ensemble average

1. The value of a meteorological variable found by averaging over many independent descriptions or realizations of that variable.

While this type of average often forms the basis of theories and simulations (numerical or physical models) for turbulence, it is usually impossible to compute in real life because we cannot control the atmosphere in order to reproduce multiple ensemble members. In real life, an ergodic hypothesis is often used, where time or space averages are assumed to be reasonable approximations to ensemble averages.

1. In numerical weather prediction, the average found by averaging over many different forecasts for the same domain and time period, but starting from slightly different initial conditions or using different numerical models or parameterizations.
   This ensemble average is usually more accurate than any single model run because it partially counteracts the sensitive dependence to initial conditions associated with the nonlinear equations that govern the atmosphere.

Any function of time f(t) is periodic with period t if f(t) = f(t + τ) for all times t, where τ is the smallest number for which this equality holds.