Electric fields are a ubiquitous feature of the ionosphere and are intimately linked with aurora through particle precipitation and field-aligned currents. They exhibit order-of-magnitude changes on temporal and spatial scales of seconds and kilometres respectively which are not easy to measure; knowing their true magnitude and temporal variability is important for a theoretical understanding of auroral processes. We present a unique method to estimate ionospheric electric fields in the region close to (kilometre scale) a dynamic auroral arc by solving the continuity equation for the metastable O+(P-2) ions, which emit as they move under the influence of electric fields during their 5 s lifetime. The main advantage of this optical method is the increase in temporal resolution over other methods such as ground-based radars. Simultaneous measurements of emission at 732.0 nm (from the O+(P-2) ions) and prompt emissions at 673.0 nm (N-2) and 777.4 nm (O), all at high spatial (100 m) and temporal (0.05 s) resolution, are used in the solution of the continuity equation, which gives the dynamic changes of the O+ ion population at all heights in a 3D volume close to the magnetic zenith. Perspective effects are taken into account by a new geometric method, which is based on an accurate estimate of the magnetic zenith position. The emissions resulting from the metastable ions are converted to brightness images by projecting them onto the plane of the ground, and the projected images are then compared with the measured images. The flow velocity of the ions is a free parameter in the solution of the continuity equation; the value that minimises the difference between the modelled and observed images is the extracted flow velocity at each time step. We demonstrate the method with an example event during the passage of a brightening arc feature, lasting about 10 s, in which the inferred electric fields vary between 20 and 120 mV m(-1). These inferred electric fields are compared with SuperDARN measurements, which have an average value of 30 mV m(-1). An excellent agreement is found in the magnitude and direction of the background electric field; an increase in magnitude during the brightening of the arc feature supports theories of small-scale auroral arc formation and electrodynamics.