Horizontal structure function and vertical correlation analysis of mesoscale water vapor variability observed by airborne lidar

Abstract

[1] Analysis is presented of airborne lidar measurements of water vapor, covering a height range from 1.5 to 10.4 km, from three field campaigns (midlatitude summer, polar winter, and subtropical summer). The lidar instrument provides two-dimensional cross sections of absolute humidity, with high accuracy (errors less than 5-7%) and high vertical ( 200 m) and horizontal ( 2 km) resolution. Structure functions, i.e., statistical moments up to the fifth-order of absolute increments over a range of scales, are investigated, and power law scaling or statistical-scale invariance was found over horizontal distances from 5 to 100 km. The scaling exponents are found to take different values, depending on whether or not the observations were taken in an air mass where convective clouds were present. The exponent of the first-order structure function in nonconvective regions, H = 0.63˙0.10, is large indicating a smooth series with long-range correlations, in contrast to the lower value H = 0.35˙0.11 found in convective air masses. Correspondingly, the moisture field in the convective regime was found to be more intermittent than for the nonconvective regime, i.e., water vapor structures in convectively influenced air mass show more jump discontinuities, which could be explained by the moistening and drying effects of updrafts and downdrafts in convective air mass. Within each regime (convective or nonconvective), the values appear to be universal, with no significant dependence on the season, latitude, or height where the observations were made. Furthermore, some evidence is found that vertical correlation lengths are longer in convective air masses.Citation: Fischer, L., G. C. Craig, and C. Kiemle (2013), Horizontal structure function and vertical correlation analysis of mesoscale water vapor variability observed by airborne lidar,

The global distribution of cloud gaps in CALIPSO data

“…Nevertheless, physically they are closely related to the distribution of relative humidity. Recently, similar power-law exponents have been reported for specific humidity variability seen in airborne lidar measurements by [5,6]. Meso-scale relative humidity variability is more strongly tied to specific humidity variability than to temperature variability, as temperature fluctuations are likely to be damped by gravity waves through their effect on buoyancy [17].…”

Structure Function Analysis of Water Vapor Simulated with a Convection-Permitting Model and Comparison to Airborne Lidar Observations

“…A well-established method for representing and quantifying scale dependence in the observed tropospheric water vapor field is the calculation of horizontal structure functions of different orders (Cho et al 1999(Cho et al , 2000Fischer et al 2012Fischer et al , 2013Lovejoy et al 2010;Pressel and Collins 2012). Over certain ranges of spatial scales, a power-law behavior has been found that allows for the determination of the power-law exponent, also called the scaling exponent, as a measure of spatial variability.…”

The structure function as new integral measure of spatial and temporal properties of multichannel EEG

“…Most likely by increasing the sampling frequency F d one can identify more distinct scaling regions with the breaks in S 1 ( τ ) slope. It should be noted that according to [41, 46], the first-order SF scaling exponent ζ is simply the Hurst exponent H that has a clear physical meaning. We have found that the average value of ζ in our analysis is 0.88 ± 0.03 for time scales less than 0.028 s. It means that one-dimensional random process (and ) is characterized at these scales by persistent increments and long-range correlations.…”

“…However, according to Fisher et al [41], the first-order SF is more robust than higher-order SFs with respect to outliers in the absolute increment. This conclusion may be partly illustrated by comparing the coefficients of variation (CV) of the first- and the second-order SF in the limiting case of “random EEG.” Since the random variable Δ Y τ is distributed according to the scaled chi-distribution, while Δ Y τ 2 is distributed according to the scaled χ 2 distribution, then one can easily derive analytical expressions for CV 1 and CV 2 as follows: …”