One of the main challenges of the atmospheric model is the proper determination of the turbulent diffusivity. In this sense, variousboundary layer parametrization have been developed along of the years. For the same closure order, many times, the bigger differences between them, are concentrated in the adjustment parameters. From the adequate physical description, to find the real value of each constant is the great challenge of the models. Them, the present work compare three different parametrization for the non-dimensional relation u2 ∗=E, that is used as a constant in the momentum diffusion coefficient in the E - l models. In the comparison with the GABLS experiment, the results show that the constant does not have a great influence over the windcomponents and over the temperature. On the other hand, the constant have a fundamental role in the behavior of the turbulence kinetic energy. This is due the fact of the constant is also present in the turbulence viscous dissipation term. Finally, it is important to stress that this is a work that is in its beginning and it aims the construction of a boundary layer parameterization for climate and weather forecasting models.