A parameter sensitivity analysis for a pre-operational 2-D barotropic application of the ROMS_AGRIF ocean model for the forecast of sea surface height (SSH) and currents at the South-Western South Atlantic Continental Shelf with emphasis in the Río de la Plata Estuary is presented. Particularly, the interest is on the simulation of extreme storm surges generated by persistent and strong southeasterly winds (<i>Sudestadas</i>) which produce strong floods. Atmospheric models show deficiencies in the forecast of winds during those events. Therefore, linear and quadratic bottom friction, wind speed and direction, and runoff were considered in the sensitivity analysis. The analysis yields to a hierarchy of the impacts of them on the simulated SSH. The most important, with non-linearity in the model response, is wind speed. It is followed by the quadratic bottom friction and the runoff, which responses are more linear, and present a regional dependence. Runoff has a larger impact than friction in the upper estuary, which decreases downstream. Non-linearity of wind speed is mainly due to the parametrization of the stress tensor, whereas the interaction with the runoff is not relevant in spite of the huge discharge of this particular estuary. This information allows an optimal calibration of the model with a minimum number of simulations.