Errors in the Estimation of Turbulence Kinetic Energy Dissipation Rate in the Atmospheric Boundary Layer

Recent findings in atmospheric turbulence research indicates that the turbulent kinetic energy dissipation rate (E) is a relevant parameter in the development of scaling laws of boundary-layer flows. Because direct measurement of E in the atmosphere is still a technological challenge, indirect estimates from the fit of inertial range laws to measured energy spectrum and structure functions remain the most used approach, despite the uncertainties inherent to them. In this study, these uncertainties are investigated in detail, including the estimation of E from the spectrum ogive, as it presents, in addition to its own model for the inertial subrange, smaller relative errors compared to the energy spectrum. Theoretical variance predictions of sample data are compared to synthetic atmospheric turbulence data generated via the Monte Carlo method. In particular, the effects of typical limitations present in atmospheric turbulence data are investigated, namely the low measurement frequency (compared to the dissipation scales) and path averaging. These effects are incorporated in the synthetic turbulence model and in the theoretical predictions of mean and variance of the spectrum, the ogive and the structure function, providing insight about the advantages and limitations of using each approach. The existence of bias in the estimation of E is investigated and corrections are proposed when necessary.