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Time-weighted magnetic indices as predictors of ionospheric behaviour
Journal
of Armospheric
Pergamon 0021-9169(95)00096-8
and Terrestrial
Physics, Vol. 57, No. 14, pp. 1763-1770, 1995 Copyright 0 1995 Elsevier Saence Ltd Printed in Great Britain. All rizhts reserved 00%9169/95-X.9.50+0.00
Time-weighted magnetic indices as predictors of ionospheric behaviour Jiping Wu and P. J. Wilkinson IPS Radio and Space Services, P. 0. Box 5606, West Chatswood, NSW 2057, Australia (Received infinalform
16 January 1995 ; accepted 17 February 1995)
Abstract-A time-weighted accumulation of the ap index, ap(z) (Wrenn, 1987; Wrenn et al., 1987, 1989), together with other similar indices, was explored as a predictor of ionospheric behaviour, usingf,F2 data for a selection of locations in Australia and Europe for September and October 1989. All the time accumulated indices showed improved linear correlations, indicative of a response time of the order of about 15 hours. The response time could be decomposed into a lag between respective time series and a persistence time, although the decomposition appeared unnecessary as the persistence time carried the same information. Of the individual indices investigated, aa appeared best and the aurora1 oval equatorward edge index (AI index) was poorest, although the differences were not statistically significant. Comparisons between the aa, ap and Kp indices, plus comparisons between different ionospheric parameters showed that forecasting may be improved using different transformations of the data. While these results a.ppear good, further studies using other stations and seasons are warranted to confirm their utility for forecasting.
1. INTRODUCTION
While it is well known that ionospheric disturbances and storms follow geomagnetic disturbances, forecasts for the responses are poor. The quality of ionospheric forecasting may be improved by finding a better way to organise the ionospheric and magnetic data. Here, this proposition is explored by investigating how well various time series accumulations of aa, ap, Kp, Dst and AI indices correlate with observed changes in the ionosphere. Since the ionospheric storm effects correspond to high levels of magnetic activity, and the severity of the effects depends more on the average index level throughout the event then on the peak value, which may occur for only a single observation, it is worth exploring accumulative indices. Wrenn (1987) introduced the following time series accumulation of the ap index : ap(z) = (l-,r)(ap+zap_,
+?apmZ+
...)
where 0 < 7 < 1 and ap_,, ap_,, . are the ap values for - 3, - 6, - 9 hours, etc. The attenuation multiplier, or persistenc’z factor z, is a value between 0 and 1 and the factor 111-z) normalises the summation. As a persistence factor, 7 determines how ap(T) will depend on the pas{ history of the ap index. The bigger the value of z, the more dependence ap(z) will have upon its history.
Similar time-weighted indices can be constructed using other geomagnetic indices such as Kp, the three hour range index from which ap is calculated, aa, similar to ap but based on two antipodal stations, and Dst, an index supposedly indicative of large scale geomagnetic activity due to the equatorial ring current and one Wrenn suggested was worth exploring. Alternatively, a direct indication of magnetospheric processes on the aurora1 region could be used. In this case the aurora1 oval equatorward edge index (AI index hereafter) calculated from precipitating electron data recorded by the Defence Meteorological Satellite Program (DMSP) was used. The AI index has higher time resolution than the other indices (20-40 minutes versus 3 hour and 1 hour) and possibly will be available in real time (Rich, 1992) in the near future. By taking a delta function in ap and comparing the subsequent decay of ap(t) for different values of T Wrenn (1987) found that 3/( 1 -z) (in hours) can be used as an approximate measure of the time required for a l/e decay of ap(z) and called it the persistence time. Following the same procedure, depending on the time division of an index, 3/(1-r), l/(1-~) and 0.55/(1 -z) hours is the persistence time for aa (and ap(z) and Kp(z) also), Dst(z) and AI(T), respectively. The persistence time for the best correlation between ,f,F2 and ap(r) (or any other index) is regarded as a typical response time for F2 region to magnetic disturbances.
1763
J. Wu and P. J. Wilkinson
1764
Table I. Station coordinates Geographic latitude,
Station Uppsala St Peter-Ording Slough Poitiers Rome Townsville Mundaring Canberra Hobart
59.8N 54.ON 51.5N 46.5N 41.9N 19.6s 32.0s 35.3s 42.98
Geographic longitude,
Geomagnetic latitude,
Geomagnetic longitude.
L
58.3N 54.8N 54.IN 49.2N 42.2N 28.43 43.5s 44.0s 51.6s
106.9E 94.8E 84.4E 83.OE 92.7E 139.5w 172.3W 134.3w 134.1w
3.3 2.6 2.4 2.0 1.6 1.3 1.9 2.0 2.9
17.6E 9.3E 0.5w 0.4E 12.6E 146.9E 1l6.2E 149.OE 147.3E
In this paper, these indices are compared with ionospheric changes to discover if they can assist in ionospheric forecasts. The simplest way in which an index can be used to assist in forecasts is to use it directly, scaling the index to give an associated ionospheric response. This information could be used as guidance, together with other indicators. For purposes of exploring and comparing the time-weighted indices as predictors of ionospheric behaviour, a linear correlation analysis was adopted. While this implies a simplistic approach to the use of indices, it is convenient for the present purposes. The objective of this paper is to discover whether indices developed following Wrenn’s suggestion can be used to assist in ionospheric forecasting.
2. DATA
Data are mainly analysed for the period September and October, 1989 when magnetic activity was often very high. Most results are presented for Canberra and these are indicative of the results obtained for other locations (see Wu and Wilkinson, 1993, for additional details). All the locations analysed are shown in Table 1. Finally, seasonal behaviour at Canberra in 1989 is summarised. Kp, aa, ap, Dst and AI indices have all been used as indicators of magnetic disturbances. Since aa, ap and Kp are 3-hour averaged indices and AI is a 2040 min averaged index, while f,F2 is an hourly measurement, interpolated fhF2 values centred on ap(z) and Kp(z) time and interpolated AI values on the hour were used in the analysis. This did not affect the results significantly as checks of data sequences showed, so the interpolation method was retained in the analysis since it was more representative of the effects being analysed. Dst is an hourly index, so no interpolation is needed.
3. RELATIONSHIP
BETWEEN
GEOMAGNETIC
THE F REGION
AND THE
INDICES
Figure 1 displays the Canberraf,F2 data and the aa index for different z, in September and October 1989. The top panel shows the variation of electron density changes over Canberra in terms of log(N/N,). Electron density, N, is calculated from the observed hourlyf”F2 values, and the N, are calculated from the monthly medians off,F2. Other panels show the variations of aa for t = 0.0, 0.5, 0.7, 0.8 and 0.9, respectively. It is clear that, apart from the pronounced diurnal variation, log(N/N,,) follows the aa reasonably well for large deviations. The interpolation of N, and the choice of ionospheric parameter, is explored in Fig. 2, which shows the correlation coefficients from linear fitting of three f,F2 parameters with aa as functions of the persistence factor z. Two options are log (N/N,) and log (N/N;), where No is the monthly median and N’, is the daily median interpolated from the adjacent monthly medians. The third option uses (f-fu)/fO, where ,f’is the hourlyf,F2 and,f, is the monthly medianfhF2. The following conclusions can be drawn from these two figures :
(1) aa(
(2)
the time-weighted accumulation, is a better index than the instantaneous aa index, aa( in ionospheric forecasting. When z changes from 7 = 0 to r = 0.80, the correlation rises from -0.50 to -0.68 for log(N/N,) and from -0.46 to -0.63 for (f‘-Q/fo. When t = 0.80, the correlations betweenf,F2 and aa are best no matter how the,f,F2 data are organised. z = 0.80 corresponds to a persistence time of 15 hours which suggests, an ionospheric response time to geomagnetic disturbances of about 15 hours, consistent with general ionospheric forecasting experience at IPS.
Predicting
ionospheric
behaviour
using geomagnetic
indices
0.5
0.0 ,-0.5
150 100 50 n 200, 150 100 50 --- 0 __I
aa(0.70)
150
100,
t
150
-
I\
I
aa(O.80)
100 -
150
aa(0.90)
100 _I50
_A
September
h
1989
October
Fig. 1. The variations of log(N/N,J for Canberra and aa in September and October 1989. Electron densities N are calculated from observed hourly foF2 values, and N, are the monthly medians. a(z) is shown for T = 0.0, 0.5, 0.7, 0.8 and 0.9.
1765
J. Wu and P. J. Wilkinson
1766
Persistence
faCtOr
Fig. 2. Correlation coefficient from linear fitting of foF2 (in three formats) with aa( as functions of persistence factor t, for September and October 1989 at Canberra and a diurnal variation in the correlation between log (N/N,) and aa(
(N/N,) are plotted as a function of their respective persistence times. Past experience had suggested that ap was a better index than Kp for ionospheric forecasting and Fig. 3 confirms this. The correlation of log(N/N,) with Kp(r) is best when T = 0.80, with a correlation coefficient of r = -0.61, slightly worse than the correlation with ap(r) (r = -0.67). Since ap is derived from the Kp, this shows that transforming the data can lead to improved relationships. The aa and ap indices are prepared from different numbers of magnetic stations and, as Fig. 3 shows, there is a marginal difference in their responses. This suggests the station set used may not be as important as the data transformation used. Similar results were obtained for Hobart, Townsville and Mundaring (Wu and Wilkinson, 1993). In all cases, T = 0.80 gave the best correlations, these being higher at Hobart and lower at Townsville than obtained for Canberra. There is a diurnal variation in the correlation between ionospheric and geomagnetic indices, as can be seen in Fig. 2 for aa( Similar results were obtained by Wrenn et al., 1989. The correlations for night time (2 1LT to 04LT) form an upper bound for aa for the complete 24 hours, and the daylight (1OLT to 16LT) correlation forms a lower bound. All three curves have the same shape and persistence time for maximum correlation, about I5 hours. This implies forecasts will have the same lead time but will have variable accuracy, depending on the time of day. Different blocks of two months of Canberra data during 1989 (Fig. 4) were used to demonstrate how
persistence time (hours) Fig. 3. Absolute values of the correlation coefficient from linear fitting of log (N/N,) with aa( ap(z), Kp(z), Dst(z) and Al(r) indices, as functions of persistence time (hours), for September and October 1989 at Canberra.
better parameter (3) log(N/N,,) is a consistently than (f-&)/f0 in transforming ionospheric data. (4) The daily median, Nb, is marginally better than the monthly median, N,, but the difference is rather small so log(N/N,) is used as the ionospheric parameter hereafter because it is easier to calculate. Also, from Fig. 1, a diurnal variation of log(N/N,,) is present and its amplitude is possibly affected by magnetic activity. In Fig. 3 correlations
between
all the indices and log
Persistencefactor(r) Fig. 4. Correlation coefficient from linear fitting of log(N/N,) with the aa index, as functions of persistence factor t, for different pairs of months and the whole year of 1989 at Canberra.
1767
Predicting ionospheric behaviour using geomagnetic indices the correlation between f,F2 and aa varies with season. In summer and equinox, the correlation coefficients are negative, consistent with the magnetic storm causing a decrease in the value of f,F2 (e.g. Rishbeth, 1975). In winter (May-August), the correlation coefficients are positive, consistent with a magnetic storm being followed by enhancements in f,F2. Clearly, there is wide variability both in expected accuracy (level of correlation) and persistence time, with the seasonal differences exceeding the diurnal differences. It appears (Fig. 1) there could be a delay between the ionospheric response and the various indices. This possibility is explore:d in Fig. 5. As the delay between the time series is increased from 3 to 6 hours, marginally better correlations can be obtained and r decreases. This is more apparent for some of the other stations analysed (Wu and Wilkinson, 1993). However the response tirne remains the same, e.g., at Canberra, the correlation coefficient maximises at z = 0.75 when the time-lag of ionospheric data is 3 hours (and r = 0.60 when time-lag is 6 hours) corresponding to a total response time (lag plus persistence time) of about 15 hours. This shows that the time accumulated indices account for any ‘delay between the ionospheric and index time series, tlhe visual delay apparent between the series being an inaccurate indicator of the actual delay. Figure 3 also shows results for two further indices; Dst(r) and AI(T). For the September-October 1989 period, the best correlation (r = 0.69) is obtained when 7 = 0.80 for the aa index and the poorest
Persistence factor(r)
Fig. 5. Correlation coefficient from linear fitting of log(N/N,) with aa( as functions of persistence factor T and time-lag of ionospheric data, for September and October 1989 at Canberra.
correlation (I = 0.60) was recorded for AI(r) (with z = 0.96). As expected, all indices give a similar level of ionospheric response time, about 15 hours. There is no improvement using Dst(z) instead of Dst(0) in the correlation analysis. The correlation relationship changes with both season and location. The indices used in this study are compared directly with the ionospheric response at several stations in Australia and Europe in Fig. 6 and the aa and Dst(z) relation is shown in Figs 7(a) and 7(b). While the results are not dissimilar to those obtained for Australian stations, there are some striking differences. The Dst index is better than the aa index for all European stations while Kp and AI are less effective. The best correlations are found for a persistence time marginally longer than for Canberra ; the persistence time being longer for the lower latitude stations and shorter for the higher latitude stations, consistent with the results for Australia (Wu and Wilkinson, 1993). The exception is the highest latitude station of Uppsala, located in the aurora1 region, which is, presumably, dominated by high latitude factors. In Europe, 7 is marginally longer for aa, ap, Kp and AI and 7 z 0.90-0.95 for Dst, corresponding to a persistence time of l&20 hours. The seasonal results for Canberra and the results here for a selection of European stations confirm that the relationship between the geomagnetic indices and the F region, while qualitatively apparent, is not easily quantified.
4. SUMMARY
AND DISCUSSION
The correlation between ionospheric disturbances and the time-weighted accumulation of magnetic indices has been shown to be better than the equivalent instantaneous indices at four Australian stations and five European stations during the period September to October 1989. This confirms Wrenn’s observation (1987) that log(N/iV,,) depends not only on the present phase of a magnetic disturbance, but also on the past history of the disturbance, with a diminishing contribution from earlier periods. Some of the consequences of this analysis are discussed here. The correlation coefficients for the ap and Kp indices, in Fig. 3, were compared and the ap index was found to be the better index for the Canberra f,F2 data. Similar results were found for other stations. Since ap has been derived from Kp, it may be possible to develop other transformations of Kp that improve ionospheric forecasts even further. Similarly, log (N/N,,) is a better ionospheric parameter than (f-fO)/fO, suggesting other transformations of the data may be possible. It will be worth exploring these
1768
J. Wu and P. J. Wilkinson
s 4
0.5 0.0
ST
Peter-Ording
-0.5 z _)
-1.0 -1.5
F
0.5
2
0.0
z s
Slough
-0.5 -1.0 -1.5
s s z s
;; z z s
0.5 Poitiers
0.0 -0.5 -1.0 -1.5
0.5 0.0 -0.5 -1.0 -1.5 -2.0’,““‘,,“““““““~“‘~“~,,,~,,,,,.,,,,,,,,~~~~,~~~~,,1 1.0
E;
0.5
4
0.0
3
s
Canberra
-0.5
-i.o -1.5 -2.0
450
11111,1111,,,,,,1,1,,,,,,,,,,,,, 5 10 15 September
Fig. 6. The variation
20
25
30 1969
, 35
40
I,,, 45
,,,,,,,,,,, 50 55
60
October
of AI(O), Kp(0) and aa(0) and Dst(0) indices and log(N/N,,) Australian stations for September and October, 1989.
at several European
and
Predicting ionospheric behaviour using geomagnetic indices
Persistence factor(r) 0.80 ,T
1
I
I
0.60
”0.60
I
d 0.60 .$ E $ 0 0.50 8 ‘Ja z 5 0.40 u
0.28.0~“‘““‘“‘0.40 ““““~
1.00
‘Persistence faCtOr Fig. 7.(a) Correlation coefficient from linear fitting of log(N/N,) with the aa index, as a function of persistence factor z, at different stations in Europe and in Australia, for September and October, 1989. (b) As (a) but for Dst(r).
transformations to discover if they improve forecasting. The improvement arises because the relationship between the time series to be forecast and the predicator series has been made clearer by the transformation. Developing a single relationship between geomagnetic disturbance indices and global ionospheric disturbances is obviously not simple. Different relationships will be more appropriate for different ionospheric locations. The most important spatial relationship is the latitudinal difference that is apparent in the data. Smaller correlations for lower latitude stations and also for the high latitude station of Uppsala suggest there is a latitude region where the correlation is best This leads to a forecasting strategy
1769
based on forecasting the storm effects for the region most responsive to the indices and then making a second forecast, based on the first, for other latitudes ; which is roughly how present ionospheric forecasts are made. Seasonal variation (Fig. 4) further highlights the problem of forecasting an ionospheric storm using magnetic disturbance indices. Behaviour during winter (May-August for Canberra) is the inverse of other seasons, corresponding to positive storm effects observed during winter. The September-October 1989 period, chosen here because it contained several geomagnetic storms, has the highest correlations. This may be a typical seasonal effect or may reflect the choice of period. Either way, it demonstrates the problems encountered using indices for forecasting. The AI index was expected to perform better than has been the case although, since the index was not designed to be used in the context reported here, its apparent failure is qualified. Initially, it seemed reasonable to expect that if Al described the location of the aurora1 oval, where the energy sources responsible for ionospheric disturbances were located, then the AI index should be a good index of ionospheric behaviour. However, visual inspection of the time series in Fig. 6 confirms, subjectively, that AI, in addition to being more variable than indices such as Dst, does not have the same general shape as the ionospheric parameters. From Fig. 3, it is apparent that AI is not as effective as the aa, ap and Kp indices, although it is similar in effectiveness to Dst. One possibility is that the other indices are global indices, whereas AI should be treated as a regional index similar to the other aurora1 oval indices; AE, AU and AL. This would limit how AI should be used in this paper. Alternatively, it may be possible to seek a transformation of the AI that will improve its performance as a forecasting index. When a delay was introduced between the magnetic indices and the ionospheric time series, the correlation was marginally improved and the persistence factor 7 reduced, confirming there was a lag between the two time series. However, the total response time of lag plus persistence time remained roughly the same ; about 15 hours. Thus the accumulated index takes account of lags between the two time series. The results presented here confirm the proposal of Wrenn and Rodger (1989) that F region forecasting can be improved using time weighted accumulation indices. While the increase in the correlation coefficients for the time-weighted accumulation indices is clear in the figures, it is not significantly larger than for the instantaneous indices. Because the correlation improvements are small, these indices may
1770
J. Wu and P. J. Wilkinson
have limited use in a forecasting environment. Further studies, with other station sets and for other periods of activity as well as other seasons are necessary. The results in Fig. 4 give an indication of this. It is also important to explore periods when the relationships fail, or give misleading advice to forecasters. Notwithstanding, all the time weighted indices show some
improvement and may therefore add a small, worthwhile advantage for the ionospheric forecaster and further analysis may improve on this. Acknowledgemenfs-We would like to thank Dr David Cole and Dr John Caruana for reviewing the draft of this paper and many valuable comments.
REFERENCES Rich F.
1992
Rishbeth H.
1975
Aurora1 activity index derived from DMSP electron boundaries now available. STEP International, 3, 18 F-region storms and thermospheric circulation. J.
Wrenn G. L.
1987
Time-weighted
atmos. terr. Phys. 37, 1055-1064
accumulations
ap(r) and K~(T). J.
geophys. Res. 92, 10,12510,129.
Wrenn G. L., Rodger A. S. and Rishbeth H.
1987
Geomagnetic storms in the Antarctic F-region, 1.Diurnal and seasonal patterns for main phase effects. J.
Wrenn G. L. and Rodger A. S.
1989
Wu J. and Wilkinson P. J.
1993
Geomagnetic modification of the mid-latitude ionosphere: Towards a strategy for the improved forecasting of foF2. Radio Sci. 24,99-l 1 I. Time-weighted accumulation of ap index-a better indicator of magnetic disturbance. IPS Technical Report TR-93-01.
atmos. terr. Phys. 49,901L913.
of Armospheric
Pergamon 0021-9169(95)00096-8
and Terrestrial
Physics, Vol. 57, No. 14, pp. 1763-1770, 1995 Copyright 0 1995 Elsevier Saence Ltd Printed in Great Britain. All rizhts reserved 00%9169/95-X.9.50+0.00
Time-weighted magnetic indices as predictors of ionospheric behaviour Jiping Wu and P. J. Wilkinson IPS Radio and Space Services, P. 0. Box 5606, West Chatswood, NSW 2057, Australia (Received infinalform
16 January 1995 ; accepted 17 February 1995)
Abstract-A time-weighted accumulation of the ap index, ap(z) (Wrenn, 1987; Wrenn et al., 1987, 1989), together with other similar indices, was explored as a predictor of ionospheric behaviour, usingf,F2 data for a selection of locations in Australia and Europe for September and October 1989. All the time accumulated indices showed improved linear correlations, indicative of a response time of the order of about 15 hours. The response time could be decomposed into a lag between respective time series and a persistence time, although the decomposition appeared unnecessary as the persistence time carried the same information. Of the individual indices investigated, aa appeared best and the aurora1 oval equatorward edge index (AI index) was poorest, although the differences were not statistically significant. Comparisons between the aa, ap and Kp indices, plus comparisons between different ionospheric parameters showed that forecasting may be improved using different transformations of the data. While these results a.ppear good, further studies using other stations and seasons are warranted to confirm their utility for forecasting.
1. INTRODUCTION
While it is well known that ionospheric disturbances and storms follow geomagnetic disturbances, forecasts for the responses are poor. The quality of ionospheric forecasting may be improved by finding a better way to organise the ionospheric and magnetic data. Here, this proposition is explored by investigating how well various time series accumulations of aa, ap, Kp, Dst and AI indices correlate with observed changes in the ionosphere. Since the ionospheric storm effects correspond to high levels of magnetic activity, and the severity of the effects depends more on the average index level throughout the event then on the peak value, which may occur for only a single observation, it is worth exploring accumulative indices. Wrenn (1987) introduced the following time series accumulation of the ap index : ap(z) = (l-,r)(ap+zap_,
+?apmZ+
...)
where 0 < 7 < 1 and ap_,, ap_,, . are the ap values for - 3, - 6, - 9 hours, etc. The attenuation multiplier, or persistenc’z factor z, is a value between 0 and 1 and the factor 111-z) normalises the summation. As a persistence factor, 7 determines how ap(T) will depend on the pas{ history of the ap index. The bigger the value of z, the more dependence ap(z) will have upon its history.
Similar time-weighted indices can be constructed using other geomagnetic indices such as Kp, the three hour range index from which ap is calculated, aa, similar to ap but based on two antipodal stations, and Dst, an index supposedly indicative of large scale geomagnetic activity due to the equatorial ring current and one Wrenn suggested was worth exploring. Alternatively, a direct indication of magnetospheric processes on the aurora1 region could be used. In this case the aurora1 oval equatorward edge index (AI index hereafter) calculated from precipitating electron data recorded by the Defence Meteorological Satellite Program (DMSP) was used. The AI index has higher time resolution than the other indices (20-40 minutes versus 3 hour and 1 hour) and possibly will be available in real time (Rich, 1992) in the near future. By taking a delta function in ap and comparing the subsequent decay of ap(t) for different values of T Wrenn (1987) found that 3/( 1 -z) (in hours) can be used as an approximate measure of the time required for a l/e decay of ap(z) and called it the persistence time. Following the same procedure, depending on the time division of an index, 3/(1-r), l/(1-~) and 0.55/(1 -z) hours is the persistence time for aa (and ap(z) and Kp(z) also), Dst(z) and AI(T), respectively. The persistence time for the best correlation between ,f,F2 and ap(r) (or any other index) is regarded as a typical response time for F2 region to magnetic disturbances.
1763
J. Wu and P. J. Wilkinson
1764
Table I. Station coordinates Geographic latitude,
Station Uppsala St Peter-Ording Slough Poitiers Rome Townsville Mundaring Canberra Hobart
59.8N 54.ON 51.5N 46.5N 41.9N 19.6s 32.0s 35.3s 42.98
Geographic longitude,
Geomagnetic latitude,
Geomagnetic longitude.
L
58.3N 54.8N 54.IN 49.2N 42.2N 28.43 43.5s 44.0s 51.6s
106.9E 94.8E 84.4E 83.OE 92.7E 139.5w 172.3W 134.3w 134.1w
3.3 2.6 2.4 2.0 1.6 1.3 1.9 2.0 2.9
17.6E 9.3E 0.5w 0.4E 12.6E 146.9E 1l6.2E 149.OE 147.3E
In this paper, these indices are compared with ionospheric changes to discover if they can assist in ionospheric forecasts. The simplest way in which an index can be used to assist in forecasts is to use it directly, scaling the index to give an associated ionospheric response. This information could be used as guidance, together with other indicators. For purposes of exploring and comparing the time-weighted indices as predictors of ionospheric behaviour, a linear correlation analysis was adopted. While this implies a simplistic approach to the use of indices, it is convenient for the present purposes. The objective of this paper is to discover whether indices developed following Wrenn’s suggestion can be used to assist in ionospheric forecasting.
2. DATA
Data are mainly analysed for the period September and October, 1989 when magnetic activity was often very high. Most results are presented for Canberra and these are indicative of the results obtained for other locations (see Wu and Wilkinson, 1993, for additional details). All the locations analysed are shown in Table 1. Finally, seasonal behaviour at Canberra in 1989 is summarised. Kp, aa, ap, Dst and AI indices have all been used as indicators of magnetic disturbances. Since aa, ap and Kp are 3-hour averaged indices and AI is a 2040 min averaged index, while f,F2 is an hourly measurement, interpolated fhF2 values centred on ap(z) and Kp(z) time and interpolated AI values on the hour were used in the analysis. This did not affect the results significantly as checks of data sequences showed, so the interpolation method was retained in the analysis since it was more representative of the effects being analysed. Dst is an hourly index, so no interpolation is needed.
3. RELATIONSHIP
BETWEEN
GEOMAGNETIC
THE F REGION
AND THE
INDICES
Figure 1 displays the Canberraf,F2 data and the aa index for different z, in September and October 1989. The top panel shows the variation of electron density changes over Canberra in terms of log(N/N,). Electron density, N, is calculated from the observed hourlyf”F2 values, and the N, are calculated from the monthly medians off,F2. Other panels show the variations of aa for t = 0.0, 0.5, 0.7, 0.8 and 0.9, respectively. It is clear that, apart from the pronounced diurnal variation, log(N/N,,) follows the aa reasonably well for large deviations. The interpolation of N, and the choice of ionospheric parameter, is explored in Fig. 2, which shows the correlation coefficients from linear fitting of three f,F2 parameters with aa as functions of the persistence factor z. Two options are log (N/N,) and log (N/N;), where No is the monthly median and N’, is the daily median interpolated from the adjacent monthly medians. The third option uses (f-fu)/fO, where ,f’is the hourlyf,F2 and,f, is the monthly medianfhF2. The following conclusions can be drawn from these two figures :
(1) aa(
(2)
the time-weighted accumulation, is a better index than the instantaneous aa index, aa( in ionospheric forecasting. When z changes from 7 = 0 to r = 0.80, the correlation rises from -0.50 to -0.68 for log(N/N,) and from -0.46 to -0.63 for (f‘-Q/fo. When t = 0.80, the correlations betweenf,F2 and aa are best no matter how the,f,F2 data are organised. z = 0.80 corresponds to a persistence time of 15 hours which suggests, an ionospheric response time to geomagnetic disturbances of about 15 hours, consistent with general ionospheric forecasting experience at IPS.
Predicting
ionospheric
behaviour
using geomagnetic
indices
0.5
0.0 ,-0.5
150 100 50 n 200, 150 100 50 --- 0 __I
aa(0.70)
150
100,
t
150
-
I\
I
aa(O.80)
100 -
150
aa(0.90)
100 _I50
_A
September
h
1989
October
Fig. 1. The variations of log(N/N,J for Canberra and aa in September and October 1989. Electron densities N are calculated from observed hourly foF2 values, and N, are the monthly medians. a(z) is shown for T = 0.0, 0.5, 0.7, 0.8 and 0.9.
1765
J. Wu and P. J. Wilkinson
1766
Persistence
faCtOr
Fig. 2. Correlation coefficient from linear fitting of foF2 (in three formats) with aa( as functions of persistence factor t, for September and October 1989 at Canberra and a diurnal variation in the correlation between log (N/N,) and aa(
(N/N,) are plotted as a function of their respective persistence times. Past experience had suggested that ap was a better index than Kp for ionospheric forecasting and Fig. 3 confirms this. The correlation of log(N/N,) with Kp(r) is best when T = 0.80, with a correlation coefficient of r = -0.61, slightly worse than the correlation with ap(r) (r = -0.67). Since ap is derived from the Kp, this shows that transforming the data can lead to improved relationships. The aa and ap indices are prepared from different numbers of magnetic stations and, as Fig. 3 shows, there is a marginal difference in their responses. This suggests the station set used may not be as important as the data transformation used. Similar results were obtained for Hobart, Townsville and Mundaring (Wu and Wilkinson, 1993). In all cases, T = 0.80 gave the best correlations, these being higher at Hobart and lower at Townsville than obtained for Canberra. There is a diurnal variation in the correlation between ionospheric and geomagnetic indices, as can be seen in Fig. 2 for aa( Similar results were obtained by Wrenn et al., 1989. The correlations for night time (2 1LT to 04LT) form an upper bound for aa for the complete 24 hours, and the daylight (1OLT to 16LT) correlation forms a lower bound. All three curves have the same shape and persistence time for maximum correlation, about I5 hours. This implies forecasts will have the same lead time but will have variable accuracy, depending on the time of day. Different blocks of two months of Canberra data during 1989 (Fig. 4) were used to demonstrate how
persistence time (hours) Fig. 3. Absolute values of the correlation coefficient from linear fitting of log (N/N,) with aa( ap(z), Kp(z), Dst(z) and Al(r) indices, as functions of persistence time (hours), for September and October 1989 at Canberra.
better parameter (3) log(N/N,,) is a consistently than (f-&)/f0 in transforming ionospheric data. (4) The daily median, Nb, is marginally better than the monthly median, N,, but the difference is rather small so log(N/N,) is used as the ionospheric parameter hereafter because it is easier to calculate. Also, from Fig. 1, a diurnal variation of log(N/N,,) is present and its amplitude is possibly affected by magnetic activity. In Fig. 3 correlations
between
all the indices and log
Persistencefactor(r) Fig. 4. Correlation coefficient from linear fitting of log(N/N,) with the aa index, as functions of persistence factor t, for different pairs of months and the whole year of 1989 at Canberra.
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Predicting ionospheric behaviour using geomagnetic indices the correlation between f,F2 and aa varies with season. In summer and equinox, the correlation coefficients are negative, consistent with the magnetic storm causing a decrease in the value of f,F2 (e.g. Rishbeth, 1975). In winter (May-August), the correlation coefficients are positive, consistent with a magnetic storm being followed by enhancements in f,F2. Clearly, there is wide variability both in expected accuracy (level of correlation) and persistence time, with the seasonal differences exceeding the diurnal differences. It appears (Fig. 1) there could be a delay between the ionospheric response and the various indices. This possibility is explore:d in Fig. 5. As the delay between the time series is increased from 3 to 6 hours, marginally better correlations can be obtained and r decreases. This is more apparent for some of the other stations analysed (Wu and Wilkinson, 1993). However the response tirne remains the same, e.g., at Canberra, the correlation coefficient maximises at z = 0.75 when the time-lag of ionospheric data is 3 hours (and r = 0.60 when time-lag is 6 hours) corresponding to a total response time (lag plus persistence time) of about 15 hours. This shows that the time accumulated indices account for any ‘delay between the ionospheric and index time series, tlhe visual delay apparent between the series being an inaccurate indicator of the actual delay. Figure 3 also shows results for two further indices; Dst(r) and AI(T). For the September-October 1989 period, the best correlation (r = 0.69) is obtained when 7 = 0.80 for the aa index and the poorest
Persistence factor(r)
Fig. 5. Correlation coefficient from linear fitting of log(N/N,) with aa( as functions of persistence factor T and time-lag of ionospheric data, for September and October 1989 at Canberra.
correlation (I = 0.60) was recorded for AI(r) (with z = 0.96). As expected, all indices give a similar level of ionospheric response time, about 15 hours. There is no improvement using Dst(z) instead of Dst(0) in the correlation analysis. The correlation relationship changes with both season and location. The indices used in this study are compared directly with the ionospheric response at several stations in Australia and Europe in Fig. 6 and the aa and Dst(z) relation is shown in Figs 7(a) and 7(b). While the results are not dissimilar to those obtained for Australian stations, there are some striking differences. The Dst index is better than the aa index for all European stations while Kp and AI are less effective. The best correlations are found for a persistence time marginally longer than for Canberra ; the persistence time being longer for the lower latitude stations and shorter for the higher latitude stations, consistent with the results for Australia (Wu and Wilkinson, 1993). The exception is the highest latitude station of Uppsala, located in the aurora1 region, which is, presumably, dominated by high latitude factors. In Europe, 7 is marginally longer for aa, ap, Kp and AI and 7 z 0.90-0.95 for Dst, corresponding to a persistence time of l&20 hours. The seasonal results for Canberra and the results here for a selection of European stations confirm that the relationship between the geomagnetic indices and the F region, while qualitatively apparent, is not easily quantified.
4. SUMMARY
AND DISCUSSION
The correlation between ionospheric disturbances and the time-weighted accumulation of magnetic indices has been shown to be better than the equivalent instantaneous indices at four Australian stations and five European stations during the period September to October 1989. This confirms Wrenn’s observation (1987) that log(N/iV,,) depends not only on the present phase of a magnetic disturbance, but also on the past history of the disturbance, with a diminishing contribution from earlier periods. Some of the consequences of this analysis are discussed here. The correlation coefficients for the ap and Kp indices, in Fig. 3, were compared and the ap index was found to be the better index for the Canberra f,F2 data. Similar results were found for other stations. Since ap has been derived from Kp, it may be possible to develop other transformations of Kp that improve ionospheric forecasts even further. Similarly, log (N/N,,) is a better ionospheric parameter than (f-fO)/fO, suggesting other transformations of the data may be possible. It will be worth exploring these
1768
J. Wu and P. J. Wilkinson
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Predicting ionospheric behaviour using geomagnetic indices
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transformations to discover if they improve forecasting. The improvement arises because the relationship between the time series to be forecast and the predicator series has been made clearer by the transformation. Developing a single relationship between geomagnetic disturbance indices and global ionospheric disturbances is obviously not simple. Different relationships will be more appropriate for different ionospheric locations. The most important spatial relationship is the latitudinal difference that is apparent in the data. Smaller correlations for lower latitude stations and also for the high latitude station of Uppsala suggest there is a latitude region where the correlation is best This leads to a forecasting strategy
1769
based on forecasting the storm effects for the region most responsive to the indices and then making a second forecast, based on the first, for other latitudes ; which is roughly how present ionospheric forecasts are made. Seasonal variation (Fig. 4) further highlights the problem of forecasting an ionospheric storm using magnetic disturbance indices. Behaviour during winter (May-August for Canberra) is the inverse of other seasons, corresponding to positive storm effects observed during winter. The September-October 1989 period, chosen here because it contained several geomagnetic storms, has the highest correlations. This may be a typical seasonal effect or may reflect the choice of period. Either way, it demonstrates the problems encountered using indices for forecasting. The AI index was expected to perform better than has been the case although, since the index was not designed to be used in the context reported here, its apparent failure is qualified. Initially, it seemed reasonable to expect that if Al described the location of the aurora1 oval, where the energy sources responsible for ionospheric disturbances were located, then the AI index should be a good index of ionospheric behaviour. However, visual inspection of the time series in Fig. 6 confirms, subjectively, that AI, in addition to being more variable than indices such as Dst, does not have the same general shape as the ionospheric parameters. From Fig. 3, it is apparent that AI is not as effective as the aa, ap and Kp indices, although it is similar in effectiveness to Dst. One possibility is that the other indices are global indices, whereas AI should be treated as a regional index similar to the other aurora1 oval indices; AE, AU and AL. This would limit how AI should be used in this paper. Alternatively, it may be possible to seek a transformation of the AI that will improve its performance as a forecasting index. When a delay was introduced between the magnetic indices and the ionospheric time series, the correlation was marginally improved and the persistence factor 7 reduced, confirming there was a lag between the two time series. However, the total response time of lag plus persistence time remained roughly the same ; about 15 hours. Thus the accumulated index takes account of lags between the two time series. The results presented here confirm the proposal of Wrenn and Rodger (1989) that F region forecasting can be improved using time weighted accumulation indices. While the increase in the correlation coefficients for the time-weighted accumulation indices is clear in the figures, it is not significantly larger than for the instantaneous indices. Because the correlation improvements are small, these indices may
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J. Wu and P. J. Wilkinson
have limited use in a forecasting environment. Further studies, with other station sets and for other periods of activity as well as other seasons are necessary. The results in Fig. 4 give an indication of this. It is also important to explore periods when the relationships fail, or give misleading advice to forecasters. Notwithstanding, all the time weighted indices show some
improvement and may therefore add a small, worthwhile advantage for the ionospheric forecaster and further analysis may improve on this. Acknowledgemenfs-We would like to thank Dr David Cole and Dr John Caruana for reviewing the draft of this paper and many valuable comments.
REFERENCES Rich F.
1992
Rishbeth H.
1975
Aurora1 activity index derived from DMSP electron boundaries now available. STEP International, 3, 18 F-region storms and thermospheric circulation. J.
Wrenn G. L.
1987
Time-weighted
atmos. terr. Phys. 37, 1055-1064
accumulations
ap(r) and K~(T). J.
geophys. Res. 92, 10,12510,129.
Wrenn G. L., Rodger A. S. and Rishbeth H.
1987
Geomagnetic storms in the Antarctic F-region, 1.Diurnal and seasonal patterns for main phase effects. J.
Wrenn G. L. and Rodger A. S.
1989
Wu J. and Wilkinson P. J.
1993
Geomagnetic modification of the mid-latitude ionosphere: Towards a strategy for the improved forecasting of foF2. Radio Sci. 24,99-l 1 I. Time-weighted accumulation of ap index-a better indicator of magnetic disturbance. IPS Technical Report TR-93-01.
atmos. terr. Phys. 49,901L913.