It is proposed to develop a new data-based model of the Earth's magnetospheric magnetic field. Modeling the geospace plasma environment is the essence of the GEM project, and one of its special tasks is an accurate representation of the distant geomagnetic configuration. The model will be specifically designed to meet the needs of the Geospace Circulation Model providing the community with flexible tools to handle magnetospheric current systems and quantitatively represent their contributions to the total field. The proposed study will be based on magnetometer data from many spacecraft, accumulated over tens of years, and will use sophisticated mathematical methods, allowing a flexible representation of the observed fields. The new model will provide a realistic quantitative description of the geomagnetic field for a wide range of distances, as a continuous analytical function of the position, Earth's dipole tilt angle, solar wind characteristics, the polar cap area, and appropriate geomagnetic disturbance indices. One of the principal goalq of this project will be to represent not just the average magnetospheric configurations, but also its large- scale time variations. Specifically, it is intended to quantitatively model such phenomena as (i) compression/expansion of the magnetopause in response to solar wind gusts, (ii) gradual re-distribution of the magnetic flux during the substorm growth phase, induced by the interplanetary magnetic field, and (iii) formation of the substorm electric current system leading to the collapse of the previously stretched configuration. The main product of this effort will be computer codes for deriving the time-varying model magnetic field.