A proof of concept for scale-adaptive parametrizations: the case of the Lorenz '96 model

Constructing efficient and accurate parametrizations of subgrid-scale processes is a central area of interest in the numerical modelling of geophysical fluids. Using a modified version of the two-level Lorenz '96 model, we present here a proof of concept of a scale-adaptive parametrization constructed using statistical mechanical arguments. By suitable use of the Ruelle response theory and the Mori-Zwanzig projection method, it is possible to derive explicitly a parametrization for the fast variables that translates into deterministic, stochastic and non-Markovian extra terms in the equations of motion for the variables of interest. We show that our approach is computationally parsimonious and has great flexibility, as it is explicitly scale-adaptive, and we prove that it is competitive compared with empirical ad-hoc approaches. While the parametrization proposed here is universal and can easily be adapted analytically to changes in parameter values by a simple rescaling procedure, the parametrization constructed with the ad-hoc approach needs to be recomputed each time the parameters of the systems are changed. The price we pay for the higher flexibility of the method proposed here is having a lower accuracy in each individual case.