  We describe CATKE, a parameterization for fluxes associated with small-scale
or "microscale" ocean turbulent mixing on scales between 1 and 100 meters.
CATKE uses a downgradient formulation that depends on a prognostic turbulent
kinetic energy (TKE) variable and a diagnostic mixing length scale that
includes a dynamic convective adjustment (CA) component. With its dynamic
convective mixing length, CATKE predicts not just the depth spanned by
convective plumes but also the characteristic convective mixing timescale, an
important aspect of turbulent convection not captured by simpler static
convective adjustment schemes. As a result, CATKE can describe the competition
between convection and other processes such as shear-driven mixing and
baroclinic restratification. To calibrate CATKE, we use Ensemble Kalman
Inversion to minimize the error between 21 large eddy simulations (LES) and
predictions of the LES data by CATKE-parameterized single column simulations at
three different vertical resolutions. We find that CATKE makes accurate
predictions of both idealized and realistic LES compared to microscale
turbulence parameterizations commonly used in climate models.
