Ionogram analysis: Least squares fitting of a Chapman‐layer peak

Abstract

A formulation is described which uses plasma frequency F as a function of real height h near a layer peak. This allows profile data from lower heights, and scaled critical frequencies from both magnetoionic components, to be combined in a single least squares solution. The scaled critical frequencies do not define the final value, but provide additional input to the least squares calculation. Results give directly the rms fitting errors for the critical frequency, the peak height and the scale height. Calculations begin with an assumed model value for the scale height near the peak. With good data the final result is independent of this model. As the amount and consistency of the data decreases, the solution automatically gives more weight to the initial (model) scale height. This greatly reduces the normal tendency for peak extrapolations to become erratic or absurd as the quality of the data decreases. With very poor data the model scale height is imposed directly. The critical frequency is still obtained from a least squares solution, using the known scale height plus some physical checks to ensure a reasonable range of extrapolation. Thus optimum results are obtained with good data, and acceptable peak profiles are obtained from all useful ionograms.