The standard error due to instrument noise is denoted by the short vertical bars on the linear fit curve The integral scale of w fluctuations retrieved with two different noise corrections and without correction. Two different techniques to extrapolate M 11( τ) to zero lag as well as the spectral method were used to determine ε 2 The inertial range is resolved by about 25 data points The M 11( τ) at three different heights for w from the HRDL. The estimates were obtained using a three-point linear fit as well as the first lag of M 31 and M 22 in (25), and (20) in combination with (40) The normalized fourth moment of humidity variance and noise variance, ρ 2 ε 2/ ( ρ 2 ε 2), which is an estimate of the correlation between instrument noise and atmospheric variance for absolute humidity. The sampling and noise errors are also shown on the curve achieved with (17) Kurtosis of absolute humidity uncorrected for noise, with correction using (17) assuming Gaussian, uncorrelated noise, and using the first lag of M 31 as well as M 22 in (22). (b) The corresponding estimation of ε 4 using linear fit, first-lag, and an estimate based on the assumption of Gaussian noise (a) The uncorrected ρ 4 = M 22(0), the corrected ρ 4 using three-point extrapolation and first-lag estimates in (22), as well as using (17) assuming Gaussian, uncorrelated noise. (b) The corresponding results for M 22(→0) (a) M 31(→0) using a three-point linear extrapolation from the right side to zero, the first-lag estimate, and the uncorrected zero lag value M 31(0). Again, M 31( τ) is slightly asymmetric around zero lag (a) M 31( τ) and (b) M 22( τ) for three heights. The statistical and sampling errors are also indicated on the linear fit curve (b) The corresponding estimation of ε 3Ībsolute humidity skewness without any correction for noise and with noise correction using a three-point linear extrapolation to zero lag or the first lag of M 21. (a) Shows M 21(0) as well as M 21(→0) for a three-point linear extrapolation from the right side to zero lag, and using the first lag. The M 21( τ) at three levels M 21( τ) is slightly asymmetric around zero lag
The standard error due to instrument noise is also shown on the 2/3 power-law fit curve The standard error due to instrument noise is also shown on the 2/3 power-law fit curveĪbsolute humidity variance profiles retrieved with two different noise corrections and without correction. The integral scale of the humidity fluctuations retrieved with two different noise corrections and without correction. The increase of the total variance at zero lag at 720 m is due both to the increase of the atmospheric variance and the noise variance The inertial range is resolved by only a few data points.
The M 11( τ) at three different heights from the MPI DIAL.
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