This paper presents an algorithm that allows physical, time-dependent, ionospheric models to reproduce the measured F2 peak electron density (NmF2). The algorithm uses the measured NmF2 to adjust the entire altitude density profile in the model as it steps in time. Thus the algorithm provides an internal constraint to the electron density in addition to the usual initial and boundary constraints. If the plasma temperatures are also well modeled, the new algorithm allows a faithful reproduction of electron density profiles throughout the entire F2 layer to high altitudes. The algorithm offers a simple method of parameterizing electron density profiles from incoherent scatter radars and also extending bottom side measurements into the topside ionosphere. The improved accuracy of the model electron density will allow more accurate studies of ionospheric emissions, energy budget, and minor species densities. There may be other non-ionospheric physical systems where a similar algorithm could be applied. Any system where remote sensing measurements provide internal constraints would be a candidate. ¿ American Geophysical Union 1995