Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales
Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales
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DOI：
10.5194/gmd-11-1683-2018
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发表时间：
2018-05-03
影响因子：
5.1
通讯作者：
Seroussi, Helene
中科院分区：
文献类型：
--
作者：
Cuzzone, Joshua K.;Morlighem, Mathieu;Seroussi, Helene
古气候代用指标正与冰盖模拟实验结合使用，以确定格陵兰冰盖如何对过去的变化作出反应，特别是在最后一次冰消期。虽然这些比较是我们理解格陵兰冰盖对过去变暖敏感性的关键组成部分，但它们通常依赖于模型实验，这些实验有利于最大限度地减少计算费用，而不是增加模型物理。在古气候时间尺度上，模拟冰盖的热结构对模拟的冰粘度有很大的影响，它可以反馈到基底滑动和冰流。为了准确地捕获热场，模型通常需要大量的垂直层。然而，这不是应力平衡计算的情况，其中不需要高垂直分辨率。因此，由于应力平衡和热方程通常在相同的网格上执行，因此在应力平衡计算上花费的时间比其他必要的时间多。由于这些原因，运行高阶冰盖模型（例如，Blatter-Pattyn）在相当于古气候记录的时间尺度上进行计算，而不产生大量的计算费用是不可能的。为了缓解这个问题，我们提出了一种方法，可以在冰盖模型中实现，其中垂直插值沿着z轴依赖于高阶多项式，而不是传统的线性插值。在冰盖系统模型（ISSM）中，使用二次和三次有限元法对理想情况下的垂直插值和一个现实的格陵兰岛配置进行了测试。一个单圆顶冰盖的冰厚度演变的瞬态实验表明，提高精度使用高阶垂直插值模型相比，使用线性垂直插值，尽管有更少的自由度。这种方法也表明，以提高模型的能力，捕捉尖锐的温度梯度在冰盖特别是接近床，相比，模型使用线性垂直插值。这一点在使用高阶模型对格陵兰冰盖进行的热稳态模拟中得到证实。一般来说，我们发现使用高阶垂直插值减少了对大量垂直层的需求，同时大大减少了瞬态模拟的模型运行时间。结果表明，当使用高阶垂直插值时，瞬态冰盖松弛的运行时间比使用具有线性垂直插值的模型快5至7倍，因此这需要更多的垂直层来实现模拟冰量，基底温度和冰划分厚度的类似结果。研究结果表明，这种方法将允许在研究古气候时间尺度上冰盖行为的研究中使用更高阶的模型，而计算成本仅为使用线性垂直插值的模型所需的一小部分。
Paleoclimate proxies are being used in conjunction with ice sheet modeling experiments to determine how the Greenland ice sheet responded to past changes, particularly during the last deglaciation. Although these comparisons have been a critical component in our understanding of the Greenland ice sheet sensitivity to past warming, they often rely on modeling experiments that favor minimizing computational expense over increased model physics. Over Paleoclimate timescales, simulating the thermal structure of the ice sheet has large implications on the modeled ice viscosity, which can feedback onto the basal sliding and ice flow. To accurately capture the thermal field, models often require a high number of vertical layers. This is not the case for the stress balance computation, however, where a high vertical resolution is not necessary. Consequently, since stress balance and thermal equations are generally performed on the same mesh, more time is spent on the stress balance computation than is otherwise necessary. For these reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn) over timescales equivalent to the paleoclimate record has not been possible without incurring a large computational expense. To mitigate this issue, we propose a method that can be implemented within ice sheet models, whereby the vertical interpolation along the z axis relies on higher-order polynomials, rather than the traditional linear interpolation. This method is tested within the Ice Sheet System Model (ISSM) using quadratic and cubic finite elements for the vertical interpolation on an idealized case and a realistic Greenland configuration. A transient experiment for the ice thickness evolution of a single-dome ice sheet demonstrates improved accuracy using the higher-order vertical interpolation compared to models using the linear vertical interpolation, despite having fewer degrees of freedom. This method is also shown to improve a model's ability to capture sharp thermal gradients in an ice sheet particularly close to the bed, when compared to models using a linear vertical interpolation. This is corroborated in a thermal steady-state simulation of the Greenland ice sheet using a higher-order model. In general, we find that using a higher-order vertical interpolation decreases the need for a high number of vertical layers, while dramatically reducing model runtime for transient simulations. Results indicate that when using a higher-order vertical interpolation, runtimes for a transient ice sheet relaxation are upwards of 5 to 7 times faster than using a model which has a linear vertical interpolation, and this thus requires a higher number of vertical layers to achieve a similar result in simulated ice volume, basal temperature, and ice divide thickness. The findings suggest that this method will allow higher-order models to be used in studies investigating ice sheet behavior over paleoclimate timescales at a fraction of the computational cost than would otherwise be needed for a model using a linear vertical interpolation.