The deviations of foF2 from the monthly median, ΔfoF2, have been calculated for each UT hour of each month for the years 2002, 2003, 2004 and 2006, for 10 ionosondes in Australia and Papua New Guinea. The linear correlation coefficients between simultaneous (same UT) values of ΔfoF2 for 45 station pairs have then been calculated for each hour for the 48 months. Since mixing up magnetically quiet and disturbed days can lead to deceptive correlations that correspond to neither quiet nor disturbed days, most of the analysis has been restricted to magnetically quiet days, defined as Ap < 25. On a monthly basis, it is found that the correlation coefficients are significantly lower for months with no magnetically disturbed days. In general, the correlation coefficients decrease with decreasing solar activity, from 2002/2003 to 2006. It is inferred that the deviations that lead to the observed correlation coefficients are due to changes in the solar wind, and the consequent effects on neutral winds, electric fields, temperature, and composition. The magnitudes of the measured correlation coefficients have implications for the F2 region correlation lengths used in global ionospheric models. For the Australian ionosondes and for quiet days, the inferred north-south correlation length would be ∼1000 km, while the east-west correlation length would be ∼1500 km, with somewhat lower values for winter and low solar activity. The lower limit is not well defined because the shortest station separation is 857 km. Shorter station separations are considered in a companion paper.
 This paper readdresses the question of the spatial correlations between the deviations of foF2 from the monthly median, ΔfoF2, because of their importance to the emerging global assimilative models of the ionosphere. The correlations have been discussed previously by Rush  in terms of the requirements for an ionospheric observational network to be used for short-term forecasting of radio propagation conditions. With the advent of the GPS navigation system, most effort in this area has been concentrated on the correlation between the deviations of total electron content, ΔTEC. One of the key papers on ΔTEC was that by Klobuchar and Johanson . A recent paper [Shim et al., 2008] presents a very detailed analysis of the ΔTEC correlations of worldwide observations of GPS TEC (for 2004), and provides extensive references to earlier papers.
 The earlier studies of spatial correlations ignored the effects of disturbances, treating all observations as part of a statistical ensemble with a continuous spectrum of disturbances. However, this approach can overestimate the correlation lengths because of the impact of outliers caused by storms. In this study, the observations have been grouped into two broad ranges: (1) all the observations, including storms, so that their impact can be demonstrated and (2) observations for quiet to moderately disturbed conditions (Ap < 25). The bulk of days for which global models are used will fall into this latter regime.
McNamara and Wilkinson  drew attention to the importance of separating the data into magnetically quiet and disturbed days, since lumping the data together can lead to correlation coefficients that apply to neither the quiet nor disturbed days. For example, a single disturbed day in a month that produces a large enhancement at one location and a large depression at another can change a correlation coefficient for the month from positive to negative. This negative correlation coefficient is clearly not relevant to the other 29/30 (quiet) days of the month. The program used to analyze the deviations in foF2 will optionally ignore any days with Ap > 25 (that we describe rather loosely as “quiet” days), which is the mode of operation used for the present study. It might be argued that a much lower value of Ap should be used to define a magnetically quiet day. However, the data sample sizes would then be reduced drastically. The Ap index itself is not an ideal index because it provides only a very simple measure of the changes to the Earth's magnetic field. The Shim et al.  analysis was for intervals in 2004 that were generally magnetically quiet. However, Rush  and Klobuchar and Johanson , do not appear to have distinguished between quiet and disturbed days.
 The ionosondes providing the observations of foF2 described in this paper are located in Australia and Papua New Guinea, as shown in Figure 1 and Table 1. The Macquarie Island values of foF2 were not actually included because of the large number of values missing due to spread F echoes on the ionograms. The station order is basically alphabetical, except that Hobart was included at a later date (after the station numbering in the analysis program had been set). Like Macquarie Island, Hobart also has a large number of missing foF2 values.
Table 1. Locations of the Ten Ionosondes Used in the Analysis
Port Moresby, PNG
Norfolk I. (Australia)
 The ionosonde data available from the IPS Radio and Space Services database (see the acknowledgments) were all manually scaled by experienced personnel, often by the ionosonde station operators. Each datum is in the standard URSI format QxxxD described by Piggott and Rawer , and slightly modified over the years by international agreement. The “Q” is a qualifying letter that qualifies the scaled value, xxx, and “D” is a descriptive letter that provides information on why the value was qualified. For foF2, the values are given in units of 0.1 MHz, and the important qualifying letters are D (greater than), E (less than) and U (uncertain). All qualified values of foF2 have been set to zero and ignored in all the analyses. The nominal scaling error for manually scaled values of foF2 is 0.1 MHz.
Section 2 of the paper gives examples of “deceptive” or storm-contaminated correlations that arise when the disturbed days are included. These examples are deceptive in that they are the result of a large storm, and thus are not typical of what happens on the ∼90% of the days of the months that are magnetically quiet (or nonstorm). Storm effects that give either a depression or enhancement at both locations can have the effect of enhancing the correlation coefficient above its value for the other days of the month. Storm effects with opposite signs can switch a positive correlation that is representative of the quiet days to a negative correlation that is not representative of either set of days.
Section 3 gives the Brisbane-Canberra (942 km apart) correlation coefficients for each month of 2004, and shows that the correlation coefficients are significantly lower for magnetically quiet months. Some of the low correlation coefficients can be traced to low variances of foF2 at one or both of the ionosonde stations. The correlation coefficients have seasonal variations that are described in section 4.
 One of the main interests in studies of the foF2 correlation coefficients is to determine the rate at which the correlation coefficients decrease with increasing station separation, and this is discussed in the section 5. While this variation is very irregular, the correlation coefficients were found to decrease approximately linearly from ∼0.7 at ∼1000 km to ∼0.4 at 3000 km. The east-west correlation coefficients were found to be larger than the north-south coefficients.
Section 6 discusses the correlation lengths that can be inferred from the correlation coefficients. The correlation lengths derived from the correlation coefficients given by Rush  are significantly larger than those derived in this paper. Section 7 presents an overall summary of the results of the paper. A companion paper [McNamara, 2009] discusses the correlations of foF2 for station separations less than the minimum separation for the Australian ionosondes, which is 857 km.
2. Examples of Deceptive Correlations
 Analyses of storm effects on foF2 for Australian stations (internal reports, no longer available) showed typical midlatitude behavior [e.g., Buonsanto, 1999]. The severity of depressions was found to be larger for summer and equinox than for winter. Except during major storms, the winter months had only small, if any, depressions in foF2. The size of the depressions usually increased with latitude from Vanimo to Hobart. Enhancements of foF2 followed the normal midlatitude pattern of starting in the late afternoon and evening following a storm sudden commencement. The Australian midlatitude ionosphere does not behave in a coherent fashion during major storms, some ionosondes showing storm effects while others do not.
Figure 2 shows the diurnal variation of the correlation coefficient for Brisbane-Canberra (942 km apart), for November 2004, when the disturbed days (days 7 through 12, excluding 11 for which Ap = 23) are excluded. The correlation coefficients are ∼0.8 for all hours except near 1700 UT (0300 LT). LT = UT + 10 for the east coast of Australia.
 Including the disturbed days in the analysis sometimes increases the correlation coefficients, but the more common effect is to decrease them. Figure 3 shows the diurnal variation of the correlation coefficients for the same data set, Brisbane-Canberra, November 2004, when the disturbed days are included.
Figure 3 shows a dramatic decrease in the correlation coefficient for 0800 to 1300 UT (1800–2300 LT). In fact the correlation coefficient went negative for 0900–1100 UT, but these values have been set to zero for plotting convenience. Figure 4 shows the individual deviations for 1000 UT, one time for which the correlation coefficient went negative. The two points in the lower right corner of Figure 4 correspond to days 08 and 10, for which Ap was 189 and 181. These points are so far removed from the points for the other days that they control the value of the correlation coefficient, in fact switching it from a high positive value (0.82) to a negative value. The values of foF2 on day 09 (Ap = 120) were very close to the median (deviations of −2.1, −1.8). November is summer in Australia, so negative storm phases would be expected at midlatitude stations, as observed at Canberra. However, foF2 was strongly enhanced at Brisbane (hence the positive values of ΔfoF2) during this event. Cases such as this illustrate the need to sort the observations into magnetically quiet and disturbed days.
3. Correlation Coefficients for 2004
 Correlation coefficients have been derived for 45 station pairs, 12 months, 4 years, and 24 UT hours. We can thus present only a small fraction of the results, and must rely on some judicious averaging. Figure 5 shows the diurnal variation of the correlation coefficient for Brisbane-Canberra (the second closest station pair) for the summer months of 2004 (January, February, November and December). This was the year for which Shim et al.  analyzed global TEC values. Corresponding plots for the other years may be found in the work by McNamara . The data points for the different months are identified by the first letter in the name of the month.
Figures 6 and 7 show the results for winter and equinox. (In Figure 7, E is June and Y is July.) The correlation coefficients tend to be lower at night (0800–2000 UT for the ionosondes near 150°E) for summer (Figure 5) and winter (Figure 6), but not for the equinoxes (Figure 7). Perhaps the most interesting feature of the seasonal plots is the generally lower values of the correlation coefficients for April (Figure 7), and for May and June (Figure 6). These are in fact all magnetically quiet months, with maximum Ap values of 23, 17 and 22 (i.e., all less than 25). The correlation coefficients are also low in the middle of the day (0100 to 0400 UT) for February (Figure 5). Days 11 and 12 were the only disturbed days in February, both with relatively low Ap values (26 and 28).
 The low correlation coefficients for the magnetically quiet months confirm that the source of the deviations that provide the correlations is changes in the solar wind associated with solar disturbances, which provide a forcing that is external to the ionosphere. The only other candidate might be TIDs, but these would not normally be expected to correlate over the large distances between the Australian ionosondes (∼1000 km or greater). TIDs might play a larger role during magnetically quite periods for closer station separations. Atmospheric tides might also be important, but have not been investigated here.
 Low correlation coefficients for a station pair can derive from a low variance of foF2 for at least one of the stations. Low variances would be more affected by foF2 scaling errors and possibly by the effects of TIDs. Figure 8 shows an example in which the variances of foF2 are low at both stations, and the correlation coefficient is also low.
Figure 8 shows a general decrease of both variances and the correlation coefficients from ∼0800 UT onward. A limited analysis of the variances has suggested that there is a threshold value of ∼0.4 that must be exceeded in order to produce a reliable correlation coefficient. Some of the low correlation coefficients for a station pair are not related to low variances, but simply correspond to uncorrelated deviations. For example, for Brisbane-Townsville April 2004, 0400 UT, the low correlations are due to significant depressions in foF2 at Brisbane on days 04 and 06, and only minor depressions at the equatorward Townsville. The corresponding values of Ap were 12 and 21. Even at these low Ap levels, the ionosphere behaved quite differently at the two locations (1074 km apart).
4. Annual Variation of the Correlation Coefficients
 In order to provide succinct summaries of the variations of the correlation coefficients, separate median correlation coefficients have been derived for day and night, for each month and year. The local time is calculated at the midpoint between the stations in each pair, and divided into day (0800–1600 LT) and night (2000–0400 LT). Median values of the correlation coefficient are then calculated for the day and night. We illustrate the results for the closest separation (Canberra-Hobart) and second closest separation (Brisbane-Canberra).
 For convenience, Klobuchar and Johanson  defined the correlation length as the separation at which the correlation coefficient for ΔTEC drops to 0.7. The same definition will be used here for ΔfoF2. Consequently, the following discussion concentrates on the attainment of a 0.7 correlation coefficient.
4.1. Annual Variation of Canberra-Hobart Correlation Coefficients
Figure 9 shows the variation of the Canberra-Hobart (857 km) median daytime correlation coefficients (multiplied by 100 for convenience) for the 4 years, calculated as above, with the numerals in the plot being the last digit of the year.
Figure 9 shows that the correlation coefficients are generally higher for the more active years, and lowest in the middle of the year (winter) and for low solar activity (2006). The 2004 values are low in winter, while the 2006 values are low all year-round. The correlation coefficient exceeds 0.7 for most of 2002, 2003 and 2004, but not for 2006. There are large numbers of foF2 values missing because of spread F at night, but the daytime conclusions seem to be applicable to the nighttime.
4.2. Annual Variation of Brisbane-Canberra Correlation Coefficients
 The Brisbane-Canberra (942 km) results are not as affected by spread F as the Canberra-Hobart results. Figure 10 shows the variation of the Brisbane-Canberra daytime correlation coefficients for the 4 years. Isolated numerals indicate lack of data for the surrounding months. There are also some missing numbers because of low sample sizes.
 In general, the correlation coefficients are lower for Brisbane-Canberra than for Canberra-Hobart (the shorter separation). The correlation coefficients exceed 0.7 for about half the months in 2002, 2003 and 2004, but they are less than 0.7 for the other half of the months. For 2006, they exceed 0.7 for only 3 summer months.
 The nighttime Brisbane-Canberra correlation coefficients for the 4 years are shown in Figure 11. The correlation coefficients exceed 0.7 for most of 2002, all of 2003 (some data points are missing), about half the months in 2004, and for only October and November in 2006. There is a general decrease in the correlation coefficients for the winter months (6, 7 and 8).
5. Correlation Coefficient Versus Ionosonde Separation
 It is well known that the correlation coefficients for ΔfoF2 decrease with increasing ionosonde separation. Unfortunately, the separations for the Australian ionosondes are quite large, as shown in Table 2, which gives the station separations for some of the closest pairs.
Table 2. Australian Ionosonde Stations With the Closest Separations
 As can be seen from Figure 1, Hobart, Canberra, Brisbane and Townsville are in eastern Australia, while Learmonth and Mundaring are in western Australia. Vanimo and Port Moresby lie to the north of eastern Australia, and are equatorial in nature. Norfolk Island lies an hour to the east of Brisbane. The medians used to define the monthly variation in section 4 have been summed over 12 months to provide the average monthly (yearly) value for each separation, separately for day and night.
Figure 12 shows the daytime variation of the averaged median correlation coefficients with station separation for 2004. As can be seen from Figure 12, the variation with station separation is rather noisy, even after averaging over 12 months. Ignoring the fluctuations, the correlation coefficient decreases approximately linearly from ∼0.7 at ∼1000 km to ∼0.4 at ∼2000 km. The high value at 1482 km is for the basically east-west pair Brisbane-Norfolk Island. The correlation coefficients are higher for an east-west separation than for the same north-south separation (q.v.). The nighttime behavior is similar (not shown).
 Comparing the results like those in Figure 12 for 2002, 2003, 2004 and 2006 shows the following:
 1. The overall correlation coefficients decrease from 2002/2003 to 2006 (i.e., with decreasing solar activity).
 2. The variability of the correlation coefficient with station separation is greatest for 2002, nighttime.
 3. The separation at which the correlation coefficients drop to 0.4 (a convenient number) is ∼2000 km for 2004 and 2006, and ∼3000 km for 2002 and 2003. These numbers are approximate because of the relatively large scatter. The longer separation distances correspond to higher solar (and magnetic) activity.
 4. The rate of decrease of the correlation coefficient with station separation out to ∼3000 km is about the same for day and night in 2002, 2003 and 2004. However, the correlation coefficients are generally low for 2006 (starting at ∼0.5 for the closest separations).
 Previous authors have found that the correlation coefficients at midlatitudes drop off with distance more slowly in the east-west direction than in the north-south direction [Rush, 1976; Klobuchar and Johanson, 1977; Shim et al., 2008]. There are three useful east-west station pairs for the Australian network, Brisbane-Norfolk, Darwin-Townsville and Mundaring-Canberra.
 Norfolk Island lies about one hour to the east of Brisbane, so the foF2 departures have been correlated at the same UT (the default) as well as at the same LT. The correlation coefficients were found to be higher for UT than for LT, which is consistent with an external (to the ionosphere) cause of the deviations.
Table 3 shows the annual average correlation coefficients for the three east-west station pairs, for daytime observations. Table 3 shows that the correlation coefficients decrease from 2002/2003 to 2006, and also (generally) decrease with increasing distance. There is no significant difference between day and night, so the night results are not shown.
Table 3. Correlation Coefficients for East-West Station Pairs, Daytimea
Times 100 for clarity.
6. Correlation Lengths Used by Global Ionospheric Models
 Global assimilative models such as USU-GAIM [Scherliess et al., 2006], EDAM [Angling and Khattatov, 2006], and JPL-USC GAIM [Wang et al., 2004] assume that the effects of a difference between an F2 region observation and the model value decrease with distance in an exponential fashion, exp(−d/D), where D is the ionospheric correlation length.
 As discussed by Angling and Khattatov  a large number of points need to be processed for these assimilative models, and the direct implementation of a Kalman filter for their own model is impossible. The evolution of only the diagonal terms of the background error covariance matrix (i.e., the variances) is tracked, while parameterizations are used for the off-diagonal elements. If it is assumed that correlations between variations of electron densities at two different points become negligible at certain distances (the correlation lengths), the matrices become sparse, and the calculations become possible.
 It is these correlation lengths that are required for global ionospheric models, whereas the observations of foF2 provide correlation coefficients. There does not seem to be a one-to-one relationship between the correlation coefficient for foF2 deviations and the correlation length for an assumed exponential decay with distance of a deviation observed at one station. However, Klobuchar and Johanson  defined the correlation length as the separation at which the correlation coefficient for ΔTEC drops to 0.7. This definition will be used here for ΔfoF2, although with a few caveats.
For a linear prediction model, this can be written in terms of the correlation coefficient, r, as
If r = 0.866, for example, PI = 50%.
 The correlation coefficient of 0.7 taken to define the correlation length would lead to a PI of only 29%. A correlation coefficient of 0.87 would be required to halve the RMS errors, and provide a PI of 50%. This level of correlation was found for only 2002 and 2003, for the closest station separations. If a correlation coefficient of 0.87 were demanded, the correlation lengths discussed here would shrink below those typically available from station networks.
 Correlation lengths may be derived from the ΔfoF2 correlation coefficients given by Rush , who listed the correlation coefficients for east-west and north-south station separations as a function of season and local time. These correlation coefficients were derived using ∼30 ionosonde stations for the IGY in 1957/1958, which was a period of very high solar activity. Most of the ionosondes were in the northern hemisphere.
 Rush did not separate quiet and disturbed days in his analysis of the IGY values of foF2. Since we have found that the correlation coefficients are higher for the high solar activity years (2002, 2003) than for the low-activity years (2006), we could expect that the correlation lengths corresponding to Rush's values of the correlation coefficient will be somewhat similar to those found here for 2002/2003, and significantly longer than those found here for 2004 and 2006, especially for the latter.
6.1. North-South (Meridional) Correlation Lengths
 The north-south correlation lengths derived from the correlation coefficients given by Rush  are listed in Table 4, broken up into his four local time zones. These are the distances at which the correlation coefficients dropped to 0.7 for the IGY data.
Table 4. North-South Correlation Lengths Derived From Correlation Coefficients Given by Rush 
 Correlation lengths corresponding to a correlation coefficient of 0.7 have also been derived from the Australian data, for the same seasonal and LT intervals. All hourly correlation coefficients for a given year have been binned into seasons and LT intervals, and the median determined for each season and LT bin.
 The Australian data for 2002/2003 give the north-south correlation length as ∼1000 km for all seasons and LT intervals. The scatter in the values is too large to allow a more detailed specification of the correlation lengths, but they tend to be smaller in winter than in the other seasons. The values in Table 4 (based on Rush ) are significantly larger than ∼1000 km for summer and equinox.
 For the 2004 data, the Australian data gives the north-south correlation length as ∼900 km for summer and equinox, and less than the smallest station separation (857 km) for winter. For the 2006 data, the correlation coefficients for the Australian data reach 0.7 only for the interval 1700–2100 LT for the closest station separation. Thus for the low solar activity years, the correlation lengths are typically less than ∼850 km.
6.2. East-West (Zonal) Correlation Lengths
Table 5 shows the east-west correlation lengths derived from the correlation coefficients given by Rush . The station pair with the smallest east-west separation for the Australian data is Brisbane-Norfolk, at 1482 km. Table 3 shows that the correlation coefficients are 0.7 or greater for 2002, 2003 and 2004, but not for 2006. The correlation coefficients for the next closest pair (Darwin-Townsville, 1875 km) do not usually exceed 0.7 for any season or LT interval. As far as can be ascertained from the limited data set, the correlation length appears to be greater than 1481 km but less than 1875 km for 2002 and 2003, for most seasons and LT intervals. The correlation lengths do not reach the large equinoctial and summer values given in Table 5. The values are lowest for winter 2004 and 2006.
Table 5. East-West Correlation Lengths Derived From Correlation Coefficients Given by Rush 
 The Australian results can be summarized as giving east-west correlation lengths of ∼1500 km for years of high solar activity (2002, 2003), and an uncertain value of ∼1000 km for years with low solar activity (2004, 2006). These are much shorter than the IGY values given in Table 5. The correlation lengths are lowest in winter.
6.3. TEC Correlation Lengths
 Using observations of TEC made in 2004, Shim et al.  found midlatitude north-south angular correlation lengths of 7°, and east-west correlation lengths of 20°. These correspond to distances of ∼800 km and 2200 km (for midlatitudes). The 800 km is somewhat lower than the ΔfoF2 value of ∼900 km given here for summer and equinox, but agrees with the “less than 857 km” value for winter. The 2200 km is too long when compared with the present values for summer and equinox, and especially for winter. There is, of course, no guarantee that the correlation coefficients for ΔfoF2 and ΔTEC will be the same, since foF2 is only one point in the profile that is integrated to get the TEC.
6.4. Equatorial Stations
 For the two equatorial stations, Vanimo and Port Moresby (separation of 983 km), the correlation coefficients are very noisy and suffer from large amounts of missing values because of spread F, especially in 2002. There was no data for Port Moresby for May through October. The clearest set of results was for winter 2004, for which the correlation coefficients were about 0.6 +/− 0.2 for all times of day, with most of the values being below 0.7. Vanimo is northwest of Port Moresby, so the stations do not fall into either the north-south or east-west category.
 Values of foF2 observed by eight ionosondes in Australian and two in Papua New Guinea have been used to investigate the correlation between deviations of foF2 from the monthly median for the 45 possible station pairs. Most of the analysis was performed for magnetically quiet days (Ap < 25). We consider it essential to avoid mixing up quiet and disturbed days, which results in deceptive correlation coefficients that are applicable to neither quiet nor disturbed days. The correlation coefficients for those 10% of days that are either “storm” days or very quiet days (Ap < 4) are not addressed here.
 The correlation coefficients were found to decrease approximately linearly with station separation, and to decrease with decreasing solar activity from 2002/2003 to 2004 to 2006. In general, the correlation coefficients for a magnetically quiet month were significantly lower than for other months. There is a large variability of the correlation coefficient, especially for 2002, which makes it difficult to provide summary conclusions.
 We have derived correlation lengths for the Australian data using the Klobuchar and Johanson  expedient of setting the correlation length equal to the distance at which the correlation coefficient decreases to 0.7. For 2002/2003, these were found to be ∼1000 km for north-south (meridional) separations, and ∼1500 km for east-west (zonal) separations. The meridional values are shorter than those derived (Table 4) on the basis of the IGY (1957/1958) correlation coefficients given by Rush . The zonal values are much shorter than those derived (Table 5) from Rush . The correlation lengths are shorter for the low-activity years 2004/2006 than for the active years 2002/2003, but the Australian grid is too coarse to determine the actual values for meridional separations for the low-activity years.
Rush  used the very active years 1957 and 1958, so his correlation coefficients and deduced correlation lengths tend to be larger than those obtained in the present study. For magnetically quiet days (∼90% of the time), the IGY correlation lengths would be overestimates. It seems likely that the much longer east-west correlation lengths for summer and equinox than for winter in Table 5 are a result of including the very disturbed days. For example, if the whole dayside ionosphere (covering many thousands of kilometers) is severely depressed during a storm, the correlation coefficients for the month will be controlled by the points for this day. This would hold for any east-west station pair, regardless of their separation.
 Some of the low correlation coefficients, and thus the deduced correlation lengths, can be traced to low variances in foF2 for at least one station of the pair. If the variances are low at both stations, the errors introduced by the use of optimistic correlation lengths would be correspondingly small. Problems would arise, however, if the variances were low only at one location. More detailed results and discussions on this topic are given by McNamara .
 In a paper that is complementary to the present one, McNamara  discusses the correlation coefficients derived from Digisonde ionograms for station separations down to 66 km. That paper integrates the conclusions of the two papers, and proposes correlation lengths for use with global ionospheric models at different levels of solar activity. Incidentally, an ionosonde was operated at Camden (−34.05, 150.67) for 1981–1984. Camden is outside Sydney, and 208 km from Canberra. The Canberra-Camden monthly correlation coefficients had average values of 0.94 for 1981 and 1984.