On the Power-law Scaling of Turbulence Cospectra Part 1: Stably Stratified Atmospheric Boundary Layer

Turbulent fluxes in the atmospheric surface layer are key input for the prediction of weather, hydrology, and carbon dioxide concentration. In numerical modelling of turbulent fluxes, a -7/3 power-law scaling in turbulence cospectra is usually assumed at high wavenumbers. In eddy-covariance (EC) measurements of turbulent fluxes, an assumed shape of turbulence cospectra is typically required for high-frequency spectral corrections, typically assuming a -7/3 power law. The derivation of -7/3 power-law scaling is based primarily on dimensional analysis, and other cospectral scaling has also been observed. Here we examine the shape of turbulence cospectra at high wavenumbers from extensive field measurements of wind velocity, temperature, water vapour and CO2 concentrations in various stably stratified atmospheric conditions. We propose a turbulence cospectral shape with -2 power law rather than -7/3 law for high wavenumber equilibrium range of the stable atmospheric boundary layer. This finding contributes to improved estimation of turbulent fluxes in both modelling and observation.