Modeling of small scale processes in Antarctic sea ice and their impact on the biological pump in the future Southern Ocean - a physical-biological coupled bi-scale approach

全球海冰覆盖的季节变化是全球气候的一个重要组成部分。然而，海冰的小规模影响在全球气候模式中仍未得到充分描述。因此，本研究旨在利用高保真双尺度模型对海冰中关键的物理(P)和生物地球化学（BGC）过程进行数学描述。然后可以将结果参数化并纳入全球气候模式（GCMs），从而提高预测能力。海洋变暖将显著改变海冰的微观结构。因此，我们建立了南极海冰的P-BGC模型，以数学方式描述冰形成、营养物质运输、盐度和盐水通道分布、光合作用和碳酸盐化学之间的复杂耦合关系。我们利用该模型模拟了不同情景下海冰形成及其对海冰藻类生长的影响，海冰藻类对垂直碳输出（生物碳泵）有显著影响。因此，本项目对研究课题’3.2有重要贡献。提高对极性过程和机制的理解。我们使用一个耦合的双尺度模型来描述与变形、盐度和盐水运输有关的冻结和融化的相关方面。在宏观层面上，在扩展多孔介质理论（eTPM）的框架内进行了连续力学描述。这允许通过一组耦合的偏微分方程（PDE）来描述变形、输运和反应过程。对于水与冰之间相变的物理现象，相场模型（PF）提供了一个微观尺度，它也是由耦合的pde组成的。这导致了PDE-PDE耦合。步骤2：与扩展的RecoM2模块耦合作为微尺度模型。这允许描述BGC现象。RecoM2模块由一个常微分方程系统组成，因此可以执行PDE-ODE与P-BGC模型的耦合。步骤3：模型方法的评估这包括使用文献和实验数据对P-BGC组合模型进行验证和验证。为了在全球气候模式中使用高分辨率二尺度P-BGC模式，必须提高计算效率。为此，应用降阶模型（ROM）来生成全阶模型（FOM）的替代品，从而降低模型的复杂性，例如通过数据驱动的机器学习（ML）技术或广义适当分解（GPD）。

The seasonal variability of the global sea ice cover is an important component of the global climate. However, the small-scale influence of sea ice is still insufficiently described in global climate models. Therefore, this proposal aims to mathematically describe the key physical (P) and bio-geo-chemical (BGC) processes in sea ice using a high-fidelity two-scale model. The results can then be parameterized and incorporated into global climate models (GCMs), thus improving the predictive power.Ocean warming will significantly change the microstructure of sea ice. Thus, we develop a P-BGC model of an Antarctic sea ice floe to mathematically describe the complex coupled relationships between ice formation, nutrient transport, salinity and brine channel distribution, photosynthesis and carbonate chemistry. We use this model to simulate different scenarios of sea ice formation and its effects on the growth of sea ice algae, which have a significant impact on vertical carbon export (biological carbon pump).Thus, this project contributes significantly to the research topic '3.2.D - Improved understanding of polar processes and mechanisms'. In detail, we address three overarching goals:Step 1: Description of the sea ice structure We use a coupled bi-scale model to describe relevant aspects of freezing and melting in connection with deformation, salinity and brine transport. On the macroscopic level, a continuum mechanical description within the framework of the extended theory of porous media (eTPM) is performed. This allows the description of deformation, transport and reaction processes via a coupled set of partial differential equations (PDE). For the physical phenomenon of phase transformation between water and ice, the phase field model (PF) provides a micro-scale, which also consists of coupled PDEs. This results in a PDE-PDE coupling.Step 2: Coupling with the extended RecoM2 module as micro-scale model This allows the description of the BGC phenomena. The RecoM2 module consists of a system of equations of ordinary differential equations, so that a PDE-ODE coupling to a P-BGC model is performed. Step 3: Evaluation of the model approaches This includes the verification and validation of the combined P-BGC model using literature and experimental data. For the use of the high-resolution two-scale P-BGC model in global climate models the calculation efficiency has to be increased. For this purpose, reduced-order model (ROM) to generate surrogates of the full order model (FOM) are applied, which decrease the model complexity, e.g. by data-driven machine learning (ML) techniques or generalized proper decomposition (GPD).