Improved techniques have been developed for empirical modeling of the high-latitude electric potentials and magnetic field-aligned currents (FAC) as a function of the solar wind parameters. The FAC model is constructed using scalar magnetic Euler potentials and functions as a twin to the electric potential model. The improved models have more accurate field values plus more accurate boundary locations. Nonlinear saturation effects in the solar wind--magnetosphere coupling are also better reproduced. The models are constructed using a hybrid technique, which has spherical harmonic functions only within a small area at the pole. At lower latitudes the potentials are constructed from multiple Fourier series functions of longitude at discrete latitudinal steps. It is shown that the magnetic (FAC) and electric potential models can be used together to calculate the total Poynting flux and Joule heating in the ionosphere. An additional model of the ionospheric conductivity is not required to obtain the ionospheric currents and Joule heating, as the conductivity variations as a function of the solar inclination are implicitly contained within the FAC model's data. The models' outputs are shown for various input conditions and are also compared with satellite measurements. The calculations of the total Joule heating are compared with results obtained by the inversion of ground-based magnetometer measurements. Like their predecessors, these empirical models should continue to be useful research and forecast tools.