Corresponding author: L. F. McNamara, Air Force Research Laboratory, AFRL/RVBXI, Kirtland AFB, Albuquerque, NM 87117, USA. (email@example.com)
 This paper describes and compares two real-time assimilative ionospheric models, with an emphasis on their ability to provide accurate profiles of the electron density below the peak of the F2 layer at a midlatitude location, given automatically processed vertical incidence ionograms at a single location. The two models are specifically oriented toward several important practical applications of high-frequency (HF) radio propagation: HF communications, single station location of HF transmitters, and coordinate registration for OTHR. Both models start with the International Reference Ionosphere (IRI) as a background ionosphere and assimilate digisonde observations (either the ionogram or the profile) and available GPS total electron content observations. The digisonde data from one site in the Republic of South Africa (RSA) provide the ionosonde assimilation data, while the other three digisondes in the RSA provide the ground-truth observations of foF2, hmF2, and the plasma frequency profile. Since the four RSA digisondes receive each other's transmissions, maximum observed frequencies have also been used as ground truth. The models tested have both been found to provide significant improvements over the IRI and to have similar accuracies for the study interval (September 2011). The errors of the models are very close to the minimum achievable errors for all the validation parameters, which seem to be set by the ubiquitous traveling ionospheric disturbances being different at the different locations. For the optimum ground-truth location ~685 km from the digisonde providing the assimilation data, the RMS errors in foF2 were found to be 0.2 MHz (night) and 0.5 MHz (day).
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 The assimilative models considered in this study are GPSII (GPS Ionospheric Inversion) and EDAM (Electron Density Assimilation Model), which are discussed in more detail in the following section. Both models can be used for global specifications, but the nature of the assimilation data, especially in the current study, often limits the effective coverage to more restricted regions.
 The analysis interval for the present study is September 2011, and the study concentrates on observations from the four digisondes in the Republic of South Africa (RSA). September 2011 was chosen for analysis mainly because it was the last full month before the study was initiated. As it turned out, September 2011 showed a large amount of solar and geomagnetic variability. For example, (1) the daily sunspot number ranged from 47 to 167, (2) the global Ap index exceeded the nominal storm threshold (25) on 6 days (253, 254, 255, 260, 279, and 270), and (3) the Dst index went down to −103 near midnight on 26/27 September.
 The models are initially compared in terms of the accuracy of their values of three peak parameters: foF2, hmF2, and h0.8 (the altitude at which the profile has a plasma frequency equal to 0.8 foF2). foF2 and hmF2 are standard metrics adopted in other analyses. The models are then compared in terms of their ability to specify the maximum observed frequency (1F MOF) for one-hop high-frequency (HF) propagation on three circuits in the RSA (i.e., the highest frequency that would be supported for oblique propagation on a point-to-point circuit). The MOF comparisons are directly relevant to the major HF applications, which all involve oblique HF radio propagation. Finally, the models are compared in terms of the accuracy of their plasma frequency profiles.
 The RSA digisondes were also used as assimilation and ground-truth data in an earlier study by McNamara et al. . Pezzopane et al.  describe how the joint use of autoscaled data and two climatologic ionospheric models can provide a useful tool for obtaining a real-time three-dimensional electron density mapping of the ionosphere in the central Mediterranean region. Settimi et al.  made limited comparisons of calculated and observed oblique ionograms for a 1235 km Rome-Crete circuit, using the ionospheric specification developed by Pezzopane et al. . They found that this ionospheric specification gave more accurate oblique ionograms than the IRI.
Section 2 of this paper reviews the GPSII and EDAM models. Section 3 describes the assimilation scenarios and introduces the observed values of the MOF and various ionogram processing issues. Section 4 briefly discusses the observed traveling ionospheric disturbances (TIDs). Because the TIDs are different at the different digisonde sites, they have a strong influence on the achievable accuracies, as discussed in section 5. The assimilated digisonde data were processed automatically (autoscaled), necessitating some filtering of that data, as described in section 6. Some obviously spurious model results are also filtered out. Sections 7, and 9 present the model results for foF2, hmF2, and h(0.8 foF2). The model values of the 1F MOF are discussed in section 10. The accuracy of the GPSII, EDAM, and IRI plasma frequency profiles are discussed in section 11. Because there are ~2800 profiles for each digisonde, the comparisons are heavily summarized into profiles of the average and standard deviation of the errors in plasma frequency. The conclusions of the study are presented in section 12.
2 The Assimilation Models
 GPSII and EDAM both use the International Reference Ionosphere IRI-2007 (http://iri.gsfc.nasa.gov/) as their background model. The latest version is IRI-2012, which is equivalent to the IRI-2007 that was used for the present study.
 The IRI is a monthly median model that draws favor because of its ease and speed of use and generally acceptable level of validity. It uses either the URSI or CCIR world maps of foF2 and M(3000)F2 to define the F2 peak parameters foF2 and hmF2, and thence the plasma frequency profile. The world maps relate the monthly median values of foF2 and M(3000)F2 to two indices, namely the 13 month running means IG12 and RZ12. The values of these indices are made available in a table IG_RZ.dat that is regularly updated. Final values of these indices for the study interval, September 2011, were not available when GPSII and EDAM were run, so the teams agreed to use IG12 = 67.4 and RZ12 = 47.3. These values were passed to the IRI as the variables oarr(39) and oarr(33), respectively, and took precedence over the values in the table IG_RZ.dat.
 In fact, neither GPSII nor EDAM showed any sensitivity to the assumed values of IG12 and RZ12, as long as they were reasonable choices. The main reason for care in selecting the values was to establish representative IRI baseline values of the F2 peak parameters for comparison with the GPSII and EDAM results.
 EDAM has been developed to assimilate ionospheric measurements into a background ionospheric model [Angling and Khattatov, 2006; Angling et al., 2009]. The background model is currently provided by IRI-2007 [Bilitza and Reinisch, 2008]. The EDAM assimilation is based on a weighted, damped least mean squares estimation. This is a form of minimum variance optimal estimation (or best linear unbiased estimation) which provides an expression for an updated estimation of the state (the analysis) that is dependent on an initial estimate of the state (provided by the background model) and the differences between the background model and the observations [Menke, 1989; Twomey, 1977].
 A magnetic coordinate system is used in this assimilation, along with a time step of 15 min. The electron density differences between the voxels of the analysis and the background model are propagated from one time step to the next by assuming persistence combined with an exponential decay. The time constant for this decay is set at 4 h. Thus, if the data feed is interrupted, the analysis will decay back to the background model.
 EDAM assimilates GPS slant total electron content (TEC) observations as well as ionosonde information in the form of the ionogram virtual height traces [Angling and Jackson-Booth, 2011]. It can also assimilate radio occultation (RO) observations of slant TEC [Angling and Cannon, 2004; Angling, 2008] and in situ electron densities, but these capabilities were not exercised for the present study. During the study period, very few RO observations were available over the RSA, which covers a relatively small part of the globe.
 This study is the first extensive analysis of EDAM results when ionogram traces were assimilated and independent ionosondes were used to provide truth data. An earlier study addressed only a single day of data and was limited to an examination of the residual errors [Angling and Jackson-Booth, 2011].
 GPSII (pronounced “gypsy”) is a recursive data assimilation algorithm [Fridman et al., 2006, 2009] that provides an electron density distribution model for a fixed geographical area. At each time step of the solution, the resulting electron density model matches all ionospheric data accumulated during the model update time interval to within the data measurement error. The updated model is obtained by modifying the solution extrapolated from the preceding step. This data-driven modification of the model is determined with the help of the Tikhonov method [Tikhonov and Arsenin, 1977]. The GPSII processing ensures that the resulting model is spatially and temporally smooth and is yet in agreement with all measurements.
 Ionospheric measurements that GPSII is able to assimilate include raw absolute and relative TEC data from ground- and space-based GPS receivers, relative TEC data obtained with LEO satellite beacons, in situ electron density measurements, and data from vertical incidence ionosondes. GPSII is also able to assimilate various HF measurements such as OTHR backscatter ionograms [Fridman et al., 2012], but these capabilities were not exploited for the present effort. GPSII assimilated only data from ground-based GPS receivers and bottomside profiles of electron density from selected ionosondes (Grahamstown). IRI-2007 [Bilitza and Reinisch, 2008] was used as the background model. The solution update interval was 15 min.
2.4 Biases in the Validations
 Assimilation of the ionogram virtual height trace (by EDAM), rather than the true height plasma frequency profile (as done by GPSII), avoids having to use an independent procedure to perform the ionogram inversion to derive the plasma frequency profile. The best known methods for inverting an ionogram to get the profile are NHPC [Reinisch and Huang, 1983] and POLAN [Titheridge, 1988]. In both cases the inversion procedure must make assumptions about the profile below the first frequency at which ionogram echoes are obtained as well as in the E-F valley.
 The different assimilation approaches used by GPSII and EDAM lead to potential biases in favor of GPSII when validating the model values of hmF2 and the profile shapes. In particular, GPSII assimilates the ARTIST/NHPC profiles (for Grahamstown), while the ARTIST/NHPC profiles at the other three digisonde sites are used as ground truth. On the other hand, EDAM assimilates the virtual height trace at Grahamstown.
 However, the model validations against the observed 1F MOF on the Hermanus and Louisvale to Grahamstown circuits are independent of the ARTIST/NHPC profiles and therefore favor neither model.
3 The Assimilation Scenario
 As with the study by McNamara et al. , the four digisondes (actually the Digisonde DPS-4D) [Reinisch et al., 2009] in the RSA provided the ionograms and derived plasma frequency profiles. Figure 1 shows the locations of the digisondes.
 For the present study, the Grahamstown (GR13L) ionograms were used to provide assimilation data, while the Hermanus (HE13N), Louisvale (LV12P), and Madimbo (MU12K) ionograms were used to provide the ground-truth observations. The ionogram observations can be downloaded from the University of Massachusetts Lowell “DIDBase” http://umlcar.uml.edu/DIDBase/.
3.1 RSA Digisonde Ionograms
 Figure 2 shows as an example the Grahamstown ionograms for 20110916 (day 259 in 2011), 1200 UT.
 Because the four digisondes are GPS-synchronized, they can receive each other's transmissions as well as their own, thus providing both vertical incidence and oblique incidence ground truths. Figure 2 shows the usual vertical incidence traces out to ~9 MHz (red: ordinary trace; green: extraordinary trace), with double-hop traces at virtual heights of ~600 to 650 km.
 The two sets of multicolored traces that go out to ~11.5 MHz correspond to one-hop oblique propagation from the digisondes at Hermanus and Louisvale. There are ordinary and extraordinary traces for each circuit. The nose of each trace is the junction frequency or MOF for that polarization and circuit. There is a partial two-hop oblique Madimbo-Grahamstown trace near 8.5 MHz, 800 km. The four MOFs in Figure 2 are as follows: LV12P (O-ray), 11.4 MHz; LV12P (X-ray), 11.7 MHz; HE13N (O-ray), 11.7 MHz; and HE13N (X-ray), 11.9 MHz.
3.2 RSA Oblique Propagation
 Figures 3 and 4 show the diurnal variation of the observed 1F MOFs (i.e., for a 1F mode) for the three Grahamstown circuits for days 253 (10 September) and 270 (27 September) of 2011.
 Days 252 and 253 were disturbed days (Ap = 36, 33). Day 253 was the only day for which the Madimbo-Grahamstown 1F MOF was lower than the digisondes' frequency limits at both locations during daylight hours. Day 270 shows a local increase in the 1F MOF near 21 UT, which should be reproduced by the two models. Both figures show the presence of TIDs, which also appear in the other observations such as foF2 and hmF2. We discuss the TIDs briefly in section 5.
 Because the circuits from Hermanus (685 km) and Louisvale (735 km) to Grahamstown are very similar in length, the MOFs are also very similar. The changes to the propagation conditions due to ubiquitous TIDs often preclude the use of the relative sizes of the MOFs to identify the two sets of traces. However, we have followed the arguments given by Davies [1990, p. 165] to identify the traces with the smaller O-X separation as corresponding to the west-east Hermanus-Grahamstown circuit. The ordinary mode 1F MOFs for the Hermanus and Louisvale circuits have been scaled manually using this criterion to identify the two circuits. The MOFs for the Madimbo-Grahamstown circuit are significantly greater than those for the other circuits, and there are no identification issues. Unfortunately, the MOFs for the Madimbo circuit exceeded the adjustable upper frequency of the Grahamstown digisondes during most of the day (the ionosonde upper frequency limits are appropriate to vertical propagation, not oblique).
3.3 Observations Available to Modelers
 The modeling teams were given free rein as to what data other than ionosonde data they assimilated, but both teams restricted themselves to ground-based GPS TEC observations available from http://gsac.ucsd.edu, in particular, the GPS sites ABPO, ADIS, CAGZ, HARB, HNUS, MAD2, MAL2, MAS1, MAT1, MAUA, NKLG, NOT1,NURK, RBAY, REUN, SEY1, TDOU, WIND, YRCM, and ZAMB. Details of the available GPS sites are available at http://igscb.jpl.nasa.gov/network/list.html. AFRL validation studies, as well as studies using EDAM, showed that RO observations of TEC tend to be too sparse to contribute usefully when GPS TEC data are also available (the RO data are more important over the oceans).
 The RSA ionograms and autoscaled data were downloaded from the University of Massachusetts Lowell DIDBase by each team member using SAO Explorer. The ground-truth ionogram traces and vertical incidence observations were thus freely available. However, the oblique ionograms were scaled manually by LFM and provided an independent set of ground-truth observations. The vertical ionograms were automatically processed (autoscaled) by ARTIST5 [Galkin et al., 2007].
4 Properties of the Observed TIDs
 TIDs are ubiquitous in the RSA observations. We have already seen them in the observations of the 1F MOF (Figures 3 and 4). Midlatitude TIDs have a wide range of periods, ranging from 15–20 min to several hours. Since the observations are made only every 15 min, short-period TIDs cannot be studied with the present data set. There is also a Catch-22 situation in that the TIDs perturb the ionogram traces and make it difficult to measure the key ionospheric characteristic (foF2) that we analyze to determine their properties.
 Preliminary analysis of the observations of foF2 using the Lomb-Scargle periodogram approach has isolated a period of ~2 h in some situations, which is consistent with the 1F MOF observations. Hunsucker  classifies TIDs with periods of 30 min to 3 h as “Large Scale TIDs”, which have horizontal velocities of 400 to 1000 m/s and wavelengths greater than 1000 km. These large-scale traveling ionospheric disturbances (LSTIDs) are generated in the polar regions during geomagnetic storms and propagate equatorward.
 Figure 5 shows by way of illustration the deviations of the Hermanus foF2 from a smoothed curve for days 259–261 (chosen because the TIDs are well defined). Ap was 32 on day 260, with very quiet days before and after. There is clearly a disturbance with a period of ~2 h. The perturbations at night are smaller than those during the day and close to the measurement error. Ignoring the extreme values (some of which could be suspect), the TID variability is about ±4% of the smoothed values of foF2.
 The Lomb-Scargle approach found an ~2 h periodicity (1.5 to 2.5 h) in the Hermanus foF2, but only for disturbed days. For example, day 260 (Ap = 32) showed a clear peak at 1.90 h, while day 269 (Ap = 67) showed peaks at 1.696, 1.667, and 1.508 h. The difference between periodicities for different disturbed days would not be unexpected if the LSTIDs are generated in the distant polar regions.
5 The Minimum Achievable Error
 Neither GPSII nor EDAM takes specific account of the perturbations in the profiles and peak parameters caused by TIDs. Subjective comparisons of the fine-scale variations of the observed daytime values of foF2 show that they are not similar in detail for different digisondes, even allowing for possible phase shifts. The same situation holds for the 1F MOF observations illustrated in Figures 3 and 4. We therefore propose that the differences between the TID effects at the driver station (Grahamstown) and the ground-truth stations (Hermanus, Louisvale, and Madimbo) will set a minimum error that can be achieved by GPSII or EDAM.
 As an estimate of this minimum achievable error, we take the standard deviation of the differences between corresponding observed values of the driver (Grahamstown) and ground-truth (such as Hermanus) values of foF2. Average differences are ignored on the basis that the models would have no systematic errors when they are working perfectly. The actual RMS values of the GPSII/EDAM errors can then be compared with the standard deviations of the differences in the observed values of foF2.
 Figure 6 indicates that the minimum achievable error in foF2 at Hermanus will have a standard deviation of ~0.4 MHz during the middle of the day, when foF2 values are highest, dropping down to ~0.2 MHz at night. The minimum achievable error is ~50% higher for Grahamstown-Louisvale, and higher still for Grahamstown-Madimbo. Since the observed midday values of foF2 are ~9 MHz (as shown in the later Figure 9), the minimum achievable error for the Hermanus foF2 at 11 UT (noon) is ~4%.
 Figure 7 shows the estimated minimum achievable error in the peak height hmF2 at the three ground-truth sites. The standard deviation of the differences has a local maximum in the middle of the day, local minima near 06 and 16 UT, and high values at night. This diurnal variation follows that of hmF2 (see the later Figure 12 for the Hermanus values of hmF2). In the middle of the day, the RMS errors in hmF2 correspond to ~6% of hmF2.
 It can be expected that the minimum achievable errors would be affected by ionogram autoscaling inaccuracies as well as by the different TID effects, but there seems to be no way to disentangle the two effects.
6 Filtering the Observations and Model Results
 The assimilated Grahamstown digisonde observations were all automatically processed (autoscaled) by ARTIST5, as were the observations for the three ground-truth digisondes. While the RSA digisondes are well maintained, the RSA ionograms are relatively simple, and ARTIST5 is a significant advance on earlier versions of ARTIST, there are still some autoscaling “blunders.” These blunders can lead to apparently large errors in the model results, so procedures have been adopted to prevent them from distorting the results of the present study.
 The first step is to filter the assimilation data. Since this process is automated, both GPSII and EDAM will produce the occasional large error which is due to undetected autoscaling issues. The GPSII/EDAM/IRI values of the validation parameters are therefore filtered before they are presented here.
6.1 Filtering the Autoscaled Assimilation Data
 The final comparison and analysis of the model outputs, including filtering of errant results, were performed by LFM. The first step in the filtering process was to run QualScan [McNamara, 2006] for all ionograms for all four sites. QualScan performs multiple checks on the likely validity of the scaled ionogram trace, calculates the POLAN [Titheridge, 1988] plasma frequency profile, and compares the POLAN and ARTIST (NHPC) profiles to establish the plasma frequency and uncertainty at a standard grid of altitudes. Profiles such as these are provided to the Air Force Weather Agency global real-time model of the ionosphere.
 For the Grahamstown ionograms, there were nominally 30 × 96 = 2880 ionograms. QualScan immediately rejected ~10% of these because ARTIST5 had determined post facto that its results were unreliable. Another ~7% were subsequently rejected mainly because POLAN would probably have failed to derive a profile from the scaled trace, even after some judicious patching of the ionogram trace by QualScan, or the derived POLAN profile was nonphysical in some way. As well as “failing” an ionogram because no POLAN profile was derived, QualScan provides a quality figure for each ionogram. In this case, ~10% of the Grahamstown quality figures were 0 (could not process ionogram) or 1 (high risk/low quality), leaving ~90% with acceptable or good quality. The autoscaling process can be affected detrimentally by the presence of spread F echoes, but extensive perusal of the ionograms suggested that this was not an issue for the current study. This conclusion is consistent with the statistical characterization of spread F over South Africa made by Amabayo et al. .
 The essential elements of QualScan's processing are saved in a file called peak_vs_time.dat, which lists ~30 characteristics of the ARTIST and POLAN profiles. These peak_vs_time.dat files for the four digisonde sites play a key role in filtering the model results. An ionogram (and a GPSII/EDAM/IRI specification) is included in the error analysis if it appears in the peak_vs_time.dat files for both Grahamstown and the digisonde location being processed. Recall that Grahamstown provides the assimilation data, while the other three sites are ground-truth sites. An ionogram at either site is also rejected if it fails some other simple sanity checks on the ARTIST values of the peak height hmF2 and the obliquity factor M(3000)F2. The test on hmF2 mainly rejects some invalid ARTIST results for Louisvale daytime ionograms.
6.2 Filtering the Model Results
 The ARTIST5 autoscaled values of foF2 are generally very reliable for the present set of ionograms, and both GPSII and EDAM yield very small RMS errors in foF2, i.e., only about a third the size of the IRI errors (as discussed in section 8). However, the situation is not so simple for the models' nighttime values of hmF2 (and to some extent the height h(0.8foF2), the height of the subpeak F2 layer at 0.8 foF2) for which a few percentages of outlier values have sufficiently large errors to severely distort the calculated RMS errors.
 In principle, the large errors can arise in two ways: undetected bad data can be assimilated, or good data can be assimilated badly. The first case includes the effects of undetected autoscaling blunders. These can cause model errors directly as the bad data are assimilated and for some time afterward, since the models have to “unlearn” the effects of bad assimilation data. Deciding whether a new observation that differs significantly from the preceding ones is valid is part of the “innovation” issue in data assimilation. Both EDAM and GPSII are affected by these errors.
 However, for EDAM, a small number of cases appear to be affected in the second way, i.e., reasonable virtual height traces are assimilated but result in grossly nonphysical vertical electron density structures within the EDAM grid. As with the bad data case, the resulting poor results can take a significant time to decay out of the grids and lead to clumping of the outliers. Figure 8 shows the corresponding EDAM and ARTIST values of hmF2 for Hermanus, illustrating the outlier EDAM values.
 It is not yet clear why such nonphysical results occasionally arise in EDAM from the assimilation of good data. It should be relatively straightforward to detect and exclude these poor assimilations, but the necessary procedures have not yet been implemented. Consequently, for the purpose of the current testing, the hmF2 results have been filtered. After several attempts, we chose to filter the model values of hmF2 by excluding values that lay outside the 2σ errors in the IRI values. Before any filtering was applied, the IRI errors in hmF2 at Hermanus had an average error of 6.63 km and a standard deviation of 20.41 km. We have therefore rejected all ionograms for which the EDAM error in hmF2 laid outside the range of −34.2 and 47.7 km, but only for the calculation of the RMS errors in hmF2 (this filter was thus also applied to the GPSII and IRI results; the same Hermanus-based filter was applied to the Louisvale and Madimbo results).
7 Model and Observed Values of foF2
 foF2 is one of the most useful characteristics of a plasma frequency (or electron density) profile. It is the highest O-ray frequency that would be reflected at vertical incidence. Ionograms were recorded with a 15 min cadence.
7.1 Observed Values of foF2
 Figure 9 shows the observed (autoscaled) values of foF2 for Grahamstown, starting at 00 UT on day 244 (1 September).
 The decreases in the daytime values of foF2 on days 253 and 270 are associated with increases in Ap on the previous day(s). The red C indicates missing ionograms. There is a general increase of foF2 throughout the month, in line with the increase of the 10.7 cm radio flux from 112 to 190 on 24 September (day 267), followed by a decrease back to 138.
7.2 RMS Errors in Model Values of foF2
 Figure 10 shows the diurnal variation of the RMS model errors in foF2 for GPSII, EDAM, and IRI. The IRI was run for the full month with a fixed value of IG12 = 67.4 to provide a reference level for figures such as this. The IRI errors were positive for the first half of the month, after which they became negative. The GPSII and EDAM specifications of the profiles and peak parameters do not retain any memory of the value of IG12 used to provide the background ionosphere used for the assimilation process.
 Figure 10 shows that the GPSII and EDAM errors are generally less than 0.5 MHz. They are larger during the day when the values of foF2 are higher, and significantly less than the IRI error except around dawn. Comparison of the GPSII and EDAM errors with the Hermanus minimum achievable errors given in Figure 6 shows that the model and estimated errors are very similar.
 One of the objectives of the present study is to determine if either GPSII or EDAM is clearly better than the other. Table 1 lists the statistics of the GPSII, EDAM, and IRI average error, standard deviation, and RMS error in foF2 for Hermanus for the three models. All valid 15 min ionogram cases have been considered. The sample size was 2188. The GPSII and EDAM errors in foF2 are very similar and are less than half that of the IRI.
Table 1. Hermanus Average, Standard Deviation, and RMS Errors in foF2 for GPSII, EDAM, and IRI
 It is of some interest to see how far GPSII and EDAM can extend the effects of the Grahamstown observations. Table 2 lists the RMS errors in foF2 for the three models and four digisonde sites (again unfiltered). The “Separation” column gives the distance from Grahamstown (the assimilation station). The Grahamstown results show how closely GPSII and EDAM fit the assimilation data, but this is actually a matter of modeling preference. The ARTIST values of foF2 (and hmF2) have finite errors.
Table 2. RMS Errors in foF2 for GPSII, EDAM, and IRI, for the Four Digisonde Sites
 It can be seen from Table 2 that EDAM has the smallest RMS errors in foF2 at Hermanus and Louisvale and (as expected) that the IRI errors are the largest. The GPSII errors are significantly smaller than the EDAM errors for Madimbo, which is 1287 km from the driver site, Grahamstown. Hermanus and Louisvale are only ~700 km from Grahamstown, and GPSII and EDAM have similar accuracy for these two sites. The increase of the errors with distance from Grahamstown is in keeping with the decrease in the cross-correlation coefficient found between the deviations of foF2 from the median values for all times: Hermanus, 0.83; Louisvale, 0.78; Madimbo, 0.69.
 The reason for the Hermanus errors being smaller than the Louisvale errors probably lies in the geometry of the digisonde network. As shown in Figure 1, Hermanus is basically west of Grahamstown, while Louisvale is to the northeast. East-west correlation coefficients for foF2 are generally higher than north-south correlation coefficients [McNamara, 2009; McNamara and Wilkinson, 2009]. Madimbo is 1287 km NNW of Grahamstown, so high correlation coefficients would not be expected.
7.3 Assimilating Only One Data Type
 Both GPSII and EDAM have also been run using either the GPS TEC or the ionogram observations (profile or trace) separately to see if the relative utilities of the two types of assimilation data can be determined. Overall, it appears that the Grahamstown ionograms are more useful than the GPS TEC observations.
 When used alone, the GPS TEC observations are used to provide the model values of foF2 indirectly by assuming some F2 slab thickness model as discussed by McNamara et al. . Since the TEC observations cannot contribute usefully to specify hmF2 (except for very dense GPS networks), both GPSII and EDAM must rely on the IRI values of hmF2. In general, the relative utilities of the GPS TEC and ionogram observations will depend on the numbers and qualities of each data type. In this particular case, the Grahamstown ionogram data are abundant and reliable, whereas the GPS TEC data are rather sparse.
8 Model and Observed Values of hmF2
 The observed values of hmF2 show much more variability than the values of foF2. This larger variability is at least partly due to inaccuracies in the ionogram autoscaling and in the derivation of the plasma frequency profile from the scaled ionogram trace. However, periodic nighttime variations of hmF2 with amplitudes up to ~30 km and a period of ~3 h were observed at all four digisonde sites on days 267 and 268, so some of the variability is real.
8.1 Observed Values of hmF2
 There are several ways to illustrate the variation of the observed values of hmF2. Figure 11 shows the diurnal variation of the individual observed values of hmF2 at Hermanus, September 2011. It illustrates the variability of the observed (ARTIST) values of hmF2 at Hermanus. The high values of hmF2 for the night of 269/270 were associated with a magnetic storm with an Ap of 67 and Dst of −103. Both GPSII and EDAM follow this storm-time variation of hmF2 very well. The values of hmF2 that lie below ~220 km are probably due to autoscaling blunders. As mentioned earlier, such blunders are most common at Louisvale during the middle of the day.
8.2 RMS Errors in Model Values of hmF2
 The EDAM values of hmF2 were compared with the observed values in Figure 8.
 Figure 12 shows the diurnal variation of the RMS model errors in hmF2 for GPSII, EDAM, and IRI. The errors have been filtered using the IRI statistics to overcome the sometimes dramatic effects of autoscaling blunders and large outliers for EDAM. If an ionogram case had an outlier EDAM error based on this filtering, the GPSII and IRI cases were also filtered out along with the EDAM case. The IRI absolute errors were generally positive throughout the month, following the increase of the 10.7 cm solar flux.
 Figure 12 shows that the GPSII errors during the day are less than the EDAM and IRI values, which are very similar. The estimated minimum achievable errors given in Figure 7 reach ~20 km in the middle of the day. The GPSII and EDAM RMS errors have local minima of ~10 km near 06 and 16 UT, which are consistent with the estimated achievable errors. The errors in the model values of hmF2 at night are significantly larger than the minimum achievable errors.
 The GPSII errors tend to be the smallest, with the EDAM errors being closer to the IRI errors. However, a comparison of the GPSII and EDAM errors in hmF2 is biased toward GPSII because GPSII assimilates the ARTIST profiles, and we are using ARTIST profiles as the ground truth. GPSII adjusts the model to achieve a reasonable agreement with the ARTIST profile (including its hmF2 value). On the other hand, EDAM assimilates the ionogram trace and basically assumes that the IRI value of hmF2 is correct, which is why the EDAM and IRI values are so similar.
 As with foF2, it is of some interest to see how far the models can extend the effects of the Grahamstown observations of hmF2. Table 3 lists the RMS errors in hmF2 for the four digisonde sites. In view of the larger errors at night, only the daytime data between 08 and 15 UT are compared (the hmF2 values have been filtered, but the effects of the filtering are marginal during the day). As with the foF2 errors, the GPSII errors in hmF2 increase with increasing distance from Grahamstown. The GPSII errors are systematically less than the IRI errors, but the EDAM errors do not show any improvement over the IRI. The systematic increase of the IRI errors seems to be fortuitous.
Table 3. RMS Errors in hmF2 for GPSII, EDAM, and IRI, for the Four Digisonde Sites, 08-15 UT Only (Daytime)
9 The Profile Altitude Corresponding to 0.8 foF2
 The autoscaled values of hmF2 are subject to the vagaries of TIDs as well as the uncertainties of ionogram autoscaling and the conversion from the ionogram to the plasma frequency profile. Thus, it is not usually possible to quantify the level of uncertainty that exists in the ARTIST values of hmF2. We have therefore included the profile altitude at a plasma frequency of 0.8 foF2 (0.64 NmF2) as another validation parameter. The more common figure of 0.5 NmF2 was avoided so as to restrain the altitude to the F2 layer. For simplicity, we call this altitude h0.8.
 The altitude h0.8 is expected a priori to suffer from less natural and processing noise than hmF2. It also has the advantage that it is a point on the F2 profile that is more relevant than hmF2 to HF radio propagation on oblique circuits. However, as with hmF2 the EDAM results include outliers that distort the RMS errors. Overall, both GPSII and EDAM provide accurate values of h0.8, as illustrated in Figures 13 and 14, and Table 4.
Table 4. Average and Standard Deviation of the GPSII, EDAM, and IRI Errors in foF2, hmF2, and h(0.8) for Hermanus
aThe values of hmF2 have not been filtered; this was done only for the RMS calculations.
 Comparison of Figures 13 and 14 shows that GPSII has fewer outliers than EDAM and that both sets of model values are biased a little high.
 Table 4 lists the average and standard deviation of the GPSII, EDAM, and IRI errors in the values of foF2, hmF2 (filtered), and h(0.8 foF2) for Hermanus. The table shows that the GPSII and EDAM h(0.8foF2) errors are smaller than those for hmF2. The models offer significant improvement over the IRI for foF2 and h(0.8foF2), but not for hmF2. The calculations confirm the slight bias in the model values of h(0.8 foF2) that appears in the figures. The EDAM errors in h(0.8 foF2) are somewhat smaller than the GPSII errors, in spite of the large outliers seen in Figure 14.
10 Model and Observed Values of 1F MOF
 The values of 1F MOF for the Hermanus, Louisvale, and Madimbo to Grahamstown circuits were manually scaled for days 251–273 inclusive, except that there were no ionograms for Grahamstown on day 262 (19 September) and parts of other days. These days covered all of the magnetically disturbed intervals, with the global Ap having values of 30 or higher on days 9, 10, 17, 26, and 27. There were 14 days with Ap less than 10. An example of oblique ionograms was given in Figure 2.
 Examples of the diurnal variation of the observed values of the 1F MOF, along with the TID effects, were given earlier in Figures 3 and 4. The GPSII and EDAM values of the 1F MOF were calculated by the respective modelers using three-dimensional ray tracing and homing with the Earth's magnetic field included. Since neither model allows for TIDs, the model values of the MOF will have a minimum uncertainty.
 Figure 15 shows the corresponding observed values of the Hermanus and Louisvale to Grahamstown 1F MOF, for both quiet and disturbed days. Figure 15 shows firstly that the Louisvale MOF is greater than the Hermanus MOF. This is consistent with the Louisvale circuit being the longer of the two (735 km versus 684 km) and the reflection point being further north than that for the Hermanus circuit (Figure 1). The scatter of the points can be attributed to the TIDs being different at the two reflection “points.” The scatter is larger during the day, when the MOFs are higher.
 Figure 16 is the GPSII equivalent of Figure 15. Comparing Figure 16 with the observations in Figure 15 shows that the model values of the Hermanus and Louisvale MOFs are almost identical on average, whereas the Louisvale observations were slightly higher than the Hermanus observations. The GPSII results also show less scatter, which is because GPSII is not accounting for the TIDs. Some of the scatter would be due to the TID effects on the assimilated Grahamstown profiles/traces. The same situation holds for the EDAM results, except for about 20 to 30 outlier points.
 Figures 17 and 18 compare the errors in the GPSII and EDAM calculated values of the 1F MOF for the Hermanus to Grahamstown circuit. They show that the GPSII errors in the calculated 1F MOF are usually smaller than the EDAM errors, with a smaller diurnal scatter. The standard deviations are largest between about 07 and 13 UT (about 08–12 LT). The largest EDAM errors are associated with ~20 outlier points. Taking the daytime values of the 1F MOF to be 11 MHz (Figure 4) gives a daytime percentage error of about 0.5/11 or ~5% for the GPSII results, and a little higher for the EDAM results. The bulk of this error is probably due to the TIDs.
 Table 5 lists the error statistics for the model values of the 1F MOF for the Hermanus and Louisvale to Grahamstown circuits, accumulated over all days and times, summarizing the results plotted in Figures 17 and 18. The sample size for the Madimbo circuit was too small to warrant detailed analysis. The GPSII results are consistently more accurate than the EDAM results.
Table 5. Error Statistics for the Model Values of the 1F MOF, All Data
 Comparing the Hermanus and Louisvale entries shows that the errors are consistently higher for the Louisvale circuit. This agrees with the comparisons of the foF2 and hmF2 errors given in and Tables 2 and 3.
 Splitting the days up into quiet (Ap < 30) and disturbed days shows that the errors in the model values of the 1F MOF are smaller for the quiet days. This is as expected since storm effects would not usually be coherent over the area covered by the digisondes.
 The 1F MOFs corresponding to the IRI plasma frequency specifications are not of great interest because the IRI is a very simplified monthly median model, whereas we have seen that there are significant changes in the observed MOFs due to TIDs. Consequently, we have calculated the IRI MOFs only for 1 day, 16 September (day 259). These MOFs confirm the inability of the IRI to track the 1 to 2 MHz effects on the MOFs of TIDs. In contrast, the GPSII and EDAM MOFs do follow the largest TID fluctuations, although not the smaller ones. The day-to-day diurnal variability of the IRI is also more limited than that of the observations, but we have not considered the effects of this variability on the IRI MOFs. Settimi et al.  found that their ionospheric specification gave more accurate oblique ionograms than the IRI.
11 Errors in the Plasma Frequency Profiles
 Before discussing the errors in the plasma frequency profiles, we illustrate some typical profiles. Figure 19 shows the observed Hermanus plasma frequency profiles for 1045 UT (about noon). Incidentally, the ray tracing results showed that at 1045 UT the ray apogee at the MOF ranged from 230 to 280 km over the month, so this is the part of the profiles that is tested in the 1F MOF validations. The rays would reach hmF2 only at vertical incidence.
 The model plasma frequency profiles can differ from the ground-truth profiles because of differences in foF2, hmF2, or the basic shape of the profile. Any comparison of sets of profiles will average over the effects of each of these differences. In this section, we first illustrate the error profiles for all times of the day as a possible way of comparing the accuracies of the models. We then consider the average errors for two fixed times of the day in order to illustrate the variability of the profile errors.
11.1 Profile Errors for All Times
 Figure 20 shows the average plasma frequency errors in the GPSII, EDAM, and IRI profiles for all days and times at Hermanus. Because the profiles are averaged over all times, the diurnal variation of the errors has been lost, but the figures provide a simple indicator of the relative merits of the three models.
 The IRI profiles rarely extended above 300 km, so the IRI curve suffers from low counts above that altitude. Most of the observed values of hmF2 lay below ~330 km (Figure 11), although they exceeded 375 km for the disturbed night of 269/270. It can be seen that the GPSII errors have a small negative bias at most altitudes, while the EDAM errors change sign at ~220 km. All three errors are very similar at ~250 km, which may or may not be fortuitous.
 The average errors do not tell the whole story, since there is wide variability of the profiles at F2 layer altitudes. Figure 21 shows by way of example the average and average ± standard deviation of the plasma frequency errors in the GPSII profiles for all days and times at Hermanus. The GPSII and EDAM errors at Hermanus are systematically smaller than the IRI errors. The 2σ width (the separation of the outside curves in Figure 21) of the profile errors in MHz for Hermanus at some representative altitudes are given in Table 6. The GPSII and EDAM errors for the F region are thus about 0+/−0.5 MHz, with only a small mean error. The errors are larger for all models at Louisvale and Madimbo, with the GPSII and EDAM average errors again being systematically smaller than the IRI errors, and the GPSII errors being less than the EDAM errors. The 2σ width profile errors in MHz for Louisvale are given in Table 7.
Table 6. The 2σ Widths at Hermanus for the IRI, GPSII, and EDAM Models
Table 7. The 2σ Widths at Louisvale for the IRI, GPSII, and EDAM Models
 Tables 6 and 7 show that the IRI profile errors are very similar for Hermanus and Louisvale, as expected. For the 2σ errors at 250, 275, and 300 km, the GPSII errors increased for Louisvale by a factor of ~18% (average over the three altitudes), while the EDAM errors increased by a factor of ~66%. Thus, GPSII seems to have been able to extend the influence of the Grahamstown ionograms to Louisvale better than EDAM did (this difference should be investigated further; it may be due simply to the way the two models use the GPS TEC observations).
 For Madimbo, the GPSII and EDAM errors were similar to the IRI errors. Thus, the Grahamstown ionograms had minimal utility for updating the Madimbo profiles 1287 km away. The increase in the errors from Hermanus to Louisvale to Madimbo is consistent with the increase in the errors in foF2 that were listed in Table 2.
11.2 Profile Errors at Fixed Universal Times
 Accumulating the profile errors over all days and times tends to hide large outlier profiles. We have therefore considered the profiles specifically for two fixed UTs. Figures 22 and 23 show the altitude dependence of the average errors in the Hermanus plasma frequency for the GPSII, EDAM, and IRI profiles for noon (1045 UT) and midnight (2245 UT), accumulated over all days for September 2011. Figure 22 shows unexpectedly large errors for the IRI between ~150 and ~250 km that are significantly greater than the errors accumulated over all days and times (Figure 20). The GPSII and EDAM errors are much lower than the IRI errors. The GPSII and EDAM errors at midnight (Figure 23) are about twice those shown in Figure 20.
 This section summarizes the important results given in previous sections.
 The main thrusts of this paper were to:
Determine the extent to which digisonde observations can be used to update the plasma frequency profiles at other locations in the same region
Compare the relative merits of two real-time assimilation models, GPSII and EDAM, which take different approaches to assimilate the digisonde observations.
 The region considered was the midlatitude Republic of South Africa (RSA), since it has four digisondes, at Grahamstown, Hermanus, Louisvale, and Madimbo. The analysis was for a month of convenience, September 2011, which turned out to have a wide range of solar variability. The digisonde observations at Grahamstown were assimilated by the two models, with the other three digisondes providing the ground truth. GPSII assimilated the digisonde plasma frequency profiles, while EDAM assimilated the ionogram trace.
 The autoscaled data were found to be sufficiently accurate for the study, although some ionograms with the more egregious errors (blunders) were excluded from the analysis. Cases for which there was no Grahamstown ionogram (or the autoscaling was classified as unreliable) were also excluded. Thus, we have not tested in detail the ability of the models to cope with missing assimilation data.
12.2 Accuracy of Model Values of foF2
 Overall, EDAM was slightly better than GPSII at specifying the values of foF2 at Hermanus and Louisvale. However, GPSII did better at the most remote site, Madimbo. The RMS errors for the models at Hermanus (our main ground-truth site, 735 km east of Grahamstown) lay between 0.2 MHz (night) and 0.5 MHz (day). For typical daytime foF2 values of ~9 MHz, a 0.5 MHz error corresponds to ~6%. These errors are consistent with the minimum expected errors, which are apparently set by the TIDs being different at Grahamstown and the ground-truth sites. The errors increased with increasing distance from Grahamstown.
12.3 Accuracy of Model Values of hmF2
 EDAM encountered difficulties with some cases that led to large errors in hmF2 even when good data had been assimilated. This resulted in nonphysical electron density profiles, mostly at night. The cause of these assimilation errors has not yet been determined, and the outlier values have simply been excluded for the present analysis. In the future, it should be relatively straightforward to detect and exclude these poor assimilations, but the required procedures have not yet been implemented.
 The GPSII errors in hmF2 during the day were less than the EDAM and IRI values, which are very similar. The estimated minimum achievable errors reached ~20 km in the middle of the day. The GPSII and EDAM RMS errors have local minima of ~10 km near 06 and 16 UT, which are consistent with the estimated achievable errors. As with the foF2 errors, the GPSII errors in hmF2 increase with increasing distance from Grahamstown. The GPSII errors are systematically less than the IRI errors, but the EDAM errors do not provide any general improvement.
12.4 Accuracy of Model Values of h(0.8 foF2)
 Because hmF2 is a noisy parameter that seems to be very sensitive to autoscaling and profile derivation issues, as well as to TIDs, we have included the profile altitude at a plasma frequency of 0.8 foF2 (0.64 NmF2) as another validation parameter. It was found that GPSII and EDAM offer significant improvement over the IRI for h(0.8 foF2) (as well as for foF2, but not for hmF2). The EDAM errors in h(0.8 foF2) are somewhat smaller than the GPSII errors, in spite of some large outliers.
12.5 Accuracy of Model Values of 1F MOF
 We chose to use the 1F MOF as a validation parameter because it is so closely related to the main subpeak applications of the ionosphere. The MOF for the oblique ionograms is not currently scaled automatically by ARTIST, so the oblique ionograms were displayed using SAO Explorer and scaled manually for the Hermanus, Louisvale, and Madimbo to Grahamstown circuits.
 The GPSII errors in the calculated 1F MOF were usually found to be smaller than the EDAM errors. The standard deviations of the errors were largest between about 07 and 13 UT (about 08–12 LT). Taking the daytime values of the 1F MOF to be 11 MHz gives a daytime percentage error of about 0.5/11 or ~5% for the GPSII results, and a little higher for the EDAM results. The bulk of this error is probably due to the TIDs, for which neither GPSII nor EDAM accounts successfully.
12.6 Accuracy of the Model Plasma Frequency Profiles
 Given that there are nominally 30 × 96 × 4 profiles for each of the three ground-truth digisondes, we have reduced the validations to accumulations of the errors in the profiles (1) over all acceptable ionograms and (2) over all 30 (nominally) ionograms at two fixed times of the day (essentially noon and midnight).
 For the accumulation over all profiles, it was found that the GPSII and EDAM plasma frequency errors for the F region at Hermanus were about 0 ± 0.5 MHz, with only a small mean error. The IRI errors were consistently larger.
 Profiles at noon and midnight were used to provide a reminder that the errors accumulated over all days and times can mask some quite large individual errors. In fact, it is quite difficult to gain a coherent impression of the accuracy of the profiles—it is much easier to characterize the errors in operationally important parameters such as the 1F MOF that are based on the profiles.
 EDAM was developed as part of the UK Ministry of Defence ISTAR and Sensors Domain Research Programme. The development of GPSII is currently funded in part by AFRL under contract FA9453-11-C-0157.
http://ulcar.uml.edu/SAO-X/SAO-X.html. SAO Explorer is used to download the digisonde ionogram files (GRM) and files of scaled data (SAO) from DIDBase, as well as to display the ionograms for scaling the 1F MOF.