  Multiscale dynamics are frequently present in real-world processes, such as
the atmosphere-ocean and climate science. Because of time scale separation
between a small set of slowly evolving variables and much larger set of rapidly
changing variables, direct numerical simulations of such systems are difficult
to carry out due to many dynamical variables and the need for an extremely
small time discretization step to resolve fast dynamics. One of the common
remedies for that is to approximate a multiscale dynamical systems by a closed
approximate model for slow variables alone, which reduces the total effective
dimension of the phase space of dynamics, as well as allows for a longer time
discretization step. Recently we developed a new method for constructing a
deterministic reduced model of multiscale dynamics where coupling terms were
parameterized via the Fluctuation-Dissipation theorem. In this work we further
improve this previously developed method for deterministic reduced models of
multiscale dynamics by introducing a new method for parameterizing slow-fast
interactions through additive stochastic noise in a systematic fashion. For the
two-scale Lorenz 96 system with linear coupling, we demonstrate that the new
method is able to recover additional features of multiscale dynamics in a
stochastically forced reduced model, which the previously developed
deterministic method could not reproduce.
