Boundedness of Turbulent Temperature Probability Distributions, and their Relation to the Vertical Profile in the Convective Boundary Layer

Abstract

Higher-order moments, minima and maxima of turbulent temperature and water vapour mixing ratio probability density functions measured with an eddy-covariance system near the ground were related to each other and to vertical boundary-layer profiles of the same scalars obtained through airborne soundings. The dependence of kurtosis on squared skewness showed a kurtosis intercept below the Gaussian expectation, suggesting a compression of the probability density function by the presence of natural boundaries. This hypothesis was corroborated by comparing actual minima and maxima of turbulent fluctuations to estimates obtained from the first four sample moments by fitting a four-parameter beta distribution. The most sharply defined boundaries were found for the minima of temperature datasets during the day, indicating that negative temperature fluctuations at the sensor are limited by the availability of lower temperatures in the boundary layer. By comparison to vertical profiles, it could be verified that the turbulent minimum of temperature near the ground is close to the minimum of potential temperature in the boundary layer. The turbulent minimum of water vapour mixing ratio was found to be equal to the mixing ratio at a height above the minimum of the temperature profile. This height roughly agrees with the top of the non-local A. Graf (B) · M. Herbst · H. Vereecken Agrosphere (ICG-4), 123 460 A. Graf et al.unstable domain according to bulk Richardson number profiles. We conclude that turbulence statistics measured near the surface cannot be solely explained by local effects, but contain information about the whole boundary layer including the entrainment zone.

Observed spatiotemporal variability of boundary-layer turbulence over flat, heterogeneous terrain

“…As part of HOPE, the Karlsruhe advanced mobile observation platform KITcube (Kalthoff et al, 2013) (Graf et al, 2010) of the Terrestrial Network of Observatories (TERENO; Zacharias et al, 2011) were used as well. The instruments whose data are used here are briefly described below.…”

Estimating random errors of eddy covariance data: An extended two-tower approach

“…8 km away from the Merken site). EC data were collected for the period of May 2009-September 2009 in the context of collaboration between Forschungszentrum Jülich and the University of Bonn, Germany (Graf et al, 2010). The distances between the EC towers and the height of the EC equipment at the towers are shown in Table 1.…”

A variational data assimilation system for soil–atmosphere flux estimates for the Community Land Model (CLM3.5)

“…Graf et al (2010) present the setting of a similar measurement campaign at the same location. The measurement station is placed on a barley field which has been harvested in the middle of June.…”

“…The instruments used were an Ultrasonic Anemometer (CSAT3, Campbell Scientific, Logan, UT, USA) 1 and a H 2 O/CO 2 gas analyser (Li7500, Li-Cor, Lincoln, NE, USA) 2 . The measurement method of a similar measurement campaign at the same location is described in Graf et al (2010). Figure 8 shows the measured and modelled sensible heat flux at the station Merken.…”