The empirical median model of the shape and position of the MIT (Main Ionospheric Trough) in the Northern and Southern Hemispheres is presented. The model is based on the topside sounding data of the Intercosmos-19 satellite (about 2000 passes in both hemispheres) and in situ electron density N_e measurements onboard the low-orbiting CHAMP satellite (more then 20 000 passes) for high and low solar activity, accordingly.

The model is applicable to the quiet geomagnetic conditions (K_p = 2), the night-time (18:00 - 06:00 LT), the winter (November-February in the Northern Hemisphere and May-August in the Southern Hemisphere) season, and different levels of solar activity (F_10.7=70-250). Model describes the dependence of trough minimum position on the local time (LT) and longitude. The resulting analytical dependence on local time and longitude for the night MIT minimum position describes its more precisely in comparison with other models.

The MIT model is practically the model of the sub-auroral ionosphere since it describes not only the trough minimum position but its shape too, i.e. the foF2 distribution in the trough region including its minimum, equatorial and polar walls of the MIT. For this purpose the N_e data obtained at CHAMP heights (400-450 km) were reduced to F2 layer peak height using the IRI model.

The MIT model input parameters are the longitude, latitude, LT and F_10.7 (the ten centimeter solar radio flux http://www.ips.gov.au/Educational/2/2/5). The output parameters are the MIT minimum positions, latitudinal and longitudinal foF2 profiles and foF2 longitude-latitude maps in the trough region (from 38^oN to 75^oN and from 38^oS to 75^oS) for different LT and F_10.7. The accuracy of the model is 2^o in latitude, 30^o in longitude, and 0.5 MHz in foF2. In the nearest future the model will be extended to the nighttime equinoctial and day time winter conditions.

ACKNOWLEDGEMENTS
The authors are grateful to sponsors and operators of the CHAMP mission: Deutsches GeoForschungsZentrum (GFZ) Potsdam, German Aerospace Center (DLR), and the US National Aeronautics and Space Administration (NASA). Some parts of this web-site and of the MIT model was developed at financial support of the Russian Foundation for Basic Research (RFBR) - Grant №14-05-00788 (Klimenko V., Klimenko M.).

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