Radio Science

Instantaneous space-weighted ionospheric regional model for instantaneous mapping of the critical frequency of the F2 layer in the European region

Authors


Abstract

[1] An instantaneous space-weighted ionospheric regional model (ISWIRM) for the regional now-casting of the critical frequency of the F2 layer (foF2) has been developed. The geographical area of applicability of the model is ranged between 35°N–70°N and 5°W–40°E. Inside this region the hourly values of foF2 are obtained, correcting the monthly medians values of foF2 predicted by the space-weighted ionospheric local model (SWILM) on the basis of hourly observations of foF2 coming from four reference stations (Rome, Chilton, Lycksele, and Loparskaya (or Sodankyla)). The performance of the model, evaluated at four testing stations (Tortosa, Juliusruh, Uppsala, and Kiruna) during some periods characterized by strong solar and geomagnetic activity, can be considered satisfactory, given that the hourly values of the residuals are almost always below 1 MHz. A comparison between ISWIRM's performance using manually validated and autoscaled data of foF2 and SWILM's performance was made for two disturbed periods. One example of instantaneous ionospheric mapping of foF2 relative to the selected disturbed periods is also shown.

1. Introduction

[2] The development of models that can provide reliable predictions of the main ionospheric parameters is very important to ensure successful radio communications. For this reason many global and regional empirical models were developed in the past to forecast the key ionospheric characteristics of the F2 layer, such as its critical frequency, foF2, the obliquity factor for a distance of 3000 Km, M(3000)F2, and the height of the F2 peak, hmF2.

[3] The empirical models are developed by using a statistical analysis of extended data records accumulated by a network of ground ionosondes over a long interval time. The statistical description of the ionosphere is carried out with the monthly median (defined as the data point with an equal number points below it and above it) that, because of the large spread of the hourly values of the ionospheric parameters, is more suitable for describing the average behavior of the ionosphere than the standard mean. Over the years, a large number of global [Jones and Gallet, 1962; Comite Consultatif International des Radiocommunications (CCIR), 1991; International Telecommunication Union (ITU), 1997] and regional models [Bradley, 1999; Hanbaba, 1999] have been developed. These models provide long-term predictions of the monthly medians of the standard ionospheric parameters, offering good guidelines for the choice of the frequencies that need be used in HF communications under “quiet” ionospheric conditions. Many efforts have been made to develop a universal definition of “quiet ionosphere” but it is very difficult [Kouris and Fotiadis, 2002]. The monthly median values of the foF2 parameter are usually used to describe the “quiet” ionosphere [Cander and Mihajlovic, 1998] even if, in many cases, they do not efficiently represent the “quiet” behavior of the ionosphere [Kozin et al., 1995; Belehaki et al., 1999].

[4] Important phenomena of meteorological nature occurring in the neutral atmosphere, such as the upward propagation of planetary waves, acoustic-gravity waves and tides, generate a wavelike motions of the ionosphere, called traveling ionospheric disturbances (TID), that can make HF communications difficult.

[5] In addition, important events occurring on the Sun, such as solar flares (SF) and coronal mass ejections (CME), severely affect the ionosphere, giving rise to a wide variety of ionospheric disturbances, such as polar cap absorption (PCA), ionospheric storms (IS) and sudden ionospheric disturbances (SID), with detrimental effects on HF communications. Solar disturbances also affect the Earth's magnetic field, causing what are called geomagnetic storms sometimes occurring in conjunction with IS.

[6] Owing to the great variability of this phenomenon and also to the many different processes at work, it is very difficult to characterize the ionospheric storms. Basically, the ionization density can either increase or decrease during disturbed conditions. This changes are denoted as positive and negative ionospheric storm respectively [Prölss, 1995]. Generally during winter there is a prevalence of positive storms, the inverse for the other seasons [Wu and Wilkinson, 1995].

[7] During such events the ionosphere deviates from its “quiet” state and thus the use of the monthly median to predict the operating frequency that has to be used on a given HF circuit fails. In these cases a very short-term forecast of the ionospheric characteristics would be necessary, e.g., on an hourly basis, to offer HF operators real-time assistance in choosing the optimal frequencies for radio links. This requires the possibility to continuously and automatically monitoring the state of the ionosphere in real time at a useful number of stations.

[8] Nowadays this is possible thanks to modern digital ionosondes. A network of digisondes provided by automatic scaling of ionograms, constitutes a very important tool for real-time ionospheric modeling, because it provides a real-time picture of the ionosphere (the so-called “now-casting”) over the whole region covered by the network [Reinisch, 1995, 1996]. The instantaneous models are based only on a few stations in Europe that provide ionospheric data in real time (Athens, Rome, Chilton, Dourbes, Juliusruh and Tromso) unlike the monthly median models. The instantaneous model here described is one of the many possible mapping procedures that can be utilized [Hanbaba, 1999; Zolesi et al., 2004]. Recently was developed another model called Storm Time Empirical Ionospheric Correction Model (STORM) that provides an estimate of the expected change in the ionosphere during periods of increased geomagnetic activity [Araujo-Pradere et al., 2002].

[9] The ISWIRM algorithm generates values of foF2, on the base of hourly measurements of foF2 provided by a network constituted by four ionosondes located in Rome, Chilton, Lycksele, and Loparskaya, or Sodankyla when data from Loparskaya is not available (reference stations). Measurements of foF2 from the ionospheric observatories of Tortosa, Juliusruh, Uppsala, and Kiruna (testing stations) were utilized to calculate the global daily error, σ, representing the performance of the model. Since “now-casting” the ionosphere is of most interest under disturbed conditions, the reliability of the model was tested calculating σ on different time periods characterized by marked solar and geomagnetic activity. Useful indications were drawn from the analysis of σ to obtain the best instantaneous mapping of foF2.

[10] The ISWIRM model development and testing procedure is described in section 2. The data analysis, the results for the reliability of the model, and the discussion of the same are presented in section 3. Concluding remarks on the ISWIRM approach are summarized and future developments for improving its accuracy are indicated in section 4.

2. ISWIRM Development and Testing Procedure

[11] The instantaneous mapping of foF2 is obtained over a geographic area extending in latitude from 35°N to 70°N and in longitude from 5°W to 40°E (Figure 1). This region is punctuated with a grid of points which step in longitude and latitude 5° and 2.5° respectively. Over each point P of the grid, the SWILM [De Franceschi and Perrone, 1999; De Franceschi et al., 2000] predicts the monthly medians of foF2 at a given epoch (month and time of day). The SWILM model is based on foF2 monthly medians from 18 stations ranged in the area 35°–70°N and 10°W–60°E and on the R12 index as indicator of solar activity [De Franceschi et al., 2000]. The ISWIRM “corrects” the monthly medians of foF2, using the hourly observations of foF2 made at various reference stations, thus providing instantaneous foF2 values for any point of the grid.

Figure 1.

Geographic area under consideration (35°–70°N; 5°W–40°E): the red labels mark the testing stations, and the green labels mark the reference stations.

[12] The ISWIRM now-casting algorithm is:

equation image

where foF2(t)RT,P is the predicted value of foF2 calculated by the ISWIRM at a given point P and at a given epoch t; foF2(t)med,P and ΔCP(t) are respectively the monthly median predicted by the SWILM and its correction at the same epoch t and location P.

[13] ΔCP(t) is initially obtained at the reference stations calculating the variation of foF2 from its “quiet ” state as:

equation image

where N is the number of reference stations, foF2(t)med,J and foF2(t)RT,J are respectively the monthly median value of foF2 predicted by the SWILM at a given reference station j, and the observed hourly value of foF2 at the same station.

[14] A geographic sector is associated with each variation ΔFJ depending on the latitudinal distance of the reference station j from the generic point P where the instantaneous value of foF2 has to be predicted.

[15] The sector width ΔS has been fixed at 5°, because inside a radius of 5°, it is assumed that the ionosphere has the same behavior [De Franceschi et al., 2000]. The reference station contained inside a radius of length Lat(P) ± ΔS, contributes with a difference, ΔFJ belonging to the first sector (K = 1); the reference station contained inside a radius of length Lat(P) ± 2ΔS contributes with a difference ΔFJ, belonging to the second sector (K = 2), etc. This means that while ΔS is always the same for each point P of the grid, the degree of association of ΔFJ in the different sectors is variable depending on the point P of the grid under consideration.

[16] The correction ΔCP(t) is taken as the weighted sum on spatial scale of K terms. Each of these terms is the average value, equation image, of ΔFJ that is the difference between the monthly median value of foF2 predicted by the SWILM and the observed value at a given reference station j (equation (2))

equation image

Λ in equation (3) is an attenuation multiplier ranged between 0 and 1. The terms ΛE = 0,1,.S−1 represent a sort of weight that determines how ΔCP(t) depends on the values of ΔFJ in the different K sectors.

[17] The prediction procedure depends on the attenuation multiplier Λ, as shown with equation (3). By varying Λ different predictions of foF2 can be generated and compared with the observations. The testing procedure is carried out calculating the root mean square (RMS). The smallest RMS given by

equation image

determines the value of Λ that has to be used to improve the predictions.

3. Data Analysis Results and Discussion

[18] All hourly foF2 data used is manually validated. A visual inspection of the hourly data of foF2 was carried out to find possible outliers. The observatories that could provide a good covering in latitude and longitude have been considered to select the reference and testing stations. The reference and the testing stations with their geographic coordinates and locations are shown respectively in Table 1 and Figure 1.

Table 1. List of Reference and Testing Stations
Reference StationsGeographic Coordinates
Rome41.9°N–12.5°E
Chilton51.5°N–359.4°E
Lycksele64.6°N–18.8°E
Loparskaya69.0°N–33.0°E
Sodankyla67.4°N–26.6°E
Testing StationsGeographic Coordinates
Tortosa40.8°N–0.5°E
Juliusruh54.6°N–13.4°E
Uppsala59.8°N–17.6°E
Kiruna67.8°N–20.4°E

[19] In order to test the performance of the model when the ionosphere is not “quiet”, different time periods characterized by intense solar and geomagnetic activity were selected (Figures 26, purple plot). An example of the testing procedure of the ISWIRM in function of Λ for the period 8–19 April 2001 is shown in Table 2.

Figure 2.

Results of the ISWIRM model for the period 29 July to 1 August 1999: the green plot shows the observed foF2 values; the red plot shows the predicted foF2 values calculated for Λ = 0.3 (at Tortosa) and Λ = 0.1 (at Juliusruh Uppsala and Kiruna); the blue plot shows the hourly values of the residuals; and the purple plot shows the values of the geomagnetic index ap. The horizontal line marks the 1 MHz level. The magenta line indicates the most disturbed period.

Figure 3.

Results of the ISWIRM model for the period 23–26 May 2000: the green plot shows the observed foF2 values; the red plot shows the predicted foF2 values calculated for Λ = 0.3 (at Tortosa) and Λ = 0.1 (at Juliusruh and Uppsala); the blue plot shows the hourly values of the residuals; and the purple plot shows the values of the geomagnetic index ap. The horizontal line marks the 1 MHz level. The magenta line indicates the most disturbed period.

Figure 4.

Results of the ISWIRM model for the period 10–19 July 2000: the green plot shows the observed foF2 values; the red plot shows the predicted foF2 values calculated for Λ = 0.3 (at Tortosa) and Λ = 0.1 (at Juliusruh); the blue plot shows the hourly values of the residuals; and the purple plot shows the values of the geomagnetic index ap. The horizontal line marks the 1 MHz level. The magenta line indicates the most disturbed period.

Figure 5.

Results of the ISWIRM model for the period 8–19 April 2001: the green plot shows the observed foF2 values; the red plot shows the predicted foF2 values calculated for Λ = 0.3 (at Tortosa) and Λ = 0.1 (at Juliusruh); the blue plot shows the hourly values of the residuals; and the purple plot shows the values of the geomagnetic index ap. The horizontal line marks the 1 MHz level. The magenta line indicates the most disturbed period.

Figure 6.

Results of the ISWIRM model for the period 4–8 November 2001: the green plot shows the observed foF2 values; the red plot shows the predicted foF2 values calculated for Λ = 0.3 (at Tortosa) and Λ = 0.1 (at Juliusruh); the blue plot shows the hourly values of the residuals; and the purple plot shows the values of the geomagnetic index ap. The horizontal line marks the 1 MHz level. The magenta line indicates the most disturbed period.

Table 2. Global Daily Error σ in Function of the Spatial Attenuation Multiplier Λ for the Period 8–19 April 2001
Tortosa, Λ8 April, σ9 April, σ10 April, σ11 April, σ12 April, σ13 April, σ14 April, σ15 April, σ16 April, σ17 April, σ18 April, σ19 April, σJuliusruh, Λ8 April, σ9 April, σ10 April, σ11 April, σ12 April, σ13 April, σ14 April, σ15 April, σ16 April, σ17 April, σ18 April, σ19 April, σ
  σσσσσσσσσσσ σσσσσσσσσσσσ
0.10,570,551,060,630,830,640,530,400,570,520,470,660.10,550,590,920,950,460,771,090,350,460,470,530,37
0.20,530,511,010,580,820,590,480,400,570,490,450,590.20,580,640,960,990,590,811,170,350,480,440,630,45
0.30,520,500,960,550,820,600,470,420,570,460,440,530.30,620,691,011,050,740,861,260,350,500,410,750,55
0.40,540,540,930,550,850,650,500,460,590,450,460,480.40,670,751,061,120,910,931,360,360,520,400,880,66
0.50,600,610,900,580,910,750,550,510,620,450,510,460.50,720,821,121,221,091,001,470,380,540,401,030,77
0.60,690,730,880,641,000,890,630,580,660,480,570,450.60,790,901,191,321,281,091,590,400,570,411,190,90
0.70,790,870,850,711,121,050,740,660,710,520,660,480.70,860,981,271,431,501,171,710,440,600,431,361,04
0.80,891,030,820,761,281,240,860,750,780,570,770,550.80,941,071,381,531,741,271,840,500,640,471,551,19
0.90,981,180,780,791,481,461,020,860,860,620,930,660.91,031,171,491,642,011,381,980,580,680,521,761,36

[20] A successive analysis carried out under the assumption that the dependence σ = σ(Λ) can be neglected for variations Δσ(Λ) < 0.2 MHz, established that each testing station can be characterized with a particular value of Λ. It was found that the lowest values of σ show the tendency to be associated with the smallest attenuation multipliers Λ in all the cases analyzed and for all the testing stations. The smallest value of σ is obtained with Λ ranged between 0.1 and 0.4 for 70% of the cases analyzed for Tortosa: for this station the minimum value of σ is obtained with Λ = 0.3 and Λ = 0.4 for about 40% and for 17% of the cases respectively. The smallest value of σ is obtained with Λ ranged between 0.1 and Λ = 0.3 for about 90% of the cases analyzed for Juliusruh: for this station the minimum value of σ is obtained with Λ = 0.1 for about 70% of the cases, more or less as for Uppsala. For Kiruna the minimum of σ is obtained for 75% of the cases for Λ = 0.1 and Λ = 0.2. On the basis of these results a good prediction of foF2 can be obtained choosing Λ = 0.3 at Tortosa and Λ = 0.1 at Juliusruh, Uppsala, and Kiruna (Figures 26, red plot).

[21] For such values of Λ the residuals given by

equation image

were evaluated (Figures 26, blue plot).

[22] The plot of the residuals shows that predictions provided by the ISWIRM at Uppsala and Kiruna (Figures 23) can be considered satisfactory if we take into account that such predictions concern fairly high latitudes, where corpuscolar effects make ionospheric modeling much more difficult.

[23] The time interval 10–19 July 2000 is one of the most disturbed of the entire solar cycle: several solar external events gave rise to important geomagnetic storms, the last of which was characterized by a value of ap index = 400 (Figure 4, purple plot). Therefore we can consider ISWIRM's performance for this period very satisfactory. In particular, the prediction for Juliusruh during the most disturbed days (15–16 July), is much more successful than for Tortosa, given that the residuals at Juliusruh are almost always below 1 Mhz (Figure 4, blue plot).

[24] The time interval 8–19 April 2001, like the previous one, was very disturbed and characterized by many solar events that gave rise to four geomagnetic storms (Figure 5, purple plot). Thus a value for the residuals (Figure 5, blue plot) below 1 MHz (except for a few hours) can be considered a satisfactory result.

[25] The period 4–8 November 2001 was characterized by a strong geomagnetic storm, and by the strongest solar proton event (SPE) occurring during the current solar cycle. For these reasons the prediction for Tortosa during the most disturbed day (6 November), can be considered very satisfactory, with the residuals below 1 MHz, while it is not successful at Juliusruh where the residuals on 6 November were always above 1 Mhz (Figure 6, blue plot). The appropriate values of Λ were selected by using manually validated data of foF2. In this way, ISWIRM's performance (Figures 26, blue plot) does not depend on the uncertainty that may derive from autoscaled foF2 data.

[26] Since a now-casting model works on real-time data, the accuracy of the ISWIRM was also evaluated by using autoscaled data coming from two DPS ionosondes located in Rome and Chilton (reference stations). The time intervals 10–19 July 2000 and 8–19 April 2001, were selected to assess the performance of the ISWIRM at the Juliusruh testing station (54.6°N, 13.4°E).

[27] ISWIRM's performance obtained over the entire periods and for the most disturbed days (15–16 July and 10–12 April) is summarized in Table 3. The value of RMS coming from ISWIRM with manually validated data is smallest than the one coming from ISWIRM with autoscaled data. Moreover the values of RMS coming from ISWIRM are smallest than the ones coming from SWILM. The light blue and blue time plots of Figure 7 shows the residuals for the period 8–19 April 2001 obtained when autoscaled and manually validated foF2 data are used respectively.

Figure 7.

Results of the ISWIRM model for the period 8–19 April 2001 at the Juliusruh testing station: the green plot shows the observed foF2 values; the red plot shows the predicted foF2 values calculated by using manually validated data; the brown plot shows the predicted foF2 values calculated by using autoscaled data; and the light blue and blue time plots show the hourly residuals obtained when autoscaled and manually validated foF2 data are used respectively. The horizontal line marks the 1 MHz level.

Table 3. RMS Errors From ISWIRM and SWILM for the Periods 10–19 July 2000 and 8–19 April 2001 and for the Most Disturbed Days (15–16 July and 10–12 April) at the Juliusruh Testing Station
RMS From ISWIRM (Manually Validated Data)RMS From ISWIRM (Autoscaled Data)RMS From SWILM (Median Model)
σ10–19 July 2000 (Λ = 0.1) = 0.50σ10–19 July 2000 (Λ = 0.1) = 0.76σ10–19 July 2000 (Λ = 0.1) = 1.18
σ8–19 April 2001 (Λ = 0.1) = 0.67σ8–19 April 2001 (Λ = 0.1) = 0.85σ8–19 April 2001 (Λ = 0.1) = 1.54
σ15–16 July 2000 (Λ = 0.1) = 0.58σ15–16 July 2000 (Λ = 0.1) = 1.19σ15–16 July 2000 (Λ = 0.1) = 2.00
σ10–12 April 2001 (Λ = 0.1) = 0.82σ10–12 April 2001 (Λ = 0.1) = 1.13σ10–12 April 2001 (Λ = 0.1) = 1.92

[28] On the basis of the results obtained at the testing stations, two different values of Λ have to be used jointly to produce instantaneous foF2 mapping by the ISWIRM. It was found that Λ = 0.3 is the most appropriate value to use for the forecasts at Tortosa. Under the assumption that the ionosphere behaves in the same way within a latitudinal distance of 5°, we could use Λ = 0.3 starting from 40.8°N (latitude of Tortosa) ±5°, i.e., in the latitude interval L1 = 35.8°N–45.8°N.

[29] As Λ = 0.1 was found to be the most appropriate value to use for the forecasts at Juliusrh, Uppsala, and Kiruna, it would be reasonable to use Λ = 0.1 starting from 54.6°N (latitude of Juliusruh) −5° up to 67.8°N (latitude of Kiruna) + 5°, i.e., in the latitude interval L2 = 49.6°N–72.8°N.

[30] The geographic area for the instantaneous mapping of foF2 extends in latitude from 35°N to 70°N. Since this area is made up of a grid of points which have a step in latitude equal to 2.5°, to forecast foF2 over each point of the grid, L1 and L2 are respectively approximated in L1a = 35°–45°N and L2a = 47.5°–70°N. The instantaneous mapping of foF2 is thus obtained using jointly Λ = 0.3 in the latitude interval L1a and Λ = 0.1 in the latitude interval L2a. On the basis of this criterion instantaneous maps can be produced. Figure 8 shows an example of the instantaneous mapping of foF2 for 11 April 2001 at 2200 UT during a ionospheric storm. In this case a very strong depletion of foF2, extending in longitude from 5° W to 40°E can be observed in the central part of the map.

Figure 8.

Instantaneous mapping of foF2 during a ionospheric storm over the geographic area from 5°W to 40°E in longitude, and from 35°N to 70°N in latitude for 11 April 2001 at 2200 UT.

4. Conclusions

[31] The predictions provided by the ISWIRM can be considered satisfactory because even though the periods selected are very disturbed, the hourly values of the residuals are almost always below 1 MHz (Figures 26, blue plot).

[32] The prediction procedure depends on the attenuation multiplier Λ of equation (3), that is used to weight the differences, equation image, between the median value and the observed value.

[33] The ISWIRM method fix different sectors: in the first sector (latitudinal distance = 5°), equation image is weighted 1; in the second sector (latitudinal distance = 10°), equation image is weighted Λ; in the third sector (latitudinal distance = 15°), equation image is weighted Λ2 and so on. So the choice of the value of Λ gives different predictions of fof2.

[34] It was found that a good hourly prediction of foF2 can be obtained assuming Λ = 0.3 in the latitude interval 35°–45°N, and Λ = 0.1 in the latitude interval 47.5°–70°N. This empirical derivation of the attenuation multiplier Λ was obtained analyzing periods characterized by strong solar and geomagnetic activity, so we cannot know if the values of Λ found would be different during quiet periods. However, during quiet periods the prediction can be performed with a certain accuracy by using median models. Moreover, at least in the cases analyzed, we have not found different values of Λ for different storms.

[35] At least for the cases analyzed, the Table 3 shows that the ISWIRM model provides good predictions if manually validated data are used. When autoscaled data are used the predictions get a bit worse. Real-time SWILM updating using autoscaled data, gives in general much improved results compared to what can be obtained by the SWILM. For the two cases presented here, it is obvious that for storm periods ISWIRM performance is much improved comparing to SWILM results (Table 3).

[36] This means that ISWIRM algorithm is able to correct efficiently the monthly medians providing a better prediction. These results are important because they support the practical use of the model in producing instantaneous ionospheric modeling of foF2 during disturbed periods.

[37] Because the region under consideration includes a rather wide longitudinal range (70°), a further improvement could be obtained by also taking geographic longitude into account in the evaluation of the K sectors.

[38] Since the real-time specification of the ionosphere can be improved using ionospheric data coming from as many real-time digisondes as possible, the addition of more reference stations, creating a more uniformly arranged network over the area under consideration, should improve instantaneous foF2 mapping. The real-time application of the proposed software for operational use is our major goal in the future.

Acknowledgments

[39] The authors thank National Geophysical Data Center (NGDC), Rutheford Appleton Laboratory (RAL), Aeronomic Division of the Sodankyla Geophysical Observatory (SGO), Leibniz Institute of Atmospheric Physics (IAP), and Ebre Observatory for providing foF2 data. The authors also thank GeoForschungZentrum (GFZ) Postdam for providing geomagnetic index ap and the referees for their useful comments and suggestions.

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