Submitted to UKSMG: 11.02.2000
One might conclude that the distribution of skip distances is a consequence
of the geographical density of 6m operators in Europe; however, this density
is unknown. The geographical distribution of sea and land areas plays a
major role in  and  because this distribution is believed to correlate
with that unknown density. This paper discusses the model of the sea/land
distribution in Europe adopted in  and its implications on the statistical
analysis of 50 MHz sporadic-E.
Figure 2 resembles a map of Europe but in fact it is a two-dimensional table in a computer spreadsheet program in which the matrix cells have been coloured depending on the actual id-number. It takes little programming effort to transform this matrix into a database in which each European grid square is given by its actual qth-locator, actual terrain id, actual distance and azimuth and actual geographical area in square kilometers. The distance and azimuth is calculated from JO40 (which is one of the reference locations in ) to a grid target point ('handle') i.e. a constant position relative to each grid square. Figure 2 might erroneously give the impression that all grid areas are identical. Calculations of grid areas must take the actual geographical latitude into consideration because the area of north European squares is smaller than those in south Europe.
Plotting land or sea areas as a function of distance (see figure 6 in ) results in a step function; this is a consequence of the Maidenhead grid overlay. Some grid area may slip in a neighbouring range gate causing some distortion in the step function. For this reason figure 6 in  also provides the exact mathematical calculation of the area increase (see line 'true' ibid.).
This method of estimating the distribution of sea and land areas in
Europe is obviously much more accurate than the method discussed in .
In particular the 'variation of land with distance' (see figure 4 in )
is not reproduced by this model. However, provision of a highly detailed
and accurate calculation is not within the scope of . Nevertheless a
certain degree of geographical resolution and accuracy is apparently required
in order to interpret the distribution of skip distances properly. Also
figure 8 in  must be considered with care because it is based on the
results of figure 4 in . On the other hand, the principle idea behind
 is worth some thought; the result should be recalculated with the geographical
model discussed above.
The dx operator cannot identify the presence of sporadic-E if a downlink station, necessary to complete the terrestrial propagation path, is unavailable. This is particulary true when the terrestrial propagation path ends in the ocean, i.e. the corresponding E-layer region may be neglected because it has no practical importance. Figure 3 shows the E-layer blanking effect caused by the continental shape of Europe and by the observer's actual location (JO40). Sporadic-E events above western Europe e.g. the North Sea, Ireland, the UK (except the very south-east) and the north-western part of France are blanked (this is indicated by missing diamonds in figure 3) as no downlink station is available in the Atlantic ocean. A remarkable feature exist in south-eastern France and northern Italy where the diamond pattern indicates a hole corresponding to missing stations in the Mediterranean Sea (except the spot at JN24, which corresponds to the island of Mallorca, JM19). This pattern explains why sporadic-E openings, e.g. into Spain and Portugal, may terminate abruptly in JO40 although other stations (even in Germany) continue to work dx. In such a case the scatter volume moves from south-west France eastwards into this particular hole, disrupting the band opening in JO40 and its adjacent squares. Therefore, we may call the diamonds in figure 3 the effective sporadic-E horizon relative to the location JO40.
Does the unexpected distribution of skip distances result from the effective
sporadic-E horizon? Figure 4 shows the range distribution of the red-circled
grid squares shown in figure 3. There is no evidence that the effective
sporadic-E horizon stimulates significant maxima and minima in the distribution,
instead there is a more or less steady increase of grid squares with increasing
distance. This result is in good aggreement with figure 6 in , although
that figure measures areas in square kilometers.
Figure 5 isolates the observations obtained at JO40 from the database,
i.e. each grid locator contributes to the distribution in accordance to
the number of times it was heard or worked at JO40. This is not the case
in figure 6, here each locator contributes only once no matter how often
the locator was actually heard or worked. Figure 6 is fully compatible
with the type of data shown in figure 4, however it is obvious that the
distributions differ to a high degree.
As already mentioned the geographical density of 6m operators in Europe is the real matter of interest. For example, large cities and densely populated regions could, of course, play a major role in the maxima and minima shown in figures 1 and 5, even when the continental shape is neglected. Those regions are characterized by a large amount of radio amateurs in the same grid square, i.e. such squares contribute significantly to the distribution of skip distances.
In figure 6, large cities and densely populated grid squares are weighted identically to small villages and remote grid squares where only one 6m operator may exist. In figure 6, geographical spots of high 6m activity are, therefore, eliminated to a very high degree. Nevertheless the principle features of figure 1 seem to be reflected in figure 6 although the amount of data is reduced to less than a fifth (figure 1 and 6 consider 979 and 174 data records, respectively). Hence, figure 6 may be considered the real mystery because, for example, grid squares at a distance of 1100 - 1200 km (see the corresponding dip in figure 6) appear less often in sporadic-E than e.g. squares at distances of 900 - 1100 km. This is a remarkable feature because figure 4 indicates that the total number of land and coastal grid squares is more or less constant in the corresponding range gates.
Therefore, there is reason to speculate that the distribution of skip
distances in figure 1 and 5 is not purely geographical in nature, but is
caused by a geophysical phenomenon related to the physics of sporadic-E.
From this point of view there is no discrepancy between  and , although
the arguments are not identical. In  it is speculated that the distribution
of skip distances is a consequence of different sporadic-E scatter modes.
In , on the other hand, it is speculated that the distribution of skip
distances is driven by the latitudinal variance of the sporadic-E probability
(which is a geophysical phenomenon). However,  requires the speculation
of an unknown sporadic-E scatter mode for which no further evidence yet
exists and  is based on results of the sea/land distribution which do
not correspond to the results discussed above. Obviously further investigations
are required in order to interpret the distribution of skip distances properly.
 Hidden Mode of Sporadic-E? More Magic with the Magic Band.
Grassmann, V., DF5AI, www.uksmg.org, October 1999
 A Critique of ”Hidden Mode of Soradic-E” by DF5AI
Grayer, G.H., G3NAQ, submitted to UKSMG, Dec. 1999
 Fractals, Form, Chance, and Dimension
Mandelbrot, B.B., Chapter IX, ISBN 0-7167-0473-0, 1977