Explicitly Stochastic Parameterization of Nonorographic Gravity-Wave Drag

摘要

We present a straightforward methodology for converting the deterministic multi-wave parameterizations of nonorographic gravity-wave drag, currently used in general circulation models (GCMs), to stochastic analogues that use far fewer waves (in our example, a single wave) within each grid box. Deterministic discretizations of source-level momentum flux spectra using a fixed spectrum of many waves with predefined phase speeds are replaced by sampling these source spectra stochastically using waves with randomly-assigned phase speeds. Using simple conversion formulas, we show that time-mean wave- induced drag diffusion and heating-rate profiles identical to those from the deterministic scheme are produced by the stochastic analogue. Furthermore, the need for bulk intermittency factors of small value is largely obviated through the explicit incorporation of stochastic intermittency into the scheme. When implemented in a GCM, the single-wave stochastic analogue of an existing deterministic scheme reproduces almost identical time-mean middle-atmosphere climate and drag as its deterministic antecedent, but with an order of magnitude reduction in computational expense. The stochastic parameterization is accompanied by natural stochastic variability about the time-mean profile that forces the smallest space-time scales of the GCM. Studies of mean GCM kinetic energy spectra show that this additional stochastic forcing does not lead to unrealistic increases in dynamical variability at these smallest GCM scales, although a systematic increase in divergent kinetic energy variability is evident.