The state of the art in the forecast of the background solar wind speed and of the interplanetary magnetic field at Earth is based on the use as boundary conditions for heliospheric models of the input data provided by solar observations. Magnetogram synoptic maps are used to obtain information on the magnetic field configuration at the solar source surface. Magnetic field inputs at the solar source surface thus constitute one of the main external sources of errors in solar wind models. The assimilation of data into forecasting models used in the terrestrial domain showed the ability to control model state errors. A sensitivity study performed through the analysis of the ensemble variances and the representers technique is used here to assess how process and model state errors propagate in a nonlinear two-dimensional MagnetoHydro Dynamic (MHD) system. The aim is to understand the impact of the source surface input parameters on the evolution of MHD heliospheric models and the potentialities of data assimilation techniques in solar wind forecasting. The representer technique in fact allows one to understand how far from the observation point the improvement granted from the assimilation of a measure propagates.