Riometers monitor the changes in ionospheric conductivity by measuring the absorption of very high frequency radio noise of galactic origin passing through the ionosphere. In this Letter the absorption of radio signals by a thin layer of ionospheric plasma, produced by ionization due to energetic precipitating electrons, is modeled by taking into account strong turbulent heating caused by instabilities. The precipitating electron population is obtained from a global MHD simulation of the magnetosphere, along with the electric fields which excite the Farley-Buneman instability and lead to turbulent electron heating. A comparison, the first of its kind, of the data from polar and sub-auroral riometers for the magnetic cloud event of January 10, 1997 shows good agreement. The ionospheric conductance modified by turbulent electron heating can be used to improve the magnetosphere-ionosphere coupling in the current global MHD models. ¿ 2001 American Geophysical Union