The time series of hourly electron density profiles N(h) obtained from 27 ionosonde stations distributed world-wide have been used to obtain N(h) average profiles on a monthly basis and to extract the expected bottom-side parameters that define the IRI profile under quiet conditions. The time series embrace the time interval from 1998 to 2006, which practically contains the entire solar cycle 23. The Spherical Harmonic Analysis (SHA) has been used as an analytical technique for modeling globally the B0 and B1 parameters as general functions on a spherical surface. Due to the irregular longitudinal distribution of the stations over the globe, it has been assumed that the ionosphere remains approximately constant in form for a given day under quiet conditions for a particular coordinate system. Since the Earth rotates under a Sun-fixed system, the time differences have been considered to be equivalent to longitude differences. The time dependence has been represented by a two-degree Fourier expansion to model the annual and semiannual variations and the year-by-year analyses of the B0 and B1 have furnished nine sets of spherical harmonic coefficients for each parameter. The spatial-temporal yearly coefficients have been further expressed as linear functions of Rz12 to model the solar cycle dependence. The resultant analytical model provides a tool to predict B0 and B1 at any location distributed among the used range of latitudes (70°N-50°S) and at any time that improves the fit to the observed data with respect to IRI prediction.