A new approach to estimate random errors in turbulence statistics

Random errors in turbulence measurements occur when the averaging time is too short for time mean to converge to the ensemble mean as required by the ergodic hypothesis. Maximum averaging times in the atmospheric boundary layer (ABL) are limited to periods not much larger than 1 hour due to the diurnal evolution of the ABL. Although it is not always common practice for authors to report random errors in their measurements, these errors are in principle possible to estimate, and can be large over typical averaging periods employed in the ABL.

A new method is proposed for estimating random errors in turbulent moments of any order. The error estimation method is based on properties of spatial filters, and does not require an estimate of the integral timescale, which can be highly sensitive to the method used to estimate it. Random errors are estimated by filtering the instantaneous flux (e.g. w'c') at different scales, directly calculating the error variance as a function of scale, and then extrapolating to determine the random error for averaging period T. The error estimation method is validated with synthetic flux data with a known ensemble mean and intercompared with existing methods using atmospheric surface layer data from the Advection Horizontal Array Turbulence Study (AHATS). Typical errors for a 27.3 minute block of data collected at a height of z=8 m are found to be approximately 10% for the heat flux and 7-15% for the variances. The error in the momentum flux is found to increase rapidly with increasing atmospheric instability, reaching values of 40% or greater for convective conditions. A new method based on filtering is also proposed to estimate integral timescales of turbulent quantities.