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Spatial correlations of foF2 deviations and their implications for global ionospheric models: 2. Digisondes in the United States, Europe, and South Africa

[1] The deviations of foF2 from the monthly median, ΔfoF2, have been calculated for each UT for a limited selection of months and times at solar minimum using ionograms recorded by Digisondes in the United States, Europe and South Africa. The linear correlation coefficients between simultaneous (same UT) values of ΔfoF2 have then been calculated, with a view to determining the correlation lengths that are important for global ionospheric models. The results presented here are for station separations ranging from 66 km to several thousand kilometers, and complement those given in a companion paper that used values of foF2 from Australian ionosondes, the closest of which were 857 km apart. The correlation lengths derived from the two sets of data are used to specify midlatitude correlation lengths that can be used with global ionospheric models for different levels of solar activity.

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[2] The paper by McNamara and Wilkinson [2009] (hereinafter referred to as Paper A) discusses the correlation coefficients and correlation lengths for ΔfoF2 for the Australian region, using manually scaled foF2 values for 2002, 2003, 2004 and 2006 (basically solar maximum to solar minimum). The closest station separation for the Australian ionosondes is 857 km, which was found to be too large to define the smaller correlation lengths that exist for solar minimum conditions. The present paper complements that study by including Digisondes in South Africa, Europe and North America that provide station separations shorter than 857 km. It also confirms the Australian results for equinoctial months for low levels of solar activity and large separations.

[3] The Australian data described in Paper A were all manually scaled over the years by experienced personnel. The present study is limited because of its restriction to the use of values of foF2 for September/October 2006 that were manually scaled by the author. No value was assigned to foF2 if a reliable value could not be obtained.

[4] The Digisondes [Reinisch, 1996] provide automatically scaled values of foF2 (and other parameters), but the use of these autoscaled values has been found to lead to confusing results, because just one bad value can drastically decrease the correlation coefficient. This bad value could arise from such things as a poor quality ionogram, interference from short wave transmitters, prohibited frequency bands, a complex ionogram that would challenge even an expert human being, or a “blunder” made by the autoscaling software, ARTIST [Reinisch et al., 2005; Galkin et al., 2007].

[5]Section 2 of the paper discusses the results for the European Digisondes, which have some of the closest separations. Sections 3 and 4 provide analyses of the results for the other two sets of Digisondes, in South Africa and North America. The three sets of results are summarized and then integrated in terms of correlation lengths with the results of Paper A in section 5.

2. European Digisondes

[6] Ionograms from European Digisondes were manually scaled for September 2006 (hourly) and October 2006 (a cadence of 4 h). The locations of the European Digisondes are plotted in Figure 1. Fairford, Chilton, Pruhonice and Dourbes are referred to here as the Northern European Digisondes, while Rome, San Vito, and Athens are referred to as the Southern Europe Digisondes.

[7]Figure 1 also shows some of the station separations. The orientations of the two sets of Digisondes are basically east-west. LT and UT are virtually identical for the Northern European Digisondes, while LT ∼ UT + 1 for the Southern European Digisondes.

[8]Table 1 shows the correlation coefficients and the variances for the Northern European Digisondes for October 2006. (The station IDs are given in the caption to Figure 1.) There are six station pairs (Juliusruh was not included because there were no ionograms available for that month). The first row in each set of data gives the correlation coefficients, while the second and third rows give the variances in foF2 at the station (with some redundant rows). The correlation coefficients tend to be low if the variances are low, but only for larger separations. This suggests that small deviations in foF2 that are correlated for small separations are not correlated over larger distances.

Table 1. Correlation Statistics for Deviations of foF2 From the Median, Versus UT, October 2006, Manually Scaled Data^{a}

Station 1

Station 2

0000

0400

0800

1200

1600

2000

Kilometers

a

The first row for each of the six sets of data gives the correlations coefficients, while the other two rows give the foF2 variances.

RL052

FF051

0.97

0.97

0.97

0.99

0.99

0.99

66

Variance

RL052

0.13

0.12

0.19

0.42

0.20

0.59

Variance

FF051

0.14

0.10

0.20

0.50

0.20

0.47

DB049

RL052

0.87

0.88

0.85

0.85

0.86

0.98

397

Variance

DB049

0.10

0.12

0.11

0.75

0.21

0.42

Variance

RL052

0.13

0.12

0.19

0.42

0.20

0.59

DB049

FF051

0.91

0.85

0.80

0.87

0.87

0.98

463

Variance

DB049

0.10

0.12

0.11

0.75

0.21

0.42

Variance

FF051

0.14

0.10

0.20

0.50

0.20

0.47

PQ052

DB049

0.72

0.46

0.83

0.89

0.91

0.88

713

Variance

PQ052

0.08

0.17

0.32

0.59

0.34

0.22

Variance

DB049

0.10

0.12

0.11

0.75

0.21

0.42

PQ052

RL052

0.44

0.20

0.81

0.82

0.68

0.80

1088

Variance

PQ052

0.08

0.17

0.32

0.59

0.34

0.22

Variance

RL052

0.13

0.12

0.19

0.42

0.20

0.59

PQ052

FF051

0.45

0.00

0.75

0.87

0.70

0.74

1143

Variance

PQ052

0.08

0.17

0.32

0.59

0.34

0.22

Variance

FF051

0.14

0.10

0.20

0.50

0.20

0.47

[9]Figure 2 shows the variation with station separation of the correlation coefficients listed in Table 1. Figure 2 can serve as a “typical” variation of the foF2 correlation coefficient with increasing station separation for solar minimum conditions. The UT and LT are very similar for these stations. The correlation coefficients drop off more quickly at night than during the day. Note that all of the station pairs are aligned basically east-west.

[10] For the three Southern Europe Digisondes, the only ionograms that were manually scaled were for Athens and San Vito, for 1200 to 1800 UT, with a 1-h cadence. The Rome data were not scaled because of the quality of the ionograms for that month. Table 2 shows the Athens-San Vito correlation coefficients for the seven times of day.

Table 2. Athens-San Vito Correlations of foF2 Deviations for October 2006, Manually Scaled

Station 1

Station 2

12

13

14

15

16

17

18

AT138

VT139

0.91

0.86

0.64

0.44

0.77

0.88

0.88

Variance

AT138

1.08

1.18

0.37

0.46

1.24

1.37

0.37

Variance

VT139

1.15

0.73

0.32

0.30

0.40

0.90

0.34

[11] The second and third rows give the variances of the deviations. The Athens-San Vito station separation is 569 km, basically east-west. Two points could be added to Figure 1 at this distance: 1200 UT, r = 0.91; 1600 UT, r = 0.77. Note that the foF2 variances are much lower for San Vito than for Athens at 1600 and 1700 UT. The variances are low at both stations for 1400 and 1500 UT, when the correlation coefficients are also low.

[12] The September 2006 hourly ionograms were manually scaled for Fairford, Juliusruh and San Vito. Figure 3 shows the correlation coefficients for Fairford-Juliusruh (1042 km, basically east-west) had a value of 0.8 ± 0.1 throughout most of the day.

[13] The dip at 0400 UT was also seen for the October data (Figure 2) for the longer circuit lengths. The correlation coefficients for Juliusruh and San Vito (1590 km) and for Fairford and San Vito (1922 km) had values less than 0.6 for most of the day.

[14] As explained in Paper A, the correlation length is taken to be the separation at which the correlation coefficient drops to 0.7. In summary, the correlation lengths given by the European Digisondes are ∼1143 km between 0800 and 2000 UT (also ∼0800–2000 LT), ∼713 km at 0000 UT, and between 463 and 713 km at 0400 UT. Table 2 (Athens-San Vito) shows the correlation length to be greater than 569 km between 1200 and 1800 UT, except that the correlation coefficients fall below the required 0.7 at 1400 and 1500 UT. The Fairford-Juliusruh September results (Figure 3) show that the correlation length exceeds 1042 km (the station separation) for most of the day.

[15] The shorter separations for the European stations have revealed spatial and temporal structure in the correlation coefficients that was not seen for the longer separations encountered with the Australian ionosondes. If we ignore the details, we can give the correlation length for these basically east-west pairs as ∼1100 km during the day, but dropping to less than 700 km during the night. These results are for equinoctial months at solar minimum.

3. South African Digisondes

[16] The South African Digisondes are located at Madimbo, Louisvale and Grahamstown. The locations are plotted in Figure 4. To a good approximation, LT = UT + 2. The Grahamstown-Madimbo separation is basically north-south, but the other two pairs have both east-west and north-south components. Recall that the correlation coefficients are usually larger for east-west separations than for north-south separations.

[17] The September 2006 ionograms for the three Digisondes were scaled manually for each hour of the day. It was found that there was little diurnal variation of the Grahamstown-Louisvale (735 km) correlation coefficients, as can be seen in Figure 5. The diurnal variation is rather noisy, but can be set at 0.7 ± 0.2. The plots for the other two station pairs are not shown here. The Louisvale-Madimbo correlation coefficients were 0.6 ± 0.1, and were less than 0.7 for 90% of the time. The correlation length was thus less than the station separation of 1185 km. The Grahamstown-Madimbo (1287 km) correlation coefficients were 0.5 ± 0.2. They reached 0.7 for 0200 to 0400 UT (∼0400 to 0600 LT), and dropped down to ∼0.2 at 0700 UT.

[18] The October 2006 Grahamstown and Louisvale ionograms were scaled on the half hour from 1300 to 1600 UT (late afternoon, when the correlation coefficients tend to be highest). The correlation coefficients lay in the range 0.80 ± 0.06. Since these values exceed the 0.7 value, the correlation length at this time of day must exceed the station separation of 735 km, as found for the September ionograms. In summary, the correlation length for September/October 2006 for these stations was found to be generally ∼735 km, and certainly less than 1185 km.

4. North American Digisondes

[19] The locations of the North American Digisondes are plotted in Figure 6. The hourly September 2006 ionograms were scaled manually for Boulder, Wallops Island and Puerto Rico, for which the station separations all exceed 2000 km. The correlation coefficients were found to be very low (consistent with the large separations) and irregular during the day, although all three station pairs showed a local peak of ∼0.7 between 0200 and 0600 UT (late evening).

[20] The only ionograms scaled manually for October were daytime ionograms for Millstone Hill and Wallops Island, which are 623 km apart. The correlation coefficients for 1200 to 2200 UT (∼0700 to 1700 LT), were found to be 0.72 ± 0.12, which indicates that the correlation length was ∼650 km.

5. Conclusions

[21] For equinoctial months at solar minimum, the European Digisonde network suggests an east-west correlation length of ∼1100 km during the day, but dropping to less than 700 km during the night. The South African Digisonde network provides one north-south pair (Grahamstown-Madimbo) and two pairs with a bearing of ∼45°. The north-south pair indicates that the north-south correlation length is less than 1287 km. The other pairs indicate that the correlation length for a station pair with a bearing of ∼45° exceeds 735 km, and is probably ∼1185 km. The most useful results obtained for the North American Digisonde network were for Millstone Hill and Wallops Island (623 km, basically north-south). These results showed that the correlation lengths were generally greater than 623 km for 1200 to 2200 UT (0700 to 1700 LT).

[22] It was shown in Paper A that the north-south correlation lengths for low solar activity years were typically less than ∼850 km. The North American data indicate that the correlation length was greater than 623 km during the day, so we propose a (midlatitude) north-south correlation length of ∼700 km for solar minimum. The east-west correlation lengths for the Australian data had an uncertain value of ∼1000 km for years with low solar activity. The European Digisonde network suggests an east-west correlation length of ∼1100 km during the day, but dropping to less than 700 km during the night, which is consistent with the Australian results.

[23]Table 3 provides a summary of the results of this paper and Paper A in terms of high/low levels of solar activity and orientation, for midlatitude locations. The correlation coefficients tend to be low for the few hours before dawn, but not for all station pairs.

Table 3. Suggested Midlatitude Correlation Lengths for Use With Global Models

Solar Activity

North-South

East-West

High

1000

1500

Low

700

1000

[24] The correlation lengths deduced in Paper A from the correlation coefficients given by Rush [1976] are generally much larger than these values, especially for summer and equinox. Rush used data from the very active IGY years (1957/1958), and did not separate the magnetically active and quiet days. We believe that not doing so led to deceptively high correlation coefficients that apply to neither the quiet nor disturbed days. Shim et al. [2008] found correlation lengths of ∼800 km and 2200 km for 2004 GPS TEC observations, but as indicated in Paper A, there is no guarantee that the correlation coefficients for ΔfoF2 and ΔTEC will be the same.

[25] More details of the analyses of foF2 correlation coefficients can be found in two internal reports [McNamara, 2008a, 2008b], which are available from the author in PDF format. These reports show that the four numbers given in Table 3 represent an oversimplification of a very complex situation. The second report gives some details of the difficulties encountered when using autoscaled data. The close spacing of the European Digisondes provides a fertile ground for investigating the properties and physical causes of the ΔfoF2 correlations for small (less than ∼1000 km) separations.

Acknowledgments

[26] The Digisonde ionograms were obtained from the University of Massachusetts Lowell ionospheric database http://umlcar.uml.edu/DIDBase/. The work was performed under an Air Force Weather Agency contract, FA8718-08-C-0012.