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A method for foF2 short-term forecast over Europe has been developed and implemented in the EUROMAP model. The input-driving parameters are 3 h ap indices (converted to ap(τ)), effective ionospheric T index, and real-time foF2 observations. The method includes local (for each station) regression storm models to describe strong negative disturbances under ap(τ) > 30 and training models to describe foF2 variations under ap(τ) ≤ 30. The derived model was tested in two regimes: descriptive when observed 3 h ap indices were used and real forecast when predicted daily Ap were used instead of 3 h ap indices—. In the case of strong negative disturbances the EUROMAP model demonstrates on average the improvement over the lnternational Reference Ionosphere STORM-time correction model (IRI(STORM)) model: 40% in winter, 24% in summer, and 39% in equinox. The average improvement over climatology is 41% in winter, 59% in summer, and 55% in equinox. In the majority of cases this difference is statistically significant. In the case of strong positive disturbances, higher-latitude stations also manifest a significant difference between the two models but this difference is insignificant at lower latitude stations. The substitution of 3 h ap input indices for the predicted daily Ap ones decreases the foF2 prediction accuracy in the case of negative disturbances but practically has no effect with positive disturbances. In both cases the proposed method manifests better accuracy than the IRI(STORM) model provides. The obtained results show a real opportunity to provide foF2 forecast with the (1–24 h) lead time on the basis of predicted Ap indices.
Short-term (1–24 h in advance) ionospheric F2 layer forecast is still an unsolved and very challenging problem despite long history and many attempts undertaken. Problems with the ionosphere forecast are due to objective reasons. Physical mechanisms forming both negative and positive F2 layer disturbances are well established by now. They are related to global thermospheric circulation, neutral composition and temperature, electric fields, and plasmaspheric flux changes. The list of all pertinent processes may be found in Rishbeth  and Prölss . The problem is assessing the relative intensity of each process in a particular ionospheric disturbance. The Earth's upper atmosphere is an open system with many uncontrolled inputs forcing it both from above and below. If solar EUV radiation, magnetospheric electric fields, and particle precipitation (impact from above) can be controlled to some extent, the intensity of internal gravity waves, dynamo and tropospheric electric fields, and planetary waves (impact from below) are uncontrolled in principle. Depending on prehistory and current state of the magnetosphere and thermosphere, the reaction will be different to the same impact from above, but no thermosphere and magnetosphere monitoring is made at present and is not expected in an observable future. Thus, the intensity of each particular process controlling the F2 region: electric fields and characteristics of particle precipitation producing high-latitude thermosphere heating, global thermospheric circulation resulting in neutral composition, and temperature variations, the internal gravity waves dissipation in the 100–120 km height range producing via eddy diffusion changes in neutral composition in the whole thermosphere above, planetary waves etc., is not well known for each particular geomagnetic storm. Therefore, there is not much hope at present to obtain a “deliberate” forecast of the F2 region using so called first principle or physical thermosphere-ionosphere models. This was well demonstrated in the framework of the CEDAR (Coupling, Energetics, and Dynamics of Atmospheric Regions) project where available both empirical and physical models were compared [Shim et al., 2011, 2012]. The monthly median International Reference Ionosphere (IRI) model [Bilitza and Reinisch, 2008, also previous versions] has turned out to be one of the best many cases. This does not mean that IRI is good to describe the disturbed conditions considered in that testing; a monthly median model is not designed for this, but it does tell us that physical models with data assimilation or without it are inadequate to describe specific geophysical conditions. An example of a poor real-time description of NmF2 and hmF2 variations with the Coupled Thermosphere Ionosphere Plasmasphere Electrodynamics model at Kwajalein during a disturbed period in August 2011 is given in Codrescu et al. [2012, Figure 5]. Present day problems with the thermosphere-ionosphere physical modeling are discussed by Schunk et al. . But it should be stressed that physical modeling is the only way to understand the mechanisms of the ionospheric changes under various geophysical conditions and its role hardly can be overestimated. Thus, theoretical modeling may be considered as a powerful tool for research rather than operational forecasting.
Therefore, we follow the empirical approach developing a foF2 prediction method. There are two main empirical approaches (i) the regression one which uses foF2 autocorrelation or foF2 regression with solar wind parameters or with indices of solar and geomagnetic activity [Wu and Wilkinson, 1995; Marin et al., 2000; Kutiev and Muhtarov, 2001, 2003; Stanislawska and Zbyszynski, 2001, 2002; Araujo-Pradere et al., 2002, Araujo-Pradere and Fuller-Rowell, 2002; Koutroumbas and Belehaki, 2005; Liu et al., 2005; Pietrella and Perrone, 2005, 2008; Perrone et al., 2007; Dabas et al., 2008; Koutroumbas et al., 2008; Tsagouri and Belehaki, 2008; Tsagouri et al., 2009; Pietrella, 2012] and (ii) and the approach using various neural networks [Altinay et al., 1997; Wintoft and Cander, 2000; Francis et al., 2000; Chan and Cannon, 2002; Tulunay et al., 2004; Oyeyemi et al., 2005; Chen et al., 2010a, 2010b, 2010c; Ban et al., 2011; Wang et al., 2013].
There also exists an aeronomic approach to the F2 layer parameter prediction [Shubin and Annakuliev, 1995] which seems to be practically unknown to the ionospheric community. It is based on the NmF2 analytical relationship with neutral composition and temperature taken from any thermospheric model, for instance, MSISE-00. Similar to the lnternational Reference Ionosphere STORM-time correction model (STORM) model [Araujo-Pradere et al., 2002, Araujo-Pradere and Fuller-Rowell, 2002, 2003], the aeronomic approach can be used in areas where ionospheric observations are absent and this is important from practical point of view.
One can find in literature exotic prediction methods, for example McNamara et al. , which is based on an analog forecast to predict NmF2 variations up to 4 days in advance. Obviously, the authors appeared to be forced to this method under the pressure of practical needs realizing the incapability of the existing prediction methods.
There is an aspect of the ionospheric forecast which is not usually discussed in publications. When observed driving parameters (e.g., historical geophysical indices) are used as the input to a model [e.g., Shim et al., 2011, 2012], one should speak about the accuracy of model description or approximation of the observations rather than the prediction accuracy. Real forecast starts when the predicted driving parameters are used as the input, and the prediction accuracy estimates will be quite different from those using historical data.
Ionospheric F2 layer disturbances are known to be related to geomagnetic ones and this is widely used in practice. But today, only daily Ap index is routinely predicted 1–3 days in advance and the accuracy of these predictions is rather low. However, this is the present day reality and any prediction method basing on the relationship with geomagnetic activity has to use this Ap index forecast. The proposed method is also based on this relationship, and we will demonstrate what foF2 forecast accuracy can be achieved on this way.
The whole territory of the globe may be divided in four classes according to the availability of ionospheric observations.
Regions of the first class are those where ionospheric observations were conducted for some decades in the past and where modern ionosondes are installed to provide real-time ionospheric observations. Such regions are Europe, America, and Australia. Two types of local prediction models can be created for the stations of the first-class regions: models based on historical observations for some solar cycles and training models which use real-time observations. The two models will supplement each other providing an acceptable prediction accuracy under various geophysical conditions as will be demonstrated in this paper.
Regions of the second class are those where ionospheric observations were conducted for some decades in the past, but current real-time observations are absent. There are many regions of this type in the world, for instance, the territory of the former USSR. Regression prediction models can be created for the stations located in such regions. Such models as it will be shown in the paper can be efficiently used.
Regions of the third class are those where newly installed modern ionosondes like DPS-4 provide real-time ionospheric data, but no historical observations are available. Training prediction models can be derived for such stations. Prediction possibility of such models will be discussed in the paper.
Regions of the fourth class are those where neither historical nor current ionospheric observations are available. These are oceans, Africa, and eastern part of Russia. Only global models like IRI(STORM) or an aeronomic one, or physical first-principle models can be used for the ionospheric forecast in such regions.
We will consider the European first-class region with eight ionosonde stations—Chilton (Slough), Juliusruh, Moscow, Rostov, Pruhonice, Athens, Rome, and Ebre (Tortosa)—for which both regression and training models can be created to demonstrate the prediction possibilities of the proposed approach.
Therefore, the aims of the paper may be formulated as follows: (1) to develop a method for foF2 short-term (1–24 h) forecast over midlatitude European stations for which both historical and real-time foF2 observations are available, (2) to estimate a description and prediction accuracy of the proposed method in comparison with the IRI(STORM) model which is considered the international standard of the ionospheric models, and (3) to evaluate whether the developed method can be used in practice for the foF2 short-term forecast.
2 Method Description
This part includes a description of the observations used in our analysis, a selection of the background level to count foF2 deviations during ionospheric perturbations, and the formalism used to create both regression and training prediction models.
Historical hourly foF2 observations on the eight European stations were taken both from Space Physics Interactive Data Resource (http://spidr.ngdc.noaa.gov/spidr/) and directly from the stations. Observations over 25–30 years are necessary to develop a regression model. This is due to a necessity to have a sufficient number of strong ionospheric storms (both negative and positive) to find statistically significant dependences for 12 months of the year and 24 UT moments. All data were visually checked to delete obvious errors as the quality of foF2 data is different on the stations considered.
For real foF2 forecast, only daily Ap can be used as this is the only index of geomagnetic activity which is predicted at present. Table 1 gives the prediction accuracy of daily Ap index 1 and 2 days in advance made at three Prediction centers over the 2003–2011 period.
Table 1. Prediction Accuracy of Daily Ap Index 1 and 2 Days in Advance at Three Prediction Centers Obtained Over 2003–2011a
aStandard (SD) and mean relative (MRD) deviations in comparison with the observations are given. Total number of points used for comparison N ≈ 3200.
SD (1 day)
MRD (%) (1 day)
SD (2 days)
MRD (%) (2 days)
Table 1 shows that the prediction accuracy is rather low—mean relative deviation (MRD) = 60–100%. These are statistical estimates obtained over 9 years. Figure 1 gives two examples of such predictions for the periods comprising strong geomagnetic disturbances in October 2000 and April 2001.
It is seen that large geomagnetic disturbances (the most important from practical point of view) are not successfully predicted. Only a general tendency in Ap variations is described with this forecast.
Despite obvious problems with the Ap index forecast, this is the only real opportunity to derive a method to predict foF2 variations with (1–24 h) lead time using geomagnetic activity indices as the driving parameter. In fact, 3 h ap indices are required to describe hour-to-hour foF2 variations but such indices are not predicted with a sufficient lead time. One can find only an ap index forecast for 1–4 h in advance ftp://ftp.swpc.noaa.gov/pub/lists/wingkp/. This ap index forecast can be used for the first 3 h interval, then the predicted daily Ap repeated 7 times to imitate 3 h ap index daily variations is used. Similarly, the predicted 2 days in advance Ap index is used in our method for foF2 forecast for the next day.
The ionosphere-thermosphere (and via it the ionosphere) reacts to the integral impact of geomagnetic activity, and the prehistory of ap index variation is important. This idea is expressed in ap(τ) index [Wrenn, 1987] used in our method
where ap–n (n = 0, 1, 2, 3…)—ap value for the current 3 h interval, −3 h, −6 h, etc. In practice, τ = 0.7–0.75 and this corresponds to the “persistence time” 3/(1 − τ) = 10–12 h. This may be considered as the characteristic time of the ionosphere reaction to geomagnetic activity variations. This integrated impact of geomagnetic activity limits to some extent the problems with the 3 h ap index forecast: observed ap indices for the previous hours noticeably contribute to the predicted foF2 variations.
2.2 Background Level
Many prediction methods deal with foF2 deviations from a background level and the choice of this level is very important for the efficiency of the method. Various approaches are used to specify the background level. Monthly median or running median calculated over previous ~ 30 days are often used as the background [e.g., Marin et al., 2000; Kutiev and Muhtarov, 2001; Tsagouri and Belehaki, 2008]. Such median gives a floating background level, which depends on the number of disturbances in the month, and this inserts an additional noise to the prediction method. Better results should give a selection of magnetically quiet days for a station with binning them in terms of hour, month, and range of solar activity. The mean values for each bin provide a quiet-time background level which can be applied with suitable interpolation to any day of a month [Wrenn et al., 1987; Perrone et al., 2007; Pietrella and Perrone, 2008; Pietrella, 2012]. The only problem related to this method is related to so called quiet-time disturbances (Q-disturbances) which occur under quiet geomagnetic conditions [Mikhailov et al., 2004, 2007a, 2007b]. They are numerous and may give a bias to the background level. Another possibility is to use model monthly median foF2 as the background [Shubin and Annakuliev, 1995; Araujo-Pradere et al., 2002, Araujo-Pradere and Fuller-Rowell, 2002]. Due to averaging (in the model) of many monthly medians obtained under various geomagnetic conditions but similar level of solar activity (e.g., the IRI(CCIRInternational Radio Consultative Committee) model), one may hope that such average median presents a reference level corresponding to a given solar activity. Both positive and negative F2 layer disturbances (including Q-disturbances) should be seen with respect to this background level.
We also follow this way in developing our prediction method. Instead of using the IRI(CCIR) model, we have derived local (for each station) monthly median foF2 models which are based on the ionospheric T index [Turner, 1968; Caruana, 1990] as an indicator of solar activity. It is well known that effective ionospheric indices of solar activity provide the best correlation with monthly median foF2 [e.g., Mikhailov and Mikhailov, 1999]. As an example, the IRI model (any version) with CCIR coefficients is compared to the derived local model for Juliusruh. The results are given for four seasons, four periods of day under solar maximum and minimum (see Appendix A, Tables A1 and A2). Tables A1 and A2 show that the derived local monthly median foF2 model provides much better approximation accuracy than the IRI especially under solar maximum conditions. Such models developed for each station are used as the background to calculate foF2 deviations. It is assumed that the median is appropriate to the sixteenth day of a month. Using foF2 medians for neighboring months, it is possible to generate a “median” for each day of a month and each UT moment [Wrenn et al., 1987].
2.3 Regression Storm Model
A regression storm model for a station presents a foF2obs/foF2bgr versus ap(τ) regression (cubic polynomial) considered for 12 months of the year and 0–23 UT moments. An example of this dependence is given in Figure 2. The whole foF2obs/foF2bgr versus ap(τ) area may be divided into three subareas with points under ap(τ) < 30 (moderate both positive and negative disturbances or quiet conditions) and points with ap(τ) ≥ 30 (strong positive and negative disturbances). The latter subarea belongs to the regression storm model which is supposed to describe strong negative disturbances. The area with ap(τ) < 30 belongs to the training model (see later). There are two types of positive disturbances at middle latitudes [Zevakina and Kiseleva, 1978; Mikhailov et al., 2012]. Type I of disturbances is referred to those followed by quiet ionospheric conditions. Positive disturbances of type II are followed by negative ionospheric storms. The disturbances of type II are shorter than those of type I, but their amplitude is larger. After the active period of the disturbances of type I, enhanced, foF2 is observed for the whole day and the active period may repeat in 24 h with decreased δfoF2. Positive disturbances of type II present the first phase of a two-phase (positive-negative) foF2 disturbance. They occur under high geomagnetic activity and cannot be distinguished from strong negative disturbances when we work in the real forecast mode: the type of future disturbance (positive or negative) cannot be predicted on the basis of Ap index forecast. The impossibility to predict this type of future foF2 disturbance is a serious limitation of the method. If the type of a disturbance could be predicted, this would strongly increase the prediction accuracy of the method. Choosing between negative and positive disturbances, we gave the priority to the prediction of strong negative ones which are more important from practical point of view. For this reason positive disturbances of type II are poorly described with our method, but fortunately, they are not a lot of such disturbances. However, they were also included in the list of tested cases (section 3.2) as, in practice, the type of future disturbance a priori is not known.
Strong negative disturbances are not numerous, and we used additional points from neighboring hours to “strengthen” the foF2obs/foF2bgr versus ap(τ) regression dependence for a given UT. All points outside the ± 2 SD (SD is the standard deviation) interval were removed from the analysis. The regression coefficients for 12 months and 24 UT moments found for eight European stations present the regression storm models which allow the calculation of δfoF2 = foF2obs/foF2bgr and correspondingly foF2 for a given ap(τ) value using available foF2bgr. Such models were tested using specially selected strong negative disturbances, and the testing results will be given later in section 3.1
2.4 Training Model
For the stations with available real-time foF2 observations, training prediction methods can be derived. It is known that δfoF2 exhibits a pretty good interhour correlation within a day. During daytime hours the e-fold time of NmF2 changes with respect to recombination (τ ~ 1/βm, where βm is the linear loss coefficient at the F2 layer maximum height) is about 1.5 h. However, daytime F2 region is strongly controlled by thermosphere (neutral composition and temperature) and the e-fold time for these parameters is longer than 1.5 h. During nighttime hours, the characteristic time with respect to the loss process is more than 10 h due to low linear loss coefficient at hmF2 heights and the NmF2 interhour correlation normally is very good for nighttime hours. Therefore, a prediction method should take into account previous foF2 observations and this is widely used in practice. Although this interhour correlation breaks down during disturbed periods, decreasing to 1–3 h, such a persistent method may be a good addition to the regression storm model even under disturbed conditions, increasing the prediction accuracy during the first 1–3 h.
The regression used in our prediction method is written as follows:
where δfoF2(UT) is the last observed deviation at UT moment, n is the lead time (1–24 h), ap(τ,UT + n) is the predicted ap(τ) index for (UT + n) moment. The unknown coefficients Ci are obtained over the previous 28 day (one solar rotation) training period using the least squares multiregressional methods.
Figure 1 shows that the δfoF2 versus ap(τ) relationship is practically absent under ap(τ) < 30. We have just a cloud of points: both positive and negative disturbances take place under the same ap(τ) values. However, the analysis has shown that some dependence still exists even under low ap(τ) values. We have selected both strong negative and positive disturbances at Juliusruh observed under ap(τ) < 30 (totally 31 cases) and checked the regression (1) for two selections: with really observed ap(τ) values and when all ap(τ) were assumed to be zero. The corresponding MRD deviations in comparison with the observations were 14.3% and 14.9% with the standard deviations 5.9% and 6.2%. The difference is seen not to be large but if it exists on average, one may think that geomagnetic activity may be important in some cases. For this reason it was included into the regression (1).
3 Testing of Models
The testing procedure includes checking the approximation accuracy of the developed models when the type of disturbance is known and observed 3 h ap indices are used as the input. Testing of the models in the real forecast mode implies the use of predicted daily Ap instead of 3 h ap indices, Ap being the only input driving information.
3.1 Testing of the Regression Storm Model
First, we will consider the approximation accuracy of the regression storm model using all available historical observations and observed 3 h ap indices. This model is designed to describe strong negative disturbances which are very important for applications to high-frequency radio. Strong negative disturbances over eight European stations and for three seasons (20–25 disturbances for each season) have been selected for testing. A disturbance was considered to be a strong one if δfoF2 deviation was ≤ δfoF2cut during at least 5 successive hours in a day. It is known that the negative disturbance magnitude decreases equatorward, therefore, δfoF2cut was 0.6 for higher-latitude stations: Moscow, Juliusruh, and Slough, 0.7 for moderate latitudes: Rostov and Pruhonice, and 0.75 for lower latitude stations: Athens, Rome, and Tortosa. The number of strong negative disturbances is sufficient in summer and equinox but they are few in winter. It should be stressed that strong F2 layer disturbances may take place under moderately disturbed or even quiet geomagnetic conditions—so called Q-disturbances [Mikhailov et al., 2004, 2007a, 2007b], and we have sufficient number of such cases among the selected ones. Of course, this decreases the accuracy of the method as it is easier to describe the ionospheric perturbations related to strong geomagnetic disturbances while no precursors for Q-disturbances have been revealed to date.
The developed regression storm model, the IRI(STORM) model [Araujo-Pradere et al., 2002, Araujo-Pradere and Fuller-Rowell, 2002, 2003], and the local (in each station) monthly median model were tested. The latter was used to illustrate the improvement over climatology presented by foF2 monthly median.
Table 2 gives mean relative MRD (in %) and standard SD (in MHz) deviations calculated over 24 h of the day and all selected storm cases. The results are given for three seasons in eight ionosonde stations. Table 2 shows that the developed storm model manifests the best results over all stations and for all seasons. Relative mean deviations are about 2 times less than the IRI(STORM) model provides. Even larger differences in MRD up to 3–5 times take place with respect to monthly median model. The improvement over climatology according to the Araujo-Pradere and Fuller-Rowell,  definition will be estimated later (Table 5).
Table 2. Mean Relative (in %) and Standard (in MHz in Brackets) Deviations Calculated Over 24 h of the Day and All Selected Negative Storm Casesa
aThe developed regression storm, IRI(STORM), and local monthly median models are compared. The results are given for three seasons on eight ionosonde stations. The best results for each station and season are given in bold.
At lower latitude stations in winter the monthly median model turns out to be more accurate than IRI(STORM). Problems with the IRI(STORM) model in winter are well known [Araujo-Pradere and Fuller-Rowell, 2002].
The newly developed model is seen to demonstrate a very good accuracy which is much better than the IRI(STORM) model provides. However, it should be stressed again that this is the model approximation accuracy when the type of disturbance (negative) is known and the observed ap indices are used in calculations. In real forecast we do not know either the former or the latter. For this reason the advantages of the developed model cannot be fully used in real forecasting, as it will be shown later.
3.2 Testing of the Summary Model
The summary model is a working version of our prediction model which comprises the training model for ap(τ) < 30 and the regression storm one for ap(τ) ≥ 30. It is supposed to work with both negative and positive F2 layer disturbances. At this stage we analyze the model approximation accuracy. As earlier this implies the use of the observed 3 h ap indices and known type (positive/negative) of a disturbance. For this testing, earlier selected strong negative disturbances were supplemented with the same amount of strong positive disturbances. A positive disturbance is considered as a strong one if δfoF2 ≥ 1.2 (≥ 40% in NmF2) during at least 5 successive hours in the day.
The testing procedure of the training model differs from that we used for the regression storm one. Starting from any UT = 0–23 moment when the “last” foF2 observation was done, the model predicts 24 foF2 values with lead time 1–24 h. This is a practical working mode which is normally used in an ionosphere prediction center. Two adjacent days “today” and “tomorrow” are considered in such prediction. Testing of two successive days is also reasonable from practical point of view. Usually, strong ionospheric disturbances last longer than 1 day [e.g., Wrenn et al., 1987; Buonsanto, 1999] partly overlapping two neighboring days and testing results obtained over 48 h give a more adequate estimate of the model performance. We will compare the developed model with the IRI(STORM) one as it may be considered the international ionospheric standard. In this testing the IRI(STORM) model is also run for 48 h.
Table 3 shows that the developed model provides systematically better results than IRI(STORM) for all stations and three seasons in the case of negative disturbances. In the majority of cases this difference is significant at the level > 97%. The developed model is seen to provide less MRD even when the difference is insignificant (the significance level is < 95%). The results for positive disturbances are different to some extent. Higher-latitude stations (Moscow, Juliusruh, and Slough) also manifest a significant difference between the two models, but this difference is insignificant at lower latitudes and the IRI(STORM) model demonstrates slightly better results for Rome and Tortosa.
Table 3. Mean Relative Deviations (in %) Calculated Over 48 h for All Selected Negative and Positive Storm Casesa
aNumbers in brackets are IRI(STORM) results. The best results are given in bold. The significance of difference (in %) between the two models according to Student criterion is given in the second line.
15.3(18.0) < 95.0
16.3(19.7) < 95.0
14.7(18.7) < 95.0
11.7(13.2) < 95.0
14.3(17.5) < 95.0
14.0(15.2) < 95.0
12.8(14.8) < 95.0
12.4(14.6) < 95.0
17.4(20.4) < 95.0
16.0(15.8) < 95.0
16.1(16.4) < 95.0
12.7(16.1) < 95.0
18.7(19.1) < 95.0
18.0(15.0) < 95.0
19.1(15.5) < 95.0
15.6(13.4) < 95.0
13.5(13.4) < 95.0
15.5(12.5) < 95.0
Table 3 shows on average some decrease of the description accuracy in comparison with Table 2 for the same negative disturbances. This is due to the following. The summary model works only with the input index ap(τ) without any a priori information on the type of the disturbance. The code uses the training model when ap(τ) < 30 while the regression storm model was used for all ap(τ) values during testing negative disturbances (Table 2). Therefore, the accuracy loss takes place in the ap(τ) < 30 area where the training model should capture both negative and positive disturbances. In both cases we lose the accuracy, but unfortunately, the disturbance type cannot be predicted on the basis of ap index.
3.3 Dependence on Lead Time
There is no dependence of the model accuracy on lead time for strong disturbances (ap(τ) ≥ 30) as the regression storm model depends only on ap(τ) value and the model approximation accuracy may be found in Table 2. It should be mentioned once again that the regression storm model is designed to describe only strong negative disturbances. Both positive and negative disturbances occurring under moderate and low (ap(τ) < 30) geomagnetic activity are described with the training model, and one can speak on the lead time dependence in this case. Strong negative and positive disturbances observed at Juliusruh during 2000–2002 were selected for our analysis. Only three strong negative disturbances under ap(τ) < 30 were found, and all three were observed in winter. Positive disturbances are more numerous and they occur in any season of the year, so we selected 16 of them for our analysis.
Figure 3 gives foF2prd/foF2obs dependence versus lead time for three negative and 16 positive disturbances observed at Juliusruh in 2000–2002. Average deviations are seen to be small <10% especially for positive disturbances, but SDs are much larger for negative disturbances (14–27%) compared to (7–17%) positive ones. The standard deviations continuously increase with lead time for positive perturbations while they are relatively small in the beginning (n = 1–2 h) and in 24 h in the case of negative disturbances. This peculiarity of negative disturbances prediction was mentioned earlier [e.g., Mikhailov, 1990; Tsagouri et al., 2009]. One may think that this peculiarity is related to the negative disturbance formation mechanism which is related to neutral composition changes. The disturbance bulge “rotates” with the Earth producing a negative storm effect at the same location in 24 h. According to Prölss , the idea that composition perturbations, once they have been generated, “rotate” with the Earth is just an idea.
Actually, the disturbance bulge will be pushed around by winds and may move back and forth in latitude and this is confirmed by the storm simulation [Fuller-Rowell et al., 1994] as well as by ESRO-4 data analysis [Skoblin and Förster, 1993].
4 Real Forecast
It was stressed earlier that one can speak about real ionospheric forecast only when predicted driving parameters are used as the input. We do not discuss small (< 2 h) lead times which are within the e-fold characteristic time of foF2 variations. Quasi-persistent methods can be efficiently used in such case. Such methods are also may be efficient in quiet conditions without strong foF2 perturbations, quiet-time foF2 perturbations (Q-disturbances) are a special problem.
Our method is based on the foF2 versus ap(τ) dependence, that is we need an ap(τ) forecast. Only daily Ap index is predicted 1–3 days in advance at present and the accuracy of this forecast is rather low (see earlier). However, this seems to be the only possibility to develop a practical method to predict foF2 with lead times up to 24 h under various geomagnetic conditions. The aim of our analysis is to demonstrate which foF2 prediction accuracy can be obtained using such an Ap index forecast, which to our knowledge has not been previously attempted.
Both strong negative and positive ionospheric disturbances observed at Juliusruh, Chilton (Slough), and Rome in 2000–2002 were used in this analysis. These years were not used during the development of the method. The list of selected disturbances is slightly different for the stations depending on the available observations but about 25 disturbances of two types were selected at each station. It should be stressed once again that strong ionospheric disturbances are not necessarily related to strong geomagnetic storms, and they may occur under moderately disturbed or even quiet geomagnetic conditions. For instance, negative disturbances were observed at Juliusruh on 11 December 2000 (Ap = 8/10), 11 October 2001 (Ap = 21/7), 05 March 2001 (Ap = 19/19), and 24 January 2001 Ap = (19/17); observed daily Ap indices are given for the current and previous days. The majority of positive disturbances take place under quiet or slightly disturbed geomagnetic conditions. Therefore, we did not pay attention to the geomagnetic activity level when selecting the disturbed cases.
Testing results for Juliusruh, Chilton, and Rome are given in Table 4. The developed prediction model (summary version) is compared to IRI(STORM) when observed 3 h ap indices and predicted at Space Weather Prediction Center (SWPC) daily Ap indices were used as the input. The results obtained with the local monthly median models (the background level) are also given for comparison. The substitution of the observed 3 h ap input indices for the predicted daily Ap ones is seen to decrease the prediction accuracy in the case of negative disturbances. However, this accuracy decrease is not catastrophic and the obtained MRD = 16–24% is still acceptable in comparison with a forecast on the basis of the local monthly median model (Table 4). This decrease in the prediction accuracy is explainable. The majority of negative disturbances are related to strong magnetic storms which are poorly predicted (see Table 1 and Figure 1), which result in the foF2 prediction accuracy decrease (Table 4). The proposed method is seen to provide better accuracy in comparison with IRI(STORM), although this difference sometimes statistically is not significant when the significance level is < 95%.
Table 4. Mean Relative Deviations (in %) Calculated Over 24 h of the Day and All Selected Negative and Positive Storm Cases When Observed ap 3 h and Predicted Daily Ap Indices Were Used as the Inputa
Observed 3 h ap
Observed 3 h ap
aThe developed model (first number), the IRI(STORM) model (second number), and the local monthly median model are compared. The significance of the difference (in %) according to Student criterion between the developed and the IRI(STORM) models is given in the second line.
16.6/20.2 < 95.0
23.5/25.4 < 95.0
16.3/18.2 < 95.0
13.5/15.1 < 95.0
The situation with positive disturbances is different. The change of the observed 3 h ap indices for the predicted Ap ones practically has no effect on the foF2 prediction accuracy. This is related to the peculiarity of foF2 positive disturbances. The majority of them belong to the positive disturbances of type I [Mikhailov et al., 2012], which occur under low geomagnetic activity. The geomagnetic forecast in this case can be done with better accuracy and with less absolute errors. Moreover, Table 4 shows that monthly median provides the same prediction accuracy and it could be efficiently used for the foF2 forecast. Unfortunately, this is impossible in practice as the type (positive/negative) of future disturbance cannot be reliably predicted on the basis of the Ap index forecast. The proposed method is seen to provide better prediction accuracy compared to IRI(STORM), the difference being statistically significant with one exception for Rome.
Summarizing the testing results, it is possible to conclude the following. A substitution of the observed 3 h ap indices for the predicted daily Ap decreases the foF2 prediction accuracy in the case of negative disturbances and has no effect in the case of positive ones. But this decrease is not catastrophic, and the foF2 prediction accuracy is still much better than can be obtained on the bases of the monthly median. The prediction accuracy obtained with the proposed method is higher than what the IRI(STORM) model provides both for negative and positive disturbances. The obtained results seem to be encouraging as they show a real opportunity for foF2 forecast with the (1–24 h) lead time on the basis of the predicted Ap indices. It should be stressed once again that daily Ap index is the only index of geomagnetic activity which is really predicted at present with the (1–3) day lead time. If it can be efficiently used for the foF2 forecast, this is a result of practical importance.
5 Mapping Over Europe
The multiquadric method [Hardy, 1971] application to global and to regional ionospheric mapping is given in Teryokhin and Mikhailov . The function describing the surface of foF2 drawn over given set of points may be written as follows:
where θi is the colatitude = (90 − ϕi) and λi is the longitude of a station, and Ci is the unknown coefficients to be specified using the ionospheric parameters in N points. Our previous analysis has shown that there is no need to add a constant to this expression as proposed in Hardy and Nelson  when we deal with a limited area like Europe. It should be pointed out that the multiquadric method draws a surface strictly over given set of points in distinction from other methods being used for ionospheric mapping.
The developed EUROMAP model is a part of the global SIMP (System of Ionosphere Modelling and Prediction) model which is under development in Russian Federation; it will be described elsewhere. For this reason the European area is surrounded by a buffer zone to provide smooth interfacing to the global foF2 model. The buffer zone points should be located at some distance from the ionospheric stations (Figure 4) and global model foF2 values are specified in these buffer zone points. Both observed or predicted foF2 values over the European ionospheric stations and buffer zone points are used in drawing the surface.
An example of such foF2 map for strongly disturbed conditions of 15 May 1969 at 00 UT (3 h ap = 154) in comparison with the IRI(STORM) model is given in Figure 4. The regression storm model foF2 values were used at the station points and are not shown here. This map is very similar to the map when observed foF2 values are used at the station points. An interesting peculiarity of this period is the main ionospheric trough which has formed over the northern part of Europe where Moscow (3.0/3.2 MHz), Juliusruh (3.3/3.9 MHz), Pruhonice (3.4/3.9 MHz), and Slough (3.1/3.2 MHz) ionosonde stations are located. Model/observed foF2 values are given in brackets and their closeness confirms the reality of the trough with very low foF2 values. It is interesting to note that the position and foF2 values in the trough minimum observed in central Europe organically match the trough parameters described by the global model: the points eastward of λ = 60°E belong to this global model. The main trough position in this model depends on the effective Kp index [Annakuliev et al., 1997] which takes into account the prehistory of geomagnetic activity variations.
The IRI(STORM) model (Figure 4, bottom) manifests a gradual poleward foF2 decrease as the main ionospheric trough is absent in this model. In general the IRI(STORM) model foF2 values (5.0–5.5 MHz) in central Europe are much larger both the observed and our model values (3.0–3.5 MHz). This is rather strange as the IRI(STORM) model was shown to be the most efficient in summer [Araujo-Pradere and Fuller-Rowell, 2002].
The undertaken analysis has shown that it is possible to develop a foF2 forecast method for the first-class regions where both historical and real-time foF2 observations are available. Europe is a region where this method can be efficiently used as there are long-working ionospheric stations and current ionospheric observations are also available, for instance, via Digital upper Atmosphere Server Project [Belehaki et al., 2005, 2006, 2007]. In such regions it is possible to derive single-station foF2 prediction models which manifest higher accuracy compared to global models like IRI(STORM) [Araujo-Pradere et al., 2002, Araujo-Pradere and Fuller-Rowell, 2002, 2003]. Using such single-station foF2 prediction models ingested with current ionospheric observations and applying foF2 mapping methods, it is possible to monitor in real time the whole European region. The proposed EUROMAP model is a part of the global SIMP model which is under development in Russian Federation to provide global ionospheric monitoring and forecast. In near future when new ionosondes are installed across the territory of Russia, the developed method can be successfully used for the ionospheric forecast.
This is not our first attempt to derive a prediction model which could be used in practice [Mikhailov, 1990; Marin et al., 2000; Pietrella and Perrone, 2005, 2008; Mikhailov et al., 2007c; Perrone et al., 2007]. Previous efforts were mainly directed toward the development of methods to describe strong negative foF2 disturbances. In this paper our previous experience has been used to derive a prediction method suitable for practical application. We have shown not only the descriptive possibilities of the developed method using historical observations but have demonstrated its accuracy when predicted Ap indices were used as the input. As far as we know, this is the first time this has been done.
Daily Ap index is far from being the best for the foF2 short-term forecast. But today it seems to be the only opportunity to derive a practical method based on geomagnetic activity to predict foF2 with the lead time up to 24 h as only daily Ap indices are predicted at present with lead time 1–3 days. Both our regression storm and training models use 3 h ap index as the driving parameter. However, this index is not predicted; therefore, it was substituted with daily Ap repeated 8 times to imitate 3 h ap index. Of course, this substitution decreases the foF2 prediction accuracy, but this decrease does not look catastrophic and it takes place only for negative disturbances while positive foF2 perturbations practically are not sensitive to this substitution. This result looks encouraging from practical point of view as it has opened the way for real foF2 forecast with the (1–24 h) lead time.
Some new features distinguish the proposed approach. First, a selection of the reference background level. Our previous attempts [Mikhailov, 1990; Marin et al., 2000; Perrone et al., 2007; Pietrella and Perrone, 2008] were based on using either running foF2 median or on foF2 averaged over magnetically quite days. Both methods as it was mentioned earlier give a flowing background and this inserts an additional noise to the analyzed foF2 deviations. Moving to local (for each station) monthly median foF2 models which depend on the effective ionospheric index T [Turner, 1968; Caruana, 1990] with an interpolation of this median on a particular day of a month gave an obviously positive result. Such foF2 median derived over many years reflects an average level of geomagnetic activity corresponding to a given level of solar activity. Therefore, such median better presents the background ionosphere under given solar activity compared to any running median of quiet days which inevitably bear the geomagnetic activity effects.
Another new feature of the proposed approach is a combination of two models: the regression storm model and the training one. The reason to do this is in the following. Strong negative foF2 disturbances are the most important from practical point of view, but they rarely occur and there are not many chances to have them in the previous 28 day training period. The use of long training periods (years) is not reasonable, keeping in mind strong seasonal variations of the ionospheric F2 region with different foF2 reaction to geomagnetic activity in different seasons. A ~30 year period with observations for each ionospheric station is required to have a sufficient number of strong negative disturbances to derive regression models for 12 months and 24 UT moments. This is a laborious process to derive such a storm model but it guarantees higher foF2 descriptive accuracy (see Table 2) compared to global models like IRI(STORM). It seems unreasonable not to use this possibility in the data-rich area like Europe while global models like IRI(STORM) or the model by Shubin and Annakuliev  can be used elsewhere (for, instance, oceans) as they are not dependent on current ionospheric observations.
The training model is designed to describe both negative and positive foF2 perturbations occurring under low and moderate (ap(τ) < 30) geomagnetic activity. The main bulk of time is under such geomagnetic conditions which with high probability occur during the 28 day training period. In practice, this prediction model is supposed to produce 24 new foF2 forecasts (n = 1–24) for each integer UT moment when new foF2 observation appear. This mode automatically switches to operate with the regression storm model under high (ap(τ) ≥ 30) geomagnetic activity.
One of the problems which is not specifically related to the proposed method is the prediction of large foF2 perturbations occurring under low geomagnetic activity, the so called Q-disturbances [Mikhailov et al., 2004, 2007a, 2007b]. Presumably, such disturbances are due to an impact from below but no precursor for their occurrence has been revealed yet. Any prediction method will be inefficient with such perturbations unless a precursor is found. An example was earlier given [Mikhailov et al., 2007c, Figure 3] for a quiet-time disturbance observed at Moscow on 23 April 1980. We have sufficient number of such cases especially among positive disturbances. All of them were included to general statistics to show which accuracy can be obtained in practice without any special selection of disturbances used for testing.
At present the type of future disturbance (negative/positive) can hardly be predicted with sufficient confidence at a particular station, although attempts are made in this direction [Tsagouri and Belehaki, 2008; Paznukhov et al., 2009]. If we succeeded with this, the foF2 prediction accuracy could be significantly increased in the ap(τ) < 30 area. Regression models could be derived separately for positive and negative foF2 deviations, and this would increase the prediction accuracy of the model. From this point of view the situation with strong geomagnetic disturbances usually considered in publications looks simpler. Normally, strong geomagnetic storms result in negative foF2 disturbances and our local storm regression models demonstrate good descriptive accuracy (Table 2) which is much better than what IRI(STORM) provides. However, there are some problems with strong geomagnetic storms as well. One is a poor geomagnetic forecast of such events (e.g., Figure 1), and this may be a serious limitation for the ionospheric forecast with our method. Another problem is the so-called positive disturbances of type II [Mikhailov et al., 2012] which present the first positive phase of a two-phase (positive-negative) ionospheric disturbance. They occur under high geomagnetic activity as well and cannot be distinguished from strong negative disturbances when we deal with real ionospheric forecast using only predicted Ap index. Although the morphology and physics of such positive disturbances are established, they cannot be predicted accurately in practice. Additional efforts are needed in this direction to find reliable precursors which could be added to our prediction method.
It is interesting to compare the developed model to other prediction models. A comparison with the IRI(STORM) model has been done at each step in this paper. This is explainable as the IRI(STORM) model may be considered as the international standard. All comparisons have shown that the developed method provides systematically better results under all conditions in question, in the majority of cases, the difference being statistically significant (≥ 95%) according to Student criterion. An additional widely used way to demonstrate the merits of a method is to give an improvement in comparison to any other model. Following the Araujo-Pradere and Fuller-Rowell  definition
where root-mean-square error (RMSE) = (1/n∑(foF2mod − foF2obs)2)0.5. This RMSE or “scatter” is different from SD (standard deviation) used in Table 2. We have specially calculated this parameter because it is used in other publications devoted to ionosphere prediction. Table 5 gives the improvement of the proposed method over the IRI(STORM) model. Earlier considered negative storms (Table 2) have been used for this comparison. The significance of the difference was estimated according to Student criterion.
Table 5. Improvement (in %) Over the IRI(STORM) Model Estimated for Three Seasonsa
aEarlier considered strong negative storms (see Table 2) were used for this comparison. Numbers in brackets = significance of the difference (in %) according to Student criterion.
8 (< 95.0)
19 (< 95.0)
Table 5 shows that the difference with the IRI(STORM) model is statistically significant (≥ 95%) in the majority of cases and the improvement varies from 20 to 48%. Of course, this is an encouraging result, but this is normal when a local model derived for a particular station demonstrates an advantage over a global one. However, this does not always the case. See, for example, Pietrella .
An improvement over climatology can be also considered as this parameter is used by Tsagouri et al. and Araujo-Pradere and Fuller-Rowell  The SWIF model manifests the same tendency both for middle- to high-latitude (Chilton and Juliusruh) and for middle- to low-latitude (Athens, Rome) stations. The improvement is maximal ~ 60% for the lead time 1 h, and it falls down to < 20% for the lead time 24 h, the results being slightly better at higher-latitude stations (their Figure 8). It was mentioned earlier that the term “lead” time is not applied to our regression storm model which depends only on 3 h ap index, therefore, we give averaged estimates obtained over all tested storm days in different seasons (Table 6). The results are accompanied by the significance of the difference according to Student criterion.
Table 6. Improvement (in %) Over Climatology Obtained With the Regression Storm Modela
aNumbers in brackets = significance of the difference (in %) according to Student criterion. The results are obtained using the same list of storms as in Table 2.
22 (< 95.0)
20 (< 95.0)
Table 6 shows the improvement over climatology varying from 20 to 72%, in the majority of cases this difference being absolutely significant (> 99%). There is a tendency to smaller improvements at lower-latitude stations (Athens, Rome, and Tortosa) in comparison with higher-latitude ones (Moscow, Juliusruh, and Slough). For comparison the IRI(STORM) model provides on average a ~ 33% improvement over climatology [Araujo-Pradere et al., 2002, Araujo-Pradere and Fuller-Rowell2002].
The obtained results can be summarized as follows.
It was shown that in a data-rich (both historical and real-time) region like Europe, it is possible to derive local (for each station) foF2 prediction models depending on 3 h ap, T indices, and real-time foF2 observations. The driving input parameter is 3 h ap while the effective ionospheric index T specifies the background level. The proposed approach is applied to eight European stations and is implemented in the EUROMAP model.
The descriptive accuracy of the derived model was shown to be better than what the IRI(STORM) model provides for all eight stations and three seasons in the case of strong negative disturbances. In the majority of cases this difference is statistically significant at the level > 97% according to Student criterion. In the case of strong positive disturbances, higher-latitude stations (Moscow, Juliusruh, and Slough) also manifest a significant difference between the two models but this difference is insignificant at lower-latitude stations (Athens, Rome, and Tortosa).
In the case of strong negative disturbances the EUROMAP model demonstrates on average the improvement over the IRI(STORM) model: 40% in winter, 24% in summer, and 39% in equinox. The average improvement over climatology is 41% in winter, 59% in summer, and 55% in equinox. In the majority of cases this difference is statistically significant.
The accuracy of the EUROMAP model depends on lead time in the ap(τ) < 30 regime.
Average MRDs are small (<10%) especially for positive disturbances, but SDs are much larger for negative disturbances (14–27%) compared to (7–17%) for positive ones. The standard deviations continuously increase with lead time for positive perturbations while they are relatively small in the beginning (n = 1–2 h) and in 24 h in the case of negative disturbances.
The latter is presumably related to the negative disturbance formation mechanism.
Practical systems need real foF2 forecast with lead time 1–24 h. Daily Ap index is the only index of geomagnetic activity which is predicted at present with the (1–3) day lead time. It was shown that the substitution of 3 h ap input indices for the predicted daily Ap ones decreased the prediction accuracy in the case of negative disturbances. However, this accuracy decrease is not substantial and the obtained MRD = 16–24% still looks as acceptable in comparison with a forecast on the basis of the local monthly median model. In the case of positive disturbances this substitution practically has no effect on the foF2 prediction accuracy. This is related to the peculiarity of foF2 positive disturbances. The majority of them occur under low geomagnetic activity when the geomagnetic forecast can be done with better accuracy.
A comparison with the IRI(STORM) model in the same testing regime has shown that the proposed method provides better accuracy both for negative and positive disturbances although this difference sometimes statistically is not significant with the significance level < 95% according to Student criterion.
The obtained results seem to be encouraging as they show a real opportunity for foF2 forecast with the (1–24 h) lead time on the basis of predicted Ap indices. As far as we know, this has been shown for the first time and this result is of practical importance. The developed EUROMAP model is a part of the global SIMP model which is developed in Russian Federation for the ionosphere monitoring and forecast.
Table A1. A Comparison of the CCIR Model to a Monthly Median Local foF2 Model for Juliusruh Based on the Ionospheric Index T for Solar Maximum and Minimum, Four Seasons, and Four Periods of Day. Mean Relative (MRD) and Standard (SD) Deviations are Given Along With Number of Comparisons.