Uncorrelated Noise in Turbulence Measurements

Abstract

We show that the error variance contributed by random uncorrelated measurement noise can be merged with the error variance contributed by real variations in the atmosphere to obtain a single expression for the total error variance when the sampling time is much less than the integral scale of atmospheric variability. We assume that the measured signal is a representation of a variable that is continuous on the scale of interest in the atmosphere. The characteristics of this noise are similar, but not identical, to quantization noise, whose properties are briefly described. Uncorrelated noise affects the autocovariance function (or, equivalently, the structure function) only between zero and the first lag, while its effect is smeared across the entire power spectrum. For this reason, quantities such as variance dissipation may be more conveniently estimated from the structure function than from the spectrum. The modeling results are confirmed by artificially modifying a test time series with Poisson noise and comparing the statistics from ten realizations of the modified series with the predicted error variances. We also demonstrate applications of these results to measurements of aerosol concentrations. A “figure of merit” is defined which is used to specify when instrument counting noise contributes more to measurement error than does atmospheric variability. For example, for measuring the vertical flux of a trace species for a small surface resistance to deposition, the specified counting rate is about 100 counts s⁻¹ for measuring flux in the surface layer and about 10³ counts s⁻¹ for measuring flux throughout the convective boundary layer.