• Nino
• Fokker-Planck
• LOM
• ENSO

El Nino-Southern Oscillation (ENSO) is the most important and studied phenomenon affecting the climate variability at interannual timescales. As the name suggests, ENSO consists of two related aspects which fluctuate periodically in an irregular way. The first, El Nino, is associated to an increase in the sea surface temperature (SST) along the coasts of Ecuador and Peru, whereas the second one, the Southern Oscillation, is related to changes in the east-west pressure gradient leading to the movement of air masses in the atmosphere along the Pacific Equator line (Walker's circulation). Over the years, a number of models have been developed in order to fully understand this phenomenon both qualitatively and quantitatively. These models usually rely on more or less strong approximations of the fluid dynamic equations which regulate the atmospheric and oceanic dynamics. These approximations are based on the fact that the ENSO phenomenon involves a very thin layer of the ocean along the Pacific Equator, i.e. a strip of water 15000km long, few hundreds km widht and with an average dept of some tens of meters. This very elongated strip of water, behaves like a river that has the source at the extreme east, the sink at the west boundary, and it is driven by the rotation of the Earth and by the westerly trade winds.
This simplifyed scheme of the ocean dynamics, along the Pacific Equator, leads to a reduced set of equations in which one or more stochastic terms are introduced. The stochastic terms are used to simulate the fluctuations in periodicity and intensity of the phenomenon, generated by the interaction between the ocean and the atmosphere (Recharge oscillator models, ROM).
In recent works, Dr. Marco Bianucci has developed a different general approach, based on projection techniques, that allows to couple a generic system under examination (in this case the oceanic variables) with a deterministic system that correctly reproduces the contribution of the stochastic forcing. This technique, applied to a model which reproduces the ENSO phenomenon, allows us to derive a partial differential equation which describe the statistics of two ENSO relevant variables: the anomalies of the average thermocline depth (h) and the estern Pacific SST (T), respectively. This last, in particular, is considered the main variable which identifies the phenomenon of Nino, when T>0, or la Nina, when T<0. Under appropriate hypothesis, this PDE can be reduced to a Fokker-Plank equation (FPE), which will be the core of this work.
The present thesis concerns mainly in the study and the realisation of a software that allows the numerical resolution of the Fokker-Plank equation for the ENSO phenomenon. This software has made it possible to obtain the probability density function (PDF) for the stationary state in the two-dimensional space (h,T) and a reduced form of it for the sole variable T. This reduced PDF was directly compared to the analytical results obtained in the foundamental work of Dr. Marco Bianucci. These theoretic results are particularly important since allow a direct and immediate comparison with the data obtained from the observation of the ENSO phenomenon. Nevertheless these result are obtained by adopting an hypothesis ("the ansatz") which is assumed to be approximately correct: one of the aim of the present thesis is to verify, through the numerical solution of the Fokker-Planck equation, the validity or not of this hypothesis.
Subsequently it was performed the numerical integration of the stochastic equations associated to the previously PDE in order to calculate the quantities related to the periodicity and the intensity of extreme El Nino events. To this end it was calculated the mean first passage time (MFPT) corresponding to El Nino events of great intensity and this result was compared with the available observations for the ENSO phenomenon and with the analytical results stemming from standard MFPT techniques applied to the reduced model.