The El Niño Southern Oscillation (ENSO) is the most intense climatic fluctuation on Earth after the seasonal cycle. The observation, understanding and forecast of this fluctuation with worldwide impacts are major scientific issues. This thesis (entitled "Simple Models for Understanding the Mechanisms and Modulation of ENSO") documents various aspects of ENSO such as its mechanisms, its modulation and its forecast. Those various aspects are tackled by developing a hierarchy of models of the equatorial Pacific, of increasing complexity, ranging from conceptual models to a data assimilation method in an intermediate complexity model. We study at first mechanisms of ENSO formation. We develop an alternative derivation of the recharge/discharge conceptual model where ENSO arises from a basin-wide adjustment of the equatorial thermocline. We also implement an original diagnostic in a model of equatorial coupled instabilities, which evidences a new mechanism of ENSO formation where reflections at the ocean boundaries are secondary. The background ocean stratification contributes to the decadal modulation of ENSO characteristics. This relation is adressed in a new reduced model that takes into account the gravest baroclinic modes of a continusouly stratified ocean. The space of model solutions is explored, indicating a control on ENSO stability by characteristics of the equatorial thermocline. The sensitivity to stratification over the recent decades is put in perspective with the sensitivity to thermodynamic and atmospheric feedbacks. We stress in particular certain limitations of usual methods of estimation of the thermocline feedback in the central Pacific. Finally, we implement an Ensemble Kalman Filter method in an already existing intermediate model of the equatorial Pacific, in order to assimilate sea level observations and to initialize retrospective forecasts. We show that the major model constraint is on the basin modes that are associated to the recharge/discharge process of the equatorial Pacific. Our work provides a formalism to diagnose the modulation of ENSO characteristics in observations, climate projections and forecasts. Results support the need to extent the understanding of ENSO mechanisms, in order to account for the diversity of observed regimes and to improve forecasts.
