On the Characterization of Intermediate-Scale Ionospheric Structure

Characterization of ionospheric structure starts with spectral analysis of one-dimensional time series. Unknown spectral density function (SDF) parameters are estimated by model-fitting procedures, which will be referred to in this paper collectively as irregularity parameter estimation. If the diagnostic SDF has a power law form, linear least squares estimation (LLE) can be used to estimate the power law parameters. In this paper simulations are used to investigate LLE estimates of diagnostic single-component and two-component power law SDFs. There is a known turbulent strength bias and a more troublesome correlation between the turbulent strength and the spectral index. We found that this intrinsic property of LLE estimators completely explains a similar correlation long observed in both in situ and radio propagation ionospheric diagnostic measurements. Maximum likelihood estimation (MLE) is superior to LLE but requires knowledge of the probability distribution function of the SDF estimator. To this end one can exploit the fact that the probability distribution function of a periodogram about the its true mean is well approximated by a (D) distribution. With an hypothesized true mean SDF defined by a small set of parameters, the parameters can be adjusted to maximize the likelihood that the periodogram was generated by the parameterized SDF. Furthermore, algorithms that adjust parameters to maximize likelihood can use functions of the defining parameters being adjusted to improve performance. Recognizing that correlation between turbulent strength and spectral index estimates is an intrinsic measurement property, error minimization is particularly important. A modified MLE procedure is presented that provides robust initiation and good two-component power law parameter estimates. Plain Language Summary This paper evaluates power law parameter estimation procedures that are routinely used to characterize intermediate-scale ionospheric structure. An intrinsic correlation between turbulent strength and a large-scale power law index is identified. A modified maximum likelihood procedure is introduced to minimize the parameter errors.