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 Ionospheric plasma frequencies at the altitude of the CHAMP satellite have been deduced from ionosonde true-height profiles for Jicamarca, Peru, and have been compared with the in situ measurements made by CHAMP. The differences between the plasma frequencies have been found to be well within the uncertainties associated with the ionosonde profiles, confirming the validity of the CHAMP measurements. For satellite-ionosonde separations of less than 250 km and for satellite altitudes below the peak of the F2 layer, the average discrepancy between the two plasma frequencies is 0.25 MHz or 4%. For the most reliable ionosonde measurements, the average discrepancies reduce to 0.18 MHz (or 1.7%), with a standard deviation of 0.16 MHz (or 1.5%). Given the validity of the CHAMP plasma frequencies, corresponding ionosonde and CHAMP observations have been used to support the practice of extending the ionosonde profile above hmF2 by assuming a Chapman layer with a constant scale height equal to that of the lower side of the F2 layer peak. The average discrepancy for CHAMP passing above the peak of the F2 layer is 0.22 MHz (or 2.6%), and the standard deviation is 0.8 MHz (or 13.3%).
 This paper presents the results of a comparison between near-coincident observations of plasma frequency made by the CHAMP satellite [Heise et al., 2002; Cooke et al., 2003] and by the ground-based ionosonde located at Jicamarca, Peru. The CHAMP orbit is almost circular and near polar, with an inclination of 87.2 degrees and an altitude of ∼400 km. The CHAMP in situ plasma density measurements are made by a Planar Langmuir Probe, which is part of the Digital Ion Drift Meter that is described in the next section.
 The ionosonde at Jicamarca is a University of Massachusetts, Lowell (UML), Digisonde DPS-4 [Reinisch, 1996]. The ionograms are routinely scaled by the UML ionogram autoscaling system ARTIST, which derives the profiles of plasma frequency versus altitude [see, e.g., Reinisch et al., 2005]. (Ionograms and their derived profiles are usually defined in terms of plasma frequency. The electron density N per cc corresponding to a plasma frequency of f MHz is given by N = 1.240 × 104f2.) Jicamarca was chosen as the comparison ionosonde site because it is an equatorial location (12.0°S, 283.2°E) with relatively high values of hmF2, the height of the F2 peak, so that CHAMP often flies below hmF2. At midlatitudes, CHAMP is usually above hmF2. The ionosonde plasma frequencies are measured only up to hmF2, and need to be extrapolated theoretically above that altitude.
 We have considered all Jicamarca ionograms for the interval September 2001 to August 2002, which have been hand scaled for another project using the University of Massachusetts Lowell application SAO Explorer (http://ulcar.uml.edu/SAO-X/SAO-X.html). Autoscaling results depend critically on the quality of the ionograms and the autoscaling algorithm, and indiscriminate use of autoscaled values is not recommended [Reinisch et al., 2004]. The hand-scaled ionograms were filtered by the program QualScan [McNamara, 2006], which scans the scaled ionogram traces (virtual height versus plasma frequency) for acceptability and prepares files of the derived plasma frequency profiles for those traces found to be acceptable. QualScan also derives the profile using the program POLAN [Titheridge, 1988], and assigns error bars to the profiles and F2 peak parameters. The CHAMP observations for locations within 250 km of Jicamarca, and occurring within 15 min of an acceptable ionogram, were then identified and the ionosonde value of plasma frequency at the CHAMP altitude found from the ionosonde profile.
 The ionogram filtering, together with the spatial and temporal coincidence requirements, but mainly the latter, reduced the number of relevant Digisonde ionograms to 142 (from the original 27,000). This number was further reduced to 100 after visual inspection of the 142 ionograms, to exclude doubtful traces affected by weak ionosonde echoes and spread F. There were 198 CHAMP observations that corresponded to 64 of the 100 ionograms and a CHAMP altitude that lay below hmF2. Obviously, there were cases in which a number of CHAMP observations corresponded to the same ionogram, typically 3 or 4, as the satellite passed by Jicamarca. Most of the comparisons are made for daytime and early evening passes of CHAMP near Jicamarca, which is when the peak of the F2 layer is highest and there is no spread F to prevent analysis of the ionograms.
Section 2 of this paper describes the Planar Langmuir Probe on board CHAMP, and how it is used to derive the CHAMP plasma frequencies. Section 3 describes the errors associated with using an ionogram to determine the altitude at which a specified plasma frequency occurs. These errors are largest at the base of the F2 layer, but reduce to small values near the peak of that layer. For Jicamarca, the peak altitude of the afternoon and evening F2 layer typically lies between 0 and 100 km above the CHAMP altitude, leading to the plasma frequency comparisons at ideal altitudes. Section 4 presents a general comparison of the CHAMP and Digisonde plasma frequencies for CHAMP passes below the peak of the F2 layer, and provides statistical descriptions of the differences between them. Section 5 describes an example of a perfect agreement between the CHAMP and Digisonde plasma frequencies, as well as examples of large differences. The large differences are attributed to errors in the Digisonde plasma frequency at the CHAMP altitude, and it is deduced that the agreement of the CHAMP and Digisonde plasma frequencies in the favorable cases (from the Digisonde point of view) confirms the validity of the CHAMP plasma frequencies. With the validity of the CHAMP plasma frequencies confirmed, section 6 uses the CHAMP values above the F2 peak to confirm the validity of the assumption that the plasma frequency profile above the peak can be estimated fairly reliably from the profile just below the peak. The general conclusions of the paper are presented in section 7.
2. Digital Ion Drift Meter
 The Digital Ion Drift Meter (DIDM) on CHAMP [Cooke et al., 2003; Roth, 2004] was provided by the Air Force Research Laboratory. It consists of two different measurement components, an ion drift meter (DM), and a Planar Langmuir Probe (PLP). The DM was a first flight demonstration of a new digital, microchannel plate (MCP) approach to imaging the ion distribution function from which the drift can be determined. The DM unfortunately sustained damage on ascent and also suffered subsequent MCP degradation, rendering the data unusable for precision measurements. However, the PLP has been functioning perfectly, measuring the spacecraft potential, ion density, and electron temperature. The PLP consists of a gold 152 × 203 mm rectangular plate with an included 106 × 156 mm sensing area that is controlled as an equipotential in a guarding and probe arrangement. There are no grids in front of the sensor. The PLP is mounted on the lower front panel of the spacecraft, with its normal aligned with the forward axis of the spacecraft. Some parts of the spacecraft are electrically conducting. The sensor plate of the PLP is alternately allowed to float for 14 s to track the spacecraft potential, and swept in voltage for 1 s to verify the floating potential and to determine the ion density and electron temperature. The sweep consists of 32 discrete nonlinear spaced steps covering ∼3 volts, with ∼0.04 volt steps near the center of the sweep, which is tuned to the plasma potential with a commanded offset. The density calculations are made from the negative portions of the 1-s voltage sweep. The PLP has the capability to adjust the voltage offset of its sweeps on the basis of the previous floating potential results, but this capability has not been used. The floating portion of the PLP operation is important in that it allows the sensor plate to return to equilibrium before the next voltage sweep.
 This paper represents the first validation results to be published for the PLP plasma density. The electron temperature is not measured by ionosondes, so that part of the validation will be accomplished by comparison with incoherent radar measurements and published at a later date. A collection of characteristic voltage-current sweeps from the PLP is shown in Figure 1. This is a dual log scale representation (with the zero current excised) showing the logarithm of both the ion (upper branch) and electron (lower branch) currents. Notice that the ion current is extremely flat over a large range of voltage. This is consistent with our conceptual model of ion collection, which is simply that with an ion ram energy of about 5 eV, the PLP should see an undisturbed cross section of the ion flux when the potential is sufficiently negative as to eliminate the electron current. Furthermore, we argue that if there were a more complicated interaction between the PLP and the environment, that interaction might be affected by the PLP potential. Since no such interaction had ever been observed, and since the PLP current-voltage curves are indeed flat at negative voltage, we have no reason to believe that the PLP is not seeing the representative flux caused by the relative motion of the spacecraft and ionospheric plasma.
 The PLP measures the current, or net flux of incoming particles, which are ions when the PLP is at sufficiently negative voltage. The particle population is assumed to be O+ only. Because the ion temperature is much less than the ram energy (0.1 eV versus 5.0 eV), the ion flux is cold and highly directional, and the flux, F, is related to the density, Ni, by F = NiVrel cos ϕ. There is no temperature dependence in these density calculations. F is the current (measured by the electrometer), divided by the electron charge and the area of the sensor plate. The angle ϕ is the angle between the PLP normal and the relative plasma flow vector, which has a magnitude Vrel. If the ion drift vector had been available from DIDM, Vrel cos ϕ and thus the density could be determined. However, since the quality of the drift data is poor, we use the orbital velocity (∼7.7 km/s) for Vrel, and set the angle ϕ to zero. During geomagnetically disturbed times at high latitudes, plasma velocities can exceed 1 km/s, in which case we could expect errors exceeding 1 (km/s)/7.7 (km/s) = 12%. In low-latitude and midlatitude regions, the drifts can be characterized by transverse drifts on the order of the corotation velocity. This leads to tan ϕ = 0.5 (km/s)/7.7 (km/s), 1.0 − cos ϕ = 0.002 or 0.2% for the low-latitude and midlatitude absolute error. The data is reported as a range-scaled linear value with 11 bits of precision, leading to a precision error of 0.5%. Adding the corotation and precision errors gives a characteristic error of about 1%. During strong geomagnetic storms in which CHAMP is below the F peak, some NO+ may be present, invalidating the assumption of O+ only.
3. Errors in Ionosonde Plasma Frequency Profiles
 The CHAMP observations provide an in situ measurement of the plasma frequency (or electron concentration) at the altitude of the satellite, which is well defined [Hwang and Born, 2005]. In contrast, the ionosonde measurements are of the virtual height at a well defined plasma frequency. The plasma frequency is equal to the ionosonde sounding frequency, since use is made of the echoes corresponding to the ordinary mode of polarization. The virtual height is the effective height of mirror reflection as if the signals had traveled at the speed of light in vacuo, and is always greater than the real (i.e., actual) height of reflection. The mathematical problem of converting an ionogram, which relates virtual height to plasma frequency, into a plasma frequency profile that relates real height to plasma frequency, is called real-height analysis, true-height analysis, or ionogram inversion.
 Techniques for the true-height analysis of ionograms have been described by Reinisch and Huang , Titheridge , and Huang and Reinisch [1996, 2001]. The program POLAN written by Titheridge is generally available and has gained wide acceptance for the inversion of physically valid ionogram traces, but this program is not stable against irregular ionogram traces that sometimes result from automatically scaled ionograms. The Reinisch and Huang technique forms part of the UML software package ARTIST that scales the ionograms automatically and then derives the plasma frequency profile [Reinisch et al., 2005]. The program that derives the profile is called NHPC, and is available from ftp://umlcar.uml.edu/SoftwareUtilities/NHPC/. Extensive comparisons of POLAN and ARTIST (more strictly, NHPC) plasma frequency profiles have shown that discrepancies between corresponding POLAN and NHPC profiles mainly arise when large sections of the ionogram trace are missing for some reason. The differences are due to the different assumptions made by the two programs to account for the missing information [see, e.g., McNamara, 2006].
Figure 2 shows the Jicamarca ionogram and profile for day 027, 2002, 1615 UT (about 1115 LT). Following the color bar at the top right, the echoes of interest are the red ones (ordinary mode). The continuous trace through these echoes is the autoscaled (not hand scaled in this case) trace, which has been fitted automatically to the leading edge of the ordinary mode echoes. The wide green trace between 11 and 14 MHz is interference from the colocated 50 MHz radar transmitter. This is a high-quality ionogram, and the scaled trace follows the echoes as required. The smooth curve with a peak at 12.55 MHz, 521.2 km is the derived plasma frequency profile. At the CHAMP altitude of 405 km, the NHPC value of the plasma frequency is 11.3 MHz, which compares very favorably with the CHAMP value of 11.4 MHz.
 Assuming that the ionosonde echoes are well defined, and not compromised by equipment problems, there are several sources of possible error in a derived plasma frequency profile:
 1. The autoscaled trace is not a good representation of the actual ordinary mode echoes.
 2. During the day, the echoes provide no direct information as to the shape, width or depth of the ionization valley that lies between the peak of the E region and the base of the F region.
 3. During the night, the echoes provide no direct information as to the distribution of the ionization for plasma frequencies below the first frequency at which F layer echoes are recorded (fminF). (If a model of the nighttime E layer is assumed, this point becomes very similar to point 2.)
 4. The echoes tend to become weaker at the highest frequencies that are reflected by the ionosphere, partly because the deviative absorption increases as the echoes become more and more delayed toward the highest frequency that is reflected by the ionosphere (foF2). The radiation pattern of the transmit antennas also changes with frequency, and many of the transmit antennas used for ionosondes do not have a radiation maximum in the vertical direction for frequencies above ∼9 MHz. The signal-to-noise ratio at these frequencies is also often affected by high interference levels.
 The errors due to point 1 are generally not relevant for the present study, because all ionograms have been rescaled by hand, although the desire to provide a result if at all possible (for another study) led to the inclusion of some unreliable scaled ionograms. Such ionograms have been rejected if it was considered that the derived profiles would not be sufficiently accurate for the CHAMP-ionosonde comparisons.
 Point 2 is known as the “valley problem.” The delays imposed on the signals at frequencies above the critical frequency of the E layer, foE, do not contain sufficient information to provide a unique description of the plasma frequency profile between foE and the first frequency reflected by the F layer. The extraordinary mode echoes contain some extra information [Lobb and Titheridge, 1977], but the combined use of ordinary and extraordinary traces does not give a unique solution (X. Huang, personal communication, 1987). Recourse is therefore made to a model of the valley such as described by Reinisch and Huang , Huang and Reinisch , Chen et al. , and Titheridge [2003a]. Following Titheridge's theoretical model, valleys are generally 10–15 km wide near noon, with a depth equal to 4–7% of foE. Both width and depth increase at larger solar zenith angle (χ), varying approximately as (secχ)0.6.
 Point 3 is known as the “starting problem.” As with the valley problem, the distribution of the ionization is not known below a particular frequency, which in this case is fminF. Again, recourse is made to a model of the underlying ionization (i.e., the ionization that exists below the altitude at which the plasma frequency is equal to fminF) [see, e.g., McNamara, 1979; Titheridge, 1986, 2003b]. Near midnight, Titheridge's [2003b] model results show an E layer peak at 105 km with a density between 2.0 and 2.6 × 103 cm−3 (foE ∼0.45 MHz) under most conditions. The peak thickness corresponds to a scale height of ∼5 km. A wide valley, with a mean density of typically 1.2–1.6 × 103 cm−3, extends from ∼120 km to the sharply defined base of the F2 layer at 190–225 km. While the uncertainty in foE has little effect on the F layer profile, significant errors can occur when the actually valley width deviates from the assumed model value. NHPC adjusts the model width to make it compatible with the measured F layer echo delays just above foE. POLAN allows multiple options, including one of using the widest valley that is consistent with the F layer echo delays.
 Point 4 becomes important for CHAMP passes above the peak of the F2 layer, because the uncertainties in the ionogram profile above the peak increase, as discussed later.
 The errors that arise from an incorrect model of the valley or underlying ionization decrease roughly linearly as the inverse of the frequency. They are greatest at the first frequency reflected by the F layer, and decrease to essentially zero at the peak of the F2 layer. They are greater for higher values of fminF/foF2, since the model is required to represent a larger part of the ionosphere.
 POLAN fits a Chapman layer F2 peak to the points below the F2 cusp [Titheridge, 1985]. NHPC avoids introducing a special fitting function near the peak; the modified Chebyshev polynomial used for the NHPC profile asymptotically approaches a parabola near foF2. The fact that the echoes get weaker toward foF2 sometimes makes it difficult to define the leading edge of the echoes up to foF2, even if the procedure is performed manually. The peak height of the F2 layer cannot then be accurately defined. This has little bearing on the bottomside CHAMP-Digisonde analysis, but affects the analysis for CHAMP passes above the peak.
4. General Comparison of Observations
 The CHAMP and ionosonde observations can be compared in terms of (1) the difference between the altitudes at which each instrument says a given plasma frequency occurs, or (2) the difference between the plasma frequencies at the same altitude. Since our initial interest is in the validity of the PLP measurements of plasma frequency, we chose the second option. The ionosonde plasma frequency at the altitude of the CHAMP satellite is found from the NHPC profile.
 There are two potential sources of error in the CHAMP-ionosonde comparisons:
 1. Lack of exact coincidence: Observations are taken to be simultaneous if the ionogram was recorded within 15 min of the CHAMP observation, and the subsatellite point was within 250 km of Jicamarca.
 2. Errors in the ionosonde heights: The ionosonde profile could be incorrect, in terms of being too high or too low at the plasma frequency equal to the CHAMP plasma frequency.
 We are mainly interested in point 2. The time and space windows given in point 1 can be reduced as required, albeit with the reduction of data. Since the CHAMP orbit is basically at a fixed longitude as it passes near Jicamarca, the 250 km allows a maximum latitude separation of 250 km, or 2.25°.
 The CHAMP altitude is defined to well within a kilometer [Hwang and Born, 2005], whereas the ionosonde altitude at a specified plasma frequency is uncertain. If the ionosonde altitude uncertainty is Δh, the uncertainty in the plasma frequency is Δfn = (dfn/dh) Δh, where fn is the plasma frequency. The profile slope dh/dfn is small at the base of the F2 layer, and infinite at the peak, so dfn/dh is large at the base of the layer, and small near the peak. This means that any error in the height of the ionosonde profile at a particular plasma frequency will lead to larger plasma frequency errors near the base of the layer than at the peak. In fact, there would be no error exactly at the peak. The most reliable comparisons of the CHAMP and ionosonde plasma frequencies would thus come from near the peak of the layer. For the profile in Figure 2, the plasma frequency near the peak changes by less than 0.1 MHz over a 50 to 100 km altitude range.
Figure 3 shows the direct comparison of the CHAMP and ionosonde plasma frequencies for the 198 points within the specified time and space windows, and when CHAMP lay below the ionosonde value of hmF2.
 For this data set, the average (signed) discrepancy between the CHAMP and ionosonde plasma frequencies is 0.25 MHz (or 4.2%), with a standard deviation of 0.41 MHz (or 8.8%). The ionosonde values are systematically higher than the CHAMP values below ∼12 MHz, but the plasma frequencies from the two instruments are in substantial agreement, generally validating the CHAMP measurements. The largest discrepancies occur below values of 8 MHz. We return to these discrepancies in the next section.
 The discrepancies in plasma frequency (ionosonde minus CHAMP) are plotted as a function of the ground separation of the subsatellite point from Jicamarca in Figure 4.
 There is no clear tendency for the discrepancies to increase with increasing separation, so the maximum value of 250 km set for the separation seems a good choice. The largest errors, 1.5 MHz or higher, occur at all separations. Decreasing the time window to 10 min (from 15) has virtually no effect on the average errors, so it will be kept at 15 min for this analysis.
 The discrepancies in plasma frequency can be expected to be less near the peak than near the base because (1) errors in plasma frequency are less sensitive to errors in the altitude of the ionosonde profile at a particular plasma frequency, and (2) the ionosonde height errors due to the valley or starting problem are largest near the base of the F2 layer, but decrease toward the peak. Figure 5 shows the discrepancies in plasma frequency as a function of the difference between hmF2 and the CHAMP altitude. As expected, the discrepancies tend to be smaller near the peak of the layer.
 There is a large cluster of small errors for cases with CHAMP altitudes less than 100 km below the F2 peak (as defined by NHPC). For these points, the average discrepancy between the CHAMP and ionosonde plasma frequencies is 0.14 MHz (1.7%), with a standard deviation of 0.33 MHz (4.9%).
 We saw earlier that the uncertainty in the ionosonde value of plasma frequency will be smallest when the slope of the profile, dh/dfn, is largest, i.e., toward the peak of the layer. Figure 6 shows the discrepancies in plasma frequency as a function of dh/dfn.
 The dispersion in the discrepancies increases to the left, which corresponds to moving further from the peak, and closer to the base of the layer.
4.1. Local Time Variation of Errors
Figure 7 shows the local time variation of the plasma frequency discrepancies. As is obvious from Figure 7, most of the comparisons are made for daytime and early evening passes of CHAMP near Jicamarca. This is partly a function of the filtering of the ionograms by the program QualScan, and partly because the F2 layer at Jicamarca is highest (with hmF2 greater than the CHAMP altitude) at these times. The drop in samples after sunset is associated with the postsunset rise of the layer because of an increased upward E × B drift, and the subsequent onset of spread F echoes that make it difficult to scale the “normal” F2 trace.
4.2. Summary of Subpeak Comparisons
 It is clearly necessary to understand the sources of error in the ionosonde values of the plasma frequency at a specified altitude (that of CHAMP), and to take account of the temporal and spatial variations of the ionosphere, before using them as ground truth for the CHAMP observations. Thus CHAMP should be close enough to Jicamarca (closer than 250 km), the ionogram should not correspond to a time very different from the time of the CHAMP observation (less than 15 min), and the comparisons should be made when CHAMP is near the peak of the F2 layer (less than 100 km, dh/dfn > 60 km/MHz). For points within the temporal and spatial windows, and with dh/dfn > 60 km/MHz, fn > 8 MHz, and heights less than 100 km from the F2 peak, the average discrepancy between the CHAMP and ionosonde plasma frequencies is 0.18 MHz (1.7%), with a standard deviation of 0.16 MHz (1.5%). The sample size is 75. This confirms the general validity of the CHAMP Planar Langmuir Probe observations of plasma frequency.
5. Analysis of Specific Observations
 It is of some interest to consider some of the outliers and “perfect fits” in Figure 3, and to confirm that the largest discrepancies in plasma frequency can be attributed to uncertainties in the ionosonde value of plasma frequency. We can expect to find the largest discrepancies near the base of the F2 layer.
5.1. Perfect Fit
 We consider first the perfect fits at 12.9 MHz. Four of the points at 12.9 MHz in Figure 3 correspond to the ionogram for 20013651845 (i.e., day 365, 1845 UT), which is shown in Figure 8.
 The scaled trace follows the echoes up to a vertical asymptote at 13.8 MHz (i.e., at foF2). The calculated profile has a peak at (13.8 MHz, 475 km). The CHAMP altitude was 405 km, which puts it comfortably in the subpeak profile, and in a region where both the ionogram and the scaled trace are well defined. There is some uncertainty associated with the Digisonde profile because there are no echoes below 6.0 MHz, which means that the program NHPC has had to assume some sort of plasma frequency distribution with altitude below this point. The program POLAN uses a different assumed plasma frequency distribution, and finds a plasma frequency of 12.6 MHz, which is still close to the CHAMP (and ARTIST) value of 12.9 MHz.
5.2. Outlier Points
 Most of the data points in Figure 3 are to the left of the line, with the ionosonde values being higher than the CHAMP frequencies, which corresponds to the ionosonde profiles being too low. The most obvious outliers are the points with plasma frequencies below 6 MHz. There are 14 points with the ionosonde plasma frequency below 6 MHz, and these have discrepancies greater than 0.7 MHz. The points correspond to one of three ionograms, 20020750014, 20020750029, and 20020770015. These ionograms are all for ∼1915 LT, which is during the postsunset height rise, and the base of the F2 layer is at heights of 400 to 450 km. Figure 9 shows the 20020750014 ionogram.
 The CHAMP plasma frequency is 3.93 MHz, at an altitude of 409 km. At this altitude, the ionosonde plasma frequency is 5.43 MHz, the discrepancy is 1.5 MHz, and dh/dfn is 26.3 km/MHz. The ionosonde profile is thus 40 km too low. This error is directly attributable to the model of the underlying ionization (i.e., below 1.6 MHz) being incorrect. In particular, the modeled valley width (see the NHPC profile between 0.5 and 1.0 MHz) is too small. The height error at 1.6 MHz has only decreased to 40 km at 3.93 MHz (but would decrease further toward foF2). The CHAMP plasma frequency changes by only 0.26 MHz for the five observations associated with this ionogram, so latitudinal gradients in the ionosphere are not a major contributor to the discrepancy. In general, the smallest discrepancies occur when the CHAMP altitude is much further from the start of the ionosonde profile, since the height errors due to the starting problem decrease linearly as the inverse of the frequency. The situation is similar for the other two ionograms.
 A second example of outliers in Figure 3 is given by the 14 points with an ionosonde plasma frequency of 7.8 MHz. These points correspond to four ionograms, 20013112359, 20020320415, 20020600130, and 20020600144. Eight of the points correspond to the last two ionograms, with the CHAMP plasma frequency decreasing from 7.6 to 7.0 MHz, as the satellite moved from −10.3° to −13.2° latitude. The discrepancies may be attributed to either an incorrect altitude from the ionosonde profile, or to latitudinal changes in the ionosphere. If all of the error is attributed to the ionosonde profile, the slope of the profile indicates that the profile is 24 km too low over the 7 to 8 MHz range of plasma frequency. This again can be traced to an error in the modeled NHPC nighttime valley width.
6. CHAMP Passes Above the F2 Peak
 There were 36 ionograms for which CHAMP was at an altitude above the ionosonde value of hmF2. These were not included in the preceding analysis because the ionosonde profile is strictly defined only up to hmF2. However, Reinisch and Huang  and Huang and Reinisch  have achieved some success in assuming that the topside profile is well modeled by an α Chapman function that has a constant scale height equal to that derived from the bottomside shape near the F2 peak. Huang and Reinisch found good agreement of the calculated total electron content (TEC) from the full ionosonde profile with incoherent scatter radar, Faraday and TOPEX TEC measurements at middle latitudes and the magnetic equator (Jicamarca). We have therefore used a Chapman function with a fixed scale height to derive the plasma frequencies for CHAMP altitudes between hmF2 and hmF2 + 3 × shF2 (the NHPC scale height). Higher altitudes are not considered.
Reinisch et al.  have shown that modeling the topside profile to larger altitudes is more accurately done with a “vary-Chap” function, i.e., a Chapman function with continuously varying scale height [Rishbeth and Garriott, 1969]. Indeed, the Reinisch-Huang technique used in NHPC fits a vary-Chap function to the entire measured bottomside profile and determines the scale height as a function of height from the E region to hmF2. The calculated scale heights consistently show a maximum at an altitude around 180 km and then level off to a near-constant value close to hmF2 [Reinisch et al., 2007], the value that NHPC uses above hmF2 for the α Chapman topside profile.
 Since we have previously validated the CHAMP observations of plasma frequency to within the expected ionosonde uncertainties, we can use them to confirm the validity of the Huang-Reinisch approach. However, the topside ionosonde profiles rely on accurate values of hmF2 and shF2, which demand strong echoes and accurate fitting of the scaled trace to the echoes. Since this is not always the case in practice, some noise can be expected in the ionosonde values of plasma frequency at the CHAMP altitude. Three of the 36 ionograms were rejected as providing a clearly unreliable peak (because of weak echoes). There were 59 topside coincidences for the remaining 33 ionograms.
Figure 10 shows the direct comparison of the CHAMP and ionosonde plasma frequencies for the 59 points within the specified time and space windows, and when CHAMP lay between hmF2 and hmF2 + 3 × shF2. Comparison of the results for passes below hmF2 (Figure 3) confirms the expected greater scatter of the data points for the passes above hmF2. The average discrepancy is 0.22 MHz (or 2.6%), and the standard deviation is 0.8 MHz (or 13.3%). Most of the data points were for local times between 03 and 09 LT, when foF2 is low and hmF2 is usually less than 400 km.
Figure 11 shows the discrepancies between the CHAMP and Digisonde plasma frequencies for the 59 cases, plotted against the height of CHAMP above hmF2 normalized to the NHPC value of the scale height for the F2 peak. The scale height is ∼60 km.
 The scatter in the data points is about the same for all heights above hmF2, up to three scale heights. A similar result is obtained from the POLAN plasma frequencies. The points in the bottom right of Figure 11 represent outliers with respect to the other points. The discrepancies for these points are ∼1.5 MHz, and correspond to the ionogram 20021120845. The next ionogram, 20021120900, gave discrepancies of 0.45 MHz, i.e., only one third the size.
 The essential difference between the two ionograms is that the ordinary-ray echoes are much better defined near foF2 for the 20021120900 ionogram. It is not possible to fit a smooth trace through the echoes in the 0845 ionogram near the F2 cusp. Thus, as with the plasma frequency comparisons for CHAMP passes below the peak of the F2 layer, the large discrepancies can be explained readily in terms of errors in the ionosonde profile. While the main source for the bottomside errors was the valley width uncertainty, the topside errors are mainly caused by ill-defined echoes at the F2 cusp.
 The results in Figures 10 and 11 confirm the general validity of the Reinisch-Huang method of extending the bottomside profile above hmF2 by assuming a constant scale height equal to the subpeak scale height, at least up to three scale heights. The scatter in the discrepancies is about the same over the range of three scale heights.
 The basic intention of the present analysis was to confirm that the AFRL Planar Langmuir Probe on board the CHAMP satellite gives valid plasma frequencies, by comparison of its values with values derived by the well established technique of inverting vertical incidence ionograms. This has been done, using CHAMP passes at altitudes below the peak of the F2 layer at Jicamarca, Peru. The discrepancies between plasma frequencies averaged ∼0.2 MHz.
 Given the validity of the CHAMP plasma frequencies, CHAMP passes at altitudes above the peak of the F2 layer at Jicamarca have been used to confirm, with somewhat larger discrepancies, that the ionosonde plasma frequency profile can be extended quite reliably up to three scale heights above the F2 peak by assuming a Chapman layer shape with a constant scale height equal to that derived for the profile just below the peak.
 The current work has been supported in part by AFRL contract FA8178-04-C-0055. We wish to thank C. J. Roth of AER, Inc., for the telemetry processing and data analysis support throughout the DIDM project [Roth, 2004], under contract F19628-00-C-0089 with AFRL. The CHAMP satellite is operated under the responsibility of the GeoForschungsZentrum (GFZ), Potsdam, Germany.