1. WRPM Sporadic E Model Development The initial model for Sporadic E has been based on the model given in ITU‐R Recommendation P.534, which has been implemented in Mathcad. Sporadic E is caused by the ions at ~90km above the Earth becoming concentrated into thin clouds with a high MUF extending into the VHF region. This region of the atmosphere is in the Ionosphere, where complex interactions between Solar radiation and the earths magnetic field develop regions of ionisation that refract electromagnetic waves. This model is concerned with predicting the effects of mid‐latitude sporadic E. Similar effects occur at the magnetic poles and for paths transiting the geomagnetic equator but are due to different ionospheric mechanisms, for example Auroral E and Trans Equatorial Propagation (TEP). This model does not yet cover these. F‐layer propagation only becomes important above 30MHz at around the solar maximum and is well modelled by existing recommendations. As sporadic E effect is by definition sporadic, it must be treated statistically. It is generally considered as an interference mechanism above 30MHz, so we express the annual statistics of in terms of the critical frequency not exceeded for more than a specified time percentage. f > fc f < fc 2000km
Sporadic E clouds
f = fc double hop
Figure 1‐1: Sporadic E To estimate the sporadic E field strength using recommendation ITU‐R P.534 we need the major parameter FoEs, which is the critical frequency of the sporadic E layer for the ordinary wave taken at the middle of the path. While paper maps of the percentage of time this parameter exceeds 7 MHz are given in the recommendation, for the purposes of the WRPM we need this data in electronic format and ideally as the cumulative distribution. This data does not appear to be readily available and so the approach taken was to generate suitable statistics from Ionosonde data. Ionosondes are radars which sweep through the HF spectrum measuring the heights and critical frequencies of ionospheric layers; an idealised ionogram showing the presence of sporadic E is shown in Figure 1‐2. Data from ionosondes is routinely collected from many sites around the world. The value of FoEs can be difficult to interpret and the quality of the results from different sites varies, however this is considered to be the best data available at this time. In order to develop global maps, Ionosonde data was obtained from the World Data Centre (WDC) database covering the period 1980 to 2007 and a program was written in C++ to extract the statistics of FoEs. Two typical distributions are shown in Figure 1‐3 for Chilton, near London in the UK and Kokubunji near Tokyo in Japan. h’ F ‐ layer returns
E ‐ layer returns
h’Es h’E fmin
fbEs foEs
f fxEs
Figure 1‐2: Idealised Ionogram (Piggott & Rawer, 1972) 100
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Kokubunji (Japan) Figure 1‐3: Typical distributions of FoEs The CDF results in Figure 1‐3 demonstrate that, for these two sites at least there appears to be a linear relationship between the log of the time percentage and the value FoEs not exceeded. The WDC database contains records from many sites with varying quality and resolution. In an initial analysis 8 sites were rejected either because they were missing important results or because the records covered less than one year which because of the monthly variability of Sporadic E was considered to be too short a time period. The resulting processed annual statistics for the remaining 104 sites were analysed. A few results appeared to be anomalous with very high values of FoEs; the most notable of these outliers being Arenosillo, Darwin, Hobart and Townsville. It was not clear if these are real ionospheric effects associated with sporadic E generated by the equatorial electrojet or a result of data problems; for the time being these sites have been eliminated from further analysis. The locations of the respective Ionosondes are shown in Figure 1‐4. The geographical spread of the resulting measurement database is concentrated in the Northern hemisphere and in Europe and North America. The statistical results are plotted in Figure 1‐5. The mean FoEs value at around 3‐4MHz is low enough for the sporadic E mechanism to be neglected for frequencies above 30MHz at 50% time percentages and below. Sporadic E is only likely to be important for systems requiring above around 90% availability. Figure 1‐4: Ionosonde measurement sites FoEs (MHz) not exceeded for 50,10,1,0.1 and 0.01%of total measurement time
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YAKUTSK
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Figure 1‐5: Sporadic E statistics The measurement coverage around the UK is good and a European estimate based on a triangular cubic interpolation between the many measurement sites in this region is presented in Figure 1‐6. The minimum percentage that can be statistically relied on is 0.1% owing to the limited data. The results compare favourably with the regional figures available from the WOMAP software available from the ITU‐R study group 3 web pages. The figures given by this program have been processed into Table 1‐1 by using the equations from ITU‐R P.534 and a log interpolation function. The results for Europe are highlighted. The validity of the log interpolation is demonstrated by the data shown in Table 1‐1 which, at least over Europe agrees quite well with the measurements. The log interpolation can therefore probably be used to extend the model to higher availabilities, for example 0.01%. Although the validity of this extension can not easily be tested, it is the only method we are likely to have available. 50% 10% 1% 0.1% Figure 1‐6: European map Sporadic E statistics Table 1‐1: Regional FoEs figures Region/Percentage
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3.5 5.0 7.7 Region Key 1 South America 7 Subequatorial Asia 2 Subequatorial America 8 Equatorial Asia 3 Equatorial America 9 Africa 4 North America 10 Subequatorial Africa 5 Europe 11 Equatorial Africa 6 Asia 10 11 The proposed model is that from ITU‐R P.534 so it is not repeated here. Figure 1‐7 shows the predicted field strength in microvolts per metre for 1kW radiated power at 30MHz for FoEs of between 4 MHz and 12 MHz. For reference, the field strength for a free space path is also shown. Es Field Strength - 1kW radiated power
Field Strength(uV/m)
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Figure 1‐7: ITU‐R P.534 predicted field strengths against FoEs Figure 1‐8 demonstrates how the field strength varies with signal frequency for an FoEs of 15 MHz which from Figure 1‐6 and Table 1‐1 is typical of the level not exceeded for more than 0.01% of time for Europe and the level not exceeded for more than 0.1% of time for Equatorial regions 1 . Note that there are two important variations shown, the height of the curves which relates to the path loss and also their width which relates to the area from which interference can arise. It is clear that the significance of sporadic E falls off very rapidly as the signal frequency increases, especially for the double skip mode, which can probably be safely ignored. This is important as it limits the interference distance that must be considered to approximately 3000km. Es Field Strength - 1kW radiated power
Field Strength(uV/m)
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V( d 30 15)
V( d 40 15) 10
V( d 60 15)
V( d 80 15)
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V( d 120 15)
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E1kw( d)
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Figure 1‐8: ITU‐R P.534 predicted field strengths against signal frequency 1
Note Equatorial here refers to the Geomagnetic Equator which is offset from the geographic equator.
Sporadic E is highly variable between months and with time of day; this is demonstrated in Figure 1‐9. It may be desirable to produce a model that accounts for time of day and month of year, though at this time the plain annual statistics will be concentrated on. The model may include advice, such as “sporadic E interference is more common around local noon in the summer months”. Chilton FoEs (Upper Decile) by Month
South Uist FoEs (Upper Decile) by Month
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Figure 1‐9: Sporadic E upper decile variability Interpolation to developing FoEs maps To make use of the sporadic E model in the WRPM we will require maps of the statistics of the sporadic E critical frequency, FoEs. This parameter may be extracted from Ionosonde measurements and the locations of the Ionosondes used are as shown in Figure 1‐4. To maintain compatibility with existing ITU‐R maps, the new maps should be presented in the traditional format which is a 1.5 degree resolution global grid stored as an ascii file. The global database of Ionosonde measurements has been analysed and the FoEs statistics have been extracted for each Ionosonde site in the form of a cumulative distribution. The value of FoEs not exceeded for 50%, 10%, 1% and 0.1% of time were then used to develop the maps. As has already been noted, the parameter FoEs is not one that is easy to measure and therefore there is a large potential for measurement error. A further consideration is the non‐uniform global coverage of the measurements, with a high concentration of measurement sites on land and in the Northern hemisphere. Owing to this uneven distribution and the inherent uncertainty in the measurements, a simple grid interpolation has been applied. Several interpolation methods were investigated using Matlab, these included the Matlab V4 method and 3 forms of triangular interpolation – Cubic, Linear and Nearest. Kriging was also tried but did not give useable results as, probably owing to the nature of the measurement data, the variogram was too noisy. The Matlab V4 method produced the smoothest results as is demonstrated by the plots in Figure 1‐10 through to Figure 1‐13. Figure 1‐10: Interpolation comparison for 50% time Figure 1‐11: Interpolation comparison for 10% time Figure 1‐12: Interpolation comparison for 1% time Figure 1‐13: Interpolation comparison for 0.1% time The ITU‐R format maps have been produced based on the Matlab V4 interpolation and are shown in the standard format as used by other current recommendations in Figure 1‐14 through to Figure 1‐15. Figure 1‐14: ITU‐R format map for 50% time Figure 1‐15: ITU‐R format map for 10% time Figure 1‐16: ITU‐R format map for 1% time Figure 1‐17: ITU‐R format map for 0.1% time