Filtering ionosphere parameters to detect trends linked to anthropogenic effects
© Elias; licensee Springer. 2014
Received: 8 April 2014
Accepted: 22 August 2014
Published: 10 September 2014
The great concern about the global warming observed in the troposphere has generated a large interest in the study of long-term trends in the ionosphere since the early 1990s, which has now become a significant topic in global change investigations. Some research works link ionosphere trends to anthropogenic sources such as the increase in greenhouse gas concentration, and others to natural causes such as solar and geomagnetic activity long-term changes, and secular variations in the Earth's main magnetic field. In all the cases, in order to analyze ionospheric trends, solar activity effect must be filtered out first since around 90% of ionosphere parameter variance is due to solar variations. The filtering process can generate ‘spurious’ trends in the filtered data series which may lead to erroneous conclusions. foF2 data series which include solar cycle 23 are analyzed in the present work in order to detect the effect of different filtering procedures on the determination of long-term trends. In particular, solar cycle 23 seems to have had an extreme ultraviolet (EUV) emission greater than that deduced from traditional solar EUV proxies during the maximum epoch and lower during the minimum epoch. When solar activity is filtered assessing the residuals of a linear regression between foF2 and Rz, or between foF2 and F10.7, this fact may bias trend values especially because it is at the end of the time series. The length of the period considered for trend assessment, the saturation and hysteresis effect of some ionosphere parameters, and the solar EUV proxy used are also considered in this study in order to quantify a possible spurious trend that may result as a by-product of a filtering process. Since trends expected as a consequence of anthropogenic effects are relatively small, these spurious effects may surely mask, or enhance, trends expected from anthropogenic origins.
Long-term changes in ionospheric parameters were analyzed by many authors since the early 1990s, and, in general, after filtering the effects of solar activity, long-term variations, or trends, were reported. These trends were attributed to solar extreme ultraviolet (EUV) radiation changes (Adler et al. 1997; Yamazaki and Yumoto 2012), geomagnetic activity variations (Mikhailov and Marin 2001; Danilov 2002; Mikhailov 2001, 2006), the increase in greenhouse gas concentration (Bremer 1992, 1998; Upadhyay and Mahajan 1998; Ulich and Turunen 1997; Jarvis et al. 1998), and/or secular variations of the Earth's main magnetic field (Foppiano et al. 1999; Elias and Adler 2006; Elias 2009; Yue et al. 2008; Cnossen and Richmond 2008, 2013; Cnossen et al. 2012).
The ionosphere varies greatly because of changes in the sources of ionization, that is, the solar EUV radiation, and changes in the neutral part of the upper atmosphere in which it is embedded which also depends on solar radiation, so that solar EUV radiation is the dominant influence on the ionosphere. In fact, solar EUV proxies such as Rz and F10.7 usually explain around 90% of ionospheric parameters' variance once the annual variation has been filtered out from ionospheric data. This 90% value is obtained considering that for most ionospheric stations, the correlation coefficient between annual or 12-month running mean data of the critical frequency of the F2 layer, foF2 (or the E layer, foE) for example, and Rz (or F10.7) is around 0.95. This means a variance explained of 0.952, that is, 0.90 or 90%. Long-term trends would represent then at most the remaining 10%. This makes necessary to filter ionospheric time series in order to enhance and make ‘significantly’ detectable these trends. Filtering procedures are based on the dependence of ionospheric parameters on solar EUV radiation which is almost linear as can be deduced from the well-known direct association of these parameters to solar EUV proxies such as Rz or F10.7. However, it should be noticed that for Rz > 160 and F10.7 > 200, a saturation effect takes place which results in a nonlinear dependence (Liu et al. 2006, 2011). The risk of not considering this effect, which is significant at some stations but weak at others, is described in ‘Saturation effect.’
Filtering is a standard mathematical operation which in our case is used to enhance features, as it is a long-term trend, otherwise not visibly apparent in the data. However, filtering can have unexpected consequences such as the introduction of spurious oscillations or a spurious trend (Chandler and Scott 2011). Special care is therefore required when making inferences from filtered time series.
foF2 data series which include solar cycle 23 are analyzed in the present work in order to detect the effect of different filtering procedures on the determination of long-term trends. The minimum of this solar cycle, between 2007 and 2009, is characterized by lower EUV solar radiation than during previous solar cycles. Well-known solar activity proxies and also measurements give diverse results regarding the true percentage decrease (Solomon et al. 2013). The fact is that cycle 23 has had a EUV emission different than that deduced from traditional solar EUV proxies such as Rz and F10.7. Emmert et al. (2010) suggested that the long-term relationship between EUV irradiance and F10.7 has changed markedly since around 2006 with EUV levels decreasing more than expected from the F10.7 proxy. This result is also suggested by Chen et al. (2011). The opposite happened to the relationship between EUV and Rz during the solar cycle 23 maximum and declining phase where Rz underestimates EUV solar radiation (Lukianova and Murusla 2011).
When solar activity is filtered assessing the residuals of a linear regression between foF2 and Rz, or between foF2 and F10.7, which is a common filtering technique used in most of the publications that analyze ionosphere trends, the relationship between foF2 and the EUV proxy considered is expected to be the same over the whole period of analysis. If this is not the case, as happens during solar cycle 23, a spurious trend may be obtained. For example, a negative trend would result due to the overestimation of EUV radiation during the last minimum, or, considering the cycle 23 maximum, if Rz is being used as a solar EUV proxy, the underestimation of EUV would result in a spurious positive trend.
The length of the period considered for trend assessment, the saturation and hysteresis effect of some ionosphere parameters, and the solar EUV proxy used are also considered in this study in order to quantify a possible nonreal trend that may result as a by-product of a filtering process in comparison to the trends expected in the upper atmosphere as a consequence of anthropogenic effects.
The data analyzed and expected results due to the departure from linearity of foF2 vs EUV proxy are presented in ‘Data analysis’, followed by the ‘Discussion and conclusions.’
Monthly median foF2 at 12 LT from three stations, which include solar cycle 23, were analyzed: Juliusruh (54.6°N, 13.4°E), Slough (51.5°N, 359.4°E), and Sodankyla (67.3°N, 26.3°E).
As a first step, the seasonal variation, present in foF2 but not in solar activity, is filtered out applying a 12-month running mean to both foF2 and the solar activity index considered. This process decreases the degrees of freedom by 1/12. Another possibility would have been to analyze annual data, and in this case, the number of data would have been reduced in 1/12, so both options are statistically equivalent.
where α and β are the regression coefficients and α is the trend we are interested in.
As can be noticed, α will depend on the steps previous to its calculation, and especially on the filtering process applied to the series involved.
There are at least five issues to consider regarding the latter filtering process: (1) saturation effect, (2) hysteresis effect, (3) nonlinearity, (4) the choice of the model or solar activity index to assess the modeled value, and (5) length of the period considered. Each of them is analyzed in the following subsections.
Results and discussion
Saturation takes place in the case of some ionospheric stations, when Rz or F10.7 exceeds a certain value, beyond which the ionosphere seems not respond to a further increase in EUV radiation (Balan et al. 1994; Liu et al. 2003; Ma et al. 2009). It is linked to a breakdown of the linearity between foF2 and EUV (or solar index), as reported in Liu et al. (2006, 2011), and the consequences may strongly influence the long-term trend reached.
This situation results in persistent negative residuals which will affect the trend value according to where this period of persistence is located within the whole period of analysis. If it is in the middle, it may not cause any spurious results, but if it is close to an extreme, it will depend if it is at the beginning, inducing a spurious positive trend, or at the end inducing a spurious negative trend.
In the case of Sodankyla, the period of saturation, that is, solar cycle 19, is at the beginning of the time series so it should be expected to be a positive or a less negative trend than the trend without considering this period. In fact, the trend from cycle 20 to cycle 23 results -0.010 and -0.008 MHz/year for the period from cycle 19 to cycle 23. Although the difference is not statically significant, it results from the saturation effect.
The hysteresis effect refers to the fact that for the same value of solar activity level, foF2 may differ for the rising and falling parts of the 11-year solar cycle. The variation of foF2 then, over a complete solar cycle, displays a curve similar to the hysteresis variation of a magnetization cycle.
This phenomenon has been known for a long time (Naismith et al. 1961; Rao and Rao, 1969; Adler and Manzano 1995) and is attributed to the behavior of geomagnetic activity throughout the solar cycle (Mikhailov and Mikhailov 1995; Apostolov and Alberca 1995). The enhanced geomagnetic activity during the falling phase of the solar cycle would produce stronger F2 layer storm effects than during the rising phase.
foF2 trend values (MHz/year) for Slough (51.5°N, 359.4°E)
1960 to 1986
1960 to 1989
1960 to 1996
1960 to 2000
1960 to 2009
Nonlinearity of foF2 vs solar EUV proxy
Nonlinearity also refers to the possibility that the factor responsible for trends in the ionosphere, whichever may be, does not act with the same intensity along the solar cycle. In fact, Emmert et al. (2008) found that there is a solar cycle dependence of the long-term trends in thermospheric density (approximately - 5 and -2% per decade at solar minimum and maximum, respectively) and Mlynczak et al. (2010) observed that the infrared radiative cooling rates by CO2 and NO in Earth's thermosphere, which are the dominant radiative cooling mechanisms for the thermosphere, also vary with solar cycle activity level.
The choice of the model or solar EUV proxy may affect the trend values as long as the model or proxy selected does not effectively reflect the real variance of foF2 due to the solar EUV radiation, which is the part one wants to filter before trend determination.
foF2 trend values (MHz/year) estimated after filtering foF2 12-month running mean at 12 LT
foF2 trend (filtered with Rz) × 10-3 MHz/year
foF2 trend (filtered with F10.7) × 10-3 MHz/year
5 ± 2
-6 ± 1
2 ± 2
-9 ± 2
0 ± 2
-10 ± 2
where σ is the standard deviation of trend α and r is the correlation coefficient of the regression between foF2res and time. The statistic t value obtained in each case is tested against the Student's t value of 1.96 which corresponds to 48 degrees of freedom (50, which results from the 50 years of monthly data divided by 12 due to the 12-month running mean, minus 2) and 0.025 significance level. As can be deduced from Table 2, in all cases except Sodankyla filtered with Rz, t results greater than 1.96.
Length of period
One of the main foci of climate science is to determine the extent to which human activities are altering the planetary energy balance through the emission of greenhouse gases and pollutants. The ionosphere is one component affected by greenhouse gases. However, this anthropogenic effect is so small that in order to detect it, all other variability must be filtered out first.
In this paper, several sources which may hinder the filtering process have been analyzed. Filtering is a critical step toward trend estimation since a bad filtering leads inevitably to a bad result unless there is compensation, which occurs randomly. Lastovicka et al. (2006), having noticed that results on long-term trends in foF2 and their interpretation did not reveal a consistent pattern, carried out a joint analysis foF2 trend estimation. One problem in fact is the filtering process selected by each author which gives different results in some cases for the same foF2 time series analyzed.
Recently, Mielich and Bremer (2013) analyzed more than 100 stations in order to detect the best index to filter solar activity from foF2 and hmF2. They conclude that F10.7 is a better index for the description of the solar activity than Rz. Damboldt and Suessmann (2012) filtered the solar cycle influence using a Comité Consultatif International des Radiocommunications (CCIR) ionospheric prediction model, which uses Rz as a solar EUV proxy. They obtained a trend reversal in hmF2 in 1963 to 1964 with negative trends from 1942 to 1963 and positive trends from 1964 to 2005, which is in contrast to the results reported in most other publications of ionospheric long-term trends. A plausible cause of this would be that CCIR uses Rz as solar activity index.
According to the results presented here, three recommendations for trend assessments which can be easily handled are suggested. One is not to include periods with F10.7 > 200, or at least test that the residuals for these periods are not systematically negative. The other two were already made by Mielich and Bremer (2013): use F10.7 instead of Rz, since it follows more closely EUV solar flux, and the length of period considered should be long enough so as to obtain a stable trend since at least the last 4 to 5 years of the data series considered (almost half a solar cycle).
Why is important to do a correct filtering of ionospheric (or atmospheric in general) parameters? We live in the Earth and we want to understand and predict the atmosphere behavior which is essential for human life. A correct filtering would guarantee a good result from which right conclusions regarding variations of small amplitudes such as long-term trends are extracted.
Regarding ionosphere, at least the five mentioned issues regarding filtering process should be taken into account in order to be sure about trend value results.
I would like to thank two anonymous reviewers for their helpful comments and to the Nagoya CAWSES-II Symposium organizers for the important financial support they gave me. This research was performed under project Prestamo BID - PICT 2011–1008.
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