Adv. Space Res. VoL12, No.6, pp. (6)279—(6)282, 1992 0273-1177/92 $15.00 Printed in Great Britain. All rights reserved. Copyright @ 1991 COSPAR REGIONAL MODELLING AND MAPPING OF THE IONOSPHERIC CHARACTERISTIC PARAMETERS BY SPHERICAL CAP HARMONIC EXPANSION A. De Santis,* G. De Franceschi,* B. Zolesi* and U. R. Cander** *fr~g~jr~r~ Nazionale di Geofisica, Via di Villa Ricotti 42, 00161-Roma, Italy ** Geomagnetic Institute, 11306, Grocka Belgrade, Yugoslavia ABSTRACT The method of Spherical Cap Harmonic Analysis, SCHA /1/, has been applied to the critical frequency of the F2 layer observed at several European vertical incident ionospheric stations. The aim was the regional mapping and modelling of this parameter in Europe. To make it possible a spherical cap including Europe, centred at 50°N, 14°E with the half-angle of 200 has been considered. The model is based on the expansion of Fourier longitudinal series and Legendre colatitudinal functions as the orthogonal basis functions over the caplike region of interest. It has been found that for the modelling of the foF2, a SCH model with only 9 coefficients (K up to 2) well portrays its basic features. INTRODUCTION Global modelling of spherically distributed data is usually made by an expansion in terms of spherical harmonics. They are based on Fourier terms in longitude, ~ and Legendre functions in colatitude, P~(O), that form orthogonal functions over the globe /2/. In the case of no radial dependence, the spherical harmonic expansion of some global function ~ 8) can be written as follows: f(.\,8) = ~~F,~’(A) .P,~(O) = > (g~cosmA+h’sinm.X) .P,~”(cos8); (1) n=O ,n=O n=O m~O where )~ and 8 respectively represent longitude and colatitude of a polar reference system placed at the Earth’s centre; m and n are integer indices, respectively order and degree of the expansion truncated at a given degree N and g~’ and h~’ are suitable coefficients evaluated by the least squares method. We are here interested to the regions.! modelling of the critical frequency of the F2 layer, f 0F2, as observed in Europe. In this case, it has to be noted that Europe represents that region characterized by the highest density of ionospheric stations, and, moreover, since a global model such as the CCIR model /3,4/ makes use of global data sets, its fit to data from a particular area is compromised by the requirement to model data over the remainder of the globe /5/. A means to solve the problem could be to find that harmonic expansion which can be still applied in a restricted area. One natural region could be a spherical cap with specific half-angle, such to bound the region of data. Unfortunately, the Legendre functions used in global analysis are no longer suitable, being non-orthogonal in the case of a limited portion of the Earth’s surface. What kind of new functions could be used as alternative? In. geomagnetism Haines /1/ has recently introduced a new technique, called Spherical Cap Harmonic Analysis (SCHA), to model geomagnetic data on a caplike region by a new kind of functions that are still Legendre functions of integer order m but (in general) non-integer degree n. Moreover Walker /6/ applied SCHA on geomagnetic data to estimate the ionospheric and induced equivalent currents, showing the possibility for this technique to be used also for sparse data. Hence, SCHA appears to be one of the most suitable model for data taken over restricted regions of the Earth. The new fractional Legendre functions and their Oo - derivatives .have, alternatively, zero value at the edge of a cap with half-angle 8~: dP,~(cos6o)/dO=0 P,~(cosOo)=0 (2) (6)279