When it comes to modelling in atmospheric and climate science, the two main types of models are taken into account – dynamical and statistical models. The former ones have a physical basis: they utilize discretised differential equations with a set of conditions (boundary conditions + present state as an initial condition) and model the system’s state by integrating the equations forward in time. The statistical models are considerably different: they are not based on physical mechanisms underlying the dynamics of the modeled system, but derived form the analysis of past weather patterns. The example of such statistical model, based on the idea of linear inverse modelling, is examined for modelling the El Nino – Southern Oscillation phenomenon with a focus on modeling cross-scale interactions in the temporal sense. Various noise parameterizations and the possibility of using multi-variable model are discussed among other characteristics of statistical model. The prospect of using statistical models with low complexity as a surrogate models for statistical testing is also discussed.