Numerical errors in the real-height analysis of ionograms at high latitudes
Article first published online: 7 DEC 2012
Copyright 1987 by the American Geophysical Union.
Volume 22, Issue 5, pages 715–727, September-October 1987
How to Cite
1987), Numerical errors in the real-height analysis of ionograms at high latitudes, Radio Sci., 22(5), 715–727, doi:10.1029/RS022i005p00715.(
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 1 MAY 1987
- Manuscript Received: 8 JAN 1987
The accuracy of real heights in the ionosphere, calculated from sweep-frequency virtual height records, is limited by numerical errors at dip angles greater than about 65° (corresponding to magnetic latitudes greater than 49°). For high-order modes of analysis, using five-point Gaussian integration, errors increase by a factor of about 10 at dip 70°, a factor of 100 at 80° and a factor of 500 at 86°. Allowance for the effect of low-density ionization, or of ionization in the valley between two layers, requires the use of combined ordinary and extraordinary ray data. These calculations become unusable at dip angles greater than 80° with normal integration procedures. A simple dual-range integration procedure is developed for use at high latitudes. This maintains accuracy in the analysis of ordinary ray data up to a dip angle of 89°. For the start and valley calculations, numerical errors are effectively zero at all dip angles up to 89.9°. Alternatively, the extreme errors which occur at high latitudes can be avoided by analyzing the ionograms using a decreased value for the dip angle. An expression is derived giving the optimum dip angle to use with different integration orders and frequency intervals.