Limits on the accuracy of correction of trans-ionospheric propagation errors by using ionospheric models based on solar and magnetic indices and local measurements

Satellite propagation data have been used to estimate the limits on the accuracy of models of the ionospheric electron content used in calculating refractive corrections. In the first series of comparisons, electron content measurements have been compared with the Penn State Mark I Ionospheric Model. The probability of making errors in estimating electron content has been derived for stations at different latitudes and different time periods. It is shown that with this model there is a 10% probability of making errors, ranging from 2.2 × 10¹⁷ m² at an equatorial station in the time period 1600-2200 hours to less than 7 × 10¹⁶ m² at a midlatitude station. In the second series of comparisons, the same satellite data base was used, but the comparisons were made to an ideal model for each station, obtained by fitting each data set, using a least squares analysis, to functions of the geophysical indices, local time, and day number. These models typically produced only a factor of 2 improvement in the accuracy for given error probabilities. In a third series of comparisons, horizontal gradient measurements were used to estimate the errors that would result if electron content measurements were available along a ray path separated from the desired ray path by 500, 1000, and 1500 km. Error probabilities are given for an equatorial station and a midlatitude station for conditions when the mean horizontal gradients are assumed to be unknown and for the limiting case, when the mean horizontal gradient can be assumed to be known exactly. It is concluded that major advances in ionospheric modeling for predictive purposes will require a much better understanding of the factors controlling the day-to-day variability.