Toward next generation sea ice models: taking the rough with the smooth?

现有的海冰模型，例如出现在环境和气候模型中的海冰模型，是建立在连续的局部热量、动量和质量平衡之上的。状态变量如冰的厚度和浓度是光滑的和连续可微的。虽然存在重要的流变差异，但这些模型在数学上与标准连续介质模型（如牛顿流体流动的Navier-Stokes （NS）方程）在类型上相似。然而，与后几种模型不同的是，连续统假设在海冰模拟中往往是无效的，因为海冰是NS方程中分子的类似物，与用于数值模拟的网格单元大小相当。在这种情况下，网格单元不能包含具有统计代表性的海冰样本（或其他特征，如引线）。连续性的破坏导致了这样的建议，即下一代海冰模型应该建立在一个离散的架构上，在那里单个浮冰的相互作用可以被表示出来。本项目将研究连续体模型中的连续性违逆问题。特别是，如果能够证明连续模式代表了离散行为的平均值，那么这将为这些模式的解释提供急需的信心，特别是在气候模拟中。将探讨现有连续模型的局限性和离散方法的可能性，以满足未来模型发展的需要。海冰模型主要是在20世纪70年代建立的，当时提出了关于连续性、各向同性和流变学的基本假设。这些模型被设计为在长度尺度上有效，其中海冰可以通过在许多浮冰上平均（~50-100公里）而被视为连续的，并且假定冰盖各向同性（现在已知在所有长度尺度上都无效）。现在气候和天气模型中使用的海冰模型与这些模型是一样的，这些模型的分辨率越来越高（低至~1km），使连续性假设失效。由于这些模型不是为如此高的分辨率而建立的，并且包含了现在已知是错误的假设，因此人们对这些海冰模型是否有效和是否可信存在根本性的担忧。这个问题在海冰模拟界得到了很好的理解，但在更广泛的气候界却鲜为人知。在这个项目中，我们将通过解决混合离散和连续建模方法的可行性，向气候模型能力的海冰离散表示迈出第一步。在之前的方法和代码的基础上，学生将开发一个离散元素海冰模型（DEM），其中离散元素是实际的浮冰，并使用它来检查海冰的破裂和流动，以获得一系列理想的几何形状和强加的边界强迫。这些模拟将与等效连续介质模拟进行比较。DEM将用于检查狭窄海峡中的海冰破裂和流动，例如使用连续体海冰模型模拟的边界条件的典型加拿大群岛。对研究区域和观测数据的嵌套DEM模拟与连续体模型的直接模拟进行了比较。

Existing sea ice models, such as those that appear in environmental and climate models, are built on continuum local balances of heat, momentum, and mass. State variables such as ice thickness and concentration are smooth and continuously differentiable. While there are important rheological differences, these models are mathematically similar in type to standard continuum models such as the Navier-Stokes (NS) equations for Newtonian fluid flow. Unlike these latter models, however, the continuum assumption is often invalidated in sea ice simulations because the sea ice floe, the analogue of a molecule in the NS equations, is of comparable size to the grid cell used for numerical simulation. In this case, the grid cell cannot be taken to contain a statistically representative sample of sea ice floes (or other features such as leads). Continuity violation has led to suggestions that the next generation of sea ice models should be built on a discrete architecture, where individual floe interactions can be represented. This project will examine the issues of continuity violation in continuum models. In particular, if it can be shown that a continuum model represents an average of the discrete behaviour then this would provide much needed confidence in the interpretation of these models, particularly in climate simulations. The limitations of existing continuum models and the possibilities of discrete approaches will be explored, with a view to the needs of future model development.Sea ice models were largely built in the 1970s, where fundamental assumptions were made concerning continuity, isotropy, and rheology. The models were designed to be valid over length scales where the sea ice could be treated as continuous by averaging over many floes (~50-100km) and the ice cover assumed isotropic (now known to be an invalid at all length scales). These are the same sea ice models being used in climate and weather models now, where there is a push to increasingly high resolutions (down to ~1km), invalidating the continuity assumption. Since the models were not built for such high resolutions, and contain assumptions now known to be wrong, there are fundamental concerns over whether such sea ice models are valid and can be trusted. This is an issue well appreciated within the sea ice modeling community, but is less well known in the broader climate community. In this project we will take the first steps towards a climate model-capable discrete representation of sea ice by addressing the feasibility of blending discrete and continuum modelling approaches. Building on previous approaches and code, the student will develop a discrete element sea ice model (DEM), where the discrete elements are the actual floes, and use this to examine sea ice breakup and flow for a range of idealised geometries and imposed boundary forcing. These simulations will be compared with equivalent continuum simulations. The DEM will be used to examine sea ice breakup and flow in narrow straits, such as are typical of the Canadian Archipelago using boundary conditions from a simulation using a continuum sea ice model. The nested DEM simulations would be compared with the direct simulations from the continuum model for the study region and observations.