Modeling El Nino Southern Oscillation and its interaction with the Atmosphere by combining the Delayed Action Oscillator and the Lorenz Models

El Nino Southern Oscillation constitutes a meteorological phenomenon with a substantial range of impacts. It influences both, hurricane and drought seasons as well as the spread of diseases along the entire Pan-American and Caribbean regions. Forecasting of El Nino and/or La Nina requires the combination of regional as well as global models, demanding a considerable amount of computer power and time. A possible intermediate solution might be the application of the so called “Toy Models”, which despite its relative mathematical simplicity are able to capture most of the physics of these phenomena. In this regards, the Delayed Action Oscillator (DAO) has been used in the literature to model El Nino, and the Lorenz model constitutes a paradigm in weather variability and the chaotic nature of some solutions preventing to do long time range forecasts. The DAO model is based on a time delayed non-linear differential equation of the first order which has been solved appealing to different external forcing in order to evaluate how they might change periodicities and intensities of El Nino and/or La Nina. Within this model, stochasticity of the weather is introduced via the Weierstrass function; a continuous and differentiable nowhere function. It differs from the traditional white noise. Even though, this model is able to account for much of the trends observed within the ocean, it is not able to capture the influence on other climatic zones neither the so called teleconnection with other regional scale meteorological events. One possible extension of the DAO model might be to couple it with the Lorenz model. The Lorenz model considers the convective heat exchange within the atmosphere and it is a system of three non-linear differential equations. This way, changes in surface temperature of the ocean are couple with changes within the atmosphere and vice versa. The model was labeled as DAOPL (DAO Plus Lorenz). The solutions of these models may be found numerically using the software Mathematica. The sensitivity of solutions commonly found for pure DAO are investigated as a function of the ocean – atmosphere coupling, as well as a function of parameters controlling the Lorenz model dynamics. The DAOPL model is solved also under the action of both, a periodic forcing and a stochastic forcing. No signatures of stochastic resonance were found within the range of considered parameters. Periodicities of El Nino slightly change, showing a robust dynamics. Even though, the presented model neglect spatial variability, it might be seen as a coarse-grained approximation of the ocean – atmosphere interaction during El Nino events.