We develop a technique to create two-dimensional maps of the field line integrated, F-layer Pedersen conductivity from images of the 630.0-nm emission at midlatitudes. By modeling the 630.0-nm and the height-integrated Pedersen conductivity, we show that the former can be used as a surrogate for the latter to within 0.2 mhos if information on the height of the F-layer is known. A simple thin-shell model is used to convert the height-integrated conductivity to field line integrated conductivity, a more useful parameter in the study of midlatitude ionospheric dynamics. Two nights are studied using this technique, one with a gradient in electron density seen to the south and one with severe depletions. In the latter case, bands of alternating low and high field line integrated Pedersen conductivity are seen to align from the northwest to southeast, just as predicted by Perkins .
 The relative importance of the E- and F-region dynamos is controlled both by the wind fields which drive the system and by the conductivities of the two regions. During the daytime, E-region conductivity so dominates that there is effectively no F-region dynamo. At night, however, the F region can dominate the electrodynamics, although not with quite so strong a control as is exhibited by the E region during the day. Burnside et al.  studied the height-integrated E- and F-region conductivities at midlatitudes for a number of nights using Arecibo data and plotted their ratio for different local times and seasons. This study showed that the ratio of the integrated F- (ΣPF) to integrated E-region (ΣPE) Pedersen conductivities was as high as 20 and almost always greater than 2.5.
 This ratio is of interest in the study of instabilities and structures in the midlatitude E and F regions as well. In his ground-breaking work introducing a new instability at midlatitudes, which has come to be called the Perkins' Instability, Perkins  used the field line integrated F-region conductivity as the primary variable he tracked in his calculation. He found that under some conditions regions of high and low perturbed conductivity would become more pronounced with time as the corresponding plasmas fell and rose in altitude, respectively. He predicted that bands of high and low height-integrated conductivity would align from the northwest to the southeast in the Northern Hemisphere. As we shall see below, this is exactly what the all-sky airglow application outlined in this paper reveals. In effect we argue that we can make two-dimensional maps of ΣPF using the airglow technique.
 In addition to Perkins' application, knowledge of the height-integrated F-region conductivity using the passive airglow technique would allow analysis of E- and F-region coupling. Swartz et al.  studied this coupling using the Arecibo incoherent scatter radar to calculate the contribution from both regions. Using the airglow method proposed here, we could study such effects without the need for an incoherent scatter radar. For example, M. C. Kelley et al. (Relationship between destabilizing polarization electric fields in the E region and midlatitude spread F: Case studies, submitted to Journal of Geophysical Research, 2003a) have used an ionosonde to determine (within limits) the E-region conductivity and the airglow method presented here for the F-region contribution in a study of the effect of sporadic E on the overhead ionosphere. Similar methods could be applied to see the effect of traveling ionospheric disturbances (TIDs) on the E region below.
 Several studies in the auroral zone have shown that the technique of using optical measurements to infer the ionospheric Pedersen conductivity to be a viable one. Mende et al.  used scanning photometer measurements of the 630.0-nm emission to derive conductances. Kosch et al.  showed that Pedersen conductivities could be inferred from observations of the aurora at 557.7-nm. These authors derived a very simple relationship between the 557.7-nm emission and the height-integrated Pedersen conductivities using an imager collocated with the EISCAT radar. They then used this relationship to create maps of the conductivity. It is important to note that these authors' work was done in the auroral region and thus the processes resulting in the emissions used, as well as the techniques derived to estimate the conductances, are unique to that region. Very little work has been done to apply airglow techniques to deduce the middle and low-latitude conductivities, as we do in this paper. We show in this paper that the 630.0-nm emission can be used as a surrogate for the F-layer integrated Pedersen conductivity for sites equatorward of 45° magnetic latitude.
 In the next section we develop the analysis techniques and test them using climatological models. Following this, we use Arecibo data taken on two quiet nights with no medium-scale structure to calculate the conductivity and then compare the results to our airglow-based prediction on those same nights. We then apply the method to a very active night to create what we believe are the first height-integrated Pedersen conductivity maps of the midlatitude ionosphere.
2. Comparison of the 630.0-nm Emission and Pedersen Conductivity: Theory
where the quantities in brackets are species density; β1D is the fraction of the dissociative recombination reactions O2+ + e → 2O(3P, 1D, 1S) that result in O(1D) atoms (rather than O(3P) or O(1S)); k1, k3, k4, and k5 are rate coefficients; and A1D is the transition coefficient for the O(1D) atoms. The values used for the coefficients in this study are given in Table 1.
Table 1. Rate Coefficients Used to Determine the 630.0-nm Emissiona
 Concerning ourselves with the F region, from which the bulk of the 630.0-nm emission originates, we can assume that the plasma is dominated by O+ and thus can assume that [O+] = [e]. By examining equation (1), we see that this emission has a dual dependence on the O2 density as well as on the electron density. Owing to this dependence on [O2], the peak of the emission typically occurs about one scale height below the F peak, and the dimming (brightening) of the emission can be due to either a decrease (increase) of the electron density or the raising (lowering) of the F layer as a whole [e.g., Makela et al. 2001]. As mentioned by Garcia et al. , this same dual dependence is seen in the Pedersen conductivity, as will be shown below, and accounts for the ability to use the 630.0-nm emission as a substitute for the Pedersen conductivity.
2.2. Pedersen Conductivity
 The Pedersen conductivity, σP, parallel to E but perpendicular to B, is defined as [Kelley, 1989]:
where [e] is the electron density, q is the electron charge, νi and νe are the ion and electron collision frequencies, and Ωi and Ωe are the ion and electron gyrofrequencies. As we are primarily concerned with the F-region component of σP in this paper, we can make quite a few simplifications to equation (2). First, above about 75 km, Ωe ≫ νe, while at the same time, in the plane perpendicular to B, the electrons are constrained to move perpendicular to any applied force. These two constraints allow us to drop the first term in the brackets of equation (2). In addition, above 150 km, Ωi ≫ νi. Thus we can simplify equation (2) in the F region to:
 All of the terms in equation (3) are straightforward parameters except for the ion collision frequency. Following Buonsanto et al. , we define the ion collision frequency in the F region to be
It is not readily evident that this equation should have the same dependence on [O2] and [e] that we see in the 630.0-nm emission. To demonstrate that this is the case, we assume that neutral densities exponentially decay with height and thus can be described by
where nz is the density at height z, n0 is the density at some reference height of z0, and H is the species dependent scale height given by:
We can now easily express [O]z and [N2]z in terms of [O2]z:
where HO, and are the scale heights for the individual neutral constituents (e.g., 26.5 km, 53.0 km, and 30.3 km, respectively, for T = 1000 K). The reference height used for [O]0, [O2]0, and [N2]0 for this study is 190 km. Substituting equations (9) and (10) into equation (6), we now have:
where the common term [O2] has been pulled out of the term in parentheses. In this form the dependence on both [e] and [O2] can be seen. However, the question remains: Is it reasonable to expect that all of the “extra” terms in equations (1) and (11) are somehow equivalent, allowing for a simple relationship between the 630.0-nm emission and the Pedersen conductivity to arise? As it turns out, this is the case in the ionosphere, as we empirically show below.
2.3. Modeling of the 630.0-nm Emission and Pedersen Conductivity
 To show that the 630.0-nm emission can be used as a surrogate for the Pedersen conductivity, we use the IRI-95 model [Bilitza, 1997] to obtain modeled plasma parameters ([e], Te, Ti) and the NRLMSISE-00 model [Picone et al., 2002], an extension to the MSISE model [Hedin, 1991], to obtain the neutral parameters ([O], [O2], [N2]). We assume that Tn = Ti. We present the results of using the parameters thus obtained in equations (1) and (6) in Figure 1, where the height profiles for both the 630.0-nm emission (thin line) and the Pedersen conductivity (thick line) are shown. The similarity between the two profiles is striking. Both peak at the same altitude and fall off at approximately the same rate above and below. There certainly are differences between the two (most notably the bump in the Pedersen conductivity's profile at 175 km), but on the whole the two share the same general characteristics.
 In Figure 2 we endeavor to demonstrate why the two quantities show such similar characteristics. Here we have plotted the 630.0-nm emission divided by [e][O2] versus σP divided by [e][O2] for a model run over one night. Each point has been color coded with the height used in the model. For the height range from about 190 km (black) to 320 km (light blue) the two exhibit a close to linear relationship. This is the same height range where the peak of [e][O2] typically occurs for nighttime conditions. Plots similar to that shown in Figure 2 for other nights show the same linear relationship.
 In practical circumstances, however, we do not have the height profiles of the 630.0-nm emission from which to calculate σP. However, using a photometer or an imager with the appropriate filter, we can measure the integrated line-of-sight emission, I6300. If a relationship between the two integrated quantities can be found, we could then substitute I6300 for the more important height-integrated Pedersen conductivity in the F-region. Before making this extrapolation, another subtlety must be taken into account. Although σP is a scalar quantity, the medium is anisotropic and it is the field line-integrated quantity that matters, not the height-integrated or line-of-sight quantity seen by the all-sky imager. To be able to view along the magnetic field lines, a ground -based optical instrument's look-angle must be equal to the magnetic field's dip angle in the thermosphere. For practical purposes, such as near field obstructions and increased atmospheric absorption at low elevation angles, look-angles less than 25° are not typically used. This consideration limits the range of latitudes where an optical field-aligned measurement can be made to magnetic latitudes poleward of roughly 13°. In the case of an all-sky instrument, although the entire image will never be field-aligned, as long as the imager is located poleward of 13° magnetic latitude, some portion of the image can be considered field-aligned. We defer for the moment a discussion of all-sky maps of ΣPF and concentrate on a local determination of the line-of-sight quantity.
 Unfortunately, the integrated forms of equations (1) and (11) do not lend themselves to straightforward analysis. So, to compare the two integrated quantities, we have modeled both the integrated 630.0-nm emission and the integrated Pedersen conductivity for nighttime conditions (between 2100 and 0400 LT) over a 2-year period (January 2000 to December 2001) for magnetic latitudes equatorward of 45° at all longitudes. On the basis of equation (11), we expect the ratio of the two quantities to have a dependence on the ratios of [O]/[O2] and [N2]/[O2] at our reference height (190 km). We thus perform a linear regression to fit the ratio of the integrated 630.0-nm emission to the height-integrated Pedersen conductivity that is dependent on the neutral densities at the reference height. On the basis of the 2 years of modeled nocturnal data, we find a best fit of:
The RMS difference between the modeled Pedersen conductivity and the 630.0-nm-derived conductivity is 0.271 mhos. In Figure 3a we present a scatter plot of the modeled Pedersen conductivity versus the airglow-derived conductivity. If no error existed in the estimation, this would be a straight line with a slope of one. In Figure 4a we present a comparison for a typical night (f107 = 171.5, f107a = 171.0, Ap = 6) over a midlatitude site corresponding to the location of the Arecibo observatory (18.34°N, 293.25°E). The agreement is quite good.
 If information on the height of the F layer is known, an improvement to equation (12) can be made. Taking into account hmF2, we find a best fit using the equation:
The RMS difference for this fit is 0.172 mhos. The modeled versus derived Pedersen conductivity is plotted in Figure 3b, while the comparison for a typical night is shown in Figure 4b. As can be seen in Figure 3b, the spread in the error using equation (13) is much less than when using equation (12). Thus if our imager is collocated with an ionosonde or images at both 630.0- and 777.4-nm are available to deduce the height [Makela et al., 2001], a marked improvement in the estimation of the ionospheric Pedersen conductivity can be made.
2.4. Conversion From Line-of-Sight to Field Line Integrated Quantities
 The important quantity to consider regarding the integrated Pedersen conductivity is the field line, rather than the line-of-sight or vertically integrated conductivity. What we have described above pertains to calculating the vertically integrated Pedersen conductivity from the vertically integrated 630.0-nm emission. As mentioned above, in practice we have measurements of the 630.0-nm emission integrated along many different line-of-sights for a single all-sky image. The technique to convert to a flat-fielded or height-integrated estimate has been described by Garcia et al. , and is the technique used here. These flat-fielded images can be used to estimate the height-integrated Pedersen conductivity using the methods described above, but a method to convert from height to field line-integrated conductivity is still needed.
 The problem in question is essentially the inverse problem encountered in using Global Positioning System (GPS)-derived estimates of the total electron content (TEC). In the GPS problem the measured quantity is the TEC along the line-of-sight from the receiver to the satellite, whereas the more useful quantity is the vertical TEC. Different methods have been developed to convert from line-of-sight TEC to vertical TEC; however, most employ the simple thin-shell approximation [e.g., Lanyi and Roth 1988]. For our purposes here we will use this simple single-shell approximation for converting from height to field line integrated Pedersen conductivity.
 In the simple shell approximation it is assumed that all of the total electron content (or in our case, the Pedersen conductivity) is located in a single thin shell at an altitude, H, above the Earth's surface. The problem is in finding the relation between a quantity measured vertically through the shell, V, and at an arbitrary angle, θ, through the shell, S(θ). The slant factor, M(θ), which relates the two, is derived from simple geometry and can be expressed as
where Re is the radius of the Earth. Using this factor, the relation between the vertical and line-of-sight quantity becomes
In the case of converting from the vertical Pedersen conductivity to the field line-integrated Pedersen conductivity, θ will become the dip angle of the magnetic field at the pierce point of the current look-angle at the shell height. The very simple relation described by equation (15) will be used below to present maps of the field line-integrated Pedersen conductivity.
3. Comparison of the 630.0-nm Emission and Pedersen Conductivity: Experimental Test
3.1. September 1999
 To study how the technique works when applied to actual data, we turn to the Combined Ionospheric Campaign held in September 1999 (e.g., J. J. Makela et al., Mid-latitude plasma and electric field measurements during Space Weather Month, September 1999, submitted to Journal of Atmospheric and Solar-Terrestrial Physics, 2003, hereinafter referred to as Makela et al., submitted manuscript, 2003; M. C. Kelley et al., Further studies of the Perkins stability during Space Weather Month, submitted to Journal of Atmospheric and Solar-Terrestrial Physics, 2003b). The Arecibo incoherent scatter radar ran for four out of five consecutive nights from 9–14 September 1999 and operated for a continuous 54-hour run from 15–17 September 1999. In addition, the Cornell All-Sky Imager (CASI) operated during this period but due to inclement weather, coincident data were collected only on three nights (14–15, 15–16, and 16–17 September). These nights will be our focus here.
 Unfortunately, during this time, CASI was not calibrated, so only the relative intensity of the 630.0-nm emission was recorded. To obtain the absolute intensity of the 630.0-nm emission, we model the expected emission based on the ISR-measured electron densities and a background neutral atmosphere from MSIS. The measured intensities were then normalized to these values in a way to minimize the RMS error. The images were flat-fielded according to the technique described by Garcia et al. . The calibration was performed on 14–15 September and was assumed to hold for the subsequent nights shown below.
 Having thus calibrated the all-sky images for 14–15 September, we wish to compare the airglow-derived ionospheric Pedersen conductivity and conductivity derived using the electron densities from the ISR for the following two nights. Only data obtained by CASI corresponding to the look-direction of the Arecibo ISR are used for this comparison. The results for the two nights using both equations (12) (top panel of each plot) and (13) (bottom panel of each plot) are shown in Figure 5. In using equation (13), the height of the F layer used was obtained from the ISR data. The agreement on each night is quite good. The RMS error, using each method for each night, is shown in Table 2. The errors on 16–17 September are significantly higher than we expect based on the modeling performed above. This result is possibly due to the significant gradients in electron density present on this night (Makela et al., submitted manuscript, 2003) or due to the added uncertainty from the calibration process described above. We believe, though, that the RMS differences seen on these two nights are still very reasonable and show that this technique is indeed viable.
Table 2. RMS Errors on Each Night Using RMS 1 and Equation (13), RMS 2
RMS 1, mhos
RMS 2, mhos
 Taking full advantage of the immense amount of data provided by an all-sky image, we present a two-dimensional map of the field line integrated Pedersen conductivity in Figure 6. Here, we have used equation (13) to calculate the airglow-derived Pedersen conductivity. As observations of both the 630-0-nm and 777.4-nm emission were made on this night, we can use the topographic technique of Makela et al.  to derive the height of the F layer. The estimate of the vertically integrated Pedersen conductivity was converted to field line integrated conductivity using equation (15). This conductivity map covers an area of approximately 1000 km × 1000 km. The area of the map corresponding to where the local height-integrated conductivity is equivalent to the field-aligned conductivity and where we expect the least amount of error from the conversion between the two quantities is denoted by the oval region to the southeast of Puerto Rico. In this image we see an increase in the integrated Pedersen conductivity to the south. As seen in the work by Makela et al. , there was both an increase in electron density and ionospheric height to the south of Arecibo on this night, which tend to counteract each other in the 630.0-nm emission. The increase in Pedersen conductivity to the south must be dominated by the density increase in this case.
3.2. February 1998
 To study the usefulness of this technique during a disturbed time, we look at data obtained on the night of 17–18 February 1998. This night of intense midlatitude spread F has been studied extensively by Kelley et al.  and Swartz et al. . The 630.0-nm emission for this night, as described by Kelley et al. , was characterized by a gradual intensifying of alternating bright and dark bands, aligned from the northwest to southeast. The bands then began to drift northeastward from about 2130 until 2300, at which time they began to slow down and reverse direction. By 2330 the bands had completely reversed direction and began to drift southwestward until the imager turned off at 0200 LT. These trends are confirmed by the Fabry-Perot interferometer that was also running on this night. The radar data for this night is equally impressive. Large Doppler shifts were observed by two VHF radar interferometers and very short-duration, line-of-sight velocities of 150 m/s were observed by the Arecibo ISR [Swartz et al., 2000].
 Two field line integrated Pedersen conductivity maps are presented in Figure 7. Unfortunately, no images were taken of the 777.4-nm emission, so height information is not available for this night, as both the 630.0-nm and 777.4-nm emissions are needed to derive the F-layer height [Makela et al., 2001]. Consequently, equation (12) is used to estimate the height-integrated Pedersen conductivity before equation (15) is used to convert to the field line-integrated quantity. This night shows the classic signatures of the Perkins instability. Specifically, we see bands of high and low field line integrated Pedersen conductivity aligned from the northwest to southeast. The ratio of the conductivity in one of the high conductivity bands to the low conductivity bands reaches about four on this night.
 In a recent study by Kelley and Makela , an explanation for the direction of motion for midlatitude F-region structures was proposed. The proposed mechanism depended upon polarization of the dark bands seen in 630.0-nm emissions. In that study the authors based their assertion that the bands polarized on ISR observations of the depleted electron density inside the dark regions. We have shown here that the dark regions seen in 630.0-nm emission are indeed regions of low field line-integrated Pedersen conductivity and thus subject to polarization from an applied electric field or neutral wind.
 In the technique above, we convert from the height to field line integrated Pedersen conductivity by employing a thin-shell model. Although simple and straightforward, it is doubtful that this is the most accurate method to employ. The method does not take into account the declination of the magnetic field in relation to the azimuth of the original line-of-sight measurement. For example, the measurements poleward of the observing site (to the north in the cases presented above) are along look angles that are nearly perpendicular to the magnetic field. They are crossing many individual flux tubes with increasingly lower integrated Pedersen conductivities, making a conversion to a field line-integrated quantity extremely difficult. Furthermore, the thin-shell approximation assumes that all of the local Pedersen conductivity is concentrated at a single height. This is obviously a faulty assumption, which is quickly evident from examining Figure 1 and noting that the Pedersen conductivity has a scale height of approximately 50 km. This is not as great a concern for the original look angles that are close to being parallel to the magnetic field lines, since the method of image flat-fielding, followed by converting to the field line-integrated quantity, essentially undoes itself. However, this will definitely introduce error into the estimate of the Pedersen conductivity for the portions of the image where the original look angles are far from parallel to the magnetic field. These problems could be mitigated somewhat by employing a multiple camera system, deployed throughout a region. In this way, tomographic methods could be employed, significantly reducing these errors.
 The technique proposed in this paper does not result in estimates of the Pedersen conductivity that are as accurate as those derived from ISR measurements. However, we feel that the benefits of having a two-dimensional map of the conductivity at a relatively high time resolution make this method useful. Whereas an ISR can provide an estimate only at a single point for a given time, the maps derived here cover an area 1000 km × 1000 km. A camera system dedicated to estimating the Pedersen conductivity could produce these maps at a time resolution on the order of 5 min. In addition the camera systems that are needed to measure the required emissions are relatively inexpensive and quite portable, making this technique even more attractive.
 JJM is supported by a National Research Council Research Associateship Award at the Naval Research Laboratory. Work at Cornell is supported by the Office of Naval Research under grant N00014-03-1-0243 and the National Science Foundation under grant ATM-0000196. The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation.
 Arthur Richmond thanks Michael Kosch and Yogeshwar Sahai for their assistance in evaluating this paper.