Horizontal electric ﬁelds from ﬂow of auroral O + ( 2 P) ions at sub-second temporal resolution

. 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 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 (km 5 scale) a dynamic auroral arc by solving the continuity equation for the metastable O + ( 2 P) 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 + ( 2 P) 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 10 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 onto the plane of the ground, which are 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 minimizes 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 (cid:0) 1 . These inferred electric ﬁelds are compared with SuperDARN measurements, which have an average value of 30 mV m (cid:0) 1 . An excellent agreement is found in 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.

1 of the flow field of the light, as well as a quantitative measure of where the constraints in the flow model break down. The robust optical flow estimator performed well for regions of turbulent motion, but less well for shear flow. The work illustrates the challenges of resolving the flow perpendicular to brightness gradients, and the difficulties of dealing with violations of smoothness and data conservation constraints, all of which are important in the present work.
The method we present here estimates plasma drift using optical measurements at high temporal and spatial resolution in a 60 region close to dynamic auroral features. The uniqueness of the method is the way that it uses three different wavelengths in the aurora to solve the continuity equation for the metastable oxygen ion. This O + ( 2 P) ion emits as it drifts under the influence of electric fields close to an auroral arc. The other unique feature of the results is that the optical measurements are close to the temporal resolution of the cameras at 0.1 s, and at a spatial resolution of 100 m, which is close to the limit of auroral structure widths (Sandahl et al., 2011). The instrument used is the Auroral Structure and Kinetics (ASK) instrument, which 65 was designed for the purpose of measuring plasma flows in a small 3.1°×3.1°field of view around the magnetic zenith. Dahlgren et al. (2009) were the first to use observations of auroral brightness from the ASK instrument to estimate plasma flow velocities, from which the ionospheric electric field was inferred. They tracked the motion of the afterglow from the metastable O + ions produced by auroral precipitation in narrow arcs by assuming a fixed emission height for the afterglow.
They inferred electric fields of a few tens of mV m −1 as an auroral event subsided. However, this method is limited by the fact 70 that tracking is not possible during the main brightening because the motions of the source and the plasma cannot be separated without solving the continuity equation for the ions.
The present method, referred to as the "flow model", overcomes the limitations of the above study through the following steps.
(1) It accurately separates the prompt emissions (673.0 nm from N 2 and 777.4 nm from O), which occur at the point of 75 impact of precipitation, from the emissions of the metastable O + ions (732.0 nm) which may have moved from the location of the source.
(2) It solves the continuity equation for the O + ions at all heights in the 3D region surrounding the zenith direction. This solution requires an accurate estimate of the magnetic zenith position in the images, and must account for perspective effects in the region away from the zenith. 80 (3) By using the flow velocity as a free parameter, the solution determines how the three-dimensional distribution of the O + ions evolves during periods of auroral electron precipitation.
(4) From this time evolving distribution, modelled images of 732.0 nm emission from the 3D distribution of O + ions are projected onto the image plane on the ground (Rydesäter and Gustavsson, 2001;Tuttle et al., 2014).
(5) The flow velocity is extracted by finding the velocity that minimizes the difference between the modelled and observed 85 732.0 nm images.

The ASK instrument: three emissions
The Auroral Structure and Kinetics instrument (ASK) is a ground-based optical instrument consisting of three low-light imagers capable of resolving the structure and dynamics of the aurora at resolutions of 20 m and 0.025 s. In the present study, each 90 imager had a field of view of 3.1×3.1°(equivalent to about 5×5 km at 100 km altitude). Each camera has a specially selected narrow passband filter to isolate chosen emissions from the total auroral brightness. All cameras are synchronised and aligned centered on the magnetic zenith which is the only direction in which the true width of an auroral feature can be measured accurately. Perspective effects are critical in this small region; a new method is applied which allows emissions that are off the zenith field line to be included in the flow model.

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The first imager (ASK1) isolates emissions from several bands of the N 2 1PG electronic band system  using a passband 14.0 nm wide centred at 673.0 nm. These emissions are due to excitation of N 2 molecules by precipitating electrons, and their brightness exhibits little dependence on the energy of the precipitating electrons. Therefore the brightness of this emission can be used to estimate the energy flux of the electron precipitation ). There are no other known auroral emissions in this wavelength region.

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The second imager (ASK2) isolates emissions from the metastable O + ( 2 P) ion using a passband 1.0 nm wide centred at 732.0 nm. These emissions are from transitions between the 2 P and 2 D states, which are discussed further in section 3.3. Auroral emissions observed by this imager are indicative of low energy (< 1 keV) precipitation (Dahlgren et al., , 2009. However, there is some contamination from the (5,3) band of the N 2 1PG band system and hydroxyl airglow. The N 2 contamination is removed using the method of Spry et al. (2014), and the hydroxyl contamination is removed by background subtraction.

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The third imager (ASK3) isolates emissions due to the transition between the 5 P and 5 S states of neutral oxygen using a passband 1.5 nm wide centred at 777.4 nm . Two processes produce the upper excited state: electron impact excitation of atomic oxygen and dissociation of molecular oxygen. Altitude variations in the abundances of atomic and molecular oxygen cause the excitative process to be more sensitive to low energy precipitation and the dissociative process to be more sensitive to high energy (> 1 keV) precipitation. This energy dependence results in emission from all precipitation en-110 ergies, but it is more responsive to low energy precipitation than the 673.0 nm emission. There are no contaminating emissions beyond the background brightness.
The observations presented here were obtained when ASK was co-located with the EISCAT Tromsø radar facility at Ramfjordmoen, Norway (69.6°N, 19.2°E) and ASK was observing in the direction of the local magnetic zenith. All data are dark and flat-field corrected, background subtracted and intensity calibrated using star fluxes. Measured intensities of tens of stars 115 per image are compared with spectral irradiances in absolute units from tabulated values (Gubanov et al., 1992;Cox, 2000;Grubbs et al., 2016).

Energy and Energy Flux
The different sensitivities of emission at 673.0 nm (N 2 ) and 777.4 nm (O) to the energy of precipitation means that the ratio of O/N 2 brightnesses provides an estimate of the characteristic energy of the electron precipitation. The Southampton auroral 120 model is described in more detail in Lanchester et al. (2009), in which the method of using this ratio was tested during an auroral event measured with the ASK instrument and with incoherent scatter radar. The characteristic energy and energy flux are parameters needed for the production term in the solution of the continuity equation of the O + ions. The 1D auroral model is time-dependent and solves the electron transport equation (Lummerzheim and Lilensten, 1994) at each time step, resulting in output height profiles of auroral ionization, excitation, and electron heating rates. These are the 125 inputs to the ion chemistry and energetics part of the model, in which the time-dependent coupled continuity equations for all important positive ions and minor neutral species are solved along with the electron and ion energy equations (Lanchester et al., 2001). Initial conditions relevant to each event include estimates of neutral densities from the Mass Spectrometer Incoherent Scatter (MSIS) model (Hedin, 1991) and solar and geomagnetic indices, such as the F 10.7 solar radio flux and the A p index.
The cross-sections used are those described in Ashrafi et al. (2009) for the ASK1 (N 2 ) emission and Julienne and Davis (1976) 130 for the ASK3 (O) emission. A filter transmission factor is applied to each emission. In the case of the N 2 1PG (4,1) and (5,2) bands, the transmission factor through the ASK1 filter has a value of 0.72 determined using synthetic spectra and the filter transmission. For the OI multiplet the transmission factor is 0.70. Modelled emission brightnesses are obtained by height integrating the emission rate profiles.
Such modelled emission brightnesses are combined with measured brightnesses of 673.0 nm and 777.4 nm, from ASK1 and 135 ASK3 respectively, to estimate the energy and flux of the electron precipitation in the magnetic zenith Lanchester and Gustavsson, 2012). The ratio of the modelled emission brightnesses is determined as a function of peak energy, under conditions appropriate for the time and date of the event. The peak energy of the electron precipitation is then estimated from the ratio of the observed emission brightnesses. The energy flux is estimated from the ASK1 N 2 1P emission brightness.
A conversion factor of 250 Rayleighs per mW m −2 is used.

SuperDARN
The Super Dual Auroral Radar Network (SuperDARN) of pairs of HF radars operates in overlapping regions mainly at high latitudes (Chisham et al., 2007). In the present work we use primarily the two CUTLASS radars that overlap the field of view of the optical and EISCAT instruments, i.e. the radars at Pykkvibaer, Iceland, and Hankasalmi, Finland. Plasma density irregularities in the F region ionosphere backscatter the HF waves emitted by the radar and the Doppler shift received gives 145 the line-of-sight velocity component of the E×B drift. During the period of interest, the radars were operating in Common Time mode, in which each radar performs a sweep of its field of view every minute. Each sweep is formed by sequentially scanning 16 beams, each of which is separated in azimuth by 3.24 degrees. Each beam is separated into 75 range gates, each with a length of 45 km. Where measurements from two radars overlap, the data can be "merged" to give the 2D horizontal flow velocity at these heights (Ruohoniemi and Baker, 1998).

Observations
The presented event is from 9 November 2006, during a time of increased auroral activity caused by the Earth entering a fast solar wind stream with negative B z at about 20 UT. At 21:25 UT bright, structured and dynamic aurora was observed in the magnetic zenith. Figure 1 is an overview of the event. Panels (a)-(c) show false color images of the observed auroral forms in the three wavelengths, at selected times during a 15 s interval. In (a) and (c) the 673.0 nm (N 2 ) and 777.4 nm (O) images, 155 which measure the presence of high energy precipitation, start with a diffuse aurora with no distinguishable features. During a 10 second interval a north-south aligned filament becomes structured and moves through the magnetic zenith. Panels (d)-(f) are stack plots (or keograms) of west-east slices across the feature through the magnetic zenith for all three wavelengths. The position of the slice is marked on the first image of panels (a)-(c). At 21:25:04 UT the aurora brightens over a two second interval, increasing from 5 kR to 12 kR at 673.0 nm and from 2 kR to 6 kR at 777.4 nm, peaking at 21:25:06.5 UT. The auroral 160 brightness then decreases to initial levels at 21:25:08 UT before further abating over the next few seconds until the feature is no longer distinguishable. To determine accurate estimates of the energy and flux of the precipitation, the exact position of the zenith within the images must be known. Models of the geomagnetic field, such as the International Geomagnetic Reference Field (IGRF), are often used to calculate the position of the magnetic zenith at auroral altitudes. However, such models do not account for dynamics of the magnetic field under auroral precipitation conditions. Variations in the direction of the magnetic field of greater than one degree have been observed (Maggs and Davis, 1968;, which is significant for narrow field of view imagers 175 such as ASK. The position of the magnetic zenith can be estimated if rayed structures are present in auroral observations. These rays are spatially confined perpendicular to the field, but can extend several hundreds of kilometers parallel to the field. Maggs and Davis (1968) first used such a method in their seminal paper on the width of auroral structures, to estimate the location of the radiant point, or magnetic zenith, and found it was within an ellipse of 1 degree by 2 degrees.
Rayed structure is present at times during the interval studied here. Figures 2(a), 2(b) and 2(c) show auroral forms that exhibit 180 rays 1.6 s before and 3.8 s and 8.5 s after 21:25 UT, respectively. A line is drawn manually along each ray; the start and end points of this line are indicated by the asterisks in the figure. The line is extended across the image and the minimum distance from each pixel to the line is calculated. The location of the magnetic zenith within the images is at the pixel which minimises the sum of the squares of the distances between that pixel and each of the ray lines. The error at each pixel is shown in Fig. 2( d) and the estimated position of the magnetic zenith is found to be at the minimum error. In Figs. 2(a), 2(b) and 2(c) the double 185 circles indicate the magnetic zenith obtained using the ray method presented here; the single circles indicate magnetic zenith calculated using the IGRF model. The difference is of the order of one degree, which makes a significant difference to the interpretation of the images. The azimuth and elevation angles of the magnetic zenith are given by the azimuth and elevation of the line of sight of the pixel at the position of the magnetic zenith. This pixel is defined as the zenith pixel, (u z , v z ).

Correction for perspective
190 At all angles away from the magnetic zenith, the emissions from each camera at a given pixel are no longer on the same field line; this perspective effect must be accounted for when using images, even within a few degrees of the zenith position. Along an individual field line, at a given time, emissions at all heights result from a single electron energy spectrum that precipitates down through the atmosphere. Under this constraint, we use simple geometrical arguments to correct for perspective effects when estimating the energy of electron precipitation in the region close to the magnetic zenith. Figure 3 depicts a situation when 195 aurora occurs along a magnetic field line that is some perpendicular distance, d, away from the magnetic zenith. Emission rate profiles produced by electrons that precipitate along that field line are shown on the right of Fig. 3, in idealised form, for the emissions observed by ASK1 (N 2 ) and ASK3 (O). The peak heights for each profile are marked by dashed lines. The pixel lines of sight through the positions of these peak heights of emission subtend angles θ 1 and θ 3 with the magnetic zenith for the emissions observed by ASK1 and ASK3, respectively.
200 Figure 4 is a representation of an image in ASK1. We define the image distance between the zenith pixel, (u z , v z ), and the pixel whose line of sight passes through the height of peak emission to be n 1 in the ASK1 image, and similarly to be n 3 in the simultaneous ASK3 image. The unit vectorr from any given pixel (u, v) toward the zenith pixel is given by: whereû andv are unit vectors in image co-ordinate directions, and the values of (u z −u) and (v z −v) are small displacements.

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As emissions observed by ASK3 originate from a slightly higher altitude than those observed by ASK1, features in ASK3 will appear closer to the zenith pixel than features in ASK1. We therefore use the image coordinates of the ASK1 image as a reference and the perspective correction is applied to the ASK3 image. The denominator in Eq. (1) is then the image distance n 1 . We define which is the image distance that the position of the ASK3 peak emission appears shifted toward the zenith relative to the position of the ASK1 peak emission. This shift is the perspective effect that is corrected by the following geometrical argument.
The variation of image distance with angle is linear and obeys the following relation: where n T is the total image distance and θ T is the total field of view of the observed image. The angles in Eq. (3) are eliminated, 215 using trigonometry and the small angle approximation, to yield the following relation between the image shifts and the altitudes of peak emission, h 1 and h 3 : The altitudes of peak emission are obtained from an initial estimate of the energy that is obtained using the methods described in Sect. 2.2. Equation (4) can be combined with Eq.
(2) to yield Combining Eq. (5) with the expression forr, the displacement of the shift toward the zenith, r s is found: where shifts along the image co-ordinate directions are given by: Therefore, to account for perspective effects, the following ratio of brightnesses should be used for each pixel (u, v): where B 1 (u, v) is the brightness in the ASK1 image at pixel (u, v) and B 3 (u + ∆u, v + ∆v) is the brightness in the ASK3 230 image at pixel (u + ∆u, v + ∆v). By taking this ratio at every pixel in the ASK1 images, a map of the peak energy of the electron precipitation is produced along all field lines in the image.
One such map of peak energy across the ASK field of view at the time of the brightening at 21:25:06 UT is shown in Fig. 5.
The black line is the 4 kR brightness contour from the observed 673.0 nm emission at this time. The estimates of the energy of the precipitating electrons are approximately 1 keV along the edge of the feature closer to zenith, increasing to 5 keV on 235 the edge further from zenith, and corresponding to the lower border of the arc. The changes in the estimated energies when the perspective correction is applied are an increase of approximately 0.2 keV (20%) in the region closer to the zenith, and a reduction of 0.5 keV (10%) further from the zenith at lower heights, consistent with the geometry of the arc.
3.3 The O + ( 2 P) ion continuity equation The dynamics of O + ( 2 P) ions are governed by a continuity equation, which has terms for production, quenching, emission, 240 drift and diffusion: where n is the density of O + ( 2 P) ions, q is the production rate of O + ( 2 P) ions, n i is the density of quenching species i, α i is the rate coefficient for quenching by species i, A j is the Einstein coefficient for radiative transfer from the 2 P state to state j, v is the velocity of O + ( 2 P) ions and D is the diffusion coefficient. The contribution each term makes in Eq. (10) is described below, as well as how each term is obtained in order to solve for the three dimensional distribution of O + ( 2 P) ions.

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The first term on the right is the production of O + ( 2 P) ions, which occurs by impact ionization of neutral atomic oxygen by precipitating electrons through the following process: with 18% of O + ion production into the 2 P state (Rees, 1982). The 2 P state is further split into J 1/2 and J 3/2 angular momentum states. Production rates of O + ( 2 P) ions are obtained using a combination of optical observations and modelling as described

255
The second and third terms on the right of Eq. (10) are the two loss processes affecting the O + ( 2 P) ion: quenching and emission. Quenching is the dominant loss process at higher atmospheric densities, and hence lower altitudes. We use the rate coefficients for quenching by electrons given by Rees (1989), and rate coefficients for quenching by oxygen and nitrogen obtained by Stephan (2003). Emission occurs when O + ( 2 P) ions de-excite by spontaneously emitting a photon; there are no stimulated emissions. There are two radiative paths, ( 2 D)-( 2 P) and ( 4 S)-( 2 P), through which there are six possible transitions.

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These transitions form emission doublets at 733 nm, 732 nm and 247 nm, with only the 732 nm doublet observed by the ASK2 filter. Einstein coefficients for these transitions are found in a study made of the O + doublets by Whiter et al. (2014). The 732 nm doublet emission has contributions from both the J 1/2 and J 3/2 states, which means that Eq. (10) must be solved for each angular momentum state. In isolation, the emission and quenching terms can be inverted to obtain altitude dependent effective lifetimes for the two angular momentum states of the O + ( 2 P) ion (Dahlgren et al., 2009). These lifetimes are calculated using: with the altitude dependence arising from the density profiles of the quenching species.
The fourth and fifth terms on the right hand side of equation (10) arise due to the flux term, ∇ · (nv), of the continuity equation. Rather than solving these terms explicitly to determine v, the velocities in the modelled region are parameterized.
This parametrization is discussed further in Sect. 3.4.
Finally, the diffusion term can be neglected for the O + ( 2 P) ion, because collisions that would ordinarily redistribute the 270 thermal motion of the ion instead cause the ion to quench. Perpendicular to the magnetic field, strong density gradients may exist. At high altitudes, where quenching is negligible, these gradients are maintained by the magnetic field.

The flow model
Equation (10)  Therefore we search for two free parameters, the components of the ion velocity perpendicular to the magnetic field.

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The optimal free parameters, P , are searched for by minimizing an error function. The error function used here is the sum of the square of the difference between the observed and modelled images, and is given by: where I obs (u, v) is the observed brightness at pixel (u, v) and I mod (u, v, n(r, P )) is the modelled brightness at pixel (u, v).
The modelled brightnesses are obtained using a forward model f : where n(r, P ) is the density of O + ( 2 P) ions, calculated from Eq. (10) using the trial free parameters, P , at the position r. The 285 forward model uses the blob-based dot projection method of Rydesäter and Gustavsson (2001) to project emission from the 3-D distribution of O + ( 2 P) ions to an image plane on the ground, forming modelled images of the 732.0 nm brightness. To allow comparison with the observed brightness, the modelled image is converted to Rayleighs using a calibration image with a uniform brightness of 1 Rayleigh. The calibration image is formed by applying the forward model to a volume with a uniform column emission rate of 10 10 photons m −2 s −1 , which is the definition of a Rayleigh (Hunten et al., 1956).

Results
The flow model is run for a 15 second interval, starting at 21:24:57.50 UT, that includes times before, during and after the arc brightening. A timestep of 0.1 s is chosen, i.e. half the resolution of the ASK measurement, which is sufficient to resolve the dynamics in this event. For the first five seconds the model is run without the optimization, and using a plasma velocity of zero, to generate an initial distribution of O + ( 2 P) ions to be tracked. In the remaining ten seconds the optimization is active and the 295 model searches for the velocity at each timestep using the methods described above. Figure 6 is a sequence of modelled images at 0.5 s cadence of the 732.0 nm emission from the convecting distribution of O + ( 2 P) ions. The corresponding observations of the 732.0 nm emission (background subtracted) are shown in Fig. 7, with the modelled brightness contours superimposed. The modelled images match the structure of the measured images well, while the brightness of the model images is about half of those observed. At the time of these observations, the SuperDARN radars at Hankasalmi and Pykkvibaer were also measuring ionospheric flows above Svalbard, so a direct comparison between the modelled and measured velocities is possible. Line of sight plasma 310 velocities from the two radars have been merged at two minute resolution to give a measure of the larger-scale flow. Figure 9 shows the magnitudes (length and color) and directions of the plasma velocities between 21:24 UT and 21:26 UT. The small black square is the approximate size and position of the ASK field of view at 200 km height. Table 6

Discussion
To resolve the full electrodynamics of auroral arc formation, high temporal and spatial resolution is a crucial requirement.

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It impacts theories of auroral acceleration in the inner magnetosphere since resulting field-aligned currents must close in the dynamic auroral ionosphere, where electric fields are measured. The high time resolution of the present method of 0.1 s places constraints on theories to resolve the dynamic nature of electric fields close to auroral precipitation, and the intimate connection between the two. Spatial resolution is also of importance, and although our measurements give optical resolution of 10s of metres, the present model is tested by using the simplest form of parametrization of the plasma velocity, which is a 325 uniform flow perpendicular to the magnetic field. Therefore the present determination of the plasma flow is an estimate over a volume corresponding to the optical field of view, which is 5 × 5 km at 100 km height, an order of magnitude smaller than the volume for the coherent radar measurement.
It is useful to set the small scale nature of this result within the large scale auroral environment. Figure  The sub-second electric fields, calculated during the 10 s passage of the arc through the field of view of the cameras, are enhanced when the arc is brighter. This result is important for theories of auroral electrodynamics, in particular how the ionospheric electric fields link to processes further out where acceleration of electrons is taking place. The theory of Birk and Otto (1996) as presented in Lanchester et al. (1997) uses a three-dimensional multi-fluid MHD model to simulate 340 the spatial variation of the ionospheric plasma velocity close to a narrow (< 1 km) and dynamic arc filament, similar to that observed in the present event. The simulation includes a magnetic and velocity perturbation at its upper boundary in the inner magnetosphere, which generates field-aligned current sheets. A field-aligned electric field is generated by a resistive term in Ohm's law if the current density exceeds a threshold value. A small-amplitude perturbation is applied to initialize the formation of the acceleration region. The resulting plasma velocities in the ionosphere, which map to a similar sized region as our field-345 of-view of a few km 2 at auroral heights, are found to be mainly tangential to the arc filaments, with inferred electric fields pointing towards regions of enhanced potential, and with increased magnitudes where the arc is brightest. The net electric field at any time will be the sum of the background electric field and the electric field due to the feature. This combination should result in changes to both the magnitude and direction of the electric fields across the field of view. In our result, we assume that velocity, and hence electric field, is uniform throughout the modelled volume. Such an assumption is therefore unable to 350 account for the very small spatial variations of electric fields, such as those that may be generated on either side of the < 1 km scale auroral feature. A future step is to apply more complex parametrizations, e.g. a shear flow across the arc, similar to the above simulations.
The comparison of the derived velocities with the SuperDARN velocities reinforces the above interpretation. Care must be taken, however, as the SuperDARN velocities are obtained by merging individual line of sight vectors from two different radars, 355 which are taken from different instants within the two minutes (and which fall outside the period covered in Fig. 8, and so are not simultaneous with the ASK measurements). We also note that the SuperDARN velocities may be underestimated as a result of uncertainty in the refractive index as shown by Gillies et al. (2012). This effect is likely to be of the order of 10%. However, the SuperDARN observations are an excellent measure of the background plasma velocities on timescales much longer than the modelled interval (10 s), as shown by the close agreement between the SuperDARN velocities and the modelled velocities 360 before and after the feature intensifies. The optically derived velocities vary between 0.4 and 1.2 km s −1 in the few seconds either side of the arc brightening, compared with the average value of 0.6 km s −1 from SuperDARN.
The presented method for determining dynamic electric fields includes several steps, all of which have inherent uncertainties which must be evaluated, in order to have confidence in the high cadence vectors of Fig. 8. An important parameter in the modeling of optical images is the magnetic field direction at auroral altitudes within the volume enclosed by the ASK field of 365 view. Field-aligned currents within auroral features cause perturbations to the background magnetic field, which means that the position of the magnetic zenith may vary. In the present event, lines which pass through field-aligned rays are drawn manually, so there are uncertainties in position of not more than five pixels in selected points on each ray line. However, all ray lines pass within two pixels of the recovered position of the magnetic zenith, suggesting this uncertainty is small in the event presented here. The rays used to reconstruct the position of the magnetic zenith are separated by up to 10 seconds. The reconstruction 370 assumes that during this interval, the position of the magnetic zenith does not vary. It is clear from Fig. 2 that the zenith position is indeed a much better estimate than is given by the IGRF. The lower panels of Fig. 11 also provide evidence for the improved zenith estimate; there is a ray visible in the prompt O emissions, which is aligned well with the zenith. The direction of the magnetic zenith is critical for the application of the geometric correction for perspective in this small region within the images.
The main assumption used in the correction for perspective is the height of the peak emissions found from modeling, using 375 an initial estimate of the energy from the uncorrected brightness ratio. For the region around the lower border of the arc the energy is 5 keV; the difference in the height of peak emissions from N 2 and O is a few hundred metres, resulting in small or negligible positional shifts, no matter how far the feature is from the zenith. In regions where the energy is 1 keV, the difference in peak emission height is a few kilometres, which could cause significant perspective effects. For the present event, the regions of the bright feature where the energy is low are close to the zenith, which reduces the magnitude of the required this event, the uncertainty in the absolute intensity calibration has been quantified at 20%.
Uncertainties arising from the auroral model include the assumption of an input neutral atmosphere, here taken from MSIS.
It is known that the oxygen density may be significantly reduced from the model profiles. However, as shown in Fig. 3 of Lanchester and Gustavsson (2012), the effect on the estimation of energies is more marked for low energy precipitation, particularly lower than 1 keV. The present event is dominated by higher energies, and the effect is estimated to be less than 10% for 395 the 1 keV electrons, and with negligible effect for energies of 5 keV. The accuracy of the model emission rates can be checked by a direct comparison between the observed images from ASK1 (673.0 nm) and ASK3 (777.4 nm) and modelled images. The latter are formed from emission rates obtained in the 3D region of the flow model, which are projected to an image plane on the ground, at the ASK location, using the same blob-based dot projection method that was used in Section 3.4 for the O + emission. Figure 11 shows this comparison. The black lines delineate the brightness extent of the discrete auroral feature in The uncertainty in the peak energies will have a negligible effect on the O + production term, but the shape of the input spectrum may affect this term. The brightness of the modelled O + is less than that measured by about 50%. The most likely 405 reason is that the model does not include a low energy contribution in the present runs. Since such a low energy tail is an arbitrary addition, we have chosen to use the Gaussian shaped spectra unless there is evidence (e.g. radar profiles) to support a different shape. (Testing of such variable shapes is the subject of a separate study.) Increasing the low energy input to the model would result in an increased brightness as well as a slight increase in the height of the peak O + emission. Therefore the present result for the magnitude of the electric fields is likely to be an underestimate. The direction would not be affected.

Conclusions
The present work demonstrates a new method for estimating plasma flows around auroral features, using measurements from a multi-monochromatic imager, and modelling. The dynamic nature of the auroral event is captured at a resolution of 0.1 s, for a 10 s interval during which the arc passed through the magnetic zenith, a typical time span for dynamic aurora. Such high temporal resolution estimates of electric fields are a fundamental building block for the theory of auroral currents. Ground-415 based measurements to date (e.g. radars) of electric fields average over much longer intervals than 10 s and therefore miss dynamic changes. The agreement found in both magnitude and direction of the flow velocities with those measured by coherent radar gives confidence that the background flow is well captured. In this instance it is of magnitude about 0.6 km s −1 in the south east direction. The increase in magnitude of the flows to 2.4 km s −1 , with equivalent electric field magnitudes of 120 mV m −1 during the brightening of the arc feature, agrees with present theories of small scale auroral arc formation.

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For the event presented, the simplest form of parametrization, that of a uniform flow perpendicular to the magnetic field, was applied through the modelled volume. The full 3D model as presented here addresses some of the issues of optical flow analysis algorithms as done in e.g. Blixt et al. (2006)