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Methodological influences on F-region peak height trend analyses
Physics and Chemistry of the Earth 27 (2002) 589–594 www.elsevier.com/locate/pce
Methodological influences on F-region peak height trend analyses M.J. Jarvis a
a,*
, M.A. Clilverd a, Th. Ulich
b
British Antarctic Survey, Madingley Road, Cambridge CB3 0ET, UK b Sodankyla Geophysical Observatory, Sodankyla, Finland
Received 18 October 2001; received in revised form 20 November 2001; accepted 23 November 2001
Abstract Published estimates of the trend in hmF2 using data from ionosondes over the last 30–40 years range from +0.8 to )0.6 km yr1 and are subject to the influence of several factors. These are considered here based upon an analysis of two southern hemisphere geomagnetically mid-latitude stations, Argentine Islands and Port Stanley. The influence of the equation used to calculate hmF2 at these stations can result in variations of 0:2 km yr1 ; choice of solar proxy has a small influence on the end result, where using E10.7 instead of F10.7 produces changes of )0.04 km yr1 ; neglecting any trends in geomagnetic activity can produce variations of +0.03 to +0.2 km yr1 at the two mid-latitude stations considered in this paper; for datasets of 30–40 years length ringing due to long memory processes can produce 0:2 km yr1 variability; the phase of the 11-year solar cycle, and its harmonics, captured by the datasets can cause variability of 0:5 km yr1 ; and the neglect of local time variations in thermospheric wind conditions could result in +0.2 km yr1 for analysis which only considers local midday data. The Argentine Islands and Port Stanley datasets show ringing terms that are still converging towards trend results of )0.25 to )0.30 km yr1 , which are in close agreement with the satellite drag trend estimates. Crown Copyright Ó 2002 Published by Elsevier Science Ltd. All rights reserved. Keywords: Global change; Ionosphere; Thermosphere; Trends
1. Introduction There are now a considerable number of publications concerning long-term trends in the height of the peak electron concentration in the F-region ionosphere. The interest in this subject stems from the suggestion by Rishbeth (1990) that global cooling of the upper atmosphere, as a consequence of increased ‘greenhouse’ gas concentration (Roble and Dickinson, 1989), would result in a lowering of the F layer peak height (hmF2). Rishbeth (1990) estimated this lowering to be approximately 20 km for a scenario of doubled ‘greenhouse’ gas concentration. This can be translated to an average decrease in altitude of less than 0.1 km yr1 if we assume that this doubling occurs over more than 200 years. Rishbeth (1990) showed analytically that trends in the F region critical frequency (foF2) caused by a greenhouse gas increase should be insignificant compared to those in hmF2 and thus we focus here only on hmF2.
* Corresponding author. Tel.: +44-1223-221-548; fax: +44-1223-221226. E-mail address: [email protected] (M.J. Jarvis).
Studies using ionosonde data from around the world have provided observationally based derivations of the change in hmF2 which range from )0.6 km yr1 (Uppsala: Upadhyay and Mahajan, 1998) to +0.8 km yr1 (Moscow: Bremer, 1998) [see Table 1]. Moreover Ulich (2000) estimated hmF2 trends for 39 stations using 20 different methods. He, too, finds a large variety of trends between +0.961 km yr1 for Khabarovsk and )0.780 km yr1 for Poitiers. For observational comparison, an estimated global average change in hmF2 of )0.25 km yr1 has been derived using the completely independent method of satellite drag analysis (Keating et al., 2000). Clearly, one of the main issues now confronting research in this area is to understand why these different hmF2 trend estimates exist and whether they are a manifestation of some geophysical process which varies spatially, whether they are the result of different data acquisition practices or whether they are the statistical consequence of data variability, continuity and longevity. This paper primarily uses the Argentine Islands and Port Stanley hmF2 data analysed by Jarvis et al. (1998) to comment on and investigate some of the issues involved.
1474-7065/02/$ - see front matter Crown Copyright Ó 2002 Published by Elsevier Science Ltd. All rights reserved. PII: S 1 4 7 4 - 7 0 6 5 ( 0 2 ) 0 0 0 4 1 - 4
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M.J. Jarvis et al. / Physics and Chemistry of the Earth 27 (2002) 589–594
Table 1 Published estimates of hmF2 trends in km yr1 derived from ionosonde data, with indications of the authors involved, and the local time period studied Station
No. of years
00–24 LT
10–14 LT
Shi (10–14 LT)
BD3 (10–14 LT)
D56 (10–14 LT)
Bil (10–14 LT)
Argentine Is. Juliusruh Kaliningrad Kiruna Lannion Moscow Ottawa Poitiers Port Stanley Sodankyla Uppsala
38 34 29 33 25 32 31 26 38 42 37
)0.16a )0.19b 0.16b 0.01b 0.38b 0.84b – )0.42b )0.5a )0.22b )0.15b
– )0.21c – – – 0.24c 0.21c – )0.33c )0.38c )0.58c
0.21 0.1 0.18 0.1 0.03 0.2 0.20 0.1 1.06 0.2 0.30 0.2 0.29 0.2 0.64 0.2 0.11 0.1 0.26 0.1 0.10 0.2
0.04 0.1 0.41 0.1 0.01 0.1 0.29 0.1 1.15 0.1 0.23 0.1 0.12 0.1 0.54 0.1 0.19 0.1 0.39 0.1 0.40 0.1
0.06 0.1 0.31 0.1 0.09 0.1 0.19 0.1 0.87 0.1 0.11 0.1 0.13 0.1 0.77 0.1 0.19 0.1 0.43 0.1 0.36 0.1
0.11 0.1 0.31 0.1 0.03 0.1 0.01 0.1 1.00 0.1 0.13 0.1 0.06 0.1 0.75 0.1 0.20 0.1 0.42 0.1 0.32 0.1
The number of years of data available is shown. We also show four different estimates of F2 layer peak height trends by means of the empirical expressions of Shimazaki (1955), Bradley and Dudeney (1973, Eq. 3), Dudeney (1974, Eq. 56), and Bilitza et al. (1979) which are referred to in the table by Shi, BD3, D56, and Bil, respectively. Probable errors were computed as described by Ulich (2000). a Jarvis et al. (1998). b Bremer (1998). c Upadhyay and Mahajan (1998).
2. Published hmF2 trend estimates Table 1 presents a list of published estimates derived from ionosonde data. The method used by different authors is essentially the same but there are significant variations in the detail of the method. The basic technique is to derive hmF2 from the scaled ionogram parameters foE, foF2 and M(3000)F2 where foE and foF2 are the ordinary wave critical frequencies of the main E and F2 regions of the ionosphere, respectively, and are directly related to the maximum electron concentration. M(3000)F2 is a transmission factor related to the highest frequency that can be propagated between two sites 3000 km apart by refraction alone; it is derived by application of standard transmission curves to ionograms (Piggott and Rawer, 1972). The monthly median values of these parameters are used for any particular hour of the day. The calculation of F2 layer peak height from these parameters is achieved using one of several simple formulae. These formulae come from the same base (Shimazaki, 1955) but have different levels of development. Once a series of hmF2 data has been derived, the data themselves are used in a time-independent fashion to derive an empirical relationship between hmF2 and solar radiation input and, for some authors only, with a geomagnetic activity index. Again, not only are there differences here as to whether geomagnetic activity is included, but some authors have used F10.7 as a solar radiation proxy and some have used sunspot number. Ulich (2000) and Ulich et al. (2001) introduced multiparameter models for trend detection which additionally include terms for annual and semi-annual variation. The empirical relationships derived are used to model the expected hmF2 variation in a time-dependent fashion based on the appropriate time series of solar input and,
if considered, geomagnetic activity. The residuals between this empirical model and the hmF2 data are taken in order to remove the large solar cycle effects from the analysis. A long-term trend in these residuals is then derived. Some authors have only used data around local midday (e.g., 10–14 LT) to calculate the average trend while some have taken the mean linearly fitted trend over a complete 24-hour day. Jarvis et al. (1998) fitted a sine wave through the day for each month to split the residuals into two parts; a long-term linear trend and a long-term change in the strength of the diurnal cycling of hmF2 due to thermospheric winds. The table of published results immediately raises two obvious questions. Firstly, why do different analyses of the data from the same site produce different trends? Examples are Port Stanley, Sodankyla and Moscow. Secondly, why do some station pairs sited very close together have very different results? Examples are Poitiers (46.6°N, 0.3°E) and Lannion (48.5°N, 3.3°W) with trends of )0.42 and +0.38 km yr1 , respectively, or Juliusruh (54.6°N, 13.4°E) and Kaliningrad (54.7°N, 20.6°E) with trends of )0.21 and +0.16 km yr1 , respectively. These apparent spatial discontinuities in trend are additional to the longitudinal change across Europe determined by Bremer (1998) and are unrelated to the geomagnetic latitude dependence of the trend in peak density, foF2, reported by Danilov and Mikhailov (1999). Factors which could possibly have a bearing on these questions include data quality, the equation used to derive hmF2, which proxy was used for solar activity, whether geomagnetic activity was accounted for, the length and period of the dataset, and whether long-term thermospheric wind changes have been removed. Each of these factors is briefly considered below.
M.J. Jarvis et al. / Physics and Chemistry of the Earth 27 (2002) 589–594
3. Data handling Impacts on data quality are more likely to be due to scaling techniques or instrumental changes, for which local knowledge is required to achieve a reasonable correction. Analyses of single stations often have that local knowledge while for others, where data have been accessed in bulk from international databases, it is seldom the case. An extensive analysis of the effects of the equation used was carried out by Ulich (2000) which showed that for some stations the equation could make a significant difference to the trend estimate and that, for a number of stations, could change the sign of the estimated trend. The effect of the choice of the empirical formula for estimating hmF2 from M(3000)F2, foF2, and foE is shown in Table 1. We used monthly median data averaged around local noon (10–14 LT). Based on these data we compute four different estimates of F2 layer peak height by means of the empirical expressions of Shimazaki (1955), Bradley and Dudeney (1973, Eq. 3), Dudeney (1974, Eq. 56), and Bilitza et al. (1979), which are referred to in the table by Shi, BD3, D56, and Bil, respectively. All four computed estimates differ from the published results for the same stations because of differences in the rejection of data values outside the bounds of the equations used, and the use of additional terms in the times series fitting described below. The probable errors of the ionosonde data were determined and the probable errors of the empirical hmF2 data were computed as described by Ulich (2000). Thereafter the time series of hmF2 were fitted by a multi-parameter model containing terms for the slope of the trend, for solar activity (F10.7), for geomagnetic activity (Ap), as well as for annual and semiannual, viz. hmF2ðtÞ ¼ x0 þ x1 t þ x2 F10:7 þ x3 Ap þ x4 sinðT1 tÞ þ x5 cosðT1 tÞ þ x6 sinðT2 tÞ þ x7 cosðT2 tÞ; where xi are the parameters to be fitted, and T1 and T2 are the angular frequencies of the annual and semiannual variation. The model was inverted using singular value decomposition taking into account the individual measurement errors. In the four rightmost columns Table 1 lists the trends and their probable errors in km yr1 for a selection of 11 stations. The trends derived here vary between 0:77 0:1 km yr1 for Poitiers and þ1:15 0:1 km yr1 for Lannion. Interestingly, these two stations are only 370 km apart from one another. Generally the table demonstrates that the trend magnitude varies with the choice of hmF2 formula. For the cases of Argentine Islands, Kaliningrad, Kiruna, and Ottawa even the sign of the trend depends on the formula. Moreover, Ulich (2000) found that a similar variation of trends for a given station can
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be expected for differently composed multi-parameter models, e.g., when substituting F10.7 with sunspot numbers. For the example of the Sodankyla ionosonde, for which F2 layer heights have been scaled by the single-polynomial method of Titheridge (1969), Ulich (2000) compared the four sets of empirical hmF2 with the scaled real height data and found that empirical hmF2 generally overestimates the heights by typically 5– 100 km depending on formula, phase of solar cycle and season. For the case of Sodankyla he found Eq. 56 of Dudeney (1974) to give the best result: it overestimates hmF2 consistently by about 20 km independent of solar activity. Consequently, the applicability of any empirical hmF2 estimate to the data of a given station needs validation, because the empirical formulae were derived under certain assumptions (e.g., foF2/foE > 1:7 for Bradley and Dudeney (1973)) and the parameters of the formulae were fitted to the data of selected ionosondes during certain phases of solar acitivity. Often the authors used data obtained during the peak of Sunspot Cycle 20 which had a much lower amplitude than more recent cycles. The need for validation emphasises that local knowledge is important in trend analyses, and a lack of it can result in large variations in trend values. The equation used must be shown to produce consistently realistic hmF2 values at any individual site. A good example is that of Jarvis et al. (1998) where the Bradley and Dudeney (1973) equation which they used was originally developed and tested using data from Argentine Islands itself.
4. The solar proxy One of two solar radiation proxies have been used in the hmF2 analyses. Some authors have used sunspot number, R, and some have used the F10.7 index based on the flux of 10.7 cm radiation. Jarvis et al. (1998) compared the two and found that they gave extremely similar results but that using F10.7 resulted in a smaller variance in the final trend estimate. Recently a new index, E10.7, has been introduced (Tobiska et al., 2000). This characterises the actual integrated EUV solar irradiance that deposits energy at the top of the Earth’s atmosphere. It is reported in units of 10.7 cm radio flux and can therefore be directly substituted for F10.7. Using an identical analysis method to Jarvis et al. (1998) but substituting E10.7 for F10.7 the effect on Argentine Islands and Port Stanley data is to reduce the month-tomonth variability of the trend estimate and, in particular, to reduce the size of the trend at Port Stanley in summer. However it makes little difference to the overall mean trend as can be seen in Fig. 1. The bar plot shows the trend estimate from the original Jarvis et al. (1998) analyses using F10.7 (J98) and also with E10.7 for
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Fig. 1. Comparison of trend estimates using four different methods: (a) using the original Jarvis et al. (1998) results [denoted by J98]; (b) as (a) but using E10.7 instead of F10.7 [E10.7]; (c) as (a) with the Ap index term excluded [no_Ap]; (d) using IRI as the comparative model to derive residuals [IRI].
Argentine Islands and Port Stanley. Both sites show a small increase in the downwards trend when using E10.7 of the order of )0.04 km yr1 . These results conform to the index comparison by Tobiska et al. (2000) who show that regarding longer-term physical variations, such as the solar cycle, E10.7 and F10.7 are virtually identical, but on timescales of a solar-rotation or less there are important differences.
5. Geomagnetic activity Some authors neglect the effect of geomagnetic activity (e.g., Ulich and Turunen, 1997) on the basis that they find its inclusion makes little significant difference to the result. Others argue, based primarily on the geomagnetic dependence of foF2 trends (e.g., Danilov and Mikhailov, 1999), that most of the trends found in hmF2 should also relate to geomagnetic activity. Most authors use Monthly Ap, however, Mikhailov and Marin (2001) argue that the use of monthly Ap is inadequate to remove geomagnetic effects because correlations occur over longer time scales; thus they use a 12-month running mean. Here we repeat the Jarvis et al. (1998) analysis but excluding the Ap index term from the derived empirical model. Thus any trends in geomagnetic activity are basically neglected and are allowed to fully influence the result. The result is shown in Fig. 1 (no_Ap) where it can be seen that there is a slight reduction in the downwards trend observed at both sites of about +0.03 km yr1 compared with the J98 value. Thus the effect of geomagnetic activity appears to be small and positive for both stations. If a highly accurate time-dependent ionospheric model existed, then the results of that model could be used when deriving the residuals between our expectations, based on the prevailing geophysical inputs, and the observed hmF2 values. The most widely used ionospheric model is the International Reference Ionosphere (Bilitza et al., 1993). While this is a valuable tool for the
estimation of environmental and other effects, testing theories and designing experiments, we note that it does not perform realistically at all sites and under all conditions (Ephishov et al., 2000). With a view to using IRI output as a model with which to derive the hmF2 residuals, we have attempted to mimic the statistical process by which the observational data were derived. Thus, using the IRI, we have derived hmF2 for every hour of every day through the same 38year data period as analysed by Jarvis et al. (1998) [i.e., 1957–1995]. The IRI monthly median hmF2 value at each hour for each month was then calculated. Direct comparison with the observed hmF2 data showed that there were significant discrepancies between data and model, highlighted by Fig. 2(a). It shows the median, full range, and inter-quartile range of the differences in monthly medians between the IRI hmF2 and observed hmF2 for Argentine Islands plotted against year of the 11-year solar cycle. This shows interquartile ranges of between 30 and 50 km and median differences of about 20 km in some years. The variations clearly show an unremoved solar cycle in hmF2 residuals. By comparison Fig. 2(b) shows the same plot by the Jarvis et al. (1998) method; the solar cycle in hmF2 residuals has been more reliably removed. The interquartile ranges lie between 10 km and 25 km and median differences are no greater than 5 km. The equivalent results for Port Stanley are very similar and thus have not been shown here. The hmF2 trend for Argentine Islands and Port Stanley using the IRI model is shown in Fig. 1. It should be noted that the IRI model does not take account of varying geomagnetic activity and thus a more direct comparison might be between the no_Ap and IRI results; both have the effect of reducing the downward trend. This comparison should be refined as atmospheric models become more accurate.
Fig. 2. Residuals between observed hmF2 data and modelled hmF2 data as a superposed-epoch against solar cycle year for Argentine Islands. Medians (crosses), interquartile ranges (boxes), and full ranges (whisker) are shown. (a) Using IRI model; (b) using Jarvis et al., 1998 method. [The equivalent (a) and (b) results for Port Stanley (not shown) are essentially the same.]
M.J. Jarvis et al. / Physics and Chemistry of the Earth 27 (2002) 589–594
6. The length and period of dataset One aspect of determining the trend in hmF2 is the length of the memory processes involved in the system being studied. Analysis of a system with short memory processes would require shorter datasets to allow the result to converge to the underlying trend. Results involving long-term memory processes converge more slowly. Weatherhead et al. (1998) showed that processes lower in the atmosphere can be described by first order auto-regression, AR(1), where memory is mid- to longterm. Thus we can expect the estimate of trend in hmF2 to show long memory convergence towards the actual trend value (Beran, 1994). Fig. 3 shows the trend estimates (diamonds) for Argentine Islands and Port Stanley starting with only 10 years of data, sequentially increasing to 38 years of data. The solid lines are fits to the data using three damped oscillatory sinewave components with periods of 11, 22, 33, and 44 years superposed. At both sites the estimate of trend is well represented as a ringing function which converges to a trend value of )0.25 to )0.30 km yr1 after about 50–60 years. This kind of convergence was first shown by Bremer (1998), whose results are qualitatively similar to those of Fig. 3. The converging values shown in Fig. 3 are both essentially from negative values
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towards 0.25 km yr1 . However, it is possible that the values would converge from positive values if the datasets were collected over a different period with different phases of the sinewave components. If a data series has not converged significantly then differences of 1 km yr1 could occur depending on which period of data was analysed. This suggests that it would be advantageous to study the same periods of data to compare the results from different stations. The result of this ringing interpretation is that both Argentine Islands and Port Stanley converge to a similar trend value which is consistent with the result of Keating et al. (2000) – indicated by a dashed line in the figure. The current difference in estimate between the two sites is due to ringing terms of about 0.2 km yr1 when only 20–40 years of data have been used. Fig. 3 shows that had Jarvis et al. (1998) used 32 years of data instead of 38 the trend results for the Argentine Islands would have been positive not negative. Weatherhead et al. (2000) suggested that different regions would require different lengths of datasets before trends could be reasonably identified. Thus the form of the convergence of the trend result shown at individual sites should provide information on the robustness of each trend estimate.
7. The effect of changing thermospheric winds
Fig. 3. The variation in the estimate of the trend at Argentine Islands and Port Stanley (diamonds). The data are fitted with a 3-component damped oscillatory sinewave (solid line) which appears to converge towards the result of Keating et al. (2000) (dashed line) in both cases.
If there is a significant long-term change in the strength of the meridional thermospheric wind, then it can have a significant effect on the hmF2 trend derived from analysis limited to around midday only. The mean of data which covers all 24 h of the day will, if the altitude variation induced by the cycling of the meridional thermospheric wind is sinusoidal (or otherwise symmetric about zero), effectively cancel any thermospheric wind effect. As an example, Jarvis et al. (1998) estimated a decrease in the amplitude of the diurnal thermospheric wind-induced quasi-sinusoidal oscillation of hmF2 at Port Stanley of 0.2 km yr1 . At this location, hmF2 reaches its minimum value near midday and so, if this thermospheric wind effect is not accounted for in a longterm trend estimate of hmF2 because only data around midday have been used, then it will produce an erroneous additional ‘mean’ hmF2 trend of +0.2 km yr1 . This is confirmed by comparing the results of Upadhyay and Mahajan (1998) and Jarvis et al. (1998) regarding Port Stanley data. The former used data between 10 and 14 LT only and obtained an hmF2 trend of )0.33 km yr1 while the latter removed the thermospheric wind effect and obtained an hmF2 trend of )0.50 km yr1 . A preliminary assessment of Sodankyla data indicates that using the same F2 layer peak height derivation formula and including all local times leads to a stronger downward trend than when only midday is considered.
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A closer analysis of the thermospherically driven diurnal cycles in the data series from all stations is needed. 8. Summary Rishbeth (1990) estimated that the trend in hmF2 driven by atmospheric CO2 changes are )0.1 km yr1 . Independent estimates of the trend made from satellite drag measurements by Keating et al. (2000) give )0.25 km yr1 . Estimates of the trend in hmF2 using data from ionosondes over the last 30–40 years range from +0.8 to )0.6 km yr1 . The trend results derived from ionosonde data are subject to the influence of several factors. In this paper we have quantified some of these factors with respect to Argentine Islands and Port Stanley data which are identified here: the influence of the equation used to calculate hmF2 at these stations can result in variations of 0:2 km yr1 ; the choice of solar proxy has a small influence on the end result, where using E10.7 instead of F10.7 produces changes of )0.04 km yr1 ; neglecting any trends in geomagnetic activity can produce variations of +0.03 to +0.2 km yr1 at the two mid-latitude stations considered in this paper; for datasets of 30–40 years length ringing due to long memory processes can produce 0:2 km yr1 variability; the phase of the 11year solar cycle, and its harmonics, captured by the datasets can cause variability of 0:5 km yr1 ; and the neglect of local time variations in thermospheric wind conditions could result in +0.2 km yr1 for analysis which only considers local midday data. The Argentine Islands and Port Stanley datasets considered in this paper have the attributes of ‘good’ stations i.e., good local knowledge, non-auroral oval locations, locally calibrated hmF2 equations, and minimisation of thermospheric wind effects. The 38-year records show ringing terms that are converging towards trend results of )0.25 to )0.30 km yr1 . These are in close agreement with current satellite drag trend estimates. References Beran, J., 1994. Statistics for long-memory processes. In: Monographs on Statistics and Applied Probability, vol. 61. Chapman and Hall, New York. Bilitza, D., Sheikh, N.M., Eyfrig, R., 1979. A global model for the height of the F2-peak using M3000 values from the CCIR numerical map. Telecom. J. 46, 549–553. Bilitza, D., Rawer, K., Bossy, L., Gulyaeva, T., 1993. International Reference Ionosphere-past, present, and future. 1. electron-density. Adv. Space Res. 13, 3–13. Bradley, P.A., Dudeney, J.R., 1973. A simple model of the vertical distribution of electron concentration in the ionosphere. J. Atmos. Terr. Phys. 35, 2131–2146.
Bremer, J., 1998. Trends in the ionospheric E and F regions over Europe. Ann. Geophys. 16, 986–996. Danilov, A.D., Mikhailov, A.V., 1999. Spatial and seasonal variations of the foF2 long-term trends. Ann. Geophys. 17, 1239–1243. Dudeney, J.R., 1974. A simple empirical method for estimating the height and semithickness of the F2-layer at the Argentine Islands, Graham Land, Scientific Reports 88, British Antarctic Survey, Cambridge, UK. Ephishov, I.I., Baran, L.W., Shagimuratov, I.I., Yakimova, G.A., 2000. Comparison of total electron content obtained from GPS with IRI. Phys. Chem. Earth C 25, 339–342. Jarvis, M.J., Jenkins, B., Rodgers, G.A., 1998. Southern hemisphere observations of a long-term decrease in F region altitude and thermospheric wind providing possible evidence for global thermospheric cooling. J. Geophys. Res. 103, 20775–20787. Keating, G.M., Tolson, R.H., Bradford, M.S., 2000. Evidence of long term global decline in the Earth’s thermospheric densities apparently related to anthropogenic effects. Geophys. Res. Lett. 27, 1523–1526. Mikhailov, A.V., Marin, D., 2001. An interpretation of the foF2 and hmF2 long-term trends in the framework of the geomagnetic control concept. Ann. Geophys. 19, 733–748. Piggott, W.R., Rawer, K., 1972. URSI Handbook of ionogram interpretation and reduction, second ed., Rep. UAG-23, 324 pp, Nat. Oceanic and Atmos. Admin. US Dep. Of Comm., Washington, DC. Rishbeth, H., 1990. A greenhouse-effect in the ionosphere. Planet Space Sci. 38, 945–948. Roble, R.G., Dickinson, R.E., 1989. How will changes in carbondioxide and methane modify the mean structure of the mesosphere and thermosphere. Geophys. Res. Lett. 16, 1441–1444. Shimazaki, T., 1955. World-wide variations in the height of the maximum electron density of the ionospheric F2 layer. J. Radio Res. Lab. Jpn. 2, 85–97. Titheridge, J.E., 1969. Single-polynomial analysis of ionograms. Radio Sci. 4, 41–51. Tobiska, W.K., Woods, T., Eparvier, F., Viereck, R., Floyd, L., Bouwer, D., Rottman, G., White, O.R., 2000. The SOLAR2000 empirical solar irradiance model and forecast tool. J. Atmos. Sol.Terr. Phys. 62, 1233–1250. Ulich, Th., 2000. Solar variability and long-term trends in the ionosphere, Ph.D. Thesis, Sodankyla Geophysical Observatory Publications, No. 87, SGO, Tahtelantie 112, FIN-99600 Sodankyla, Finland. Ulich, Th., Turunen, E., 1997. Evidence for long-term cooling of the upper atmosphere in ionosonde data. Geophys. Res. Lett. 24, 1103–1106. Ulich, Th., Turunen, E., Karinen, A., 2001. Global change and changing upper atmosphere – Observations. In: Beig, G. (Ed.), Long-term Changes and Trends in the Atmosphere. New Age International Publishing Company, Pune, India. Upadhyay, H.O., Mahajan, E.E., 1998. Atmospheric greenhouse effect and ionospheric trends. Geophys. Res. Lett. 25, 3375–3378. Weatherhead, E.C., Reinsel, G.C., Tiao, G.C., Jackman, C.H., Bishop, L., Frith, S.M.H., DeLuisi, J., Keller, T., Oltmans, S.J., Fleming, E.L., Wuebbles, D.J., Kerr, J.B., Miller, A.J., Herman, J., McPeters, R., Nagatani, R.M., Frederick, J.E., 2000. Detecting the recovery of total column ozone. J. Geophys. Res. 105, 22201– 22210. Weatherhead, E.C., Reinsel, G.C., Tiao, G.C., Meng, X.L., Choi, D.S., Cheang, W.K., Keller, T., DeLuisi, J., Wuebbles, D.J., Kerr, J.B., Miller, A.J., Oltmans, S.J., Frederick, J.E., 1998. Factors affecting the detection of trends: Statistical considerations and applications to environmental data. J. Geophys. Res. 103, 17149– 17161.
Methodological influences on F-region peak height trend analyses M.J. Jarvis a
a,*
, M.A. Clilverd a, Th. Ulich
b
British Antarctic Survey, Madingley Road, Cambridge CB3 0ET, UK b Sodankyla Geophysical Observatory, Sodankyla, Finland
Received 18 October 2001; received in revised form 20 November 2001; accepted 23 November 2001
Abstract Published estimates of the trend in hmF2 using data from ionosondes over the last 30–40 years range from +0.8 to )0.6 km yr1 and are subject to the influence of several factors. These are considered here based upon an analysis of two southern hemisphere geomagnetically mid-latitude stations, Argentine Islands and Port Stanley. The influence of the equation used to calculate hmF2 at these stations can result in variations of 0:2 km yr1 ; choice of solar proxy has a small influence on the end result, where using E10.7 instead of F10.7 produces changes of )0.04 km yr1 ; neglecting any trends in geomagnetic activity can produce variations of +0.03 to +0.2 km yr1 at the two mid-latitude stations considered in this paper; for datasets of 30–40 years length ringing due to long memory processes can produce 0:2 km yr1 variability; the phase of the 11-year solar cycle, and its harmonics, captured by the datasets can cause variability of 0:5 km yr1 ; and the neglect of local time variations in thermospheric wind conditions could result in +0.2 km yr1 for analysis which only considers local midday data. The Argentine Islands and Port Stanley datasets show ringing terms that are still converging towards trend results of )0.25 to )0.30 km yr1 , which are in close agreement with the satellite drag trend estimates. Crown Copyright Ó 2002 Published by Elsevier Science Ltd. All rights reserved. Keywords: Global change; Ionosphere; Thermosphere; Trends
1. Introduction There are now a considerable number of publications concerning long-term trends in the height of the peak electron concentration in the F-region ionosphere. The interest in this subject stems from the suggestion by Rishbeth (1990) that global cooling of the upper atmosphere, as a consequence of increased ‘greenhouse’ gas concentration (Roble and Dickinson, 1989), would result in a lowering of the F layer peak height (hmF2). Rishbeth (1990) estimated this lowering to be approximately 20 km for a scenario of doubled ‘greenhouse’ gas concentration. This can be translated to an average decrease in altitude of less than 0.1 km yr1 if we assume that this doubling occurs over more than 200 years. Rishbeth (1990) showed analytically that trends in the F region critical frequency (foF2) caused by a greenhouse gas increase should be insignificant compared to those in hmF2 and thus we focus here only on hmF2.
* Corresponding author. Tel.: +44-1223-221-548; fax: +44-1223-221226. E-mail address: [email protected] (M.J. Jarvis).
Studies using ionosonde data from around the world have provided observationally based derivations of the change in hmF2 which range from )0.6 km yr1 (Uppsala: Upadhyay and Mahajan, 1998) to +0.8 km yr1 (Moscow: Bremer, 1998) [see Table 1]. Moreover Ulich (2000) estimated hmF2 trends for 39 stations using 20 different methods. He, too, finds a large variety of trends between +0.961 km yr1 for Khabarovsk and )0.780 km yr1 for Poitiers. For observational comparison, an estimated global average change in hmF2 of )0.25 km yr1 has been derived using the completely independent method of satellite drag analysis (Keating et al., 2000). Clearly, one of the main issues now confronting research in this area is to understand why these different hmF2 trend estimates exist and whether they are a manifestation of some geophysical process which varies spatially, whether they are the result of different data acquisition practices or whether they are the statistical consequence of data variability, continuity and longevity. This paper primarily uses the Argentine Islands and Port Stanley hmF2 data analysed by Jarvis et al. (1998) to comment on and investigate some of the issues involved.
1474-7065/02/$ - see front matter Crown Copyright Ó 2002 Published by Elsevier Science Ltd. All rights reserved. PII: S 1 4 7 4 - 7 0 6 5 ( 0 2 ) 0 0 0 4 1 - 4
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Table 1 Published estimates of hmF2 trends in km yr1 derived from ionosonde data, with indications of the authors involved, and the local time period studied Station
No. of years
00–24 LT
10–14 LT
Shi (10–14 LT)
BD3 (10–14 LT)
D56 (10–14 LT)
Bil (10–14 LT)
Argentine Is. Juliusruh Kaliningrad Kiruna Lannion Moscow Ottawa Poitiers Port Stanley Sodankyla Uppsala
38 34 29 33 25 32 31 26 38 42 37
)0.16a )0.19b 0.16b 0.01b 0.38b 0.84b – )0.42b )0.5a )0.22b )0.15b
– )0.21c – – – 0.24c 0.21c – )0.33c )0.38c )0.58c
0.21 0.1 0.18 0.1 0.03 0.2 0.20 0.1 1.06 0.2 0.30 0.2 0.29 0.2 0.64 0.2 0.11 0.1 0.26 0.1 0.10 0.2
0.04 0.1 0.41 0.1 0.01 0.1 0.29 0.1 1.15 0.1 0.23 0.1 0.12 0.1 0.54 0.1 0.19 0.1 0.39 0.1 0.40 0.1
0.06 0.1 0.31 0.1 0.09 0.1 0.19 0.1 0.87 0.1 0.11 0.1 0.13 0.1 0.77 0.1 0.19 0.1 0.43 0.1 0.36 0.1
0.11 0.1 0.31 0.1 0.03 0.1 0.01 0.1 1.00 0.1 0.13 0.1 0.06 0.1 0.75 0.1 0.20 0.1 0.42 0.1 0.32 0.1
The number of years of data available is shown. We also show four different estimates of F2 layer peak height trends by means of the empirical expressions of Shimazaki (1955), Bradley and Dudeney (1973, Eq. 3), Dudeney (1974, Eq. 56), and Bilitza et al. (1979) which are referred to in the table by Shi, BD3, D56, and Bil, respectively. Probable errors were computed as described by Ulich (2000). a Jarvis et al. (1998). b Bremer (1998). c Upadhyay and Mahajan (1998).
2. Published hmF2 trend estimates Table 1 presents a list of published estimates derived from ionosonde data. The method used by different authors is essentially the same but there are significant variations in the detail of the method. The basic technique is to derive hmF2 from the scaled ionogram parameters foE, foF2 and M(3000)F2 where foE and foF2 are the ordinary wave critical frequencies of the main E and F2 regions of the ionosphere, respectively, and are directly related to the maximum electron concentration. M(3000)F2 is a transmission factor related to the highest frequency that can be propagated between two sites 3000 km apart by refraction alone; it is derived by application of standard transmission curves to ionograms (Piggott and Rawer, 1972). The monthly median values of these parameters are used for any particular hour of the day. The calculation of F2 layer peak height from these parameters is achieved using one of several simple formulae. These formulae come from the same base (Shimazaki, 1955) but have different levels of development. Once a series of hmF2 data has been derived, the data themselves are used in a time-independent fashion to derive an empirical relationship between hmF2 and solar radiation input and, for some authors only, with a geomagnetic activity index. Again, not only are there differences here as to whether geomagnetic activity is included, but some authors have used F10.7 as a solar radiation proxy and some have used sunspot number. Ulich (2000) and Ulich et al. (2001) introduced multiparameter models for trend detection which additionally include terms for annual and semi-annual variation. The empirical relationships derived are used to model the expected hmF2 variation in a time-dependent fashion based on the appropriate time series of solar input and,
if considered, geomagnetic activity. The residuals between this empirical model and the hmF2 data are taken in order to remove the large solar cycle effects from the analysis. A long-term trend in these residuals is then derived. Some authors have only used data around local midday (e.g., 10–14 LT) to calculate the average trend while some have taken the mean linearly fitted trend over a complete 24-hour day. Jarvis et al. (1998) fitted a sine wave through the day for each month to split the residuals into two parts; a long-term linear trend and a long-term change in the strength of the diurnal cycling of hmF2 due to thermospheric winds. The table of published results immediately raises two obvious questions. Firstly, why do different analyses of the data from the same site produce different trends? Examples are Port Stanley, Sodankyla and Moscow. Secondly, why do some station pairs sited very close together have very different results? Examples are Poitiers (46.6°N, 0.3°E) and Lannion (48.5°N, 3.3°W) with trends of )0.42 and +0.38 km yr1 , respectively, or Juliusruh (54.6°N, 13.4°E) and Kaliningrad (54.7°N, 20.6°E) with trends of )0.21 and +0.16 km yr1 , respectively. These apparent spatial discontinuities in trend are additional to the longitudinal change across Europe determined by Bremer (1998) and are unrelated to the geomagnetic latitude dependence of the trend in peak density, foF2, reported by Danilov and Mikhailov (1999). Factors which could possibly have a bearing on these questions include data quality, the equation used to derive hmF2, which proxy was used for solar activity, whether geomagnetic activity was accounted for, the length and period of the dataset, and whether long-term thermospheric wind changes have been removed. Each of these factors is briefly considered below.
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3. Data handling Impacts on data quality are more likely to be due to scaling techniques or instrumental changes, for which local knowledge is required to achieve a reasonable correction. Analyses of single stations often have that local knowledge while for others, where data have been accessed in bulk from international databases, it is seldom the case. An extensive analysis of the effects of the equation used was carried out by Ulich (2000) which showed that for some stations the equation could make a significant difference to the trend estimate and that, for a number of stations, could change the sign of the estimated trend. The effect of the choice of the empirical formula for estimating hmF2 from M(3000)F2, foF2, and foE is shown in Table 1. We used monthly median data averaged around local noon (10–14 LT). Based on these data we compute four different estimates of F2 layer peak height by means of the empirical expressions of Shimazaki (1955), Bradley and Dudeney (1973, Eq. 3), Dudeney (1974, Eq. 56), and Bilitza et al. (1979), which are referred to in the table by Shi, BD3, D56, and Bil, respectively. All four computed estimates differ from the published results for the same stations because of differences in the rejection of data values outside the bounds of the equations used, and the use of additional terms in the times series fitting described below. The probable errors of the ionosonde data were determined and the probable errors of the empirical hmF2 data were computed as described by Ulich (2000). Thereafter the time series of hmF2 were fitted by a multi-parameter model containing terms for the slope of the trend, for solar activity (F10.7), for geomagnetic activity (Ap), as well as for annual and semiannual, viz. hmF2ðtÞ ¼ x0 þ x1 t þ x2 F10:7 þ x3 Ap þ x4 sinðT1 tÞ þ x5 cosðT1 tÞ þ x6 sinðT2 tÞ þ x7 cosðT2 tÞ; where xi are the parameters to be fitted, and T1 and T2 are the angular frequencies of the annual and semiannual variation. The model was inverted using singular value decomposition taking into account the individual measurement errors. In the four rightmost columns Table 1 lists the trends and their probable errors in km yr1 for a selection of 11 stations. The trends derived here vary between 0:77 0:1 km yr1 for Poitiers and þ1:15 0:1 km yr1 for Lannion. Interestingly, these two stations are only 370 km apart from one another. Generally the table demonstrates that the trend magnitude varies with the choice of hmF2 formula. For the cases of Argentine Islands, Kaliningrad, Kiruna, and Ottawa even the sign of the trend depends on the formula. Moreover, Ulich (2000) found that a similar variation of trends for a given station can
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be expected for differently composed multi-parameter models, e.g., when substituting F10.7 with sunspot numbers. For the example of the Sodankyla ionosonde, for which F2 layer heights have been scaled by the single-polynomial method of Titheridge (1969), Ulich (2000) compared the four sets of empirical hmF2 with the scaled real height data and found that empirical hmF2 generally overestimates the heights by typically 5– 100 km depending on formula, phase of solar cycle and season. For the case of Sodankyla he found Eq. 56 of Dudeney (1974) to give the best result: it overestimates hmF2 consistently by about 20 km independent of solar activity. Consequently, the applicability of any empirical hmF2 estimate to the data of a given station needs validation, because the empirical formulae were derived under certain assumptions (e.g., foF2/foE > 1:7 for Bradley and Dudeney (1973)) and the parameters of the formulae were fitted to the data of selected ionosondes during certain phases of solar acitivity. Often the authors used data obtained during the peak of Sunspot Cycle 20 which had a much lower amplitude than more recent cycles. The need for validation emphasises that local knowledge is important in trend analyses, and a lack of it can result in large variations in trend values. The equation used must be shown to produce consistently realistic hmF2 values at any individual site. A good example is that of Jarvis et al. (1998) where the Bradley and Dudeney (1973) equation which they used was originally developed and tested using data from Argentine Islands itself.
4. The solar proxy One of two solar radiation proxies have been used in the hmF2 analyses. Some authors have used sunspot number, R, and some have used the F10.7 index based on the flux of 10.7 cm radiation. Jarvis et al. (1998) compared the two and found that they gave extremely similar results but that using F10.7 resulted in a smaller variance in the final trend estimate. Recently a new index, E10.7, has been introduced (Tobiska et al., 2000). This characterises the actual integrated EUV solar irradiance that deposits energy at the top of the Earth’s atmosphere. It is reported in units of 10.7 cm radio flux and can therefore be directly substituted for F10.7. Using an identical analysis method to Jarvis et al. (1998) but substituting E10.7 for F10.7 the effect on Argentine Islands and Port Stanley data is to reduce the month-tomonth variability of the trend estimate and, in particular, to reduce the size of the trend at Port Stanley in summer. However it makes little difference to the overall mean trend as can be seen in Fig. 1. The bar plot shows the trend estimate from the original Jarvis et al. (1998) analyses using F10.7 (J98) and also with E10.7 for
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Fig. 1. Comparison of trend estimates using four different methods: (a) using the original Jarvis et al. (1998) results [denoted by J98]; (b) as (a) but using E10.7 instead of F10.7 [E10.7]; (c) as (a) with the Ap index term excluded [no_Ap]; (d) using IRI as the comparative model to derive residuals [IRI].
Argentine Islands and Port Stanley. Both sites show a small increase in the downwards trend when using E10.7 of the order of )0.04 km yr1 . These results conform to the index comparison by Tobiska et al. (2000) who show that regarding longer-term physical variations, such as the solar cycle, E10.7 and F10.7 are virtually identical, but on timescales of a solar-rotation or less there are important differences.
5. Geomagnetic activity Some authors neglect the effect of geomagnetic activity (e.g., Ulich and Turunen, 1997) on the basis that they find its inclusion makes little significant difference to the result. Others argue, based primarily on the geomagnetic dependence of foF2 trends (e.g., Danilov and Mikhailov, 1999), that most of the trends found in hmF2 should also relate to geomagnetic activity. Most authors use Monthly Ap, however, Mikhailov and Marin (2001) argue that the use of monthly Ap is inadequate to remove geomagnetic effects because correlations occur over longer time scales; thus they use a 12-month running mean. Here we repeat the Jarvis et al. (1998) analysis but excluding the Ap index term from the derived empirical model. Thus any trends in geomagnetic activity are basically neglected and are allowed to fully influence the result. The result is shown in Fig. 1 (no_Ap) where it can be seen that there is a slight reduction in the downwards trend observed at both sites of about +0.03 km yr1 compared with the J98 value. Thus the effect of geomagnetic activity appears to be small and positive for both stations. If a highly accurate time-dependent ionospheric model existed, then the results of that model could be used when deriving the residuals between our expectations, based on the prevailing geophysical inputs, and the observed hmF2 values. The most widely used ionospheric model is the International Reference Ionosphere (Bilitza et al., 1993). While this is a valuable tool for the
estimation of environmental and other effects, testing theories and designing experiments, we note that it does not perform realistically at all sites and under all conditions (Ephishov et al., 2000). With a view to using IRI output as a model with which to derive the hmF2 residuals, we have attempted to mimic the statistical process by which the observational data were derived. Thus, using the IRI, we have derived hmF2 for every hour of every day through the same 38year data period as analysed by Jarvis et al. (1998) [i.e., 1957–1995]. The IRI monthly median hmF2 value at each hour for each month was then calculated. Direct comparison with the observed hmF2 data showed that there were significant discrepancies between data and model, highlighted by Fig. 2(a). It shows the median, full range, and inter-quartile range of the differences in monthly medians between the IRI hmF2 and observed hmF2 for Argentine Islands plotted against year of the 11-year solar cycle. This shows interquartile ranges of between 30 and 50 km and median differences of about 20 km in some years. The variations clearly show an unremoved solar cycle in hmF2 residuals. By comparison Fig. 2(b) shows the same plot by the Jarvis et al. (1998) method; the solar cycle in hmF2 residuals has been more reliably removed. The interquartile ranges lie between 10 km and 25 km and median differences are no greater than 5 km. The equivalent results for Port Stanley are very similar and thus have not been shown here. The hmF2 trend for Argentine Islands and Port Stanley using the IRI model is shown in Fig. 1. It should be noted that the IRI model does not take account of varying geomagnetic activity and thus a more direct comparison might be between the no_Ap and IRI results; both have the effect of reducing the downward trend. This comparison should be refined as atmospheric models become more accurate.
Fig. 2. Residuals between observed hmF2 data and modelled hmF2 data as a superposed-epoch against solar cycle year for Argentine Islands. Medians (crosses), interquartile ranges (boxes), and full ranges (whisker) are shown. (a) Using IRI model; (b) using Jarvis et al., 1998 method. [The equivalent (a) and (b) results for Port Stanley (not shown) are essentially the same.]
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6. The length and period of dataset One aspect of determining the trend in hmF2 is the length of the memory processes involved in the system being studied. Analysis of a system with short memory processes would require shorter datasets to allow the result to converge to the underlying trend. Results involving long-term memory processes converge more slowly. Weatherhead et al. (1998) showed that processes lower in the atmosphere can be described by first order auto-regression, AR(1), where memory is mid- to longterm. Thus we can expect the estimate of trend in hmF2 to show long memory convergence towards the actual trend value (Beran, 1994). Fig. 3 shows the trend estimates (diamonds) for Argentine Islands and Port Stanley starting with only 10 years of data, sequentially increasing to 38 years of data. The solid lines are fits to the data using three damped oscillatory sinewave components with periods of 11, 22, 33, and 44 years superposed. At both sites the estimate of trend is well represented as a ringing function which converges to a trend value of )0.25 to )0.30 km yr1 after about 50–60 years. This kind of convergence was first shown by Bremer (1998), whose results are qualitatively similar to those of Fig. 3. The converging values shown in Fig. 3 are both essentially from negative values
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towards 0.25 km yr1 . However, it is possible that the values would converge from positive values if the datasets were collected over a different period with different phases of the sinewave components. If a data series has not converged significantly then differences of 1 km yr1 could occur depending on which period of data was analysed. This suggests that it would be advantageous to study the same periods of data to compare the results from different stations. The result of this ringing interpretation is that both Argentine Islands and Port Stanley converge to a similar trend value which is consistent with the result of Keating et al. (2000) – indicated by a dashed line in the figure. The current difference in estimate between the two sites is due to ringing terms of about 0.2 km yr1 when only 20–40 years of data have been used. Fig. 3 shows that had Jarvis et al. (1998) used 32 years of data instead of 38 the trend results for the Argentine Islands would have been positive not negative. Weatherhead et al. (2000) suggested that different regions would require different lengths of datasets before trends could be reasonably identified. Thus the form of the convergence of the trend result shown at individual sites should provide information on the robustness of each trend estimate.
7. The effect of changing thermospheric winds
Fig. 3. The variation in the estimate of the trend at Argentine Islands and Port Stanley (diamonds). The data are fitted with a 3-component damped oscillatory sinewave (solid line) which appears to converge towards the result of Keating et al. (2000) (dashed line) in both cases.
If there is a significant long-term change in the strength of the meridional thermospheric wind, then it can have a significant effect on the hmF2 trend derived from analysis limited to around midday only. The mean of data which covers all 24 h of the day will, if the altitude variation induced by the cycling of the meridional thermospheric wind is sinusoidal (or otherwise symmetric about zero), effectively cancel any thermospheric wind effect. As an example, Jarvis et al. (1998) estimated a decrease in the amplitude of the diurnal thermospheric wind-induced quasi-sinusoidal oscillation of hmF2 at Port Stanley of 0.2 km yr1 . At this location, hmF2 reaches its minimum value near midday and so, if this thermospheric wind effect is not accounted for in a longterm trend estimate of hmF2 because only data around midday have been used, then it will produce an erroneous additional ‘mean’ hmF2 trend of +0.2 km yr1 . This is confirmed by comparing the results of Upadhyay and Mahajan (1998) and Jarvis et al. (1998) regarding Port Stanley data. The former used data between 10 and 14 LT only and obtained an hmF2 trend of )0.33 km yr1 while the latter removed the thermospheric wind effect and obtained an hmF2 trend of )0.50 km yr1 . A preliminary assessment of Sodankyla data indicates that using the same F2 layer peak height derivation formula and including all local times leads to a stronger downward trend than when only midday is considered.
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A closer analysis of the thermospherically driven diurnal cycles in the data series from all stations is needed. 8. Summary Rishbeth (1990) estimated that the trend in hmF2 driven by atmospheric CO2 changes are )0.1 km yr1 . Independent estimates of the trend made from satellite drag measurements by Keating et al. (2000) give )0.25 km yr1 . Estimates of the trend in hmF2 using data from ionosondes over the last 30–40 years range from +0.8 to )0.6 km yr1 . The trend results derived from ionosonde data are subject to the influence of several factors. In this paper we have quantified some of these factors with respect to Argentine Islands and Port Stanley data which are identified here: the influence of the equation used to calculate hmF2 at these stations can result in variations of 0:2 km yr1 ; the choice of solar proxy has a small influence on the end result, where using E10.7 instead of F10.7 produces changes of )0.04 km yr1 ; neglecting any trends in geomagnetic activity can produce variations of +0.03 to +0.2 km yr1 at the two mid-latitude stations considered in this paper; for datasets of 30–40 years length ringing due to long memory processes can produce 0:2 km yr1 variability; the phase of the 11year solar cycle, and its harmonics, captured by the datasets can cause variability of 0:5 km yr1 ; and the neglect of local time variations in thermospheric wind conditions could result in +0.2 km yr1 for analysis which only considers local midday data. The Argentine Islands and Port Stanley datasets considered in this paper have the attributes of ‘good’ stations i.e., good local knowledge, non-auroral oval locations, locally calibrated hmF2 equations, and minimisation of thermospheric wind effects. The 38-year records show ringing terms that are converging towards trend results of )0.25 to )0.30 km yr1 . These are in close agreement with current satellite drag trend estimates. References Beran, J., 1994. Statistics for long-memory processes. In: Monographs on Statistics and Applied Probability, vol. 61. Chapman and Hall, New York. Bilitza, D., Sheikh, N.M., Eyfrig, R., 1979. A global model for the height of the F2-peak using M3000 values from the CCIR numerical map. Telecom. J. 46, 549–553. Bilitza, D., Rawer, K., Bossy, L., Gulyaeva, T., 1993. International Reference Ionosphere-past, present, and future. 1. electron-density. Adv. Space Res. 13, 3–13. Bradley, P.A., Dudeney, J.R., 1973. A simple model of the vertical distribution of electron concentration in the ionosphere. J. Atmos. Terr. Phys. 35, 2131–2146.
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