  We consider the numerical approximation of stochastic partial differential
equations (SPDEs) based models for a quasi-periodic climate pattern in the
tropical Pacific Ocean known as El Ni\~no phenomenon. We show that for these
models the mean and the covariance are given by a deterministic partial
differential equation and by an operator differential equation, respectively.
In this context we provide a numerical framework to approximate these
parameters directly. We compare this method to stochastic differential
equations and SPDEs based models from the literature solved by Taylor methods
and stochastic Galerkin methods, respectively. Numerical results for different
scenarios taking as a reference measured data of the years 2014 and 2015 (last
Ni\~no event) validate the efficiency of our approach.
