Stochastic Superparameterization in Quasigeostrophic Turbulence

Superparameterization is a multiscale method for modeling the impact of small-scale processes on resolved large scales in general circulation models; it couples a low-resolution general circulation model to high-resolution simulations embedded within the coarse grid. Although it is effective in representing the effects of small-scale convection, it is computationally expensive, the coupling framework precludes important small-scale instabilities (e.g. baroclinic instability), and it imposes a severe scale separation between large and small scales.

We present an alternative framework for superparameterization that allows a wider range of small-scale instabilities, including baroclinic instability, significantly decreases the computational cost, and lessens the severity of the large/small scale gap. The improved representation of the small-scale dynamics (allowing baroclinic instability) is achieved through a new framework for coupling the large and small scales, called the 'point approximation.' Massive computational savings are achieved by modeling the small-scale dynamics with quasilinear stochastic PDEs instead of nonlinear deterministic PDEs. The large/small scale gap is lessened by representing the small-scale variables as spatially-homogeneous stochastic processes in embedded domains that are formally infinite. (The small scales are nevertheless guaranteed not to have large-scale variation.)

We implement the new method in the relatively simple setting of two-layer doubly-periodic quasigeostrophic turbulence, but we emphasize that the method does not rely in any way on periodic geometry. The method absorbs the forward cascade of potential energy to small scales and generates an inverse cascade of kinetic energy from small scales, and is able to generate correct large-scale energy spectra, heat flux, and jet structure. It is only minimally more computationally expensive than conventional parameterization, and its stochastic nature suggests that it could increase ensemble variability and therefore improve the skill of ensemble-based predictions and reanalyses.