The semigeostrophic equations are a frontogenesis model in atmospheric science. Existence of solutions both from the theoretical and numerical point of view is given under a change of variable involving the interpretation of the pressure gradient as an optimal transport map between the density of the fluid and its push forward. Thanks to recent advances in numerical optimal transportation, the computation of large scale discrete approximations can be envisioned. We study here the use of entropic optimal transport and its Sinkhorn Algorithm companion.