Sea ice acts as an iron (Fe) reservoir in the Southern Ocean (SO) where primary productivity is largely Fe limited. The mechanisms leading to Fe enrichment in sea ice result from the combination of poorly understood and largely unexplored physical and biological processes. We analyze the biogeochemical impacts of three plausible idealized formulations of dissolved Fe (DFe) incorporation into sea ice corresponding to (i) constant Fe concentration in sea ice, (ii) constant ocean-ice Fe flux, and (iii) ocean-ice Fe flux linearly varying with seawater Fe concentration in a global ocean-sea-ice-biogeochemical model, focusing on the SO. The three formulations simulate different geographical distributions of DFe concentrations in sea ice. Iron in sea ice remains largely uncertain due to the limited number of spatial and seasonal observations, poorly constrained Fe sources and sinks, and significant uncertainties in simulated sea ice and hydrography. Despite these differences, the fertilization effect by sea ice on phytoplankton photosynthesis is qualitatively similar regardless of the formulation considered. Iron incorporation during sea-ice formation, transport, and melt release, common to all formulations, dominates over differences in sea-ice Fe concentrations. Formulating the Fe incorporation rate as proportional to seawater Fe concentrations gives the closest agreement to field observations. With this formulation, sediments work in synergy with Fe transport to fertilize the waters north of the continental shelf. Southern Ocean primary production and export production increase by 5-10% and 9-19%, respectively, when Fe incorporation into sea ice is considered, suggesting a moderate effect of Fe-bearing sea ice on marine productivity. A large part of the SO is under the influence of the cryosphere, which involves several forms of ice: sea ice (pack ice and landfast ice), icebergs, and melting ice shelves. These cryospheric elements reduce light availability at the ocean surface. However, they are also iron laden, which is thought to stimulate productivity and carbon export (