Extrapolating EISCAT Pedersen conductances to other parts of the sky using ground-based TV auroral images

Ionospheric conductivity is not very easily measured directly. Incoherent scatter radars perhaps offer the best method but can only measure at one point in the sky at any one time and are limited in their time resolution. Statistical models of average conductivity are available but these may not be applied to individual case studies such as substorms. There are many instances where a real-time estimate of ionospheric conductivity over a large field-of-view is highly desirable at a high temporal and spatial resolution. We show that it is possible to make a reasonable estimate of the noctural height-integrated Pedersen conductivity, or conductance, with a single all-sky TV camera operating at 557.7 nm. This is not so in the case of the Hall conductance where at least two auroral wavelengths should be imaged in order to estimate additionally the energy of the precipitating particles.


Introduction
The STARE bistatic coherent-backscatter radar system (Greenwald et al., 1978) has been employed to estimate the average statistical spatial distribution of horizontal E-region electric ®elds over Scandinavia. From this, in conjunction with the ionospheric Pedersen conductivity, Joule heating (Kosch and Nielsen, 1995) and Birkeland current (Nielsen, private communication) average global estimates have been made. Although STARE produces reasonable estimates of the ionospheric electric ®elds Schlegel, 1983, 1985) with high temporal (typically 20 s) and spatial (typically 20´20 km) resolution over a large ®eld-of-view (520´520 km), it cannot provide the ionospheric conductivity. For this reason, it was necessary to use a global, statistically averaged, model of ionospheric conductivity. Several such empirical models are available for height-integrated conductivities, or conductances (e.g. Wallis and Budzinski, 1981;Spiro et al., 1982;Hardy et al., 1987). All such models are essentially static except for some fairly crude range steps in Ae or K p . Especially for nocturnal conductivities at high latitudes, local perturbations such as auroral precipitation may dominate, making statistical conductivity models inappropriate for case studies. Brekke and Moen (1993) point out that an urgent need exists to produce detailed global conductivity maps for the study of auroral substorm phenomena.
To study real-time Joule heating and Birkeland currents during substorms, it is necessary that an estimate of the Pedersen conductance be made within the STARE ®eld-of-view at the same temporal and spatial resolution as the radar. The EISCAT radar (Folkestad et al., 1983;Rishbeth and van Eyken, 1993), which is conveniently located within STARE's ®eld-ofview, can make height-resolved estimates of both the ionospheric Hall and Pedersen conductivities (e.g. Brekke and Hall, 1988;Schlegel, 1988). However good the measurement is though, it can only be made at a single point in the sky at any one time with a limited time resolution, hence the need for a method of extrapolation to a wider ®eld-of-view. Although the aurora can¯uctuate on a time scale of seconds or less, the EISCAT data is normally integrated for 2 min in order to achieve an acceptable signal-to-noise ratio.
It is well known that nocturnal ionospheric conductances can be inferred from optical data. Robinson et al. (1989) used satellite auroral images although these are rarely useful for real-time studies. Mende et al. (1984) used ground-based meridian-scanning photometers but they have a very small ®eld-of-view. They suggested that monochrome auroral imagers could be used to extend the ®eld-of-view to two dimensions. Kaila et al. (1993) have demonstrated that it is possible to use white-light TV images to expand the ®eld-of-view of photometer measurements, thereby enabling them to estimate the auroral energy¯ux in a large ®eld-of-view and hence obtain total electron density and, in principle, conductance. Rothwell et al. (1992) reported a linear dependence between variations in the peak value of electron density pro®le, from EISCAT, and auroral luminosity. It has been demonstrated that the vertical luminosity pro®le of an auroral form can sometimes be converted into ionisation rate and electron density pro®les in agreement with EISCAT (Kaila, private communication). Although an incoherent scatter radar can make a much more accurate estimate of conductance, the same measurement by optical means is much easier to make on a large spatial scale with high time-resolution (Mende et al., 1984). In the present work, we seek to make conductance measurements from a single auroral imager with a large ®eld-of-view, with high temporal and spatial resolution, at a single convenient wavelength.

Methods and instrumentation
The theoretical equations expressing ionospheric conductivity are well established (e.g. Brekke and Moen, 1993, and references therein) and will not be reiterated here. The application of these equations to incoherent scatter radar data is also well established (e.g. Schlegel, 1988). Instead, we derive the relationship between conductance and optical intensity. The continuity equation for the E-region electron densities (N e ) measured at a given altitude is given by (Brekke et al., 1989a): where Q p is the ion production rate due to auroral precipitation, Q s is the ion production rate due to solar radiation, a is the height dependent eective recombination coecient and " m is the electron bulk velocity. Rearranging, we have: Assuming night-time, steady-state conditions and that the last term (x e Á " m) can be neglected when compared to ax 2 e (Brekke et al., 1989a), the equation simply becomes: ax 2 e p X 3 Auroral particles bombarding the atmosphere will lose energy at the rate of about 35 eV per ion pair formed (Rees and Luckey, 1974). Upon recombination, only a small fraction (%4%) of the energy thus deposited results in spectroscopic emissions observable from the ground (Rees and Luckey, 1974). However, for a given precipitation rate by particles of a certain energy, it is reasonable to expect the production of auroral photons to remain constant. To ®rst order, we can assume that auroral optical intensity (I) is proportional to Q p . That conductivity (C) is proportional to N e is well established (e.g. Egeland et al., 1973). Hence, for conductivity variations associated with particle precipitation we have: Still assuming night-time, it is worth noting the likely consequence of a breakdown of the other assumptions. Using Eq. (2) with s G p and g G x e we have: Clearly, during non-steady-state conditions and any signi®cant divergence associated with the electron bulk velocity, the conductivity will be less than that expected from Eq. (4). A single auroral imager cannot make an unambiguous height determination of the aurora. Since we can only measure Rs, which is a column integral, altitude dependent eects are neglected. Of course, this is not strictly correct as the ion-neutral collision frequency, which appears as terms in the conductivity equations (e.g. Egeland et al., 1973), increases with decreasing altitude. It is largely for this reason that Pedersen conductivity peaks at a higher altitude than Hall conductivity, depending on the precipitating particle energy (Robinson et al., 1989;Vickrey et al., 1981). EISCAT data show that main contribution to the Pedersen and Hall conductivities from precipitating particles comes from 120±150 km and 80±130 km altitudes, respectively (Senior, 1991). High energy particles penetrate to lower altitudes in the atmosphere thereby contributing to both conductivities, whereas low energy particles do not penetrate so deeply and hence mostly only contribute to the Pedersen component. As a result of this, the Hall and Pedersen conductivities are strongly and weakly, respectively, energy dependent. Vickrey et al. (1981) show that the Hall and Pedersen conductances vary by factors of about 10 and 2, respectively, for an order of magnitude change in characteristic energy of the precipitating particles. Of course, both conductances are equally¯ux dependent. Several empirical formula have been produced from optical data for conductance (Hardy et al., 1987;Robinson et al., 1989;Spiro et al., 1982). They all show a stronger dependence on energy for the Hall component than for the Pedersen component.
The ratio of Hall to Pedersen conductance is widely used as an indicator of the energy of precipitating electrons in the auroral zone (Brekke et al., 1989a and references therein;Brekke et al., 1989b). An estimate of the energy can also be made spectroscopically if at least two wavelengths are measured simultaneously (Rees and Luckey, 1974). For this purpose, the ratio 630.0/427.8 appears to be the best although other auroral emissions also suce. Comparisons between photometric and incoherent scatter radar techniques for estimating the energy of precipitating particles show good agreement (Wickwar et al., 1975;Vondrak and Sears, 1978).
The Digital All-Sky Imager (DASI) (Kosch et al., 1998) has been designed to complement STARE, and include EISCAT, for studies of the aurora. The detector consists of a monochrome low-light-level TV camera ®tted with an all-sky lens. An interference ®lter at 557.7 nm selects the strongest auroral emission. The camera has been calibrated, as well as¯at-®eld corrected, in Rayleighs at 557.7 nm using a radioactive light source. The Rayleigh is a non-SI unit still commonly used in auroral physics: By de®nition, 1 Rayleigh 10 6 photons/cm 2 /s, which is the number of photons emitted per second in 4p steradian as viewed through a one square centimetre column integrated vertically through the emitting region at the selected wavelength (Hunten et al., 1956).
DASI is fully unmanned and is automatically operated by a PC for all dark and moon-free periods. The TV images are digitially integrated in real-time with a user-de®ned temporal resolution (normally 10 s), transformed from all-sky format into any spatial grid (currently the ®eld of view of STARE at 10´10 km resolution for 100 km altitude) and saved to disk for later analysis. The spatial orientation of the camera and lens is ®xed through star observations. The frequent gain changes necessary are computer controlled and recorded by the software, thus permitting each processed image to be recalled in Rayleighs at 557.7 nm. DASI has been located at Skibotn, Norway (69.35°N, 20.36°E), which is near the centre of STARE's ®eld-of view and about 50 km from EISCAT (69.59°N, 19.23°E) because of the superior local night-sky viewing conditions. Figure 1 shows the STARE ®eld-of-view (67.6±72.6°N, 13.5±26.0°E) at an assumed altitude of 100 km as seen by DASI from Skibotn in geographic coordinates. The position of EISCAT's beam (cross), when magnetic ®eld aligned, is also shown for the same altitude.
DASI is well suited to make Pedersen conductance estimates everywhere within STARE's ®eld-of-view as it is calibrated, automatically makes column integrals of total optical intensity (Rs), has a better temporal and spatial resolution than STARE and includes EISCAT.

Data analysis and discussion
EISCAT is operated for only about 2000 h per year. DASI operates for about 1500 h per auroral season but only about 100±200 h of useful data result due to the frequently heavy cloud cover over northern Scandinavia. Hence, it is not always easy to ®nd suitable simultaneous data sets, especially of longer runs. For this study we have used data from the nights of 28 February to 2 March 1995 (K p 4±6 A ), the night of 28±29 March 1995 (K p 2 A ±3 + ) as well as the night of 13±14 February 1996 (K p 3 A ±4 A ). The four recording nights represent a good spread of low to moderate geomagnetic activity (K p 2 A ±6 A ). On all these occasions, EISCAT was operated in the CP1 mode whereby the transmitter beam is kept continuously pointing along the magnetic ®eld line direction. In this mode, conductivity estimates are made between 87 and 269 km altitude every 2 min (Schlegel, 1988). The total data set consists of 794 points with 316 pre-and 478 postmagnetic midnight (%21:30 UT). Calibrated DASI data was extracted from the 10´10 km spatial cell that overlaid the EISCAT beam. The 10 s optical measurements were averaged down to 2 min intervals which exactly correspond to the EISCAT data. Figure 2 shows scatter plots of conductance, from EISCAT, versus auroral optical intensity, from DASI, using the entire data set. Figure 2A shows the Hall component, Fig. 2B the Pedersen component and Fig. 2C the Hall to Pedersen ratio. Figure 2B also shows the least-squares ®t of Eq. (4) to the data. The data has been divided into two ranges with solid squares for K p < 4 and crosses for K p ³ 4. For K p < 4 the auroral intensity is restricted to approximately 500±3500 Rayleighs whereas for K p ³ 4 all auroral intensities are represented in the data set. The lack of data below about 500 Rayleighs is partly due to the approaching sensitivity limit of the imager (Kosch et al., 1998).
It is clear that the Hall to Pedersen conductance ratio varies signi®cantly for any auroral intensity. Since this ratio is an indicator of the energy of precipitating particles whereas auroral intensity relates directly to thē ux of precipitating particles, Fig. 2C implies a signi®cant spread in the energy of the precipitating particles which does not relate simply to the¯ux of auroral photons. This is re¯ected as a large spread in the scatter plot of Fig. 2A since the Hall conductivity is sensitive to the energy of precipitating particles. Although Hall conductance bears some relationship to auroral intensity, we are unable to make a meaningful curve ®t using optical data at one wavelength alone. At least two auroral wavelengths need to be imaged in order to make an estimate of the energy of the precipitating particles.  6±72.6°N, 13.5±26.0°E) at an assumed altitude of 100 km as seen by DASI through an all-sky lens from Skibotn (69.35°N, 20.36°E) in geographic coordinates. The data grid is shown at the lower 20´20 km resolution only for clarity. The position of EISCAT's beam (cross) when magnetic ®eld aligned is also shown for the same altitude. The circle is the ideal horizon whilst the heavy irregular circle is the actual horizon The Pedersen conductance, shown in Fig. 2B, does relate to auroral intensity rather well although the spread in the scatter plot is probably, at least partly, also due to the energy of the precipitating particles. Ignoring energy, the least squares ®t of Eq. (4) gives:

0X34 0X18
Rs p 6 where is Pedersen conductance (Siemens) and Rs is Rayleighs at 557.7 nm. Equation (6) predicts a minimum Pedersen conductance of 0.34 for no auroral precipitation. During night-time, a small residual conductivity is expected from cosmic and galactic EUV radiation and is consistent with the value of 0.2 adopted by Senior (1991). Above about 4000 Rayleighs, the ®t appears to be consistently too high. This intensity range results only from data taken at higher geomagnetic activity (K p ³ 4). Hence, it is not unexpected that the assumptions of steady state and negligible divergence used in deriving Eqs. (3) and (4) may be violated. Indeed, it is expected, from Eqs. (5), that the measured conductance should be less than predicted for nonsteady state conditions, which is consistent with our results. The standard deviation from the mean is shown in Table 1 for dierent intensity ranges. The accuracy of the curve ®t is approximately 30±45% for lower auroral intensities (<4000 Rayleighs) improving to around 20± 25% for higher intensities. The lower accuracy at lower intensities partially re¯ects the increasing noise in the TV image as the gain of the camera is increased. For low to moderate auroral intensities (<4000 Rayleighs), Eq. (6) is a good representation of Pedersen conductance. For high auroral intensities (>4000 Rayleighs) additional eects, which have not been accounted for, results in Eq. (6) being an overestimate. Figure 3 shows an example of using a DASI auroral image in conjunction with Eq. (6) to achieve an instantaneous map of Pedersen conductance throughout STARE's ®eld of view.
The analysis was repeated using pre-and postmagnetic midnight data only to check for any systematic dierences. The pre-midnight ®t gives 0X47 0X17 Rs p and post-midnight the ®t gives 0X13 0X19 Rs p . Given the achievable accuracy, there is no signi®cant dierence in the ®t for pre-or post-magnetic midnight Pedersen conductances. Solid squares correspond to data for K p < 4 whereas crosses are for K p ³ 4 There are several sources of potential uncertainty in this study including: 1. The steady state assumption may be violated. This is clearly the case during substorms. 2. Assumptions are made in producing the EISCAT conductivity estimate, for example, the ion-neutral collision frequency is taken from a model. 3. The accuracy of the camera intensity calibration depends on the con®dence one has in the reference source. Radioactive light sources make relatively good standards and age fairly slowly. Low-light-level TV cameras do not lend themselves well to an absolute intensity calibration due to the inherently noisy nature of their image intensi®ers which also suer from degradation with time. Regular recalibration is necessary. 4. Some optical intensity dependence at 557.7 nm on the precipitating particle energy spectrum can be expected. 5. Some geometric ambiguity due to the camera not being exactly co-located with EISCAT is expected. Also, the selected 10´10 km optical data cell does not exactly correspond to the radar beam only which has a 2 km diameter at 100 km altitude due to beam divergence. 6. When using ground-based optical images, perspective eects due to the vertical extent of the aurora will give an increasingly poor result the further one deviates from the local magnetic ®eld line. In particular, aurora in one data cell but at a much greater height than 100 km may map into an adjacent data cell. This problem can not be avoided with a single imaging system. Similarily, when viewing an auroral arc not in the local magnetic zenith, the total column emission, and hence conductance, may be under-or overestimated depending on the geometry.
We have tried to ®t EISCAT conductances using white light optical data from DASI for the nights of 18±20 October 1993. However, this proved to be impossible because the spread in the scatter plot was much too large. At this time, it is not known if using any wavelength other than 557.7 nm will give a better result.

Conclusion
We have shown that it is reasonable to use all-sky auroral images at 557.7 nm for estimating nocturnal ionospheric Pedersen conductances. No other additional observations are needed. The equivalent Hall conductances cannot be reasonably estimated from a single wavelength optical image. This is due to the greater dependence of the Hall conductivity on the energy of the precipitating particles. In order to use optical auroral images for estimating ionospheric Hall conductances, at least two wavelengths would have to be imaged simultaneously. A second all-sky imager, to operate at 630.0 nm, is already under construction.
All-sky auroral imagers are relatively simple and cheap to build and oer a very high temporal and spatial resolution over a large ®eld of view. Typical CCD technology can easily image the aurora at 557.7 or 630.0 nm. Given the large numbers of all-sky cameras available at northern high-latitudes, it should be possible to produce large-scale real-time maps of nocturnal conductance. The use of tomographic reconstruction from multiple optical observing sites would ultimately permit the vertical pro®le of ionospheric conductivity to be determined also.
Combining data from the STARE and DASI experiments will permit real-time computation of highlatitude ionospheric Joule heating, as well as Birkeland current estimates, with high time and spatial resolution. Such studies are planned.