Boundary-Layer Meteorology

, Volume 157, Issue 1, pp 61–80 | Cite as

Quantifying the Influence of Random Errors in Turbulence Measurements on Scalar Similarity in the Atmospheric Surface Layer

  • Kang Sun
  • Dan Li
  • Lei Tao
  • Zhongkuo Zhao
  • Mark A. Zondlo


The influence of random errors in turbulence measurements on scalar similarity for temperature, water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\) is investigated using two eddy-covariance datasets collected over a lake and a cattle feedlot. Three measures of scalar similarity, namely, the similarity constant in the flux–variance relationship, the correlation coefficient between two scalars and the relative transport efficiency, are examined. The uncertainty in the similarity constant \(C_{s}\) in the flux–variance relationship resulting from random errors in turbulence measurements is quantified based on error propagation analyses and a Monte-Carlo sampling method, which yields a distribution instead of a single value for \(C_{s}\). For different scalars, the distributions of \(C_{s}\) are found to significantly overlap, implying that scalars are transported similarly under strongly unstable conditions. The random errors in the correlation coefficients between scalars and the relative transport efficiencies are also quantified through error propagation analyses, and they increase as the atmosphere departs from neutral conditions. Furthermore, the correlation coefficients between three scalars (water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\)) are statistically different from unity while the relative transport efficiencies are not, which highlights the difference between these two measures of scalar similarity. The results suggest that uncertainties in these measures of scalar similarity need to be quantified when using them to diagnose the existence of dissimilarity among different scalars.


Eddy-covariance fluxes Flux–variance relationship  Monin–Obukhov similarity Random errors Scalar similarity 



The authors acknowledge the research group of Azer Yalin at Colorado State University for providing laboratory space and Jay Ham, Kira Shonkwiler, Christina Nash for the set-up and operation of the tower at the feedlot site. The feedlot work was supported by the Center for Mid-Infrared Technologies for Health and the Environment (MIRTHE) under National Science Foundation Grant No. EEC-0540832. Kang Sun acknowledges support by a NASA Earth and Space Science Fellowship (NN12AN64H). Dan Li acknowledges support from the NOAA (U.S. Department of Commerce) Grant NA08OAR4320752 and the Carbon Mitigation Initiative at Princeton University, sponsored by British Petroleum. Zhongkuo Zhao acknowledges support from the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA11010403). The statements, findings, and conclusions are those of the authors and do not necessarily reflect the views of the NOAA, the U.S. Department of Commerce or British Petroleum. The lake dataset was kindly provided by the Environmental Fluid Mechanics and Hydrology Laboratory of Prof. Marc Parlange at The École polytechnique fédérale de Lausanne.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Kang Sun
    • 1
    • 2
  • Dan Li
    • 3
  • Lei Tao
    • 1
    • 2
  • Zhongkuo Zhao
    • 4
    • 5
  • Mark A. Zondlo
    • 1
    • 2
  1. 1.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Center for Mid-Infrared Technologies for Health and the EnvironmentNSF-ERCPrincetonUSA
  3. 3.Program of Atmospheric and Oceanic SciencesPrinceton UniversityPrincetonUSA
  4. 4.Institute of Tropical and Marine Meteorology/Guangdong Provincial Key Laboratory of Regional Numerical Weather PredictionChina Meteorology AdministrationGuangzhouChina
  5. 5.State Key Laboratory of Severe WeatherChinese Academy of Meteorological SciencesBeijingChina

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