Abstract
Abstract. A high-fidelity lidar turbulence measurement technique relies on accurate estimates of radial velocity variance that are subject to both systematic and random errors determined by the autocorrelation function of radial velocity, the sampling rate, and the sampling duration. Using both statistically simulated and observed data, this paper quantifies the effect of the volumetric averaging in lidar radial velocity measurements on the autocorrelation function and the dependence of the systematic and random errors on the sampling duration. For current-generation scanning lidars and sampling durations of about 30 min and longer, during which the stationarity assumption is valid for atmospheric flows, the systematic error is negligible but the random error exceeds about 10 %.
Highlights
The difference between the errors of variance of vr and vR varies with line of sight (LOS) orientation and turbulence model, errors associated with vR are consistently higher than those related to vr, indicating that volumetric averaging increases errors associated with radial velocity variance estimates
The systematic error es(Tn, T ) and random error variance er2(Tn, T ) associated with sampling duration Tn derived from a time series of length T are estimated using the following stationary bootstrap method (Politis and Romano, 1994), where the sample numbers associated with T and Tn are denoted as N and Nn, respectively
The second factor, (ii), the volumetric averaging, is dictated by the probe length that is determined by the lidar properties; it causes the radial velocity autocorrelation function to increase, and increases errors in radial velocity variance estimates
Summary
Coherent Doppler lidars (hereafter called lidars) are increasingly being deployed to measure flow in the atmospheric boundary layer (ABL) for applications to wind engineering (Banta et al, 2013). The theoretical framework used to quantify errors in radial velocity variance from lidar measurements leverages the theory developed to characterize uncertainties in statistical moments estimated from a time series of sonic anemometer measurements in Lenschow et al (1994), and is modified to incorporate the effect of volumetric averaging and the slow sampling rate of lidars The difference between the errors of variance of vr and vR varies with LOS orientation and turbulence model (i.e. the turbulence structure), errors associated with vR are consistently higher than those related to vr, indicating that volumetric averaging increases errors associated with radial velocity variance estimates. Field experiment are used to show the effects of volumetric averaging and sampling duration on the errors
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