Abstract
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 discretized 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.
Models of this type are currently used e.g. as a numerical weather prediction models. The statistical models are considerably different: they are not based on physical mechanisms underlying the dynamics of the modelled system, but rather derived from the analysis of past weather patterns.
An example of such a statistical model based on the idea of linear inverse modelling, is examined for modelling the El Niño - Southern Oscillation phenomenon with a focus on modelling cross-scale interactions in the temporal sense. Various noise parameterizations and the possibility of using a multi-variable model is discussed among other characteristics of the statistical model.
The prospect of using statistical models with low complexity as a surrogate model for statistical testing of null hypotheses is also discussed.