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The method of characteristics for obtaining spatial distributions of ionospheric electrodynamic parameters from ground-based spatial observations of the ground magnetic disturbance and the ionospheric electric field is presented in spherical geometry. The method includes tools for separation of the external magnetic disturbance, its continuation to the ionosphere, and calculation of ionospheric equivalent currents. Based on these and the measured electric field distribution, the ionospheric Hall conductance is calculated as the primary output of the method. By estimating the Hall- to-Pedersen conductance ratio distribution, the remaining ionospheric electrodynamic parameters are inferred. The method does not assume ∇×E=0 to allow to study time-dependent situations. The application of this method to a Harang discontinuity (HD) situation on 27 October 1977, 17:39 UT, reveals the following: (1) The conductances at and north of the HD are clearly reduced as compared to the eastern electrojet region. (2) Plasma flow across the HD is observed, but almost all horizontal current is diverted into upward-flowing field-aligned currents (FACs) there. (3) The FACs connected to the Hall currents form a latitudinally aligned sheet with a magnitude peak between the electrically and magnetically defined HD, where break-up arcs are often observed. Their magnitude is larger than that of the more uniformly distributed FACs connected to the Pedersen currents. They also cause the southward shift of the magnetically defined HD with respect to the electrically defined one. (4) A tilt of the HD with respect to geomagnetic latitude as proposed by an earlier study on the same event, which used composite vector plot technique, and by statistical studies, is not observed in our single time-step analysis.<br><br><b>Key words. </b>Ionosphere · Electric fields and currents · Instruments and techniques · Magnetospheric physics · Current systems