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Power-Law Scaling of Turbulence Cospectra for the Stably Stratified Atmospheric Boundary Layer

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Abstract

Surface turbulent fluxes provide a key boundary condition for the prediction of weather, hydrology, and atmospheric carbon dioxide. The turbulence cospectrum is assumed to typically follow a −7/3 power-law scaling, which is used for the high-frequency spectral correction of eddy-covariance data. The derivation of this scaling is mostly grounded on dimensional analysis. The dimensional analysis or cospectral budget analyses, however, can lead to alternative cospectral scaling. Here we examine the shape of turbulence cospectra at high Reynolds number and high wavenumbers based on extensive field measurements of wind velocity and temperature in various stably stratified atmospheric conditions. We show that the cospectral scaling deviates from the −7/3 scaling at high wavenumbers in the inertial subrange of the stable atmospheric boundary layer, and appears to follow a −2 power-law scaling. We suggest that −2 power-law scaling is a better alternative for cospectral corrections for eddy-covariance measurements of the stable boundary layer.

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Acknowledgements

PG would like to acknowledge funding from the National Science Foundation (NSF CAREER, EAR-1552304), and from the Department of Energy (DOE Early Career, DE-SC00142013). The lake data were collected by the Environmental Fluid Mechanics and Hydrology Laboratory of Professor M. Parlange at l’Ecole Polytechnique Fédérale de Lausanne. We would like to thank Prof. M. Parlange and Prof. Elie Bou-Zeid for sharing Lake EC data. Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) program was funded by the Office of Naval Research (N00014-11-1-0709). Dome C data were acquired in the frame of the projects Mass lost in wind flux (MALOX) and Concordia multi-process atmospheric studies (COMPASS) sponsored by PNRA. Special thanks to P. Grigioni and all the staff of Antarctic Meteorological Observatory of Concordia for providing the radio sounding data used in this study, and to Dr. Igor Petenko of CNR ISAC for running the field experiment at Concordia station.

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Authors and Affiliations

  1. Department of Earth and Environmental Engineering, Columbia University, New York, NY, 10027, USA

    Yu Cheng & Pierre Gentine

  2. School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, 14853, USA

    Qi Li

  3. Department NOAA Earth System Research Laboratory/Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO, 80305, USA

    Andrey Grachev

  4. Institute of Atmospheric Sciences and Climate, CNR, Rome, Italy

    Stefania Argentini

  5. Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    Harindra J. S. Fernando

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  1. Yu Cheng
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Cheng, Y., Li, Q., Grachev, A. et al. Power-Law Scaling of Turbulence Cospectra for the Stably Stratified Atmospheric Boundary Layer. Boundary-Layer Meteorol 177, 1–18 (2020). https://doi.org/10.1007/s10546-020-00545-6

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