Assessing statistical fitting methods used for estimating turbulence parameters

Many turbulence estimates require fitting model forms, typically nonlinear expressions, to observations that have been converted into spectra. Choosing a fitting method usually depends on user preference, such as calculation ease under the spectra's presumed statistical nature or reducing computation demands when turbulence quantities must be estimated onboard expendable instruments. Six different methods are assessed by fitting a known model against synthetic spectra with variability generated from two different statistical distributions. The assessment uses an inertial subrange model to estimate the turbulent kinetic energy dissipation rate from velocity spectra. However, the results and conclusions are relevant to fitting other turbulence inertial subrange models that follow a power law where is the spectral slope and contains the sought‐after turbulence parameter. The two most accurate methods require linearizing the spectral observations by taking the logarithm of the wavenumbers and the dependent spectra power density . These methods are less sensitive to outliers and deviations of the observations from a known statistical distribution. Some methods returned that deviated from the prescribed value by more than 50% depending on the number of samples fitted and the level of uncertainty of the spectra. Methods for estimating the spectral slope, , were also assessed to provide recommendations on using this parameter to flag data which deviates from the expected form so that the spectra (or wavenumbers) can be excluded from further analysis.