In this paper the optimal interpolation method, in conjunction with empirical orthogonal function (EOF) bases and the maximum likelihood method for online error covariance parameter estimation, is successfully implemented for the objective analysis of large-scale high-latitude ionospheric electrodynamic variables. This study demonstrates how this methodology can be used to extract information about the temporal and spatial coherence of the large-scale electric field for a magnetic cloud event on 10--11 January 1997. Compared with the temporal persistence of the interplanetary magnetic field (IMF) and solar wind parameters, the timescale of the spatially coherent part of the electric field, on the spatial scale of the EOFs, is shorter. The principal components of the high-latitude electric field are analyzed during two periods when either the IMF BY or BZ component was relatively steady while the other component varied. The first principal component, not surprisingly, generally reflects the change in the ionospheric convection pattern predicted by IMF-dependent empirical models and thus tends to represent changes in the convection that are directly driven by solar wind--magnetosphere interactions. However, it is the second principal component that is more strongly correlated with the westward auroral electrojet, suggestive of a link to substorm phenomena.