Higher-order closure

From Glossary of Meteorology

higher-order closure

An approximation to turbulence that retains prognostic equations for mean variables (such as potential temperature and wind) as well as for some of the higher-order statistics including variance (such as turbulence kinetic energy
or temperature variance) or covariance (kinematic fluxes such as for heat and momentum).

Regardless of the statistical order of the forecast equations, other high-order statistical terms appear in those equations, the solutions of which require approximations known as turbulence closure assumptions. While usually considered more accurate than first-order closures (K-theory), higher-order closure solutions are computationally more expensive. Turbulence closures are often classified according to two attributes: the order of statistical closure, and the degree of nonlocalness. Common types of higher-order closure include (in increasing statistical order): one-and-a-half order closure (also known as k-ε closure), second-order closure, and third-order closure. All turbulence closures are designed to reduce an infinite set of equations that cannot be solved to a finite set of equations that can be solved approximately to help make weather forecasts and describe physical processes.
See Reynolds averaging;
compare zero-order closure, half-order closure.