of Ice-Sheet Evolution

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。冰川学界缺乏对滑动和河床变形的定量预测理解。pi提出了一项建模工作，以开发粘塑性床上的粘弹性冰流模型，以及相关的数据同化技术，以帮助约束描述该床的基本流动规律。对于冰，麦克斯韦模型（由弹簧和阻尼器串联组成）预计在标准牛顿（线性）阻尼器被符合格伦（非线性）流动定律的阻尼器取代时证明是足够的。麦克斯韦模型允许瞬时弹性响应，以及应力松弛，其中维持材料中给定应变率所需的应力随着时间的推移而减小。因此，麦克斯韦模型非常适合于粘性和弹性行为相对独立的材料，因此将粘性模型更改为麦克斯韦粘弹性模型可能被视为在现有模型上添加弹性“覆盖层”。先前在模拟纯弹性冰流的潮汐强迫方面取得的成功为这种方法提供了支持。然而，如果麦克斯韦模型被证明是不充分的，pi准备研究一个由麦克斯韦单位和开尔文单位串联组成的汉堡模型（它本身由一个弹簧和一个并联的阻尼器组成）。除了麦克斯韦模型的粘性和瞬时弹性行为外，Burgers模型还显示出在某些频率下对力的延迟弹性响应。然而，在对冰川流动感兴趣的更长的时间尺度上，pi预计强迫和（非局部）响应之间的任何滞后都将由弹性波的有限传播速度造成。他们计划首先将Maxwell粘弹性特性添加到深度集成、宽度平均的冰流-冰架模型中。这种一维模型允许相对直接地结合新的物理学，但它足够复杂，可以评估冰架支撑和基底融化的影响。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Alley 0909335Pennsylvania State UniversityThe glaciology community lacks a quantitatively predictive understanding of sliding and bed deformation. The PIs propose a modeling effort to develop viscoelastic ice-flow models overlying a viscous-plastic bed and associated techniques for data assimilation to help constrain basal flow laws describing this bed. For ice, the Maxwell model (consisting of a spring and dashpot in series) is anticipated to prove sufficient when the standard Newtonian (linear) dashpot is replaced by one obeying Glen's (nonlinear) flow law. The Maxwell model allows instantaneous elastic response, as well as stress relaxation, in which the stress required to sustain a given strain rate in the material diminishes over time. Thus, the Maxwell model is well-suited to materials for which viscous and elastic behavior are relatively independent, so that changing a model from viscous to Maxwell viscoelastic may be viewed as adding an elastic "overlay" to the existing model. Prior success in modeling tidal forcing of a purely elastic ice stream lends support to this approach. However, should the Maxwell model prove inadequate, the PIs are prepared to investigate a Burgers model, which consists of a Maxwell unit in series with a Kelvin unit (itself consisting of a spring and dashpot in parallel). In addition to the viscous and instantaneous elastic behavior of the Maxwell model, the Burgers model also displays delayed elastic response to forcing at certain frequencies. At the longer timescales of interest for glacial flow, though, the PIs expect that any lag between forcing and (nonlocal) response will result from the finite propagation speed of elastic waves. They plan to begin by adding Maxwell viscoelastic behavior to a depth-integrated, width-averaged ice stream-ice shelf model. This type of one-dimensional model allows for relatively straightforward incorporation of new physics, yet is sophisticated enough to assess the effects of ice shelf buttressing and basal melting.