1. Introduction

Figure 1. Range distribution of 979 stations worked or heard via 6m sporadic-E. The width of each of the range gates is 100 km e.g. range gate "800 km" refers to stations in the range 800-900 km from the amateur radio station DF5AI, which was located in JO52CJ, JO31PG and JO40DF respectively [1].

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 [1] and [2] 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 [1] and its implications on the statistical analysis of 50 MHz sporadic-E.
 

2. Modelling the sea/land distribution in Europe

Figure 2. Types of terrain based on Maidenhead grid locators. "Sea only" grid squares are labeled 0 and "land only" squares are labeled 2. Remaining squares are defined as "seacoast" (label 1). The black square JO40 indicates the point of reference, see text.

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 [1]) 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 [1]) 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 [1] 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 [2]. In particular the 'variation of land with distance' (see figure 4 in [2]) is not reproduced by this model. However, provision of a highly detailed and accurate calculation is not within the scope of [2]. 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 [2] must be considered with care because it is based on the results of figure 4 in [2]. On the other hand, the principle idea behind [2] is worth some thought; the result should be recalculated with the geographical model discussed above.
 

3. Analysing the "effective sporadic-E horizon"

Figure 3. Selection of all land and coastal grid locators in the range 700-2400 km (red circles) in reference to JO40 (black square). The corresponding E-layer scatter regions are indicated by diamonds ("effective sporadic-E horizon").

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 [1], although that figure measures areas in square kilometers.
 
 

Figure 4. Range distribution of the grid squares (see red circles in figure 3) corresponding to the effective sporadic-E horizon in reference to JO40. The count numbers in bins beyond 2000 km underestimates the grid squares because circles larger tham 2000 km are beyond the locator map (see figure 3).

4. Removing double counts in the observation data

Figure 5. Range distribution of JO40-data isolated from figure 1.

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.
 
 

Figure 6. Square count corresponding to figure 5, i.e. each grid locator is considered once even when worked or heard several times from JO40.

5. Conclusions

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 [1] and [2], although the arguments are not identical. In [1] it is speculated that the distribution of skip distances is a consequence of different sporadic-E scatter modes. In [2], 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, [1] requires the speculation of an unknown sporadic-E scatter mode for which no further evidence yet exists and [2] 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.
 

6. Call for observation data

7. References

[1] Hidden Mode of Sporadic-E? More Magic with the Magic Band.
 Grassmann, V., DF5AI, www.uksmg.org, October 1999

[2] A Critique of ”Hidden Mode of Soradic-E” by DF5AI
 Grayer, G.H., G3NAQ, submitted to UKSMG, Dec. 1999

[3] Fractals, Form, Chance, and Dimension
Mandelbrot, B.B., Chapter IX, ISBN 0-7167-0473-0, 1977