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 Poiss...