The CHAMP performed electron temperature, Te, measurements during its mission period from 2000 to 2010. For the validation of these Te data comparisons with incoherent scatter radar observations at Arecibo and Tromsø (EISCAT) have been performed. Data from 94 (143) close encounters of the satellite with the Arecibo (Tromsø) radar are available for the validation. Results at Tromsø were reasonable, but at Arecibo significant differences, in particular for low temperature, were observed. Investigations showed that CHAMP Te measurements have a bias which switches sign between northbound and southbound orbit arcs. The global distribution of the bias shows systematic latitudinal structures antisymmetric to the magnetic equator. After correction of this effect, CHAMP Te data show a good agreement with the radar observations at both sites. From the mean relative deviation we deduce that CHAMP Te data are low by 3% with a standard deviation of 8%. Validated CHAMP Te data are available for the period 20 February 2002 through 20 February 2010.
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 The electron temperature plays an important role for the dynamics of the particles in the ionosphere and thermosphere. Due to the high thermal conductivity along the magnetic field lines electrons transport energy from the sources to the sinks. Regions of high electron temperature, Te, are generally indications of flux tubes with a heat source on one end. Although the heat capacity of the electron gas is by several orders of magnitude lower than that of the ions and neutral particles, the heat transport is significant.
 At low and midlatitudes, solar extreme ultraviolet (EUV) radiation is the main source for heating the electrons in the ionosphere. This photoionization process creates energetic electrons which heat up the ambient electrons by elastic collisions [e.g., Schunk and Nagy, 1978]. The heat gained by solar EUV keeps the electron temperature above the ion and neutral temperatures. As Schunk and Nagy  describe in their section 9.7 the electron heat loss terms surmount the source terms for altitudes below about 400 km. This means, the electron heat flux is directed downward in the altitude range we sampled and the electron gas is getting cooler at lower heights. Part of the electron energy is transferred to the neutral particles by elastic and inelastic collisions. For altitudes above 300 km, which are of interest for this study, Coulomb collision with ions, however, is clearly the most effective electron cooling process. This is lifting the ion temperature significantly above that of neutrals.
 At high magnetic latitudes also other processes can become important for heating the electrons. During disturbed conditions particle precipitation or wave-particle interactions in the auroral region and the cusp may even dominate the electron heating. In that area the field lines are almost vertical. Here flux tubes connect largely separated regions, and electrons provide a significant heat flux capability over distances of several thousand kilometers. A prominent example is the Te enhancement in the cusp region [e.g., Prölss, 2006].
 For all these reasons it is of interest to know the Te distribution in the ionosphere. Extensive series of Te measurements have been performed by incoherent scatter radars (IS). Important discoveries/results from them are, for example, the E region heating by plasma instabilities [e.g., Schlegel and St.-Maurice, 1981; Igarashi and Schlegel, 1987; Saito et al., 2001] and the modification of F region electron temperatures by powerful radio waves [e.g., Stocker et al., 1992; Robinson et al., 1996]. In addition, the electron temperature control of Polar Mesospheric Summer Echos (PMSE) [e.g., Rapp and Lübken, 2000] is being investigated using high-power radio wave facilities and incoherent scatter radars. Unfortunately, such radar facilities are available only at a few locations.
 There have been a number of spacecrafts providing Te measurements in the low-Earth orbit. A comprehensive list of relevant satellites launched before 1976 is given by Schunk and Nagy  in their Table 3. In spite of the sizable number of missions many of the pending questions were left open due to limitations in sampling, data quality or data processing. Results from more recent missions like the Japanese Hinotori have been reported [e.g., Oyama, 1991; Watanabe et al., 1995] or from the Dynamics Explorer, DE-2 [e.g., Brace et al., 1982]. Likewise there have been reports from the Russian Intercosmos missions [e.g., Truhlík et al., 2001].
 A comprehensive set of globally distributed Te data has been gathered by the CHAMP satellite. With the help of a planar Langmuir probe electron density and electron temperature readings were acquired along the orbit during the mission from 2000 to 2010. This continuous data set from an altitude range between 300 and 400 km covering all latitudes and local times is unique. It spans the time period from the solar maximum of cycle 23 to its deep minimum. Especially the latter part is not expected to be well represented by ionospheric models. Before the CHAMP data set is seriously considered in scientific studies or used for comparison with models like the International Reference Ionosphere (IRI) a validation of the Langmuir probe readings is recommended. In case of the electron density data this was performed by McNamara et al. . They used for comparison the plasma frequency measurements of the Jicamarca digisonde, which is near the magnetic equator. From nearby satellite passes, with CHAMP orbit heights below the F2 peak, they report an average discrepancy between the onboard planar Langmuir probe and ionosonde recordings of only 4%, with a standard deviation of 8.8%.
 In this study we focus on the validation of the CHAMP Te measurements. Our approach is to perform direct comparisons with incoherent scatter radars. We make use of standard observations performed by the IS radars Arecibo and EISCAT. Satellite passes within a longitudinal separation of about 15° were considered. In the sections to follow, we first introduce the data from the different facilities, then present the results from the comparison, subsequently a correction of readings is performed and a validation of the final Te data set presented.
2. CHAMP Data and Te Processing
 The CHAMP satellite, launched on 15 July 2000, cycles the Earth on a near-polar (inclination 87.25°) circular orbit [Reigber et al., 2002]. The orbit altitude has decayed from 456 km at the beginning of the mission to below 300 km by 2010. The orbital plane precesses through 1 h of local time in 11 days. Thus, it takes CHAMP 130 days, when combining ascending and descending orbital arcs, to cover all local times. Among other instruments onboard CHAMP the Planar Langmuir Probe (PLP) provides measurements of the electron density and electron temperature. The sensing area of the PLP is a rectangular gold-plated surface of 106 x 56 mm size pointing into the ram direction. This instrument was provided for CHAMP by the Air Force Research Laboratory, Hanscom AFB, MA, USA and also the data processing has been performed routinely by that group. Further details of the design and performance are summarized by Cooke et al.  and McNamara et al. . The PLP is operated every 15s for 1s in the voltage sweep mode. Thus CHAMP Te data are available every 15s. This corresponds to a spatial resolution of about 115 km considering the satellite velocity of 7.6 km/s.
 The electron temperature can be found from the slope in the region of the current-voltage curve where the electrons are still retarded. Locating that point and controlling a fitting process was found to be challenging so an alternative procedure was developed and found to be more robust and reasonably accurate. Typical examples of I-V curves are presented by McNamara et al.  in their Figure 1. The method for retrieving the electron temperature from these curves is quite sophisticated. It is based on the balance between the currents entering the probe, IP, and the satellite, IS.
The equations for arriving at Te are:
where e is the elementary charge, AP is the probe area, ASe and ASi are the effective satellite areas collecting electrons and ions, respectively, VP and VS are the probe and satellite voltages with respect to the ambient plasma, k is the Boltzmann constant, Ne is electron density, vOrb is the velocity of the satellite and Je = Ne with the electron mass me.
 In a first step, equation (1) is normalized by eASeJe. We define: Re = AP/ASe, Ri = ASi/ASe, C = NevOrb/Je, and a = e/k. For the voltage applied to the PLP we can write: V = VP − VS. Thus we get:
 By considering equation (10) for several PLP voltage steps we can derive Te. The terms in parenthesis in equation (10) can be seen as a correction for finite size ratio, Re. In practice, this ratio is difficult to determine because the collection characteristics of the solar arrays is not simply understood. So, it is presented as an effect that should lead to erroneously high Te if not accounted for, but left us a fitting parameter pending on the outcome of validation.
 An initial comparison between CHAMP and Arecibo radar Te data revealed systematically too high values of the satellite data before 19 February 2002, as can be seen in Figure 1. On this day the PLP settings were changed. We switched from a broader search sweep to fine spacing of the sample points in the region where the electron current exceeds the ion current, but is still retarded from the random thermal flux. The PLP accomplishes this with a variable spacing sweep. By tuning the PLP offset potential we account for spacecraft potential so as to maintain the fine spacing in the region of interest. This study has indicated that the computed Te is no longer trending high, so we have neither implemented curve fitting nor the correction factors of equation (10). For our subsequent analyses we make use only of data recorded after the improvement was implemented. At the end of its mission life CHAMP had to be turned about the yaw axis by 180° for attitude stability reasons on 22 February 2010. After that date, with the PLP looking backward, no reliable measurements of electron temperature and density are available any more.
3. Incoherent Scatter Radar Data
 For the validation of the CHAMP-derived electron temperatures we make use of measurements from two widely separated incoherent scatter radar facilities. Since one is located at low latitudes and the other in the auroral region, recordings are expected to complement each other.
3.1. Arecibo Data
 According to CHAMP's orbital characteristics the satellite passes close to a certain point on the globe twice within about 93 min on successive ascending orbits separated by about 23° in longitude (see Figure 2). About 12 h later a similar situation occurs on descending orbits but with somewhat different distances. The 23° longitudinal track separation corresponds at the Arecibo location (18.4°N., 293.25°E.) to a distance of ≈2420 km. Thus in the optimal case CHAMP passes the Arecibo radar 4 times a day within a distance of about 1200 km. In order to obtain a sufficient number of data points we searched the Arecibo-MADRIGAL database for Te data when CHAMP passed the radar within a distance of R < 1500 km.
 The corresponding electron temperature was determined in the following way. From the measured height profile of Te (usually between about 150 and 650 km, in 15 steps) we interpolated Te at the CHAMP cruising height from an exponential fit to Te through 5 height points centered around the CHAMP height (e.g., if the CHAMP height was 380 km we used Te values from the heights of 294, 330, 368, 405, 442 km). We did this for five successive profiles, usually separated by 80 s, around the time chosen for each pass (see below). We then averaged the corresponding five Te values at the CHAMP height and used this mean for the comparison. In total we obtained in this way 104 Te values between October 2002 and February 2009. (The Arecibo radar was not operating most of 2007 and 2008.) For later times there are still no data in the Arecibo MADRIGAL database.
Figure 3 (bottom) shows an overview of the Te values used for the comparison as a function of solar zenith angle. The large scatter of the data is a consequence of the large solar zenith angle variation at this location. In order to illustrate the typical diurnal variation of the data we overplot as examples the Te variations within 24 h from the International Reference Ionosphere (IRI) for the 2 solstice days of the year 2004 (which is in the middle of our data interval). From the IRI curves it becomes evident that the diurnal variation is dominating the temperature changes at this location. Further support for this statement is provided by the measurements themselves. In Figure 4 the electron temperature measurements at three different heights over the whole day, 27 June 2006, are plotted. Particularly prominent is the steep rise in the morning starting shortly before 0500 h local time (LT). At Arecibo LT is lagging about 4.5 h behind UT. Peak temperatures are attained around 0800 h LT. After that time the curves gradually decrease, reaching the nighttime flat plateau around 2000 h LT. The shape of the LT variation is about the same at all three altitudes.
 In order to reduce the disturbing influence local time that gradients may have on our analysis, we have taken the longitudinal separation between CHAMP and Arecibo into account. Rather then considering the Arecibo temperatures at the time of CHAMP closest approach, we take the radar measurements from a slightly different time, calculated as
where tArec and tCHA are the UT times in hours of the samples to be compared, lonCHA is the longitude of CHAMP during closest approach. De facto this means, CHAMP and Arecibo data are from the same local time, but not taken at the same UT time.
3.2. EISCAT Data (Tromsø)
 EISCAT is used solely for ionospheric observations and therefore the suitable database is much larger than that of Arecibo. The selection and the processing of the Te samples for the comparison were performed in the same way as for the Arecibo data (except for the time assignment). Due to the higher latitude radar location (69.58°N, 19.23°E) the longitudinal distance between two successive CHAMP passes is only ≈900 km. Accounting for the expected larger variability of Te in the auroral zone we limited the comparison to horizontal CHAMP distances of R < 750 km from the radar line of sight. This yielded Te data for 221 overpasses between February 2008 and end of 2008.
 In the same way as for the Arecibo data we plotted the used Te samples as a function of solar zenith angle (Figure 3, top). It is obvious that the range of encountered solar zenith angles is much more restricted here compared to that at Arecibo. The curves deduced from IRI data, confirm a smaller change with local time. Due to the smaller diurnal variation we compared CHAMP and EISCAT data from the same point in time independent of longitudinal separation.
3.3. Avoiding Perturbed Te Data
 It is obvious that we have to eliminate cases from the comparison when large temporal changes of Te values occur. In case of Arecibo steep spatial gradients occur after sunrise as shows in Figure 4. Since this can be regarded as a local time effect, we have taken care of it with the adjusted sampling time (see equation (11)). Large temporal Te variations are not expected at Arecibo during not too disturbed geomagnetic conditions.
 The situation is quite different for Tromsø. During moderately disturbed conditions we can have perfectly smooth Te curves during daytime, but at night when EISCAT is located in the auroral oval even during slightly disturbed conditions we may have large Te gradients. Therefore the geomagnetic activity index alone is not a sufficient criterion for avoiding perturbed samples. We adopted another strategy explained with the help of Figure 5. In Figure 5 we plotted as a thin dashed line the radar-derived Te readings at CHAMP altitude for a period of about 20 min around the time of closest approach. From a narrower interval (±3 min around the time of closest approach) the mean value is calculated (horizontal thick dashed line). We discarded all cases where the standard deviation of Te readings within the 6 min interval was greater than 10% of the mean value. In the lower part of Figure 5 we plotted the three nearest Te readings from the PLP onboard CHAMP (asterisks), and also here discarded the cases where the relative standard deviation of the three samples was greater than 10%. In all other cases we used the averaged Te samples from the radar and the PLP (both indicated in Figure 5 by horizontal thick dashed lines) for further analysis. This method gives us some confidence that spatial variations did not occur over a distance of about 350 km along the CHAMP track and that we had a temporal stability overhead the radar for about 6 min. This strategy was applied to all cases of the EISCAT overpasses. It led to quite a reduction of the reliable Te samples for the validation study: for the Tromsø database 143 cases survived out of 221, for the Arecibo database 94 cases remained after eliminating cases with large gradients. All these cases are from quiet or moderately disturbed geomagnetic periods with ap < 40 (Kp < 4.7).
 Histograms of the relative Te standard deviations of the employed samples are shown in Figure 6 separately for the three facilities. It is obvious that the variability of the Arecibo Te samples is much smaller than the ones from EISCAT. This is partly due to the huge collecting area of the Arecibo radar, but primarily due to the much larger natural fluctuation of Te at auroral latitudes compared to midlatitudes. The mean standard deviation of the PLP Te values is in between those of Arecibo and Tromsø because the satellite samples both latitudes regions.
4. Comparison Between CHAMP and Radar Data
 For an assessment of the CHAMP measurements we compute the relative difference, Δ, between the satellite and radar Te samples. The differences are normalized by Te,CHAMP
 Obtained differences, Δ, are plotted in Figure 7 versus Te,CHAMP for Tromsø (Figure 7, top) and Arecibo (Figure 7, bottom). Both Figures 7 (top) and 7 (bottom) show significant scatter, but there are systematic differences between the results from the two sites. The spread of points seems to be more random at Tromsø, while at Arecibo we observe a bifurcation of the deviation toward lower temperatures. This specific feature at Arecibo may be seen as an indication for an instrumental effect influencing the Te measurements on CHAMP. First we regarded spacecraft charging as a possible source for Te biases. The spacecraft potential may differ between sun light and darkness. For that reason the results obtained under illumination are plotted in Figure 7 as asterisks and those in the Earth's shadow as diamonds. It is quite evident from Figure 7 that the difference in illumination is not causing systematic biases of the temperature measurements. The two different symbols are closely located.
 We also checked whether a passage of CHAMP to the west or to the east of the radar produced differences in the deviations, but without success. Finally we discovered that there is a difference in the CHAMP Te readings between northbound and southbound orbits. We further investigated that effect. Figure 8 shows the average global distribution of the differences between temperatures obtained from northbound minus those obtained from southbound tracks at same locations. The result is quite surprising. At low and midlatitudes we find latitudinal bands aligned with the dip equator with different polarities in the two hemispheres. Largest amplitudes of about 400 K are attained around ±20° magnetic latitude. Toward the North Pole the difference vanishes. While at high southern latitudes a bipolar feature emerges with maximum at 110°E and minimum at 290°E longitude. The shape of this global pattern turns out to be independent of local time, season and solar activity. The amplitude of differences is slightly higher during the day compared to nighttime; but only by a small fraction of the ambient temperature. For the two locations of the considered radars (see black dots in Figure 8) we find rather different values. At Tromsø there is almost no effect predicted, while at Arecibo large differences between upleg and downleg passes are found. This is consistent with the distribution of deviations shown in Figure 7.
 The obvious relation of Te differences with the geomagnetic field geometry suggests an interaction of the spacecraft with the ambient field as the cause for the biases of the temperature estimates. At this time, however, we cannot give a convincing explanation for the modification of the PLP results. The configuration properties will be tested more rigorously in a separate study looking also at individual PLP sweeps.
 For the time being we regard the effect of directional dependence to first order as constant over the course of the mission. We thus applied a straight forward correction approach to the CHAMP Te readings. All measurements from southbound tracks were enhanced by half the temperature value shown in Figure 8 at the location of the satellite. Northbound readings were reduced by half the value from Figure 8. The newly processed CHAMP Te data set has been subjected to a repeated comparison with the radars as described in section 3. Deviations resulting from the corrected satellite data are shown in Figure 9. It is quite evident that there is a big improvement compared to Figure 7 (the separation between sunlit and shadow points has been omitted here since it had no effect as stated above). The bifurcation of the points at Arecibo has vanished. At Tromsø the distribution of deviations stays almost unchanged, as expected. We regard this very positive result at both radar sites as a confirmation for our correction procedure. From the distribution of points in Figure 9 we compute a mean value for the relative deviations Δ of −0.012 with a standard deviation of 0.083 for Arecibo, and for Tromsø we get −0.041 and 0.084, respectively. The deviations show no trend depending on the ambient temperature at any of the radars.
5. Discussions and Summary
 We have used radar data from two very different ionospheric regions for validating the CHAMP electron temperature measurements. Samples have been carefully selected in order to obtain reliable results. Only those CHAMP measurements were considered where the satellite passed by the Arecibo radar at a distance less than 1500 km and in the case of Tromsø by less than 750 km. At Arecibo we took the local time difference between CHAMP and the radar site into account before comparing the readings. This helped to reduce the scatter. At auroral latitudes, however, no improvement was achieved by this method due to the higher temporal variability of the temperature. Therefore this procedure was not applied to the Tromsø data. Periods of high magnetic activity with Kp > 4.7 were not considered for the comparison. Also those satellite overpasses were discarded where the standard deviation of neighboring samples exceeded 10% of the mean value. These selection criteria yield for the considered time period, February 2002 to end of 2008, about 100 samples for comparison at each radar sites.
 An important finding of this study is an obvious bias of the CHAMP Te measurements depending on the flight direction of the satellite. The pattern of the differences suggests a relation to the geomagnetic field (see Figure 8). The pattern of the differences shows no obvious dependence on environmental conditions like local time, season, or solar flux. For that reason we treated it as a true additive term. All CHAMP Te data have been corrected by adding half the effect shown in Figure 8 to the temperature readings of southbound passes and subtracting half the effect from northbound measurements. The success of this procedure is confirmed by comparison with the Te measurements of the Arecibo and Tromsø radars (see Figure 9). There are several points worth mentioning. The scatter of relative deviations is practically the same from the two very different radar sites. Both mean value and standard deviation are small (average −0.03 ± 0.08) and agree within statistical limits. There is no dependence of deviations on the ambient electron density and temperature. Also the illumination of the satellite has no effect on the Te data. We checked whether electron density readings, also derived from PLP measurements, show a dependence on flight direction. Fortunately, no such effect was determined. Thus Ne data do not require a correction.
 In summary, CHAMP has provided reliable electron temperature measurements for the period 20 February 2002 through 20 February 2010. The orbit covered all latitudes and longitudes at altitudes between 300 and 400 km. A full local time sweep is completed in 130 days. This corrected global data product covering 8 years is available at the CHAMP data center, ISDC, (product identifier CH-ME-2-PLP, version 21) for further studies of global Te behavior.
 We thank the Directors and the staff of EISCAT and Arecibo for providing the data and allowing the use of the MADRIGAL database. The CHAMP mission is sponsored by the Space Agency of the German Aerospace Center (DLR) through funds of the Federal Ministry of Economics and Technology, following a decision of the German Federal Parliament (grant code 50EE0944). The data retrieval and operation of the CHAMP satellite by the German Space Operations Center (GSOC) is acknowledged.