Uncorrelated Noise in Turbulence Measurements

We show that the error variance contributed by random uncorrelated measurement noise can be merged with the error variance contributed by real variation 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. The authors assume that the measured signal is a representation of a variable that is continuous on the scale of interest in the atmosphere. Uncorrelated noise affects the autovariance 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. The authors also demonstrate applications of these results to measurements of aerosol concentrations