Modeling freezing and BioGeoChemical processes in Antarctic sea ice

Abstract

The Antarctic sea ice, which undergoes annual freezing and melting, plays a significant role in the global climate cycle. Since satellite observations in the Antarctic region began, 2023 saw a historically unprecedented decrease in the extent of sea ice. Further ocean warming and future environmental conditions in the Southern Ocean will influence the extent and amount of ice in the Marginal Ice Zones (MIZ), the BioGeoChemical (BGC) cycles, and their interconnected relationships. The so‐called pancake floes are a composition of a porous sea ice matrix with interstitial brine, nutrients, and biological communities inside the pores. The ice formation and salinity are both dependent on the ambient temperature. To realistically model these multiphasic and multicomponent coupled processes, the extended Theory of Porous Media (eTPM) is used to develop Partial Differential Equations (PDEs) based high‐fidelity models capable of simulating the different seasonal variations in the region. All critical variables like salinity, ice volume fraction, and temperature, among others, are considered and have their equations of state. The phase transition phenomenon is approached through a micro‐macro linking scheme. In this paper, a phase‐field solidification model [4] coupled with salinity is used to model the microscale freezing processes and up‐scaled to the macroscale eTPM model. The evolution equations for the phase field model are derived following Landau‐Ginzburg order parameter gradient dynamics and mass conservation of salt allowing to model the salt trapped inside the pores. A BGC flux model for sea ice is set up to simulate the algal species present in the sea ice matrix. Ordinary differential equations (ODE) are employed to represent the diverse environmental factors involved in the growth and loss of distinct BGC components. Processes like photosynthesis are dependent on temperature and salinity, which are derived through an ODE‐PDE coupling with the eTPM model. Academic simulations and results are presented as validation for the mathematical model. These high‐fidelity models eventually lead to their incorporation into large‐scale global climate models.