Vol49,4_5,2006 945 ANNALS OF GEOPHYSICS, VOL. 49, N. 4/5, August/October 2006 Key words ionospheric variability – radio wave propagation – space and satellite communications 1. Introduction Perturbations of ionization density at the heights of the ionospheric F-region are perma- nent features. Therefore, meaningful longer term predictions can only have statistical char- acter, i.e. specify probabilities (e.g., Rawer, 1957, 1993). Systematic studies on the day-to- day and hour-to-hour variability of the critical frequency of the F-region, foF2, and of the To- tal Electron Content, TEC, have shown that these perturbations, with negative and positive response, depend on local time, season and lo- cation (Kouris et al., 1998, 1999, 2002, 2006; Rawer et al., 2003; Fotiadis et al., 2004). Regarding variations of foF2 in the time in- terval of an hour have been reported in different papers (Kouris et al., 2000; Fotiadis et al., 2001; Zolesi et al., 2001; Buresova and Lašto- vička, 2001) showing that a variation of foF2 around 12% (positive or negative) with respect to the hourly daily value measured at the stan- dard-hour time is always present. This ionos- pheric variability «within-the-hour» or other- wise «ionospheric density noise» can be esti- mated from the variation of the relative devia- tions of 5-min daily foF2 measurements with respect to the standard hour daily value of foF2 measured at the corresponding standard hour. The diurnal variation of these 5-min relative de- viations shows clearly that in certain hours and under particular circumstances, values of vari- ability greater than 12% (in absolute value) of the corresponding hourly daily value can occur (Kouris et al., 2000; Buresova and Laštovička, 2001; Fotiadis et al., 2001). Moreover, varia- tions in TEC in the time interval of an hour Within-the-hour variability: levels and their probabilities Stamatios S. Kouris (1), Kostas V. Polimeris (1), Vincenzo Romano (2), Bruno Zolesi (2) and Ljiljana R. Cander (3) (1) Division of Telecommunications, Department of Electrical Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Greece (2) Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy (3) Radio Communication Research Unit, Rutherford Appleton Laboratory, Chilton, Oxon, U.K. Abstract The study of foF2 data measured every 5-min and of TEC measurements made every 10-min shows that the within-the-hour variability is different in the two parameters. Deciles of this variability for foF2 and for TEC are determined together with the probabilities of exceeding a given level of variability. Furthermore, considering hourly values, it is found that the variability in TEC is like an «intrinsic noise» throughout the day of the order of less than 5% of the hourly value; but at sunrise and often at sunset large values take place. A seasonal depend- ence is evident. Besides, a within-the-hour variability in foF2 is always present with large values at sunrise or sunset depending on the season, and also during disturbed ionospheric conditions. Mailing address: Prof. Stamatios S. Kouris, Division of Telecommunications, Department of Electrical Enginee- ring, Faculty of Engineering, Aristotle University of Thes- saloniki, Box 435, GR-54 124 Thessaloniki, Greece; e- mail: kouris@vergina.eng.auth.gr 946 Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander were reported as preliminary results in a previ- ous paper (Polimeris et al., 2004) considering a limited number of data. It was then shown that the variability in TEC is rather negligible, ex- cept at sunrise and sunset where values up to 20% higher or lower of the corresponding daily standard hour value have been observed. In the present work we investigate the vari- ability within-the-hour in TEC at different Eu- ropean locations and, for comparison, in foF2 at the location of Rome. The statistical study of their variations in the interval of an hour allow us to determine bounds of the within-the-hour variability in foF2 and in TEC for all hours of the day in each month and season. 2. Data and analysis We use foF2 5-min data measured at Rome (41.9°N, 12.5°E) during the years 1997-2001 and 10-min TEC data obtained from GPS meas- urements made mainly at Matera (40°N, 16°E) during the years 1993 to 1999, and at Hailsham (50.9°N, 0.3°E) during 1998 to 2004. We have also examined TEC data measured every 10- min during August to December in 2002 to 2004 at the locations of Brussels (50.8°N, 4.3°E) and Nicosia (35.1°N, 33.2°E). First we evaluate the 10-min relative devia- tions of TEC from the measured every 10-min daily values in each interval time of an hour (half an hour before and after each standard hour) of each day/month/year/location using the expres- sion (2.1) where dT is the 10-min relative deviation, T10 is the measured value of TEC every 10-min and Th is the hourly measured value corresponding at the standard hour of the examined one hour in- terval time. A similar expression is used to cal- culate the variability within-the-hour of foF2 (Fotiadis et al., 2001) that is (2.2) with df the 5-min relative deviation, f5 the value of foF2 measured every 5-min and fh the corre- d f f f f h h5 = − d T T T T h h 10= − sponding hourly daily value of foF2 in the con- sidered one hour interval. In this analysis for each ionospheric param- eter we deal with the relative deviations with re- spect to the standard hour value in the interval time of one hour, in order to remove the regular daily variation and to avoid any effect of the variability from hour-to-hour and from day-to- day on the obtained 5-min/10-min relative devi- ation, and so we may consider the totality of relative deviations as a whole. Since we also compare the variability of within-the-hour with the variability from day-to- day, that is their deciles. Hourly TEC data and monthly median are also used from measure- ments made at the above referred locations and during the same periods. Then, the hourly rela- tive deviation is estimated using the expression (2.3) where dT is now the hourly relative deviation, Th is the hourly measured value and Tm is the corresponding monthly median value. Evident- ly, the variation of dT from day-to-day de- scribes the day-to-day variability of TEC at the given hour. Of course a similar procedure is used in the case of foF2. 3. Results and discussion The counted relative deviations are first stud- ied month by month and then by season to inves- tigate any annual or seasonal dependence. To in- quire whether deviations as high as 20% of the corresponding standard hour value are related to magnetic disturbances, the calculated df and dT values have been studied day by day. Variability in TEC – The analysis shows that the within-the-hour variability in TEC has a dif- ferent behavior from that in foF2. It is found that a variation in TEC of 10% with respect to the standard hour value has a probability much less than 10% if not zero, contrary to what is found for foF2. Indeed, only an «intrinsic» vari- ability of the order of less than 5% is found, comparative to the one found for all other ionospheric characteristics, e.g. foE (Kouris and Fotiadis, 2002). Table I reports probabilities d T T T Th m m= − Within-the-hour variability: levels and their probabilities 947 Table I. Probability the level of variability within-the-hour in TEC exceeds the value of 0.05 (A), 0.10 (B), 0.15 (C), 0.20 (D). Data measured at Hailsham during 2002 (80 < R 12 < 120). A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 6.7 12 7.3 6 15 22 16 98 100 85 53 14 1.3 2 6 23 53 81 91 81 49 24 17 13 F 1.9 13 16 13 22 14 50 99 98 77 32 2.2 1.5 0 0 6.7 21 56 63 68 60 44 27 10 M 3.3 6.7 11 12 27 26 95 89 73 52 21 1.3 0 0 0.7 2.7 6 11 32 57 59 45 29 17 A 3.4 14 18 17 30 72 68 46 41 32 20 6.2 1.4 1.4 2.1 2.1 4.1 4.8 9.7 29 44 46 26 15 M 12 11 17 18 63 59 33 18 11 6 4 6 1.3 2 2.7 0.7 1.3 2 8.7 6.7 17 21 23 10 J 3.4 15 1.4 17 50 33 9 4.1 2.8 2.8 0.7 0 0 0.7 0 0 0 0.7 0.7 1.4 9.7 3.4 2.8 3.4 J 15 12 15 9.3 61 51 13 9.3 5.3 2.7 0 0 1.3 2.7 1.3 2 0.7 2 1.3 0 4.7 10 16 15 A 12 27 14 16 38 82 56 41 28 7.7 4.5 2.6 0.6 0.6 0 2 0.6 0.6 1.3 8.4 32 54 42 23 S 5 9.3 21 17 27 72 91 65 43 35 9.3 5.3 2.7 0 1.3 2 4 4 27 53 56 50 25 13 O 37 23 17 21 35 28 97 89 66 56 43 11 2.7 1.3 3.3 7.3 25 52 64 77 62 33 16 17 N 31 22 22 28 18 21 55 100 97 72 46 8.3 4.1 2.8 7.6 35 61 78 87 75 43 28 32 40 D 9.7 29 16 11 19 31 21 97 100 89 41 7.6 3.4 4.8 22 43 70 93 83 59 27 24 35 21 B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 3.3 2 0 1.3 0.7 0.7 1.3 87 93 48 9.3 0 0 0 0 0.7 12 41 54 38 6.7 3.3 2.7 0.7 F 0 1.5 0.7 1.5 0 2.2 30 91 66 35 0 0 0 0 0 0 0.7 6.7 19 17 10 4.4 0.7 0 M 0 0 0 1.3 2.7 13 69 55 33 9.3 1.3 0 0 0 0 0 0 0.7 2 9.3 13 0 0.7 2 A 3.4 4.1 3.4 5.5 14 35 28 17 9 6.9 2.8 1.4 0 0 0 0.7 0.7 0 0.7 3.4 5.5 5.5 4.8 4.8 M 5 1.3 4 4 23 15 4.7 3.3 1.3 3.3 0 1.3 0 0 0.7 0 0 1.3 1.3 0 0.7 2.7 1.3 0.7 J 0 0 0 0 12 4.1 0 0 0 0.7 0 0 0 0 0 0 0 0 0 0 0.7 0 0 0 J 0 0 2 0 21 6 1.3 0 0 0 0 0 0 1.3 0 0 0 0 0 0 0 0 1.3 0 A 1.6 3.2 1.3 3.2 16 42 20 5.2 1.3 0 0 0 0 0 0 0 0 0 0 0 3.9 15 6 1.4 S 0 1.3 2 2 4.7 42 53 26 11 1.3 0.7 0 0 0 0 0 0.7 0 3.3 8 14 8.7 6 2.7 O 25 9.3 7.3 7.3 6.7 12 71 56 27 21 7.3 0 0 0 0 1.3 5.3 17 19 38 23 2.7 0 4 N 14 4.8 2.8 7.6 4.1 3.4 29 93 61 29 9 0 0 0 0.7 4.1 20 39 50 32 7.6 4.1 11 17 D 0 2.6 1.3 3.9 5.2 9.7 5.2 74 85 51 5.5 1.4 0 0 2.8 4.8 29 57 44 21 9.7 9.7 7.6 4.1 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 0 0 0 0 0 0 0 58 63 20 0.7 0 0 0 0 0 1.3 17 25 8 0.7 0.7 2.7 0 F 0 0 0 0.7 0 0 18 66 47 7.4 0 0 0 0 0 0 0 0 1.5 2.2 0.7 0 0 0 M 0 0 0 0.7 1.3 8.7 46 36 4.7 0.7 0 0 0 0 0 0 0 0 0 0.7 0.7 0 0 0 A 1.7 2.8 2.8 3.4 6.2 15 10 3.4 0 0.7 1.4 0 0 0 0 0 0 0 0 0 2.8 2.1 0.7 4.1 M 3.3 0 2 2 8.7 2 0.7 2 1.3 2 0 0 0 0 0 0 0 0 0 0 0 0.7 0 0 J 0 0 0 0 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0 0 0 6.7 1.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 1.6 1.3 0 1.3 5.8 14 3.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6 2 0 S 0 0 0 0 0 26 25 7.3 1.3 0 0 0 0 0 0 0 0 0 0 2 2 1.3 0 1.3 O 13 2.7 4 0.7 1.3 5.3 45 31 8.7 5.3 0 0 0 0 0 0.7 2 4 2.7 13 2.7 0.7 0 2 N 8.6 0.7 0 0.7 1.4 0.7 19 70 46 4.1 0.7 0 0 0 0 0 0.7 12 23 10 0 1.4 2.8 10 D 0 0 0 0.6 1.9 3.9 1.9 52 62 19 0 0 0 0 0 0 11 26 23 2.8 3.4 5.5 2.8 2.1 948 Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander Table I (continued). D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 0 0 0 0 0 0 0 43 55 6 0 0 0 0 0 0 0 2.7 6 0.7 0 0.7 2.7 0 F 0 0 0 0 0 0 12 52 24 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M 0 0 0 0 0.7 4.7 29 17 2 0.7 0 0 0 0 0 0 0 0 0 0 0.7 0 0 0 A 1.7 1.4 2.8 2.8 3.4 6.9 1.4 0 0 0 0.7 0 0 0 0 0 0 0 0 0 2.1 0.7 0 2.8 M 3.3 0 1.3 2 3.3 0 0 1.3 1.3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 1.6 0.6 0 0.6 1.9 3.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7 0 S 0 0 0 0 0 13 8.7 1.3 0 0 0 0 0 0 0 0 0 0 0 0.7 1.3 0.7 0 0.7 O 6.7 2 0 0 0.7 2 32 14 2.7 1.3 0 0 0 0 0 0.7 1.3 0.7 0 4 0.7 0 0 1.3 N 3.4 0.7 0 0 0.7 0 12 56 19 0 0 0 0 0 0 0 0 2.1 9.7 0.7 0 0.7 2.1 5.5 D 0 0 0 0 0 1.9 0 40 43 3.3 0 0 0 0 0 0 2.1 6.9 5.5 0 4.1 4.1 0.7 0 Table II. Probability the variability in TEC may exceeds the bounds 0.05 (A), 0.10 (B) or 0.20 (C). Data from Matera 1996 (R 12 < 10.5). A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 16 19 22 28 25 27 80 45 37 39 17 8.4 14 7.1 29 34 31 29 11 14 12 13 18 2.7 F 30 24 22 20 31 39 94 29 18 13 11 7.1 6.4 6.4 8.6 25 45 26 16 19 5.7 5.7 2.1 4.3 M 38 20 30 14 18 87 70 42 28 18 12 8 11 6.5 14 14 9.7 34 48 39 19 9 9.2 7.6 A 22 16 15 25 68 75 42 31 27 16 9.7 2.9 6.2 9.7 7.6 4.8 6.2 6.9 28 51 47 21 13 18 M 28 25 18 33 99 76 33 17 8 6 3.3 6 2.7 0 4.7 2 6 10 5.3 13 32 43 41 19 J 11 42 44 57 92 75 33 11 7.3 7.4 3.4 2.7 0.7 3.3 4.1 4.1 3.3 11 7.3 19 36 27 22 20 J 50 26 40 42 96 63 44 19 18 19 9.2 8.6 11 6.4 9.3 4.3 7.1 8.6 7.1 30 58 41 19 20 A 54 57 36 43 82 74 43 41 36 20 14 15 6 6 8 1.3 4.7 2.7 6.7 35 62 42 24 22 S 50 23 35 21 52 85 49 41 30 9.5 19 16 11 13 8.7 11 5.4 6.4 22 43 55 33 21 12 O 62 26 12 43 31 95 82 60 22 28 19 6.7 23 13 18 26 40 64 43 31 31 53 58 46 N 13 20 28 35 36 41 100 40 24 14 11 11 15 15 25 41 52 23 11 7.7 7.7 1.5 3.1 6.2 D 18 15 16 15 15 32 82 47 47 25 14 10 4 13 23 49 49 12 12 9.3 6.7 10 6.7 6.7 B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 5.2 4.5 2.6 4.5 2.6 7.7 48 12 9 8.7 0.6 0.6 0.7 1.9 3.9 6.7 6.7 3.3 1.3 5.2 2.6 1.3 2.7 0.7 F 3.6 5.7 5 3.6 7.9 21 58 5.1 2.1 1.4 0.7 0.7 0 0 0.7 5 7.1 5 2.1 2.1 0 0 0 0 M 18 7.1 12 5.2 0 50 25 7.7 2.6 2.6 0 0.7 1.3 0 2.6 1.3 1.9 9 11 8.4 0 0 1.3 2.1 A 6.7 4.7 1.3 6 41 37 11 4 1.3 0.7 0.7 0 0 2.1 0.7 0.7 0 0 5.5 19 13 1.4 2.2 3.6 M 12 3.9 4.1 13 60 33 5.3 0 0.7 0.7 0 0 0 0 0 0 0 0 0 2.7 8.8 13 9 1.4 J 5.6 13 14 38 55 30 4.9 0 0.7 1.4 0 0 0 0 0 0 0 0.7 0.7 4 6 5.3 4.1 3.5 J 24 9.6 13 26 64 22 11 5.8 3.3 8.2 3.1 2.1 2.9 1.4 1.4 0 0 0.7 0 7.9 19 8.6 2.3 4.4 A 31 29 14 18 56 37 16 18 6 5.3 3.3 0.7 0 0 0 0 0.7 0 0 9.5 18 10 4.4 2.9 S 32 4.4 15 6.1 28 46 12 7.7 7.6 0 4.5 6.1 4.3 3.5 2.6 4.3 1.8 1.8 7.3 16 22 5.5 3.8 2 O 21 6.7 1 9.5 7.6 63 43 15 3 6 3 1 5.7 5.7 5.9 8 20 36 25 15 18 30 52 34 Within-the-hour variability: levels and their probabilities 949 Table III. Probability the within-the-hour variability in TEC be greater than 0.10 (A, C) or 0.20 (B, D). Data measured in 1999; Matera (A, B) and Hailsham (C, D). High solar activity (80 < R 12 < 120). A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 10 7.1 8.4 5.2 3.9 4.5 76 39 12 6 0 0 0.6 0.6 3.9 17 31 21 5.2 1.9 3.2 0 0.6 0 F 6.3 2.4 0 0 0 26 82 15 5.7 2.1 0 0 0 0 0 4.3 20 29 8.6 8.6 0.7 0 0.7 1.4 M 0 0.7 0 2.2 3 69 40 19 7.2 4.7 0 0 0.6 1.4 0 0.7 4.5 12 28 14 2.6 0.6 0 3.2 A 0 0.9 0.9 6.1 40 39 18 9 6.2 0 0 0.7 0 0 0 0 0 0 12 13 4.4 2.2 0 0 M 0 0 0.7 7.1 50 11 2.7 0 0 0.7 0 0 0 0 0 0 0 0 0 3.3 1.4 0 0 0 J 1.7 0 0 16 30 2.1 0 0 0 0 0 0 0 0.7 0 0 0 0 0 0 0 0.7 0 0 J 0 0.7 2 4 25 3.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7 2 2 0 A 1.7 0.7 0.7 0.7 40 26 3.4 0 0.7 0 0 0 0 0 0 0.7 0 0 0 4.8 4.1 2.1 0 0 S 0 0.7 1.4 0.7 23 52 12 6.5 4.3 0.7 0.7 0 0 0 0.7 0.7 0 5 8.6 2.1 2.9 0 0 0 O 0 0.8 0 0 1.6 73 57 18 1.6 0.8 0 0 0 0 0 3.2 19 26 10 2.4 2.3 0 0 2.3 N 0 0 0.7 2.1 0 41 81 43 11 0 0.7 0 0 0 1.3 17 38 24 8 2.7 0 0 0 0.7 D 1.7 1.3 0.7 1.3 0 15 86 39 21 4.7 2.1 0 0 0 2 22 42 19 6.7 2.7 2 0 0 0 B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 0 2.6 1.3 0 0 0.6 34 3.2 0 0 0 0 0 0 0 0 0 0.6 0 0 0 0 0 0 F 0 0.8 0 0 0 11 39 0.8 0 0 0 0 0 0 0 0 0.7 0 0 0 0 0 0.7 0 M 0 0 0 0 0 28 7.4 2.1 0 0 0 0 0 0 0 0 0 1.3 0.6 1.3 0 0 0 0 A 0 0 0 0 11 6.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M 0 0 0 0 7.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0 0 0.7 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Table II (continued). B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 N 0 1.3 2.5 16 11 21 60 10 7.5 1.3 2.5 0 3.8 6.3 9.1 10 11 1.5 1.5 0 1.5 0 0 0 D 3.3 4.7 4 3.3 2.7 10 41 11 15 3.3 0 2 0 0.7 3.3 15 13 0.7 0.7 0.7 0.7 1.3 0.7 0.7 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 5.2 1.3 0.7 0 0 1.9 19 1.3 0.6 0.7 0 0 0 0 0 0 0 0 0 3.2 0.6 0 0 0 F 0 0 0.7 0 1.4 4.3 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M 5.4 0 1.9 1.3 0 16 0.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 0 0.7 0 0 15 5.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7 0 1.4 0.7 M 1.7 0 0 4.7 18 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7 0 0 J 3.7 2.1 0.7 17 16 2.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.3 0 0 0 J 9.5 3.5 1.8 6.7 24 1 7.9 0 0 6 0 0 0 0 0 0 0 0 0 0 3.6 0 0 1.5 A 12 7.9 11 6.8 26 5.3 6 6 0.7 1.3 0 0 0 0 0 0 0 0 0 0.7 1.4 0 0 1.4 S 7.1 0 5.2 1 7 13 1 0 0 0 3.6 3.5 0.9 0 0 3.5 1.8 0.9 0.9 2.7 0 0.9 2.9 0 O 4.8 1 0 1.9 3.8 23 2.9 0 0 1 0 0 1 1.9 2 2 4 14 12 5.9 2.5 18 42 21 N 0 0 0 7.5 5 10 13 0 1.3 0 0 0 0 1.3 6.5 4.4 0 0 0 0 0 0 0 0 D 0 1.3 0.7 0 0 0 8 0.7 0.7 0 0 2 0 0 0.7 1.3 0 0 0 0 0 0 0 0 950 Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander that the level of variability in TEC exceeds giv- en bounds during 2002, a year of high solar ac- tivity (80 < R12 < 120) at Hailsham while table II reports probabilities from data measured at Matera during 1996, a year of low solar activi- ty (R12 < 10.5). It can be seen that the variability exceeds the limit of 5% mostly during the night-time hours (table I) and also under dis- turbed ionospheric conditions (table II). Thus, we may deduce that the variability in TEC with- Table III (continued). B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 0 0 0 0 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 0 0 0 0 13 1.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.4 0 0 S 0 0 0 0 4.3 9.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 32 8.8 0 0 0 0 0 0 0 0 0 0.8 0 0 0 0.8 0 0 0.8 N 0 0 0 0 0 20 38 2.1 0 0 0 0 0 0 0 0 1.3 0 0 0 0 0 0 0 D 0 0 0.7 0 0 2 40 2 0 0 0 0 0 0 0 1.3 2 0.7 0 0 0 0 0 0 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 3.3 0 2.7 0 1.3 0.7 0 58 73 38 0 0 0 0 0 3.3 15 34 37 12 4.9 1.4 0 3.6 F 0 0 0 1.6 1.6 2.4 26 78 52 15 3.2 0.8 0 0 0.8 6.8 6.8 5.8 23 27 18 3.3 0 0.8 M 0 0.7 0.7 0 2.8 15 70 47 19 12 2 0 0 0 0 0 0.7 2 6 18 24 18 2 2 A 0 0 0.7 3 8.9 51 32 13 1.5 1.5 0 0 0 0 0 0 1.5 0.7 0 0.7 5.9 12 3.7 2.2 M 0 0 0 2 22 17 2.7 0.7 0 0 0 0 0 0 0 0 0 0 0 0.7 0.7 0.7 0 0 J 0 0 0 0 10 6.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0.7 2 1.3 13 12 0 0 0 0 0.7 0 0 0 0 0 0 0 0 0 0.7 1.3 0.7 2.7 A 5.4 5.7 6.2 5.5 20 43 13 9.3 2 0 0 0 0 0 0 0 0 0 0 0 1.4 8.3 3.4 4.1 S 7.4 4.4 2.2 5.2 2.2 39 50 19 3 5.2 0.7 0 0 0 0.7 0 2.2 0 0.8 7.7 16 11 3.1 0 O 10 2.7 0.7 4.7 4.7 13 71 58 29 13 2.7 0 0 0 0 1.3 2 8.7 15 33 25 7.3 1.3 0 N 8.6 0 3.4 0 2.1 0 28 88 64 37 12 0 0 0 0 4.8 21 42 46 23 2.8 0.7 0.7 0 D 0 5.3 0.7 0 0 0 0.7 62 78 43 2.7 0 0 0 0.7 11 29 39 38 18 1.3 2 5.4 9.7 D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 0 0 0 0 0 0 0 32 30 1.3 0 0 0 0 0 0.7 2 2 2.7 2.7 1.4 0 0 1.4 F 0 0 0 0 0 0 12 36 4 0.8 0 0 0 0 0 0 0 0 2.5 0.8 0 0 0 0 M 0 0 0 0 0 2 31 6 2 2 0 0 0 0 0 0 0 0 1.3 0 0 0 0 0.7 A 0 0 0 0 0 16 2.2 1.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7 0 0 M 0 0 0 0 0.7 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J 0 0 0.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 0 0 1.4 0 5.4 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.4 S 1.9 0 0 0 0 13 8.9 1.5 0 0 0 0 0 0 0 0 0 0 0 0.8 1.5 0 0 0 O 3.3 0 0 1.3 0 4 33 15 1.3 0 0 0 0 0 0 0 0 0 0.7 2.7 3.3 0 0 0 N 1.7 0 0 0 0 0 9.7 48 19 1.4 0 0 0 0 0 0 0.7 2.8 3.4 0 0 0 0 0 D 0 2 0 0 0 0 0 32 35 0.7 0 0 0 0 0 0 0.7 1.3 2.7 0 0 0 2 2.8 951 Within-the-hour variability: levels and their probabilities in the interval of an hour, if any, is very low ex- cept around the sunrise hours and often around sunset too. The latter usually occurs in winter and equinoxes as can be seen from table III, where the probabilities that the within-the-hour variability in TEC be greater than given levels at two locations of different latitude and during 1999 a year of rather high solar activity (80< R12 < 115) are shown. At sunrise and sunset the probability of value of variability within- the-hour greater than 10% and less than 30% is very high reaching values up to 60%-80%. These high values of variability are observed during winter months and even during local dis- turbed conditions (tables I and II). Figure 1 illustrates from measurements made at Hailsham the probability level that the variability within-the-hour be greater in ab- Fig. 1. Probability the variability within-the-hour in TEC, positive (right) or negative (left), be greater than 0.10, 0.15, 0.20 or 0.30, in absolute value. Data from Hailsham. 952 Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander solute value than 0.10 or 0.15 or 0.20 or 0.30 with respect to the hourly value of the corre- sponding standard hour. It can be seen that high values of probability of a variability greater than 10% are found around sunrise and also at sunset during winter and equinoxes, otherwise the variability can be assumed to be an «intrin- sic noise» during all the other hours of the day. Figure 2 shows the probability the variabili- ty within-the-hour, positive or negative, be greater than a given level at different seasons. The data used are those measured at Matera during the period from 1993 to 1999. The dif- ference with season, regarding the time of ap- pearance of high probabilities and the value of probability is evident. Clearly, the variability is rather negligible during day-time hours. Figure 3 illustrates the upper and lower deciles of the variability in TEC from hourly measurements and from 10-min measurements made at Matera and Hailsham. They are deter- mined for each of the two locations from the re- spective relative deviations counted according to eq. (2.1) and (2.3) and from all the avaliable data measured at each one location, respective- ly. Figure 3 clearly shows the difference be- tween bounds of variability from day-to-day and those of the within-the-hour variability. In this last case the variability is limited within a range of values less than ± 0.05 except at sun- rise and also at sunset in winter or during local disturbed conditions (see also tables I and II). It can be stated that the present analysis shows clearly that the within-the-hour variability in TEC is very low, practically negligible, except at sunrise and sunset. We may therefore assume that TEC is stationary in the interval time of one hour contrary to foF2, which seems to have a stationarity of less than 10 min. Variability in foF2 – The analysis points out that the within-the-hour variability in foF2 may reach values greater, in absolute value, than 20% Fig. 2. Probability the variability within-the-hour in TEC, positive (right) or negative (left), be greater than 0.10, 0.15, 0.20 or 0.30, in absolute value. Data measured at Matera 1993-1999. 953 Within-the-hour variability: levels and their probabilities Fig. 3. Deciles of TEC from hourly daily values and deciles from TEC measured every 10-min at Matera (left) and Hailsham (right). Table IV. Probability the variability within-the-hour in foF2 be greater than 0.10 (A), 0.15 (B), 020 (C). Data from Rome measured during 1997 (November, December), 1999 (June, July, August, September), 2001 (Janu- ary, February, March, April). Black lines are due to missing measurements in May and October. A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 9.8 9.4 9.1 20 23 20 68 39 4.6 24 16 16 16 12 12 12 35 35 24 24 33 17 22 12 F 8.1 17 16 14 14 17 68 19 5.6 5.9 11 19 15 18 6.9 8.7 16 17 8.1 23 24 25 24 18 M 13 11 12 12 11 37 30 7 8.6 12 14 15 29 13 15 6.6 12 15 27 12 20 22 16 16 A 14 11 15 7.7 10 14 7 8.4 11 14 11 12 9.2 11 11 2.4 7.6 10 27 17 12 13 16 17 M J 24 13 12 14 7.8 10 6 6.4 7.3 14 12 13 13 6.8 8.5 9.6 8.8 4.4 7.6 18 20 16 25 21 J 16 11 13 8.2 8.8 9.7 13 9.9 12 8.8 5.2 6.1 8.7 6.5 8 9.6 8.4 13 7 18 19 13 15 12 A 26 9.6 22 20 12 22 11 10 10 7.3 6.6 9.1 9.1 1.9 4.8 1.3 0.6 6.2 6.7 21 20 34 20 14 S 13 19 18 9.8 8 39 18 13 5.7 4.4 2.2 1.3 5.5 6.6 4.9 1.6 7.1 14 9.4 11 15 15 13 14 O N 13 10 16 20 28 22 71 16 11 9.5 9.5 15 17 8.2 15 27 58 39 24 26 21 20 2.9 7.2 D 6.4 10 3.5 16 25 32 70 26 28 24 17 19 18 20 21 24 42 29 23 7.7 11 20 15 15 954 Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander and less than around 30% of the corresponding hourly value measured at the standard hour dur- ing disturbed conditions or around sunrise and sunset (table IV). It is also clear that a within- the-hour variability around 12%, positive or neg- ative, is always present throughout the day. Figure 4a,b reports the curves of probabili- ties which show that the variability within-the- hour could exceed a given value. It can be seen that the probability of high values of variability exist during winter and equinoxes. They are more frequent from sunset up to sunrise and seem to be related to disturbed conditions (Bu- resova and Laštovička, 2001). On the other hand, the probability of variability values greater than 0.30 (in absolute value) of the cor- responding hourly value is very small except at summer and usually after sunset up to mid- night. Figure 5 illustrates the probabilities in each season that the variability in foF2 exceeds a given value. This figure confirms the above mentioned statements. It is evident that the vari- ability within-the-hour in foF2 is bounded be- tween a positive and a negative level of 0.10 to 0.15. Values of variability greater than 0.30 may appear mostly in summer after sunset, but the probability is small, less than 10%. Figure 6 shows the upper and lower deciles of variability in foF2 from hourly measurements and from 5-min made in Rome. They are calcu- Table IV (continued). B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 3.8 4.4 1.5 10 6 9.1 48 20 0.7 6.3 7.3 3.3 8 3.7 1.8 3.2 19 24 12 11 14 6 8.4 4.9 F 3.7 9.1 9.2 9.4 4.2 9.2 49 4.9 0.4 1.5 4.5 8.6 1.6 6.5 1.7 5.2 6.6 6.1 2.1 6.6 13 13 12 9.6 M 6.5 8.3 7.6 5.3 5 22 13 0.9 3.2 3.5 4 4.2 11 3.2 6.6 0.3 5.3 4.7 9.7 7.3 7.9 11 9.4 8.8 A 11 9.2 12 5.2 7.1 6.1 2.9 3 4.3 6.2 3.4 5.2 1 2.5 1.6 0.9 0.3 0.9 9.7 7 7.1 6.1 15 12 M J 17 11 7.3 11 2.9 6.5 1.4 0.8 0.8 3.8 3.8 2 3.2 1.1 4.8 5 7.7 2.2 3 16 14 10 19 13 J 12 9.2 6.8 3.4 3.4 3.8 9.7 7.4 3.1 4.4 2.6 0 6 3.2 3.8 2.6 4.8 9.9 4 15 17 10 9.7 9 A 22 6.8 17 15 5 7.6 5 5.6 3.4 3.7 2.6 2.9 2.8 0.4 0.7 0.3 0 2.5 3.2 16 14 22 14 9.4 S 7.2 15 12 4.4 3.5 22 2.3 1.5 2.7 2.6 0.4 0.4 0.7 4.5 1 0 1.3 6.7 4.5 5.3 7 3.8 8.3 7.1 O N 5.5 3.7 11 9.4 8.3 8.4 47 5.5 2.3 3.6 1.5 3.1 4.1 0 11 7.2 36 21 8.2 11 8.1 12 1.4 4.1 D 0 6.4 1.8 5.8 11 17 52 11 14 12 5.8 7.5 8.7 6.6 12 9 27 14 16 3.8 2.7 8.8 8.9 8.3 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 J 3.3 3.2 0 6.2 3 1.8 34 8 0.3 1.9 1.5 2.2 3.8 0.7 0.7 1.2 12 15 5.2 4.9 6.2 2 2.3 2.5 F 1.9 6.7 4.9 5.5 1.6 3.6 30 1.5 0 0 1.2 1.6 0 2 0 3.6 4.5 3.6 0.4 1.6 5.7 8.8 5.6 6.2 M 5.9 5.3 4.7 2.6 2.6 11 4.4 0.6 1.6 1.7 1.8 1.4 3.8 0.4 4.6 0 3.2 2.4 2.7 3.5 4.4 7.6 5 5.9 A 10 7.3 9.7 3.1 6.2 2.8 1.3 2 1.4 2.4 1.6 1.3 0.3 0.6 0.6 0 0.3 0 5.5 3.6 5.5 3.7 13 5.2 M J 9.8 9.8 4 8.9 2 3.9 1.1 0 0 1 1.4 0.4 0.7 0 2.6 3.7 6.4 1.3 2 15 13 5.9 13 10 J 9.2 7.2 2.1 2.4 1 3.1 7.4 5.4 0.5 1.3 1.5 0 4.1 0.5 1.3 1.7 1.3 8.3 3.7 13 13 7.5 9 5.8 A 15 5.6 13 12 2.4 3.4 3.8 3.3 1.5 2 0.4 0.4 0.4 0.4 0.3 0.3 0 1.2 1.3 13 9.6 14 11 7.9 S 4.8 11 6.6 3.7 1.7 9.7 0 0.7 0.4 0.4 0 0 0.4 3.8 0 0 0 3.9 1 1.7 0.6 1 7.3 3.4 O N 3.6 0.9 4.5 1 0.9 3.2 26 2.3 0 2.2 0.7 0.8 0.8 0 2.5 2.2 23 13 2.2 1.7 0 2.9 0 1 D 0 0.6 0 3.5 5.7 7.6 37 4 8.6 4.7 1.7 0.5 6.7 2.7 2.2 3.4 13 4.1 6.7 0.6 1.8 3.5 8.1 5.1 955 Within-the-hour variability: levels and their probabilities F ig . 4a ,b . P ro ba bi li ty t he v ar ia bi li ty w it hi n- th e- ho ur i n fo F 2, po si ti ve ( ri g h t) o r ne ga ti ve ( le ft ), be g re at er t ha n 0. 10 , 0. 15 , 0. 20 o r 0. 30 , in a bs ol ut e va lu e. D at a m ea su re d at R om e: a) 1 99 8- 19 99 ; b) 2 00 0- 20 01 . a b 956 Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander lated from all the available measurements using eq. (2.2) and a similar one for the hourly deciles (Fotiadis et al., 2001). Figure 6 shows clearly the existing difference between day-to-day and with- in-the-hour variability. The bounds of variability for the 90% of the time are around 20% in ab- solute value in the case of the day-to-day vari- ability (Kouris and Fotiadis, 2002) whereas for Fig. 5. Probability the variability within-the-hour in foF2, positive (right) or negative (left), be greater than 0.10, 0.15, 0.20 or 0.30, in absolute value, using all the available data from Rome. Fig. 6. Deciles of foF2 from hourly daily values and deciles from foF2 5-min measurements made in Rome during 1997-2001. 957 Within-the-hour variability: levels and their probabilities the within-the-hour these bounds are around 10% in absolute value with respect to the stan- dard hour value. Exceptions occur again at sun- rise in winter and equinoxes, and around sunset in summer (fig. 6) where these limits are more pronounced. Variability and disturbances – Buresova and Laštovička (2001) selecting strong geo- magnetic storms found that during ionospheric disturbances there is a considerable daytime within-the-hour variability in foF2. The results reported here confirm the strong variability. In- deed, although table IV refers to monthly con- ditions, it clearly shows that a substantial vari- ability exists throughout the day, being more pronounced around sunrise and sunset. On the contrary, the within-the-hour variability in TEC is around 5% of the corresponding hourly daily value except around sunrise and sunset, and during local disturbed conditions where values of the order of 20%-30% are reached. However, it is known that ionospheric disturbances may follow magnetic disturbances (fig. 7) but there is no simple direct relationship between them. Indeed, we have observed that when Kp is much greater than 2 the level of the within-the- hour variability in foF2 could be that of the «quiet variability» (fig. 8), that is about 0.12 or less, which is of the same order of the variations observed in the critical frequency of the E-lay- er (Kouris and Fotiadis, 2002). On the other hand, the variability in TEC is around 5% or less, except at sunrise (figs. 7 and 8). Figure 9 shows clearly that although the Kp index is less than 2, the variability in foF2 is quite substantial, reaching values around 0.20; whereas that in TEC is negligible apart from around sunrise. We may therefore state that there is nearly always a substantial variability in foF2 in the interval time of an hour, whereas the with- Fig. 7. Relative deviations of 5-min foF2 measurements (Rome, 22-23 September 1999) and 10-min relative deviations of TEC measurements (Matera, 22-23 September 1999). Values of Kp index. 958 Fig. 9. Relative deviations of 5-min foF2 measurements from Rome (upper) and 10-min TEC measurements from Matera (upper middle) and Hailsham (low middle); values of Kp index (bottom). Fig. 8. Relative deviations of foF2 from measurements made in Rome (upper) and of TEC made at Matera (up- per middle) and Hailsham (low middle); values of Kp index (bottom). Stamatios S. Kouris, Kostas V. Polimeris, Vincenzo Romano, Bruno Zolesi and Ljiljana R. Cander 959 Within-the-hour variability: levels and their probabilities in-the-hour variability in TEC is about 5% or less apart from during local disturbed conditions (table II) and at sunrise and sunset. In these last cases the pronounced variations in TEC are sim- ply due to its rapid increase or decrease during its diurnal normal variation, that is at sunrise and sunset when rapid changes in the atmospheric conditions occur. The present study also points out that ionospheric disturbed conditions are more marked in foF2 rather than in TEC and this is in agreement with previous findings regarding other ionospheric parameters (Kouris and Fo- tiadis, 2002). 4. Conclusions The obtained results lead to the conclusion that the deciles of the within-the-hour variability in foF2 are 12% higher/lower than the correspon- ding standard hourly value of foF2, at least re- garding the region of Rome. Variations higher, that is of the order of 20%-30%, are usually ob- served at sunrise and sunset due to changes in the atmospheric conditions. Moreover, large varia- tions (positive/negative) in the interval time of one hour of the same order (0.20 to 0.30) due to disturbed conditions are also observed, but their probability of appearance is less than 5% per month. The variations in TEC for 90% of the time are usually less than ±5% of the corresponding hourly value. However, at sunrise and also at sunset in winter variations of the order of 20%- 30% are observed and should be attributed to the rapid increase/decrease of TEC during its diurnal normal variation. They depend strongly on sea- son.The analysis shows also that a stationarity in TEC of about one hour may be accepted. In addition ionospheric disturbances affect the F2 layer maximum electron density rather than TEC in the interval time of one hour. 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