March 31, 2001 geomagnetic storm
Locating the positions of Auroral backscatter
by Volker Grassmann, DF5AI, May 27, 2005
By using ionospheric radar systems, the actual position of Aurora backscatter may be derived from range gate measurements and from the actual antenna direction in azimuth and elevation. In amateur radio, however, distance measuring capabilities are principally not available. We may alternatively use the antenna heading of at least two amateur radio stations to triangulate the Aurora position but this approach is not applicable either, unfortunately. The typical beamwidth of ham radio antenna systems varies between, say 10 and 40 degree, insufficient to support an appropriate accuracy when locating the geographical position of the Aurora scatter volumes. Even worth: information on the antenna elevation is typically not available and even the azimuth information, if available, is more or less useless for analysis purposes. In the hot phase of an Aurora band opening, the radio operators do not optimize the antenna heading to obtain maximum fieldstrength, in a 'strong opening' there is actually no need to do so because high fieldstrength is available even with a considerable antenna offset. Thus, even if the actual azimuth reading is available it does not necessarily correspond to the Aurora's 'true' azimuth.
In the 1980s, the author has therefore developed an alternative approach supporting the estimation of Aurora positions in realtime without using any range and any directional information. That method was first published with the AURORA software ,  and was successfully used with high accuracy in many Aurora openings. Nowadays, an enhanced version is available with the BeamFinder software  which is also used in this project. In this chapter, we will discuss the method in detail because it plays a major role in the analysis of the March 31, 2001 geomagnetic storm.
Receiving radio echoes from field-aligned backscatter, the actual geographical position of the scatter volume is already determined to a certain degree. Because of the specific geometry in Aurora backscatter (which is controlled by the direction of the Earth magnetic field and by the geographical position of the transmitter and the receiver), the Aurora position is restricted to a geographical corridor which typically extends over, say 1.000 kilometers in the east-west direction and 100-200 kilometers, or so, in the north-south direction. Thus, any pair of radio stations communicating via Aurora backscatter is associated with an exclusive geographical band that includes the geographical position of the scatter volume - so far, we however lack information in which part of that geographical band the Aurora may be actually found.
In an Aurora band opening, we have hundreds of QSOs and each of them contributes an individual band of potential Aurora positions. Assuming a highly localized scatter volume enabling all this Aurora QSOs, all bands must overlap at the true position of the Aurora backscatter. Thus, by analysing the overlap areas of the bands (including some statistical considerations), we may estimate Aurora positions without using antenna headings or any other type of directional information.
The scatter curve
Aurora radio propagation corresponds to the bistatic scatter case which is associated with the geometrical picture of the so-called scatter cone, see fig. 3. The width of the cone depends on the angle between the Earth magnetic fieldlines penterating the scatter volume and the line-of-sight from the transmitter to the scatter volume. The radio station TX in fig. 3 may therefore communicate with all stations RX which are positioned along the so-called scatter curve that denotes the intersection of the scatter cone with the Earth surface.
For example: Assuming a given position of Aurora backscatter, e.g. between Scotland and Norway (see fig. 1), and assuming a fixed transmitter in the south of Sweden (see the TX location), the scattering process would distribute the radio echoes along a curve extending from western Ireland to Scotland, into the North Sea and, finally, to northern Germany (see the blue crosses in fig. 1 which correspond to the scatter curve displayed in fig. 3).
Analysing QSO data
Analysing QSO data, we however meet a different scenario: here, we know the actual transmitter and receiver location (see TX and RX in fig. 2) but the Aurora position remains unknown. We may conclude that the Aurora is located somewhere within the overlap area of the transmitter's and the receiver's individual radio horizon, see the red circles in fig. 2.
Within this overlap area, we need to identify all positions in the E region of the ionosphere which can support Aurora dx QSOs between the locations TX and RX in accordance to the above mentioned geometrical rules of field-aligned backscatter. Carrying out this calculation manually indeed represents a cumbersome procedure but the BeamFinder software can manage the same task within seconds. Depending on the actual TX and RX location, we finally obtain an ensemble of scatter volumes which can all support Aurora backscatter communication between this two radio stations, see the green area in fig. 2. Thus, if the receiver RX can detect any Aurora backscatter from the transmitter TX, the radio echo originates from some location(s) within that green area and nowhere else.
To understand the method of locating Aurora positions, the following conclusions are in particular important, i.e.
Considering QSO reports from many dx stations
In fig. 2, Auroral backscatter originates from E region irregularities located somewhere in that green area, the scatterer's exact position remains unknown though. Another example is displayed in fig. 4: here, we have two transmitters TX (located in Denmark and in northern England, respectively) which are all received by the same receiver RX in Germany. The two pairs of radio stations TX-RX result in two independent green areas, each indicates potential positions of Aurora backscatter. The northern band extends from the North Sea to the southern tip of Norway, to the south of Sweden and, finally, into the Baltic Sea. The southern band, on the other hand, extends from Scotland to Denmark, into the far south of Sweden and terminates in the Baltic Sea too. Thus, one center of Aurora backscatter could exist above southern Sweden (corresponding to the QSO, say between Denmark and Germany) and another center of Auroral backscatter could exist above Scotland (corresponding to the QSO between northern England and Germany). In this case, the receiver RX probably needs to adjust its antenna heading from north-east to north-west, or vice versa, in order to receive one or the other transmitter TX.
Assuming both Aurora QSOs would result from an identical center of Aurora activity, we may very easily identify the Aurora's true geographical position at the intersection of the two green bands. Assuming we would have 100 Aurora QSOs which are all enabled by the same scatterer in the E region of the ionosphere, the 100 curves must all intersect at the scatterer's geographical position. If two centers of Auroral backscatter would exist, the 100 curves will result in at least two intersection areas, 40 curves would correspond to intersection area A and 60 curves would correspond to area B, or so. With three scatterers, we will find at least three intersection areas A, B and C corresponding to, say 25, 35 and 40 QSOs. Although an important information, the number of intersection areas cannot provide a reliable guideline to identify the number and the position of Aurora backscatter accurately. In fig. 4, for example, we indeed find an intersection above southern Sweden and even within the Baltic Sea region. However, we cannot exclude the above mentioned case which considers two independent scatterers, i.e. one above Scotland and another one above southern Sweden - the existence of an intersection does not necessarily implies the existence of a common scatter volume, in fact. At this stage of investigation, we need to introduce some statistical considerations in order to reduce the ambiguity of the results.
BeamFinder's score method
Note that all green areas in the above figures are composed by little dot markers which actually represent BeamFinder's internal grid system. All grid positions are associated with an individual counter which increments whenever the corresponding position may be considered a potential scatter location. Initially, all counters are zeroed but, when analysing dx reports QSO by QSO, a certain amount of counters become incremented in the course of the analysis. Finally, we find counters which were never incremented at all, others were incremented a few times and some counters were incremented quite often, perhaps. The actual counter value is referred to as the grid position's score value which measures the probability of finding a scatterer at this particular position.
In BeamFinder's graphical presentation, all non-zero score positions are displayed on the screen map resulting in the green bands displayed in fig. 2 and 4. This is the user's perspective - from BeamFinder's perspective the same scenario is represented by a three-dimensional bar chart (see fig. 5), similar to a mountain ridge composed by the two-dimensional size of the potential Aurora scatter area and by mountain heights corresponding to the score values. In BeamFinder's "Aurora/FAI analyser" dialog box, the user may however vary the threshold value to be displayed on the screen map. Adjusting the slider to the score value of 10, for example, the screen map will only display scores higher than 9, i.e. 10, 11, 12 etc.
Interpreting a real example
With only one QSO information, the score method cannot estimate the true Aurora position within the green area. The positioning accuracy however increases with the increase of QSO information. With 10 or 20 QSO reports, the 'score mountain' typically shows distinct peaks and maxima which may be interpreted as the most likely Aurora positions.
Fig. 6 displays a real data example of the March 31, 2001 geomagnetic storm. All panels indicate the same Aurora QSOs between 2300 and 2330 UT. The blue lines denote the great circle path between the QSO stations, i.e. the true backscatter path is not shown here. The red and yellow colour displays the POES data from 2325 UT, see the section data analysis tools for more details.
The left panel displays all grid positions (green) corresponding to non-zero score values (Score > 0), i.e. all Auroral backscatter has originated from the green area. However, we cannot identify which parts of the green areas may be considered 'true' Aurora positions: is the backscatter scenario from March 31, 2001 represented by only one of the many dot markers or do all dot markers represent true backscatter positions? At this stage of investigation, we cannot answer this question. However, it is unlikely that any Aurora backscatter has occured outside of that green area because of the many dx stations considered in the analysis, i.e. blind spots (see the above bullet points) may be excluded to a certain degree.
The panel in the center of fig. 6 displays all scores exceeding the value of 4. Note that the green areas have collapsed to a much smaller area above southern Norway. In the right panel, the threshold has been further increased, i.e. we may now identify a small region east of Oslo which BeamFinder considers to most likely center of Aurora backscatter in the observation period between 2300 and 2330 UTC. However, it is important to understand that the spot of highest Auroral backscatter activity does not exclude the existence of secondary activity centers. Those centers might indeed exist in the March 31, 2001 scenario between 2300 and 2330 UTC but it is very unlikely that those centers may be found at an arbitrary position within the green area of the left panel: if they exist, we may find them within the green area of the central panel in fig. 6, in fact.
Notes on practical applications
By manipulating the score threshold, we may x-ray a given band opening to identify the centers of Aurora backscatter activity. In this process, it is indeed advantageous to consider azimuth information from the radio operators too. Selecting a too high threshold, the resulting green areas no longer correspond to the antenna headings reported by the radio stations. An optimum threshold is obtained if all antenna headings target at least one green area.
In realtime applications, BeamFinder also offers an unique feature to predict dx opportunities based on the above analysis. Having identified the most likely geographical positions of Aurora backscatter, we may reverse the model calculation to identify all dx targets currently available in the band opening. BeamFinder displays the dx prediction by placing blue crosses on the screen map similar to fig. 2. Thus, receiving Auroral backscatter from dx stations in, say Denmark or Sweden, BeamFinder may indicate an open dx path to Scotland or Finland even if you haven't yet noticed any GM- or OH-station at all.
Reverse modelling provides another opportunity to adjust the score threshold accurately. Entering dx data from many radio stations and performing a dx prediction based on this information, the prediction must at least reproduce the positions of those stations: imagine you have received Auroral backscatter from a station located in the, say JO40 grid square, the prediction however excludes that grid square in the dx target area, we are obviously facing an inconsistency between observation and prediction - in this case, the user has selected a too high score threshold (except he has selected that threshold by purpose which makes sense in some applications not discussed here).
Notes on the positioning accuracy
To identify the method's accuracy, we actually need to employ ionospheric radar systems capable to measure the true position of Aurora backscatter - even worse: we actually need to involve hundreds of ionospheric radars. Note that even an Aurora radar is blind to Aurora backscatter in wide geographical areas because of the backscatter geometry (similar to the Aurora dx QSOs which all show a specific band of potential scatter locations, i.e. the same restrication applys to ionospheric radar systems). From this perspective, the score method exceeds the radio horizon of Aurora radars considerably because it can identify Aurora backscatter on continental scale lengths. From this perspective, we can hardly compare the method's findings to real observation data which is a disadvantage, in fact.
We may however perform consistency checks whenever possible. The author applies this method successfully for more than 15 years, by using the AURORA software ,  in the 1980s and 1990s, and by using the BeamFinder software  nowadays (both programs refer to the same computer subroutines). During the years, many consistency checks were carried out in many analyses, in all cases a more or less perfect match was found between the observational findings and the numerical results. By using this method, we were able to reveal the nature of the so-called unusual Aurora QSOs  and we have identified the maximum dx radius in Aurora and FAI radio propagation ,  (a detailed paper will soon appear which documents the very good agreement between BeamFinder's model calculations and practical results in Aurora dx communication). When analysing Aurora band openings in 2003 and 2004, the author however got the impression of a systematical error resulting in an azimuthal deviation of 2 to 3 degree compared to the antenna headings reported by radio amateurs. This deviation may result from the subroutines calculating the International Geomagnetic Reference Field (IGRF) because the software does not yet consider the latest parameters in the spherical expansion of the geomagnetic field. However, this deviation is still under investigation.