Sea ice in the polar oceans plays a significant role in regulating global climate and biological ecosystems. During the winter months, seawater freezes to form porous ice, which also serves as a habitat for sea ice algae to survive in harsh winter conditions. However, accurate description of mechanisms and interactions associated with formation of ice, and its interaction with photosynthesis and carbon assimilation have not been well understood. This paper presents a modeling framework to describe coupled small scale Physical (P) and BioGeoChemical (BGC) processes associated with sea ice. Critical processes associated with photosynthesis along with growth and loss of algal carbon are considered. Appropriate parametrization for environmental factors such as temperature, light, salinity, and nutrients are employed to model the photosynthetic rate. Summer and winter environmental conditions are presented and discussed in detail. Finally, monthly data is taken from literature to simulate a typical year in the Southern Ocean.