Radio Science

Simultaneous inversion of total electron content and UV radiance data to produce F region electron densities



[1] The High Resolution Airglow and Aurora Spectroscopy (HIRAAS) experiment was launched aboard ARGOS on 23 February 1999. The HIRAAS experiment operated from mid-May 1999 through March 2002. One of the HIRAAS instruments, the Low Resolution Airglow and Aurora Spectrograph (LORAAS), gathered limb scans over the 750–100 km altitude range of the 911-Å emission during the daytime and the O I 1356 Å emission at night; these emissions are useful for characterizing the ion density distribution in the F region. The Coherent Electromagnetic Radio Tomography (CERTO) experiment, a coherently emitting radio beacon operating at 150 and 400 MHz, also flew on the ARGOS. The slant total electron content (TEC) between ARGOS and the ground was measured, using the CERTO beacon emissions, by a receiver located at the Naval Research Laboratory during early 2001. During the mission life of ARGOS, the ARGOS and TOPEX/Poseidon satellites occasionally crossed paths, permitting additional validation of the ARGOS measurements against TOPEX vertical total electron content measurements. We present a comparison of the UV-derived TEC and the radio beacon–derived TEC over the Naval Research Laboratory during January–April of 2001, based on LORAAS and CERTO measurements; we also present the electron densities derived by simultaneously inverting both the UV radiances and the CERTO-derived TEC. These results are validated against ionosondes. The TOPEX and UV measurements are also inverted tomographically and are used to demonstrate enhanced spatial resolution of the ionospheric reconstructions.

1. Introduction

[2] Ultraviolet imaging of the Earth's limb has proven to be a robust and accurate means of determining the global distribution of electrons in the F region ionosphere. Recent measurements by the Advanced Research and Global Observing Satellite (ARGOS) [Dymond et al., 2001a, 2001b; Coker et al., 2004], the Global Ultraviolet Imager instrument on the NASA TIMED satellite [DeMajistre et al., 2004], and the Special Sensor Ultraviolet Spectrographic Imager (SSUSI) and Special Sensor Ultraviolet Limb Imager (SSULI) instruments aboard the Defense Meteorological Satellite program satellites have provided measurements of the nighttime electron density in the F region. Additionally, the ARGOS satellite measurements have demonstrated the feasibility for daytime ionospheric sensing using the 911-Å emission produced by radiative recombination of electrons and O+ ions [Dymond et al., 2001b]. However, the main drawback of ultraviolet limb sensing is the long horizontal lines of sight through the ionosphere which tend to average out any density gradients along the instrument's line of sight. Because of this line-of-sight averaging, direct inversion of limb measurements using Abel inversion schemes, which assume spherical symmetry, can result in significant error in regions where high gradients exist, such as in and near the Appelton anomalies. To mitigate the effects of ionospheric gradients, tomographic inversion schemes have been developed; these schemes have been demonstrated and validated and have been shown to substantially reduce the reconstruction errors in high-gradient regions [Dymond and Thomas, 2001; Coker et al., 2004; Kamalabadi et al., 1999]. However, a fundamental limit to the ability of tomographic reconstruction schemes that rely solely on limb scan data is the limb scan sample spacing, which is typically 5°–6°. Thus ionospheric reconstructions in regions of high-density gradients will only show structures that are larger than about two limb scans across [Coker et al., 2004]. Bernhardt et al. [1998, 2001] suggested that the simultaneous inversion of UV limb scan data with coincident radio tomography data would produce higher-fidelity ionospheric reconstructions, especially in regions with large electron density gradients.

[3] In this work, we explore the injection of higher-resolution spatial information via the use of vertical or near-vertical total electron content measurements. Figure 1 shows the limb viewing lines of sight and the near-vertical lines of sight of the radio beacon-beacon receiver system overplotted on an ionosphere. The multiple intersections of the various lines of sight through the ionosphere permit tomographic reconstruction of the ionospheric electron density field. In the regions where the UV and radio lines of sight intersect, a higher-fidelity reconstruction is possible because of the orthogonality of the lines of sight and the abundance of intersections. We demonstrate the increased fidelity of the UV-radio reconstructions compared to UV-only reconstructions.

Figure 1.

Radio beacon and UV lines of sight. This is a representation of the satellite-to-ground radio beacon lines of sight (dash-dotted curves) and the overlapping ultraviolet limb scan lines of sight (solid curves). The straight lines of sight become curves in this type of projection. A background ionosphere is superimposed for scale (dashed contours with spacing 5 × 105 cm–3). For clarity, every 30th limb scan line of sight and every 20th radio beacon line of sight are shown. The satellite is moving from the left to the right in this representation, with the UV sensor viewing toward the left. North is toward the left. The roughly oval-shaped region at –1.4 × 104 km is the northern crest of the Appelton anomaly.

2. Data Analysis

[4] The principal data source used in this work is ultraviolet limb scans. A limb scan is essentially a vertical sounding of the ionosphere. A limb scanner views the Earth's horizon and sweeps its field of view above the disk of the Earth while measuring the ultraviolet radiance, which, depending on the emission, is related to a physical property of the ionosphere; the ultraviolet limb radiance in this work is proportional to the integral of the square of the electron density along the instrument's line of sight through the ionosphere. The Low Resolution Airglow and Aurora Spectrograph (LORAAS) on ARGOS observed the ionosphere by scanning the Earth's limb looking aft of the vehicle; the LORAAS is a copy of the SSULI instruments designed to fly on the Defense Meteorological Satellite Program (DMSP) satellites [McCoy et al., 1994]. The ARGOS satellite orbited at an altitude of ∼830–850 km in a Sun-synchronous (fixed solar local time) orbit, at 98° inclination. A limb scan consisted of sweeping the instrument's field of view from essentially the satellite's local horizon to the edge of the hard disk covering angles 10°–27° below the satellite's local horizon; thus a limb scan covered tangent point altitudes from 750 to 100 km. A limb scan normally takes approximately 90 s, followed by a rapid flyback of the field of view. The LORAAS gathered a limb scan approximately every 5°–6° of latitude. The limb-viewing geometry enhances the airglow signals by as much as a factor of 20 over a nadir-viewing geometry because of the long path through the atmosphere near the tangent point. This signal enhancement is not without a price, however. The limb-viewing geometry effectively integrates along the line of sight so that electron density gradients are averaged out. When viewing either ahead or behind the satellite, the limb-scanning approach samples a given volume of the ionosphere and then resamples that same volume; thus a given volume in the ionosphere is viewed from slightly different aspects. This oversampling permits some characterization of the along-track gradients, permitting reconstruction of the electron density maps.

[5] In this work, we will concentrate on using the 911-Å emission, which is produced solely by radiative recombination. The 911-Å intensity, I911 (in Rayleighs), at look angle ϕ is given by

equation image

where ne is the electron density at altitude z, nion is the O+ density at z, s is the path length from the observer, ds is the differential path length, and α911 is the radiative recombination rate coefficient, which is 3.5 × 10−13 cm3 s−1 at 1160 K [Meléndez-Alvira et al., 1999]. The radiative recombination rate coefficient scales as Te−1/2, where Te is the electron temperature. We assume that the ionospheric electron temperature is isothermal at the electron temperature at 350 km given by the Reference Ionosphere [Bilitza, 1990]. This assumption is rarely valid, but we have found that it does not affect the retrievals. The retrieved peak density (nmF2) is fairly insensitive to temperature as it is proportional to the square root of the radiance, which scales as the radiative recombination rate coefficient (a Te−1/2 dependence). The net effect is that the nmF2 scales as Te−1/4, which is a weak dependence.

[6] The other source of data we used in our model was the total electron content, TEC(ϕ). This is just the line-of-sight integral of the electron density, namely,

equation image

The constant, 10−12, converts from electrons per centimeter squared to total electron content units (TECU, 1 TECU = 1012 el cm−2), ne(z(s)) is the electron density in cm−3, and ds is the line element in cm. The TEC data come from two sources: TOPEX vertical TEC measurements [Imel, 1994] or near-vertical relative TEC measurements acquired by a radio beacon-receiver combination.

[7] The TOPEX absolute TEC data are derived via the use of a two-frequency altimeter operating at 13.6 and 5.6 GHz. The TOPEX is in a 1336-km altitude 66° inclination orbit. The altimeter measurements are made only over water at a 1-s time spacing for a spatial sampling of ∼6 km. The altimeter lines of sight are very nearly vertical. As the TOPEX orbital altitude is greater than the ARGOS orbital altitude, we allowed for a potential TEC bias to account for the TEC that occurred between the satellite's orbital altitudes, 850 and 1336 km. This TEC bias was a retrieved parameter during the joint TEC-UV inversions.

[8] The other source of TEC data we used was relative TEC measurements from a dual-frequency radio beacon on the ARGOS satellite and a single receiver at the Naval Research Laboratory in Washington, D. C. The ARGOS beacon radiates coherently at 400 and 150 MHz. The relative TEC is determined from the observed phase data by removing the 2π ambiguities. The TEC is relative to the overhead point. The observation angles vary over the range of about 40°. When fitting the relative TEC data, the TEC bias required to convert the relative TEC to an absolute TEC is a retrieved parameter of the joint TEC-UV inversions.

[9] We parameterize the ionosphere by placing uncoupled Chapman layers [Chamberlain and Hunten, 1987] every 5°–6° of orbit phase angle along the satellite's orbit; this spacing matches the limb scan sample spacing. We also assume that the electron and O+ densities are equal, which is an accurate assumption below the H+/O+ transition height in the F region. Each Chapman profile uses three parameters to characterize the ionosphere: the altitude where the density peaks, hmF2; the density at the peak, nmF2; and the O scale height, HO, which is one half the plasma scale height for the form of the Chapman layer given below. The Chapman function for describing the O+ density, nion(z), is

equation image

where z is the altitude. The variation of the electron density between the Chapman profiles is characterized by using a bicubic interpolating polynomial; the Chapman profiles are otherwise uncoupled. When the signal-to-noise ratio is very high, the profiles naturally couple to produce a smooth solution. Under typical ionospheric conditions and typical signal-to-noise ratios, a smooth solution is achieved through the addition of a side constraint that enforces smoothness of the solution. This is accomplished by requiring the electron density solution to be “regular” or smooth in the first derivative [Dymond and Thomas, 2001]. This regularization can sometimes suppress regions of high gradient [Coker et al., 2004] by forcing the solution to be too smooth. However, we have found that in most cases, regularization produces adequate solutions under typical gradient conditions observed during the daytime. The fitting process iteratively adjusts the Chapman parameters for the profiles to determine the best fit to the data subject to the smoothness constraint.

[10] The inversion algorithm uses the iterative Levenberg-Marquardt scheme [Press et al., 1992] to seek the maximum likelihood estimate (minimum of the chi-square statistic) of the ionospheric parameters on the basis of the fit of the forward model to the data. The inversion is initiated by using an initial guess at the Chapman parameters used to calculate the two-dimensional electron density structure of the ionosphere. These electron densities are then squared, and the line-of-sight integrals are evaluated to produce the predicted intensities; the TECs are also calculated at this time by integrating through the density field. Then, the “goodness of fit” is evaluated by minimizing a generalization of the χ2 statistic [Dymond and Thomas, 2001], X2:

equation image

where dj represents the data, UV radiances, and near vertical TECs; yj(μk) represents the fit to the data; μk is the vector of model parameters; σj represents the variance in the data; L is the regularization operator; and W is the regularization weight. The regularization operator that we use is the density field minus the smoothed version of the density field; the smoothing is a 3 × 3 boxcar average of the electron density. This version of the regularization operator yields a first derivative along latitude that has been averaged over three altitude cells. A good fit occurs when the X2 changes by less than 0.1% between iterations. If the fit is deemed to be “good,” the calculation terminates; otherwise, new values for the model parameters are chosen, and the whole process is repeated. This form of the generalized chi-square is designed to achieve a balance between the conventional chi-square goodness of fit (first term in equation (4)) and the smoothness of the solution (second term in equation (4)) [Press et al., 1992]. During the fitting procedure, W is held fixed, and the best fit solution is found. To determine the optimal value for W that produces the best compromise fit that balances the solution smoothness and goodness of fit, we first fit the data without any smoothness constraint imposed (W = 0) and then evaluate the reduced chi-square (chi-square divided by the number of degrees of freedom allowed in the fit). This usually produces an unusually rough fit, but one with a reduced chi-square that is nearly zero. We then increase the regularization weight and refit the data and again evaluate the reduced chi-square. This process is repeated until a fit with a reduced chi-square of approximately unity is found; this procedure has been found [Dymond and Thomas, 2001] to produce fits that are consistent with those found using the L curve criterion [Schimpf and Schreier, 1997]. Our approach to regularization is adopted from Press et al. [1992], where it is called “zeroth-order regularization.” Our algorithm is nonlinear, since the 911-Å emission is proportional to the square of the electron density. Once the best fit values have been determined and the model covariance matrix has been calculated, the variances of the densities at each altitude can be calculated using standard techniques for error propagation [Bevington, 1969].

3. Results

3.1. UV Limb Scan and Beacon TEC (UV-BTEC)

[11] The data presented here were acquired by the LORAAS and the radio beacon receiver at the Naval Research Laboratory (NRL, 38.6°N, 77°W) during January–April 2001. Figure 2a shows the TEC data and fit, and Figure 2b shows the reconstructed electron density. The receiver measured the TEC relative to the minimum TEC when the beacon made its closest approach to NRL. This TEC bias was determined during the joint TEC-UV fitting procedure and was added to the relative TEC to produce the absolute TEC. The asterisk in Figure 2b represents the hmF2 measured by the Millstone Hill ionosonde (41°N, 71°W), 271 km, and the ionosonde nmF2 was 1.4 × 106 cm−3; the UV-BTEC retrieved nmF2 and hmF2 were 1.5 × 106 cm−3 and 286 km, respectively. The uncertainties in the retrieved peak densities are ∼15%, and the uncertainties in the retrieved peak height are ∼25 km. In light of these uncertainties, the agreement is excellent. Figure 2c shows the contour map resulting from the UV-only reconstruction. The northern crest of the Appelton anomaly is not obvious in Figure 2c, although it is evident in the UV-BTEC contour map. This was caused by the UV-BTEC reconstruction pulling the peak height and peak density downward south of the beacon receiver to better match the observed TEC. The UV-only reconstruction reproduced the peak height observed by the ionosonde (Figure 2e). Figure 2d shows that the UV-only reconstruction overestimated the peak density in the region above the Naval Research Laboratory by ∼20%. Figure 2f shows that the UV-BTEC reconstruction pulled the scale height below that derived by the UV-only reconstruction to better match the observed beacon TEC. Table 1 shows the four comparisons made during January–April 2001; all show excellent agreement between the UV-BTEC and ionosonde measurements. We found, however, that the ionosonde-inferred TEC was somewhat lower than what we reconstructed. This bears further research but is most likely due to either the UV-BTEC or ionosonde inferring an incorrect slab thickness for the ionosphere. Comparison of the bottomside ionosonde trace with the UV-BTEC profile in the Millstone Hill region should shed some light on this disagreement. However, the information injected by the beacon TEC data better constrained the UV-BTEC reconstructions compared to the UV-only results.

Figure 2.

UV-BTEC reconstruction results. (a) Measured (solid curve) and reconstructed (dashed curve) total electron content from the ARGOS pass on 18 March 2001; the TEC bias retrieved during the fitting procedure has been added to both to produce the absolute TEC. (b) Reconstructed electron density contour map from the UV-BTEC reconstruction (units are cm–3) covering –5° to 60° latitude. The asterisk indicates the peak height measured at Millstone Hill, Massachusetts, and the peak density measured by the ionosonde is 1.4 × 106 cm–3. (c) Electron density contour map from the UV-only reconstruction; as in Figure 2b, the asterisk indicates the ionosonde peak height. In both Figure 2b and Figure 2c, the dashed curve indicates the retrieved peak height. The UV-TEC reconstruction shows an improved reconstruction of the electron density in the vicinity of the northern Appelton anomaly (∼10°N). The UV-only reconstruction shows weak variation northward of the Appelton anomaly. (d) Comparison of the UV-only (dashed curve) and UV-BTEC (solid curve) nmF2 results. (e) The hmF2 results. (f) Scale height (1/2 plasma scale height) results.

Table 1. Results of Four Inversions Using the UV-BTEC Algorithma
DateUV-BTEC nmF2, 106 cm−3MH nmF2, 106 cm−3UV-BTEC hmF2, kmMH hmF2, kmUV-BTEC TEC, TECUMH TEC, TECU
  • a

    The agreement between the UV-BTEC algorithm results and the Millstone Hill (MH) ionosonde measurements is excellent.

8 Jan 20011.51.428627144.432.3
22 Jan 20011.51.730428152.037.7
5 Feb 20011.71.630227648.833.7
17 Mar 20011.31.531229443.437.1


[12] The data presented were obtained on 2 December 1999. To show how the vertical TEC increases the fidelity of the reconstructions, we fit the UV data with and without the TOPEX TEC data. Figure 3a shows the UV radiance map that was fit. Figures 3b and 3c show the reconstructed ionospheres; Figure 3b shows the UV-only result, and Figure 3c shows the UV-TTEC result. The most striking aspect when Figures 3b and 3c are compared is the greater slab thickness evident in the Appelton anomalies seen in Figure 3c. Second, the locations and densities in the anomalies do not differ significantly from each other in the two reconstructions. We had expected to see the UV-TTEC algorithm produce a greater variation of electron density between the Appelton anomalies than the UV-only inversion. We also expected to see that the UV-only algorithm would reconstruct the vertical distribution of the electrons as accurately as the UV-TTEC because the TEC measurements add horizontal information and little vertical information. This was not what was observed. Figures 4a–4c show how the retrieved ionospheric parameters compare with and without the TOPEX TEC in the fit, and Figure 4d shows the improvement of the fit to the TOPEX-measured TEC. Figures 4a and 4b indicate that both algorithms derived similar latitudinal variations of the nmF2 and hmF2, respectively. Figure 4c, however, indicates that the UV-only algorithm did not accurately reconstruct the topside scale height or slab thickness. When the TOPEX data were included, the UV-TTEC algorithm more accurately adjusted the scale height variation to match the measured TOPEX TEC. This was a surprise, as the vertical distribution of the UV radiance was thought to be the strength of the measurement technique. The similarity of the latitudinal nmF2 and hmF2 variations means that the most important information used in the UV-only inversion came from near the peaks of the limb profiles. Although the TOPEX TEC data provided additional horizontal information, they really helped better constrain the topside scale height.

Figure 3.

UV-TTEC inversion results. (a) Ultraviolet radiance image. (b) Electron density map from the UV-only inversion. (c) Electron density map from the UV-TTEC inversion.

Figure 4.

UV-TTEC derived parameters. (a) Comparison of the nmF2 values derived during the UV-only inversion and the UV-TEC inversion. (b) Peak height comparison. (c) Scale height comparison. (d) Comparison of the retrieved TECs.

4. Summary

[13] We presented results of a new algorithm for simultaneously inverting near-vertical total electron content measurements and ultraviolet limb radiances. As expected, this algorithm showed improved performance in regions where the electron density gradient is large. We applied the technique to the inversion of radio beacon-receiver measurement of the relative TEC and found good agreement of the derived density field with coincident ionosonde measurements. Application of the algorithm to inversion of UV- and TOPEX-derived TEC showed improved performance in the region of the Appelton anomalies and an improvement in the specification of the ionospheric slab thickness.


[14] This work was supported by the Office of Naval Research.