Power-Law Scaling of Turbulence Cospectra for the Stably Stratified Atmospheric Boundary Layer
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Power‑Law Scaling of Turbulence Cospectra for the Stably Stratified Atmospheric Boundary Layer Yu Cheng1 · Qi Li2 · Andrey Grachev3 · Stefania Argentini4 · Harindra J. S. Fernando5 · Pierre Gentine1 Received: 17 February 2020 / Accepted: 4 July 2020 © Springer Nature B.V. 2020
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. Keywords Eddy covariance · Stable boundary layer · Surface fluxes · Turbulence cospectra
1 Introduction Turbulence cospectra of surface fluxes are typically assumed to follow a −7/3 power-law scaling in the isotropic inertial subrange (Kolmogorov 1941) according to derivations based on dimensional analysis (Lumley 1964, 1967). The −7/3 power-law scaling has
* Yu Cheng [email protected] 1
Department of Earth and Environmental Engineering, Columbia University, New York, NY 10027, USA
2
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
3
Department NOAA Earth System Research Laboratory/Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80305, USA
4
Institute of Atmospheric Sciences and Climate, CNR, Rome, Italy
5
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
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been validated with laboratory experiments (Saddoughi and Veeravalli 1994) and field measurements in the atmospheric boundary layer (e.g., the Kansas experiment) (Kaimal et al. 1972; Wyngaard and Coté 1972). The exact shape of the cospectra is important for field observations as well as theoretical modeling. Indeed, in eddy-covariance (EC) measurements of turbulent fluxes in the atmospheric surface layer (ASL), an assumed cospectral shape is used for the spectral correction of momentum, heat, water-vapour, and CO2 fluxes (Moore 1986; Leuning and Moncrieff 1990; Horst 1997; Moncrieff et al. 1997; Aubinet et al. 1999; Massman 2000). Recently, Mamadou et al. (2016) showed that the calculated long-term CO2 fluxes from EC observat
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