Direct Manual Calculations of Ionospheric Parameters Using a Single‐Polynomial Analysis

Two extensions of the basic polynomial analysis are described. Firstly the polynomial representation of the real‐height curve is modified to include a parabolic peak; this greatly increases the accuracy of calculations near the peak of the ionospheric layers. Secondly the analytic expression for the real‐height curve is used to obtain expressions for the height of the peak ( h m ) and the scale height at the peak ( H ). Integration of the real‐height curve also gives an expression for the effective subpeak thickness of the ionosphere ( T ), defined as the total amount of ionization below the peak divided by the density at the peak. These three expressions are then used to obtain coefficients relating h m , H , and T to the virtual heights at any required frequencies. Eighty‐four sets of coefficients are given for analyzing h' ( f ) records taken anywhere in the world, with critical frequencies between 1.5 and 20 MHz. These coefficients give the values of h m , H , T , and the real heights of reflection directly in terms of the virtual heights at five or six different frequencies. For calculations on a single ionospheric layer the accuracy is extremely high, being equivalent to that obtained with a lamination analysis using more than 50 points. For calculations on the daytime F layer, coefficients are provided with alternative sampling points chosen to reduce the effects of the E and F 1 layer cusps, so that the height, scale height, and total content of the F layer can be determined with an accuracy equivalent to a lamination analysis using more than 20 points. Finally, coefficients including an extraordinary‐ray correction for the underlying ionization are given, to enable accurate calculations for the nighttime F layer.