The Tiny Ionospheric Photometer: An Instrument for Measuring Ionospheric Gradients for the COSMIC Constellation

We describe the specifications for an ultraviolet radiometer for mea­ suring the F-region electron density gradients from the Constellation Ob­ serving System for Meteorology, Ionosphere, and Climate (COSMIC). We also present a technique for determining the two-dimensional structure of the ionosphere using the measured ionospheric gradients inf erred from observation of the radiative recombination emission at 1356 A in conjunc­ tion with occultations of Global Positioning System satellites observed from the COSMIC satellites. Our scheme uses a nadir viewing UV photometer to characterize the F-region gradients while obtaining altitude information about the F-region from the GPS occultation measurements. We present the results of simulations that demonstrate the applicability and accuracy of the technique and observational concept. (


INTRODUCTION
The use of total electron content measurements acquired during occultation of the Global Positioning Satellites (GPS ) by a receiving platform in low Earth orbit has recently been dem onstrated as a viable technique for determining the ionospheric electron density (Hajj et al., 1994).The cornerstone of the technique is use of the Abel inversion to convert the total electron content measurements made by the GPS receiver into electron density profiles.This technique assumes that the ionosphere is spherically symmetric with no horizontal density gradients.The Abel technique works well under certain viewing conditions but its accuracy is generally limited by the spherical symmetry assumption.When there are substantial iono-spheric density gradients present, the Abel inversion technique yields poor results due to an inability to handle the gradients (Hajj et al., 1994).As the GPS occultations occur sporadically around the globe, it is difficult to use them in a systematic way to gather information about the global structure of the ionosphere.Thus, alternative techniques must be used to infer the gradients and to account for them in the inversion process.
Several techniques have been proposed for inferring the ionospheric gradients.On the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC), the GPS occultation measurements will be complemented by ultraviolet radiometric measure ments, measurements of the total electron content between the satellites and ground using computerized ionospheric tomography receivers, and ground-based GPS total electron con tent measurements.The use of UV radiometers provides an accurate measurement of the gradients on a global basis as it does not rely on ground-based receivers.
Naturally occurring ultraviolet and visible emissions from the night sky have been used since the late 1960' s as means of determining the densities of electrons and o+ ions in the F region ionosphere.The emissions are produced by radiative recombination of o+ ions and electrons to produce atomic oxygen in an excited state that subsequently decays by emitting a photon.These emissions have been observed at visible wavelengths (7774 and 8446 A) from the ground (Tinsley et al., 1973;Tinsley and Bittencourt, 1975) and at ultraviolet wavelengths (911, 1304, and 1356 A) from space (Hicks and Chubb, 1970;Barth and Shaffner, 1970;Chakrabarti et al., 1984;Feldman et al., 1992).The use of the nighttime 0 emissions to remotely sense the F-region electron density is described by Tinsley and Bittencourt (1975), Chandra et al. (1975), Dymond et al. (1996Dymond et al. ( , 1997)), and Meier (1991).The UV emissions are of most interest for space based ionospheric sensing.The Earth's atmosphere absorbs all UV emissions, with wavelengths less than 1800 A, at an altitude of approximately 90 km.Thus, there is no UV background.The Earth's atmosphere is transparent to the visible emissions and, therefore, there is a visible background due to city lights, forest fires, thunderstorms, noctilucent clouds, and reflection of moon light; these background emissions would require measurement and subtraction from the nightglow signal.This background subtraction can lead to large uncertainties in the derived airglow signal.The problems caused by background emission are far worse on the dayside because the background emissions can originate above 100 km.
The radiative recombination emissions cannot be used for ionospheric sensing on the dayside, even though the emissions are always present.The 0 emissions, with the exception of the 911 A emission, are excited by photoelectron impact on the dayside, which renders them insensitive to the ionospheric state.The 911 A emission could, in principle, be used for day time ionospheric sensing, as it is not affected by photoelectron impact.However, during the daytime, the spectral region lying near the 911 A emission is contaminated by emission from neutral and ionized nitrogen; this effectively renders the 911 A measurements useless for day time ionospheric sensing.
We present the results of a study to demonstrate the use of UV radiometry with GPS occultations for the COSMIC program.The COSMIC program is being built by the National Space Program Office (NSPO) of the Republic of China (Taiwan), the University Consortium for Atmospheric Research (UCAR), the Jet Propulsion Laboratory, and the Naval Research Laboratory.We describe the results of a design study undertaken to specify the desirable characteristics of an ultraviolet radiometer capable of accurately measuring the nighttime iono spheric gradients.We also describe an algorithm that can be used to simultaneously invert the UV nadir data and the GPS occultation data.This algorithm can accurately retrieve the elec tron density distribution over the region where the occultation occurs regardless of the gradi ents.

RADIATIVE RECOMBINATION PROCESS
There are several candidate emissions that can be used to determine the electron density in the nighttime ionosphere.These emissions occur at 911, 1304, and 1356 A. The 91 1 A is the easiest of these three emissions to interpret.The emission is optically thin and therefore no radiative transport modeling is required.The emission is produced solely by radiative recom bination.The 1356 A emission is the result of a spin forbidden transition in atomic oxygen and as such is largely optically thin.However, although the transition is forbidden, the large abundance of atomic oxygen in the earth's thermosphere causes the optical depth for resonant scattering of this emission to reach unity near 100 km, which requires some radiative trransport modeling for accurate interpretation.The 1304 A emission is produced by an allowed transi tion in atomic oxygen.Thus, this emission is optically thick with a vertical optical depth exceeding several thousands near 100 km.Interpretation of the 1304 A requires extensive radiation transport modeling.This makes it difficult to use for ionospheric sensing.In addi tion to the radiative recombination process, the 1304 and 1356 A emissions can also be pro duced by neutralization of o+ by o•.This complicates the use of these emissions as the density of o• is related to the density of 0. We have found that this complication is not important as the 0 density gradients are much smaller than the o+ gradients.Thus, an algorithm that uses the gradient in the UV intensity rather than the intensity is relatively insensitive to the 0 density gradient, as is presented below.
The 911 A emission is easily modeled and interpreted.The volume emission rate for the emission is proportional to the product of the electron and ion densities.In the nighttime F region ionosphere, the electron and Q+ densities are nearly equal.The vertical UV radiance (Feldman et al., 1992), /911, is given by: z, , where n0 is the electron density at altitude z, n o + is the Q+ density at z, dz is the differential path length from the observer, Z,, is the satellite altitude, and a911 is the radiative recombination rate, which is 3.5 x 10-13 cm3 s•1 at 1160 K (Melendez-Alvira et al., 1999).The constant, 10•6, converts the radiance from units of photons cm•2 s•1 to Rayleighs.(A Rayleigh is the number of photons emitted per second into 4 7C steradians by a column with a 1 cm2 cross-section ex pressed in megaphotons; typical airglow radiances range between 0.1 and 105 Rayleighs.)We assume that the ionospheric electron temperature is isothermal at 1160 K.This assumption is rarely valid, but we have found that it does not affect the retrievals.Equation ( 1) can be rewritten to express the overall radiance in terms of the peak electron density (and hence the peak Q+ density by charge neutrality) in the F-region, nmF2.Thus the retrieved nmF2 is pro portional to the square root of the intensity / 911 and is inversely proportional to the radiative recombination rate coefficient.Since the radiative recombination rate coefficient is propor tional to Te-112, the retrieved nmF2 scales as Te114, which is a very weak dependence on the electron temperature.
The 1356 A emission is slightly more complicated than the 911 A emission.The emis sion shows mild opacity effects due to multiple scattering of the radiation by atomic oxygen in the thermosphere.The emission is also a doublet emission originating in a singlet upper state with wavelengths 1356 and 1358 A. The two lines have slightly different opacities that must be included in the model.The volume emission rate, .s0(z),for the emission is given by (Tinsley and Bittencourt, 1975): where r is the branching ratio for the 1356 or 1358 A line (0.79 1 and 0.209, respectively, (Meier, 1991)), a1356 is the radiative recombination rate 7.5 X 10-13 cm-3 s-1 (Melendez-Alvira   et al., 1999), /31356 is the fraction of neutralizations that produce atoms in the 5 S state, 0.54, and the coefficients K1 K2, and K3 are 1.3 x 10-15, 1. x 10-1, and 1.4 x 10-1 0, respectively, all in units of cm3 s-1 (Tinsley and Bittencourt, 1975).The relevant reactions and their rates summarized in Table 1.To calculate the volume emission rate including multiple scatter ing, .s(z ) , the following integral equation is solved (Strickland and Rees, 1974;Strickland, 1979;Anderson and Meier, 1985; and Meier 199 1): Zmil:\ .s(z ) = .s0(z) + n0(z )<Y J .s(z ')H( i r (z ) -r (z ')/, l t(z )-t(z ')j )dz ', where CY is the line-center scattering cross-section (2.499 x 10-18 cm2 and 1.242 x 10-18 cm2 for the 1356 and 1358 A lines, respectively (Meier, 1991)), r is the vertical resonant scatter ing optical depth, t is the vertical pure absorption optical depth, and His the Holstein function.The vertical optical depths for scattering anc;!, pure absorption are given by: r(z )=u Jn0 (z ')dz 1, where u;:" is the absorption cross-section for02 (7.6 X 10-18 cm2 and 8.0 X 10-18 cm2 for the 1356 and 1358 A lines, respectively, at 1160 K taken from Wang et al., (1987)) and n 02 is the density of 02, the only absorber of the 1356 A radiation.The Holstein H function is given by: where xis the photon's frequency, e-x is the Gaussian line shape appropriate to a Doppler CX.1Js6=7.3xl0-13(1160trer112cm3 s• 1 Melendez-Alvira et al.  and Stegun, 1972).The H function is proportional to the probability that a photon will propa gate from region z', z' + dz' to the region z, z + dz.
A variety of approaches have been used to solve the integral equation, 3.In this work, the integral equation has been solved by A iteration (Duderstadt and Martin, 1979).In this scheme, the iteration is started using £0 (z) as the first guess at the solution.The new scattered volume emission rate is calculated and substituted into the integral, which is then evaluated.The iteration process is stopped when the volume emission rate changes by less than 0.01 % be tween iterations.A typical set of volume emission rates for the 9 11 A and 1356 A emissions are included in Fig. 1.After the volume emission rate has been calculated, the column inten sities must be calculated by evaluating: z., / 1 356 = 1 0-6 I, J T(lr(z) -r(Zs)I ), Clt(z) -t(ZJl)£(z)dz , The radiation transport contribution to the 1356 A radiance is generally small.The scat terer of the 1356 A radiation is 0 and the 0 density peaks below 150 km.The ionospheric o+ and electron densities generally peak above 300 km at night.This is due to the overall collapse of the ionosphere at night due to recombination processes.At night, the o+ charge exchanges with neutral molecules to produce molecular ions.The subsequent recombination of those molecular ions rapidly eats away the bottomside of the electron density profile (Chamberlain and Hunten, 1987); this reduces the overlap of the ionosphere with the 0 layer.This, in turn, reduces the amount of resonant scattering the 1356 A photons undergo before they escape to space.Therefore, reduced scattering means less entrapment of the 1356 A photons and an overall decrease in the 1356 A emission intensity .However, the entrapment of the 1356 A photons by resonant scattering increases the emission intensity by at most 5%.We have in cluded it in our modeling because the UV radiometer for the COSMIC program should be able to measure 1356 A radiance with less than 1 % uncertainty over a wide range of ionospheric conditions.
The typical radiances seen in the nighttime ionosphere at either 1356 or 911 A drive the design of the UV instrument.These radiances were simulated using the International Refer ence Ionosphere (IRI-90) to provide the electron and o+ densities and the electron tempera ture.The Mass Spectrometer and Incoherent Scatter model (MSIS-86: Hedin, 1987) was used to produce the 0 densities used in the calculation of the neutralization component at 1356 A.
The radiances were estimated for the minimum of the 11 year solar cycle as the ionospheric densities, and hence the radiances, are lowest at that time.The minimum radiances were of order 0. 1 Rayleigh at 911Aand0.2Rayleigh at 1356 A.

INSTRUMENT
The UV instrument for the COSMIC program has to provide precise and accurate mea surements of the radiance in a compact, low power package.The simplest and most sensitive option for the COSMIC was the use of a narrow band radiometer.The most difficult part of the design was the selection of a filter.Filter technology is not as advanced in the vacuum UV as it is in the visible and infrared.Narrow band filters with a compact design are not yet commercially available .At 911 A, the instrument's passband is determined by the choice of a thin metal film filter and photocathode combination.At 1356 A, a similar choice is possible using a window that blocks short wavelengths and a photocathode to eliminate long wave length sensitivity.We considered two design options.The first option was to use the 911 A emission.The second option was to use the 1356 A emission.Both options assumed that the instrument would consist of an off-axis parabolic telescope with a photon counting detector and electronics .
An instrument's sensitivity is defined as the number of photons detected per second at an input radiance of I Rayleigh: where Q is the quantum efficiency of the photocathode on the detector (number of photons detected I number of photons incident), Tis the filter transmittance, R is the reflectance of the telescope, A is the collecting area of the telescope in cm2, and D. is the instrument's field-of view in steradians.The factor 106 /4 n converts the radiance from units of Rayleighs to pho-tons s-1 cm-2 steradiau-1 (the 4 n factor is required here to convert from the omnidirectional radiance, expressed in Rayleighs, to a specific radiance per steradian).We selected a field-of view Q based on the desired spatial resolution for determining the ionospheric gradients.The field-of-view that was selected is 3° x 15° (along the orbit track x across the satellite's ground track).This field-of-view results in a spatial coverage of approximately 20 km x 100 km when projected to 350 km, the average height of the F-region peak, when viewed from a satellite at 750 km.The 23 km resolution is smeared out to 30 km when the integration time of the instrument (1 second) and the vehicle's speed are included.The instrument's field-of view, !J, is then approximately 0.014 steradians.We have assumed a 5 cm diameter for the collecting optic; thus, the collecting area is 19 .6 cm2• We now estimate the efficiency of a radiometer operating at 91 1 A. The detector we chose for this estimate is a channeltron.The quantum efficiency of a channeltron at 91 1 A is about 10% .The channeltron's quantum efficiency drops by roughly an order of magnitude to 1 % at 1216 A. The transmittance of an indium thin film has been measured at the Naval Research Laboratory and found to be 3% at 911 A and 0.5% at 1216 A (G. R. Carruthers, private communication, 1996).Silicon carbide has the highest reflectivity at 911 A of any substance.Its reflectance has been measured at NRL and found to be 35%; this reflectance increases slightly at 1216 A, but the difference is of little consequence here.When we substi tute these numbers into equation (9), we calculate the sensitivity at 91 1 A to be 23 counts s 1 Rayleigh-1 and 0.35 count s-1 Rayleigh•1 at 1216 A. Thus, we find that an instrument will detect 2. 3 counts s-1 at 911 A at our desired minimum signal of 0.1 Rayleighs.However, the bright 1216 A (Hydrogen Lyman-a) emission can be fairly bright even at night.The 1216 A is scattered over from the dayside to the nightside by atomic hydrogen in the Earth's geocorona.
This means that the 911 A radiometer will see 600 counts s-1 due to Lyman-<X with a 2.3 count s-1 due to 911 A superimposed.Clearly, this is not a desirable situation.
We now estimate the efficiency of a radiometer operating at 1356 A. The detector we chose for this estimate is a photomultiplier tube with a cesium iodide photocathode and mag nesium fluoride window.The quantum efficiency of a photomultiplier of this type at 1356 A is about 10% .We have opted to block the bright HI 1216 A emission and the 0 I 1304 A emission by using a heated strontium fluoride filter.The short wavelength transmission cut off for strontium fluoride occurs at 1280 A at a temperature of 25° C. The transmittance of a 5 mm thick strontium fluoride filter has been measured at a temperature of 80° C by the NRL.
The transmittance was 40% at 1356 A, less than 4% at 1304 A, and 0% at 1216 A. The reflec tance of a magnesium fluoride over aluminum coating for the telescope mirror at 1356 A is about 80% (Samson, 1967).When these numbers are substituted into equation (10 ), we calcu late the sensitivity at 1356 A to be 700 counts s-1 Rayleigh-1 and less than 70 count s•1 Rayleigh-1 at 1304 A. Thus, we find that an instrument will detect 140 counts s•1 at 1356 A at our desired minimum signal of 0.2 Rayleighs.However, the signal is slightly contaminated by the 0 I 1304 A emission.As this emission is also produced by radiative recombination, the contami nation to the 1356 A signal by the 1304 A emission is deemed acceptable.Thus, the 1356 A radiometer produces a higher quality measurement than the 911 A radiometer does.
The primary difficulty with the 1356 emission measurements is the contribution to the signal by o+-o-neutralization.Since neutralization component is related to the 0 density, the neutralization contribution to the ionospheric gradients inferred from the 1356 A emission was examined.The nadir radiances for the 911 A and 1356 A emissions were simulated using the International Reference Ionosphere (IRI-90: Bilitza, 1990) for the Q+ and electron densi ties and the electron temperature.The 0 density w as taken from the Mass Spectrometer and Incoherent Scatter model (MSIS-86: Hedin, 1987)  The COSMIC photometer will operate at 1356 A. This is based on the accuracy of the gradients as seen in Fig. 1, on the stron g contamination of the 91 1 A signal by Lymana, and the higher sensitivity possible at 1356 A.

1 Algorithm Introduction
The use of UV radiometric data to correct OPS occultation data for ionospheric density gradients has been simulated.We developed and tested an algorithm that jointly inverts both types of data to produce a high fi delity ionospheric reconstruction along the orbit track.The GPS total electron data are in the form of an occultation or "limb scans" and therefore the OPS data provides high quality altitude information.However, the OPS data are integrated elec tron densities along the line-of-sight to the OPS satellite and therefore may be affected by gradients along the line-of-sight.The intensity measured by the radiometer is proportional to the vertical column integral of the square of the ele ctron density and, therefore, contains no altitude information.But, the radiometer data contains high quality gradient information.The use of the two data sets together offsets the weaknesses in each data set while taking advantage of their strengths.In this work, we will assume that the photometer images the 911 A emis sion, which tracks the nmF2 gradients as well as the 1356 A radiance does.
The OPS receiver measures the total electron content given by: � TEC(<p);:::; J n.(z(s)) ds, (10) where ne is the electron density at altitude z and ds is the differential path length from the observer.The derivation of the radiometer radiances is described above.
The altitude distribution of the Q+ and electron density was parameterized using a gener alized Chapman layer (Chamberlain and Hunten, 1987).We assume that the electron and o+ densities are equal, which is a very good approximation below the H+/Q+ transition height in the nighttime F-region.We used five parameters to characterize the ionosphere: the altitude where the density peaks, hmF2; the density at the peak, nmF2; and three parameters to char acterize the scale height, H(z), 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, n + (z), is: where z is the altitude.The scale height is assumed to be a constant below hmF2 and to vary quadratically with the difference in altitude above the peak: , where H 0, H1, and H 2 are parameters.This form of the Chapman layer is an extension to the linearly varying scale height proposed by Picone et al. ( 1997) and is a reasonable ap proximation for describing the ionospheric density.
The along-track variation of the electron is parameterized by placing Chapman profiles spaced every degree along the orbit track.The profiles are all uncoupled and no smoothing or regularization is used; this causes the inversion to be more sensitive to point to point variations in the photometer data.These point-to-point variations are due to photon shot noise added to the simulated along-track radiance.The same altitude variation is assumed for all of the pro files, as the altitude variation is determined at one location near the tangent point locus of the GPS occultation.The individual profiles are scaled by nmF2 to characterize the along track electron density variations.The nmF2 variation between the profiles is given by a quadratic Lagrange interpolation polynomial (Press et al., 1992).These are reasonable approximations to make as the GPS occultations provide accurate altitude distribution information while the photometer data provide accurate information on nmF2 and no information about the altitude distribution.However, both the scale height and peak height of the electrons are known to vary with latitude in the ionosphere.The deficiencies in this approximation will be discussed later.
The line-of-sight of a GPS occultation spans 56° degrees of latitude from a satellite at an altitude of 750 km when the tangent altitude of the line-of-sight is 100 km.Thus, our model has 56 parameters to describe the along-track nmF2 variation and 4 additional parameters to describe the shape of the profiles.
The inversion algorithm uses an iterative approach, based on Discrete Inverse Theory (Menke, 1989), to seek the maximum likelihood estimate (minimum of the chi-squared statis tic) of the ionospheric parameters based on the fit of the model to the data.The DIT approach starts by estimating the "data" based on the current parameter values.The o+ densities are used to calculate the intensity seen by the photometer and the total electron content measured by the GPS receiver.The X 2 statistic (Bevington, 1969) is then calculated and used to com pare the model to the "data".If the fit is deemed to be acceptable, the algorithm terminates and calculates the "best fit" ionosphere; otherwise, new values for the model parameters are cho sen and the whole process is repeated.A fit is considered to be acceptable when the X 2 changes by less than 0.1 % between steps.Since the radiative recombination emissions are proportional to the square of the electron density, the algorithm is non-linear.The parameters are iteratively adjusted using the Levenberg-Marquardt scheme (Press et al., 1992) to seek the minimum X 2 • In addition to the ionospheric parameters that obtained the "best fit", the uncer tainties in those parameters are also estimated and outputted.Errors in the retrieved densities are calculated from the best fit parameters and their uncertainties using conventional error propagation techniques (Bevington, 1969).

2 "Data" Simulation
Evaluations of the algorithm's performance against "realistic data" were made using the IRI-90 (Bilitza, 1990) to generate the "data" which were inverted using the algorithm.IRI-90 was run for a set of solar activities and geomagnetic conditions characteristic of the maximum of the 11 year solar cycle, which should be applicable to the COSMIC program (expected launch 2003).The "data" were simulated using the electron temperature to determine the appropriate recombination rate coefficient and the o+ and electron densities to calculate the 911 A intensities and total electron content.
Uncertainties in the "data" were generated by assuming that the photometer "data" are shot noise limited (uncertainty equal to the square root of the number of counts) and that the TEC data had a random variance of 0.003 TECU (Hajj et al., 1994).(A TECU or total electron content unit is defined to be 1016 electrons m-2 • The nighttime limb viewing TEC is expected to be on the order of 100 TECU, during the GPS occultation measurements made by the COS MIC GPS receiver.)The shot noise limit assumption is valid because the photometers count photons and have negligible dark count rates.The synthetic photometer "data" without noise were converted from units of Rayleighs, to units of counts.per bin per second by applying an intensity scaling factor (100 count second-1 Rayleigh-1, which is typical of the photometers being designed for the COSMIC program) and multiplying by the integration time (10 sec onds).These uncertainties were then superimposed on the "data" by generating Poisson ran dom deviates.New uncertainties, which accurately represent the "noisy photometer data'', were derived by taking the square root of the noisy count rate "data".The "noisy data" and their error bars were then converted back to intensities in Rayleighs.A similar approach was used for the TEC data; however, Gaussian random deviates were used instead of Poisson deviates.These synthetic "data" and their uncertainties were used in the inversion.
We have assumed that the vehicle is at 750 km altitude in a polar orbit and the GPS occultations are occurring in the orbit track.This gives us a reasonable geometry with which to test the algorithm and maximizes the effects of ionospheric gradients.shows the GPS TEC "data", while the dashed line shows the fit using our algorithm.The solid line in Fig. 3b shows the photometer "data", while the dashed line shows the fit to the "data".

3 Algorithm Test Results
The algorithm accurately fits both sets of "data".Figure 4a shows a comparison of the IRI-90 density along the tangent ray trajectory (solid line) to the two-dimensional algorithm fit (dashed lin e) , the Abel inversion retrieval ( dash-dot), and a discrete inverse theory fit assuming spheri cal symmetry and our modified Chapman layer parameterization (dash-triple dot).Note that the two-dimensional algorithm does a much better job of retrieving the density than either techn i que that relies on the spherical symmetry assumption.Panel 4b shows the fractional ((20 -IRI-90) I IRI-90) error between the two-dimen sional retrieval and the IRI-90 iono sphere.A large island of low retrieval error (less than 15%) is seen to exist from roughly 10° to 30° latitude.In this figure, negative values denote that the two-dimensional retrieval is below the IRI-90 ionosphere .Figures 4c and 4d show the IRI-90 ionosphere and the retrieved ionosphere, respectively .Note that the ionospheric peak height does not change with latitude in the retrieval, while it does in the IRI-90 ionosphere .This is caused by the assumption, in the two-dimensional algorithm, that the altitude distribution of the electrons does not change with latitude .This assumption causes the "tongue" of enhanced electron density evident in Fig .3d above 20° latitude.It also results in the topside scale height being overestimated by the two dimensional algorithm, as seen in Fig. 4a.

CONCLUDING REMARKS
We have presented the ionospheric physics relevant to making nighttime measurements of the density gradients in the F-region ionosphere .Then we described the Tiny Ionospheric error between the two-dimensional retrieval and the IRI-90 ionosphere.
In this panel, negative values denote that the two-dimensional retrieval is below the IRI-90 ionosphere.Panels 4c and 4d show the IRI-90 iono sphere and the retrieved ionosphere, respectively.Note that the iono spheric peak height does not change with latitude in the retrieval, while it does in the IRI-90 ionosphere.The smooth curve rising from approxi mately 24° Nin panel b represents the tangent point trajectory.

Fig. 1 .
Fig. 1.This figure shows the gradients in the 1356 A and 911 A radiances and the twice the nmF2 gradient (9 11 and 1356 A gradients are proportional to (nmF2) 2 ).The logarithmic derivatives are plotted as these remove the dependencies on the radiative recombination rate coefficients.Note how closely both the gradients in the 911 and 1356 A radiances track the nmF2 gradient Differences are attributed to the variation of the scale height, peak height of the layer, and the electron temperature.The spikes in the gradients at high latitudes are due to the IRI-90 model and will not be present in the ionosphere.
and used to calculate the Q+ -oneutraliza tion contribution to the volume emission rate at 1356 A. To compare the gradients without having to scale results to remove the effects of the different radiative recombination rate coef ficients, the logarithmic derivatives are used.Figure 1 shows the comparison of the nmF2 variation and the 1356 and 91 1 A gradients.The 1356 A logarithmic deri vative closely tracks the nmF2 logarithmic derivative indicating that the neutralization component does not signifi can tly affect the 1356 A gradient measurements.Furthermore, this Figure suggests that gradi ent of the radiometer data should be used in an algorithm to invert the OPS occultation data and correct for the gradients.

Figure 2
Figure 2 shows the instrument viewing geometry though the IRl-90 ionosphere used in the simulation.The curved lines across the image represent every 10th GPS occultation ray path and the vertical lines represent every 1 Oth photometer exposure.The dashed curve in the figure shows the trajectory of the tangent ray point through the ionosphere.This particular simulation occurs in a region with strong electron density gradients.The solid line Fig. 3a

Fig. 2 .
Fig. 2.This is the instrument viewing geometry though the IRl-90 ionosphere used in the simulation.The curved lines across the image represent ev ery l01h GPS occultation ray path and the vertical lines represent every 10th photometer exposure.The dashed curve in the figure shows the trajectory of the tangent ray point through the ionosphere .

Table 1 .
This table contains the reactions rate coefficients relevant to the iono spheric nightglow processes.The first four rows pertain to the 1356 A emission.The last row pertains to the 91 1 emission.Te indicates the electron temperature in Kelvins.