Modelling and mapping Sporadic E using Backscatter Radar

R.J. Norman⁽¹⁾, P.L. Dyson⁽¹⁾ and J.A. Bennett⁽²⁾

⁽¹⁾ School of Physics
La Trobe University
Bundoora, Victoria 3083
Australia

r.norman@latrobe.edu.au
Phone +61 3 9479 2637

(2) Department of Electrical and Computer Science Engineering
Monash University
Clayton, Victoria 3168
Australia

ABSTRACT

Sporadic E, abbreviated Es, is a very thin ionized layer and as its name suggests, it occurs sporadically at E region heights. To a radio wave Es often behaves as a smooth HF reflector. However, because of its complex structure and large spatial and temporal variability Es is a major problem, especially, for HF propagation predictions where the main emphasis is on the maximum electron density of the layer and an accurate description of the ionosphere. In this study it will be shown that many features of oblique propagation via Es can be both successfully modeled and mapped.

1 INTRODUCTION

The aim of this study is to develop techniques to both model Es echo traces on, and map Es from, sporadic E traces on a Backscatter Ionogram (BSI). Thus, these modeling techniques can play an important role in the frequency management system of over-the-horizon radar facilities.

Preliminary work by Houminer et al, (1996) proposed that sporadic E clouds or patches could be mapped using Backscatter Sounders (BSS). Their technique has been developed further in this study (see also Norman et al 1998) such that synthesized backscatter ionograms in conjunction with an ionospheric model containing a sporadic E layer are used to map and model different types of Es.

The Quasi-Parabolic Segment (QPS) model (Dyson and Bennett, 1988) is an analytic ionospheric model and is commonly used to represent the Earth’s ionospheric profile. The QPS model, consists of 5 QPS’s, and produces integrable terms when solving for the ray parameters. The 5 QPS’s represent the three ionospheric layers namely the E, F1 and F2 layers. The required inputs of the QPS model are the peak plasma frequencies, the peak heights and the semi-thickness of each of the three ionospheric layers. In this study a further layer is added to the QPS model representing a Es layer. This new analytic ionospheric model is referred throughout this study as the 4 Layer or 4L model. The only added inputs that this model requires are the peak plasma frequency foEs and the height of the peak plasma frequency of the Es layer, hmEs.

The method of mapping Es in this paper is very simple and makes use of the thickness, and maximum operating frequency, of the Es echo traces on the BSI and assumes that the Es behaves as a spherical mirror. The equations determining the distance of the Es cloud from the transmitter/receiver location as well as the peak plasma frequency and the extent of the Es clouds are presented. The effects of patches of Es and some examples of partial reflection from Es are also presented.

Two example backscatter ionograms from the Jindalee Stage B data (after Houminer et al 1996) containing Es echo traces are also presented and clearly demonstrate the ease and effectiveness of the modeling and mapping techniques.

It should be noted that the effects of beam spreading, multiple hops, antenna patterns and absorption, on the BSI, have been ignored throughout this study.

2 THE 4L IONOSPHERIC MODEL

The 4L ionospheric model is simply an extension to the QPS ionospheric model in that it contains an extra layer, which represents the Es. The 4L model consists of 8 QP segments, one for each of the ionospheric layers and 4 QP segments representing the joining layers. The 4L model is an analytic ionospheric model, producing integrable equations when solving for the ray parameters. The joining segments which attach the Es layer to the E layer as well as the equations for the Es layer are given below :-

The QP layers representing the E and Es layers and the two joining segments, joining the E and Es layers, are of the form :

where

is the maximum electron density occurring at the peak height

of the layer,

is the base height of the layer and

is the layer semi-thickness.
The electron concentration gradients in each of these segments are given by :

Assuming that the joining layer attaches smoothly to the other layers the parameters of the joining layer can now be readily determined. The 4L model fits the joining layer, which is represented by two QP segments smoothly attached, between the E layer and Es layer in the following manner :
Firstly, the joining segment is fitted to the Es layer at a height,

, such that

The joining segment is given a minimum plasma frequency of :

where

The height of the minimum plasma frequency of the joining segment is given by :

and

where

The height at which the joining layer smoothly attaches to the E layer is given by :

and

Adding these equations to those of the QPS model produces the 4L model.

If hmEs > hmE, a similar approach to that described above can be implemented or a 4 layer ionospheric model using the same criteria as the 3 layer, or QPS model can be used. Using the latter option there will be know valley regions between the layers so if hmE < hmEs < hmF1, and

foEs > foF1 then the F1 layer is ignored and the sporadic E layer fits directly to the F2 layer. Both methods work well, producing realistic results.

3 THE EFFECTS OF Es ON SYNTHESIZED BSI’s USING THE 4L MODEL

Figure 1 shows an example of a profile obtained using the 4L model with the following layer parameters.

foF2 = 4.9 MHz ymF2 = 125.0 km hmF2 = 230.0 km

foF1 = 4.0 MHz ymF1 = 20.0 km hmF1 = 142.6 km

foE = 3.12 MHz ymE = 11.0 km hmE = 102.0 km

foEs = 4.0 MHz ymEs = 1.0 km hmEs = 90.0 km

A very narrow QP layer in Figure 1 represents the sporadic E. This sporadic E layer has a semi-thickness of 1 km, peak height of 90 km and peak plasma frequency of 4 MHz. Figure 2 shows a blow up of the Es. Clearly, a parabolic layer smoothly attached to the rest of the ionospheric profile represents the Es. The valley region between the E and Es consists of two smoothly attached QPS’s.

Figure 1.An ionospheric profile containing a sporadic E layer.

Figure 2. A magnification of the sporadic E layer in Figure 1.

Figure 3 represents a synthesized BSI determined using the QPS ionospheric model, which produced the profile in Figure 1, without the Es layer.

Figure 4 represents a synthesized BSI determined using the 4L ionospheric model, which produced the profile in Figure 1. Blanketing sporadic E was assumed in this case i.e., there was no partial reflection by the Es layer. Notice that in Figure 4 the F-layer trace contains ray paths reflected in the F layer where the plasma frequencies must have been greater than foEs.
Figure 5 shows the ray take-off elevation as a function of both group path and frequency for the case of blanketing Es. The elevation contours basically show where the sporadic E, is relative to the transmitter location. For example if there is a patch of Es situated so only ray paths with elevation angles between 0 and 4 degrees intersect this cloud then one would expect to obtain an Es echo trace with the width of the lightest shaded contour in Figure 5. The heights, or altitudes, of the Es clouds occur in a relatively small range. If the approximate height of the Es cloud is known, then using simple geometry the extent and distance from the transmitter/receiver location, of the Es cloud can be mapped. If multiple traces of Es appear on a BSI, then this approach can be used to map each cloud separately. The case of multiple echo traces on the BSI is not uncommon.

In this example a QP layer with a semi-thickness of 1 km is used to represent the Es. The semi-thickness in these results has little affect on the Es echo trace. Increasing the semi-thickness of the Es to 10.0 km produces very little change in the shape of the Es echo trace appearing on the BSI. The sporadic E behaves similarly to that of a spherical mirror. The only noticeable difference when increasing the semi-thickness of the Es occurs near the peak operating frequency of the Es echo trace where there is a slight upward bending in the Es echo trace. This upward bending may be of some use in determining the actual thickness of the sporadic E cloud from real BSI’s.

4 MODELING THE Es FROM THE BSI

4.1 Determining hmEs from a BSI when Es is present over the entire coverage area

Sporadic E occurs at altitudes between 90 and 130 km above the earth’s surface. Depending where you are positioned, this range can normally be reduced even further. It is more than likely that this parameter would be known to the frequency management system of over-the-horizon radar facilities and would not need to be determined. We have developed a relatively simple method to calculate the hmEs for the special case of when the Es is present over the entire coverage area. The minimum detectable elevation angle that the receiver can receive is also required in order to determine hmEs.

The hmEs can be determined from the BSI by assuming the Es behaves in the manner of a spherical mirror. The synthesized BSI in Figure 4 is used as an example to illustrate the procedure to determine hmEs.

Firstly, the maximum group path from the leading edge of the BSI is determined. In this case the maximum group path is approximately 2250 km.

Secondly, assuming the Es behaves as a good mirror model, then the following equation, which determines the group path,, for the ray from the transmitter to the base of the Es layer, can be rearranged as follows to produce a simple equation to calculate hmEs.

(1) where

is the smallest angle of elevation that the receiver can detect from the Es layer,

represents the radius of the earth and

represents the radius from the centre of the earth to the Es cloud, hmEs .

Then equation (1) can be rewritten as:-

Depending on the antennas and their location, in practice, , at best. However, the synthesized BSI in Figure 4 displays ray paths with elevation angle beginning at. From the BSI in Figure 4, 2150 km.

Then km which is close to the correct value of 90 km for the peak height of the Es layer used in producing the synthesized BSI in Figure 4. Using a more accurate estimate of would produce a more accurate value of hmEs. In the following sections, equations for foEs, the length of the Es cloud and the distance the Es cloud is away from the transmitter/receiver location are presented and show that they are in terms of and not hmEs. This means that a high accuracy in the value of hmEs is not crucial for the modeling and mapping of Es and depending on the desired accuracy in the modeling and mapping required an educated guess of hmEs is in practice normally sufficient.

4.2 Determining foEs from a BSI

The peak plasma frequency should be determined for each of the Es clouds. The equation used to determine the peak plasma frequency of an Es cloud, foEs, is derived as follows:-

At reflection, we know

where

represents the refractive index, r represents the height of the ray in this case

and

represents the radius of the Earth (

= 6370.0 km). In the absence of an imposed magnetic field and collisions, the refractive index is given by

where

represents the plasma frequency (at height hmEs,

= foEs) and f represents the operating frequency or wave frequency. Then

(2) and from the BSI the highest wave frequency, f, reflected from the Es can easily be measured. The parameter

is the lowest angle of elevation for a ray that intersects the Es cloud. By substituting these values into equation 2,

can be determined. As an example, the foEs for the BSI in Figure 4 will be determined. Firstly, from the BSI, f = 24 MHz and,

. The lowest detectable elevation angle in this case is 0.1 degree. Thus,

= foEs = 4 MHz which is the correct value.

5 MAPPING Es

In order to map Es from a BSI one must determine the distance the transmitter/receiver location is away from the Es cloud. The extent of the Es cloud in the transmitter/receiver also needs to be determined from the BSI. Sometimes more than one Es echo trace is present on the BSI where each echo corresponds to a cloud of Es. It is highly likely that the foEs differ from one cloud to the next. The following procedure should be performed on each cloud separately.

Firstly, calculate the maximum and minimum elevation angles that are reflected from the Es clouds. This is achieved by reading the maximum and minimum group path of the Es echo trace and rearranging equation 1 for a spherical mirror model, as follows:-

where is the maximum elevation angle of ray paths which transverse the Es cloud, is the minimum elevation angle of ray paths which transverse the Es cloud, is the maximum group path of the Es echo read from the BSI, is the minimum group path of the Es echo read from the BSI, represents the radius of the earth and represents the radius from the centre of the earth to the Es cloud, hmEs .

The extent or length, L, of the Es cloud in the transmitter/receiver direction is given by this simple equation:-

where

and

where is the angle of incidence at the base of the ionosphere (Es patch). The parameter is the angle between the transmitter and the Es cloud relative to the centre of the earth, andare the angles of the ray paths with the lowest and highest elevation angles, which intersect the Es cloud.

The equation below determines the ground distance, D, in kilometers, from the transmitter/receiver location to the position on the ground directly below the edge of the Es cloud nearest the transmitter/receiver location:-

The actual location of the Es cloud in terms of geographic or geomagnetic coordinates can now be readily determined.

6 TESTING THE TECHNIQUE ON REAL BSI’s

Two examples are presented here which clearly demonstrate the ease and effectiveness of the modeling and mapping techniques developed in this study. Figures 6 and 7 show the two Backscatter ionograms from the Jindalee Stage B data (after Houminer et al 1996) which we will attempt to model and map. They are both nighttime cases and clearly show a weak background ionosphere.

Figures 6 and 7. Examples of Jindalee backscatter ionograms with pronounced sporadic E echoes (arrows), (after Houminer et al 1996). Times in UT.

6.1 Example1 Modeling and mapping the BSI in Figure 6

The BSI in Figure 6 shows three distinct Es echo traces at group paths in the range 400-1700 km, indicating three distinct Es clouds were present at this time. The three traces are quite narrow indicating that the patches of Es were relatively small. The three traces extend out to nearly 27 MHz indicating that they are quite dense.

In order to model the Es, one must firstly, measure the maximum operating frequency and the maximum and minimum group paths of each of the Es echo traces on the BSI in Figure 6. The results in Table 1 display these measured values. The maximum operating frequency is used to calculate the maximum plasma frequency of each of the three Es clouds. The maximum and minimum group path measurements are used to calculate the extent of each of the Es clouds. Let Es1 represent the Es cloud closest to the receiver location, represented by the Es echo trace with the smallest group paths. Let Es2 represent the cloud second closest to the receiver and let Es3 represent the Es cloud furthest from the receiver location.

Table 1

Es Cloud	Max. Frequency [MHz]	Min. Group Path [km]	Max. Group Path [km]
Es1	25.7	350	600
Es2	26	900	1150
Es3	26.5	1450	1700

It is assumed in this case that hmEs for each of the patches is 90 km, again noting that Es generally occurs at altitudes between 90 and 130 km.

Secondly, the maximum and minimum elevation angles that are reflected from the Es clouds and the extent or length, L, of the Es cloud in the direction of the BSI as well as the ground distance, D, in kilometers, from the transmitter/receiver location to the Es cloud are calculated using the equations described earlier, and are presented in Table 2.

The actual location of the Es cloud in terms of geographic or geomagnetic coordinates can be readily determined.

Table 2

Es Cloud	Min. [degree]	Max. [degree]	Length of Cloud L [km]	Distance D [km]
Es1	16.2	30.2	137	149
Es2	6.5	9.5	128	438
Es3	2.3	3.9	127	715

Thirdly, the peak plasma frequency for each of the Es clouds was calculated using the equations derived earlier, along with and the maximum operating frequencies of the ray paths which were reflected from each of the Es echo traces. The peak plasma frequencies for each of the Es clouds are shown in Table 3.

Table 3

Es cloud	Max. Frequency [MHz]	foEs [MHz]
Es1	25.7	8.25
Es2	26	5.2
Es3	26.5	4.53

Then placing these parameters into the new 4L analytic ionospheric ray tracing model, the synthesized BSI in Figure 8 was produced. The Es echo traces, in this BSI, match well to the actual Es echo traces in the BSI shown in Figure 6.

There is very little curvature in the Es echo traces in Figures 6 and 7 indicating very thin Es clouds. Thus, a semi-thickness of 1 km was used in synthesizing the Es clouds.

Figure 8 shows our first attempt at modeling the traces of the BSI in Figure 6, where we have assumed blanketing patches of sporadic E.

Figure 9 shows the synthesized BSI when assuming only partial reflection from the Es clouds. This synthesized BSI matches very well to that shown in Figure 6. In this case it is assumed that all ray paths are only partially reflected from the Es clouds. The method used is designed so that there is about a 20 dB transmission loss for ray paths reflected from (hmEs – 0.2) to hmEs and a 7 dB transmission loss for ray paths reflected from the base of the Es clouds to (hmEs – 0.2). An antenna gain of 10 dB was also included in the synthesized BSI shown in Figure 9.

6.2 Example 2 Modeling and mapping the BSI in Figure 7

The BSI in Figure 7 has one well-defined Es echo trace in the 900-1900 km group range. This means that only one large Es cloud is present. The trace appears to have a stronger region of backscatter clutter at a group range of 1600 km. This stronger region is due to a dense patch of ionization within the Es cloud. This can easily be modeled using the technique used previously in modeling the BSI in Figure 6. However, in this section the Es echo trace is modeled as a single spherically stratified Es cloud.

The maximum operating frequency of the ray paths reflected from the Es cloud is 27.5 MHz. The maximum group range is approximately 1700 km. Since we do not have the received angles of arrival of these ray paths, let us assume that the lowest detectable elevation of the antenna array is . Then hmEs and foEs are determined using equations 1 and 2 and found to be 90 km and 5.0 MHz respectively.

Then placing these parameters into the new 4L analytic ray tracing model, the synthesized BSI shown in Figure 10 resulted. The shape of the Es echo trace in this synthesized BSI matches well with the actual Es echo trace in the BSI shown in Figure 7.

Applying the same conditions of partial reflection, to those that were used in modeling Figure 6, the synthesized BSI in Figure 11 was obtained, which compares reasonably well to the real BSI in Figure 7. Knowing the actual antenna gains would produce even better results.

Not only is it now possible to model the Es, it is also possible to estimate the size and distance from the transmitter/receiver location of the Es clouds.

7 SUMMARY

The new 4L ionospheric model which is simply an extension of the QPS model, in that, another spherically stratified layer is added at the base of the ionosphere to represent Es, produces realistic results.

The equations, determining the distance of the Es cloud from the transmitter/receiver location as well as the peak plasma frequency and the extent of the Es cloud, produce encouraging results. The Es echo traces on the BSI’s compared reasonably well with the synthesized BSI’s, where the synthesized BSI’s were determined using the 4L ionospheric model.

The techniques of both mapping and modeling Es, developed here, are relatively simple, require few input parameters and may be useful in the frequency management system of over-the-horizon radar facilities.

REFERENCES

Dyson, P. L., and J. A. Bennett, "A model of the electron concentration in the ionosphere and its application to oblique propagation studies", J. Atmos. Terr. Phys., 50, 251-262, 1988.

Houminer, Z., Russell, C. J., Dyson, P. L., and J. A. Bennett, "Study of sporadic-E clouds by backscatter ionograms", Ann. Geophysicae 14, 1060-1065, 1996.

Norman, R. J., Dyson, P. L., and J. A. Bennett, "Modeling and mapping sporadic E using backscatter ionograms", Report to the Technical Steering Group, Jindalee Project, Telstra Corporation pp. 21, 1998

CONTENTS
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Date last altered: 2 Nov 99