Publishers version - DTU Orbit

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〈v ′ iv′ i 〉lidar/〈v′ iv′ i 〉
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Height (m)
Height (m)
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
〈v ′ iv′ i 〉lidar/〈v′ iv′ i 〉
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
〈v ′ iv′ i 〉lidar/〈v′ iv′ i 〉
Figure 165: ZephIR systematic errors under different atmospheric stability conditions in the
eastern sector. Very unstable (top left), unstable (top right), near neutral unstable (bottom
left), and neutral (bottom right). The markers indicate measurements. The solid lines are the
theory without the low-pass filter, and the dashed lines are with the low-pass filter.
is due to a large variation in the length scales of different velocity components resulting
in varying attenuation of the variances.
• The systematic errors increase with height under all atmospheric stability conditions –
This is due to a quadratic increase in the sample volume with height (Lindelöw, 2007).
The diameter of the scanning circle also increases with height.
• The systematic errors in w variance are much larger (approximately 3-5 times) than that
of the u and v variances – This is due to the very small length scales of the w component
as compared to those for u and v, resulting in the attenuation of the w variance of up
to 90%. The u and v variances are attenuated up to 70%.
• There is a significant spread (first and third quartiles) in the systematic errors of u and
v variances – These are the random errors and most likely occur due to the disjunct
sampling (Lenschow et al., 1994) of the ZephIR. A thorough scientific investigation is
needed to quantify random errors, but is not the focus of this paper.
• The trend of the systematic errors predicted by both models is in agreement with the
observations at all heights.
• With the exception of very stable conditions, the model with the low-pass filter (Eqs.
300–302) is in better agreement with the measurements at all heights than without the
low-pass filter.
250 DTU Wind Energy-E-Report-0029(EN)
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