How long is long enough when measuring fluxes and other turbulence statistics?

Abstract

It is determined how long a time series must be to estimate covariances and moments up to fourth order with a specified statistical significance. For a given averaging time T there is a systematic difference between the true flux or moment and the ensemble average of the time means of the same quantities. This difference, referred to here as the systematic error, is a decreasing function of T tending to zero for T → ∞. the variance of the time mean of the flux or moment, the so-called error variance, represents the random scatter of individual realizations, which, when T is much larger than the integral time scale τ of the time series, is also a decreasing function of T. This makes it possible to assess the minimum value of T necessary to obtain systematic and random errors smaller than specified values. -from Authors