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HF Propagation tutorial

by Bob Brown, NM7M, Ph.D. from U.C.Berkeley

Critical frequency maps of the E- and F-regions (IV)

Now, in your mind's eye, think of a spherical earth and the sun situated over some point between the Tropic of Cancer and the Tropic of Capricorn. Circles on the earth's surface centered on the sub-solar point would be locations having equal solar zenith angles and thus would have the same value for foE. Of course, the highest foE value would be at the sub-solar point. At the time of the recent equinox, when the effective SSN was about 75, that would give foE as 4.1 MHz for local noon at the equator. And foE would have the same value at local noon for times of the summer and winter solstices at the Tropics of Cancer and Capricorn, respectively, if the SSN remained the same.

Side-view of the ionospheric layers boundaries. These profiles are acquired using a "digisonde" that sends short pulsed signals aloft and records their reflections. The resulting plot is called an ionogram.

If your QTH were on the sunlit hemisphere, you would be able to find foE for the ionosphere overhead by finding which circle your QTH was located on. Better yet, if you know about great-circle navigation, like some boating enthusiasts, you could calculate foE yourself. All you need to know is the date, time and your own coordinates to find the solar zenith angle with the aid of the your hand-held calculator or, better yet, the U.S. Navy Nautical Almanac computer program; the equation above tells the rest.

This last point brings to the fore that discussions making use of "Flat Earth Physics" must come to an end. To do things right, we really need to put in the curvature of the earth and the ionosphere. So from here on, we'll be treating the ionosphere as spherical and concentric with the earth. And while we're at it, we'd better put a bottom on the ionosphere, up there around 60-70 km where the D-region ionization rapidly heads toward zero. If nothing else, that is needed to find the correct angle for the effective vertical frequency calculation or the fraction of a path that goes through ionization in the D-region.

Those who know great-circle navigation can pretty well see how it would go but other geometers, skilled with a graduated compass and straight edge, can still see some important facts. For example, it is fairly easy to show that the angle of approach for RF incident on a curved ionospheric layer is smaller than for a plane layer, thus raising the effective vertical frequency and making it more likely that RF can punch through the region. It's also easy to show that the slant path through a curved ionosphere is longer than for a plane layer, thus having RF pass through more electrons along a path and increasing the amount of ionospheric absorption.  

At left the E-region critical frequency at fall equinox. The LUF can be identical or higher in frequency. At right the MUF in the same conditions. Maps created with HFProp from G4ILO.

Whether the E-region is a problem or not depends on the operating frequency. Thus, at the high end of the amateur spectrum where MUFs of the F-region are important, the operating frequency is greater than foE and it is possible for RF to go right through the layer, on to the F-region at greater heights. But that is not to say that some bending/refraction does not occur in the passage through the E-region. It is just small compared to the refraction that brings oblique signals back down to ground level.

At the low end of the amateur spectrum, the E-region is the enemy, keeping signals on paths with short hops and high absorption. It is to be avoided at all costs by DXers so their operating times are all in hours when there is full darkness along the paths of interest. So come sunset, operations begin and come sunrise, they come to an end. It's as simple as that but a lot of sleep is lost in the process.

It is the transition bands, 10-18 MHz, where both the E- and F- regions are important. Thus, operations are often arranged to coincide with dawn or dusk on the E-region but while critical frequencies of the F-region are still high. This is termed "gray line" operation and is particularly helpful to DXers interested in long-path propagation. More on that later.

Reference Notes

Numerical algorithms for critical frequencies are found in most ionospheric references that have any quantitative aspect to them. It should be recognized that while the various algorithms may appear different, they all give good representations of the experimental data.

An excellent discussion of ionospheric sounding and ionograms is given in Chapter 5 of McNamara's book, Radio Amateurs Guide to the Ionosphere. Davies' book, Ionospheric Radio, also has a good discussion of ionogram scaling and interpretation in Section 4.9.

 While I bought my copy of the International Reference Ionosphere, I remember that University of Leicester, U.K., provides an online web form of IRI that calculates the electron concentration (TEC) of the ionosphere and display results on a world map. NSSDC also provides a form, but simpler and at professional usage. The original program accessible for download from NSSDC does no more exist. It is today replaced by CODE GIM at Université de Berne.

Mapping of RF propagation

So far, we've been down in the D- and E-regions, talking about how electron collisions are responsible for absorption or attenuation of signals. Also, we got into comparing the effective vertical frequency of a signal with the critical frequency of the E-region to determine whether the signal would be blocked or go up into the F-region. We even have an algorithm for the critical frequency for the E-region, at least when the sun is up.

Now, at this point, any progress up into higher regions of the ionosphere has to wait until we settle some pressing questions: about paths from point A to B and how, when the sun is up, they are affected by ionization in the E-region. Put another way, we have to do some mapping - showing details of the path from point A to B and where it lies relative to the regions which are sunlit.

Of course, mapping brings up the question of coordinates and how RF is propagated. Coordinates are easy; you just need a good atlas. But those are not always easy to find. For example, I spent a small fortune on a new atlas from the National Geographic Society only to learn that it did not have any information on coordinates. I mean "NONE!"

I did get a Rand McNally atlas, "Today's World", as a birthday present and found that it had coordinate grids in it, 1 degree latitude by 1 degree longitude. I suppose that can be considered "Good enough for Government Work" or ionospheric propagation but I rely on Goode's World's Atlas that high schools used years ago.

As for paths, they are taken, to a first approximation in radio work, as being along great-circles on the globe. That would be good except for the fact that I pointed out earlier that RF can suffer lateral deviations, skewing one way or the other, due to gradients of the electron density across the path. But in the HF range, that skewing is relatively minor so we can, at least for a start, go with the idea of great-circles being appropriate to show where RF goes.

 In simplest terms, a great-circle is the trace on a sphere that results when it is sliced by a plane that also goes through the center of the sphere. Perhaps the best known great-circle is the terminator which divides the earth into regions which are sunlit and those which are not. So the sun illuminates half the earth and if you take the trace of that boundary, it also happens to be the intersection of a plane and the spherical earth. OK?

Now radio paths are different in that they are only parts of the great-circle on the earth, that from A to B. That is called the short-path from A to B and the spherical arc can be up to about 20,000 km in length. But how does that path appear on maps is an interesting question; it depends on the type of projection.

 Now I should say at the outset that if you look in the early part of any atlas, you will be treated to a discussion of the various types of map projections. The one we see often is the Mercator or rectangular projection. There, distortions increase with latitude and what are in reality two points, the North and South Poles, are ultimately distorted into lines at the top and bottom of the map. The division of sunlit and dark regions, given by the terminator, shows up as something resembling a sine curve, at least for times of the year away from the equinoxes. And, depending on length, a radio path will have that curved character too.

What is needed for our purposes is both a path and the terminator, for the date and time of interest. The part of the path in darkness will not suffer absorption to any extent while the part in the sunlit region is at risk, ionospherically speaking. Those who operate on the low bands, 40 meters down to 160 meters, are interested only in times when the entire path is in darkness. While sunrise/sunset tables are of some help, this is really where mapping becomes important.  

Some among the many ways to display the earth in projection : from left to right in spherical, Mercator and equi-distant projections. Documents created with DX4Win.

But, first, pause and look at sunrise/sunset tables, like the ones in the ARRL Operating Manuals. Assuming that a path falls fully within the dark hemisphere, operating times without the peril of severe absorption depend on whether the path is to the west or east of primary QTH. For a path toward DX to the west, there will be total darkness on the path after DX sunset and until the sun rises at your QTH. For DX to the east, it is just the opposite, from your sunset until the sun rises in the east. I have to say the use of tables is tedious and give not much resolution in time and locations, really a poor substitute for a mapping program. But some people still use them.

The mapping program I like best is one included in the MINIPROP PLUS propagation program. The entries are simple, date and time, and coordinates of the terminii. Usually one's coordinates are default to the calculation and the far terminus is either given by the call prefix, districts, if the country happens to cover a large area, or actual coordinates. The program then gives a Mercator map, with the terminator and sun clearly shown, and both short-and long paths. It also gives the times of sunrise and sunset at each end and it is a simple matter to find when the path would open and close as well as the number of hours of darkness.

In that projection, paths and the terminator are sine-like curves and the terminator moves east to west with time. There are other programs, like DXAID, HF-Prop or WinCAP Wizard 3, in which the position of the terminator actually advances as you watch it in real-time. Some people swear by that option but I'm not very excited by it, being more interested in what I'm hearing on the air.

Radiation pattern of a 1/2l antenna superposed on an azimuthal equidistant map. Created by LX4SKY with AC6LA's MultiProp.

There is another type of map which I find most helpful in my propagation work, the azimuthal equidistant projection like the one displayed at left, somewhat enhanced. You see that type of map in the back of the ARRL Operating Manual, with the first one centered on W1AW. In contrast to the Mercator projection, where distortions increase in going toward the poles, the azimuthal equidistant map is centered on one point and the distortions increase with distance toward the antipodal point on the opposite side of the earth. In fact, the antipodal point is distorted into a circle, in contrast to the straight lines for the geographic poles in the Mercator projection.

The advantage of the azimuthal equidistant map is that all great-circle paths going out from a QTH in the center are given by straight lines. In addition, the distance along the path is linear, out to the antipodal distance of 20,000 km. But the disadvantage of the azimuthal equidistant map is that it has to be created for each QTH.  

There is another projection in which ALL great circles are straight lines, no matter where on the map. That is the gnomonic projection, used occasionally in propagation work.

The gnomonic projection is centered on one geographic pole or the other and its disadvantage is non-linearity, with distortions which increase in going to lower latitudes and the maps usually only cover 30-45 degrees of latitude going equatorward from the poles.

Myself, I prefer the azimuthal equidistant projection in the DXAID program as it includes auroral zones based on the model used to display the NOAA auroral maps on the Internet. The NOAA auroral maps on the Internet are given in terms of auroral activity while the maps in DXAID use K-indices for the corresponding levels of magnetic activity. So in using it, one can tell whether a path is more tangential to the auroral zone, for a given level of magnetic activity, or actually passes across the polar cap. With that kind of knowledge, one understands conditions far better just on hearing a signal.

In spite of that preference for propagation purposes, I have to admit that I find the shape and motions of the terminator a bit odd in the azimuthal equidistant map projection, something that I have a hard time getting used to. In contrast to that, I have no problem with the terminator in the Mercator projection, its changes with time seem quite natural. So I have to say that each projection has its function as well as virtues and that one really needs a familiarity with both to deal with propagation problems.

Having said all of that, we have to move on, above the E-region and into ionization that's largely responsible for propagation, toward the F-region peak. That will take us right into the matter of propagation predictions by bands, from fundamentals as well as computer programs.

Of course, I've already made the point that a full-service propagation program would include noise, say as signal/noise ratios. Now, I think you can understand it when I say a person interested in propagation cannot get along without a good mapping program. In the ideal case, both the forecasting and mapping programs would be on the same computer disk. Failing that, at least both ought to be readily available to a DXer.  

Reference Notes

The MINIPROP PLUS program by W6EL has been available for some years as a DOS program and is now available for Windows 16 and 32 bit under the name W6ELProp. The Mercator projection maps in this program are extremely agile and fast, making it easy to make rapid comparisons of paths in time. Today, there are however programs much more accurate on the market.

DXAID for example has excellent graphics, particularly  the azimuthal equidistant mapping version with auroral zones included. It also has a propagation module that is based on the F-layer algorithm due to Raymond Fricker of the BBC. However, like always in computing, today the auroral oval calculated by DXAID is outmoded and it can be advantageously replaced by the one provided by DXAtlas, one of the seldom application that matches exactly the auroral oval prediction calculated by SEC/NOAA.

MUF map calculated by the VOACAP engine provided with GeoAlert-Extreme from Kangaroo Tabor Software.

All these programs and algorithms are of course regularly improved, making them more comparable to predictions that would be obtained from the International Reference Ionosphere. Earlier tests for example made in the '80s, show that Fricker's work, in MINIPROP and other programs, comes closer to mimicing propagation predictions by IONCAP than other programs available at the time. Today VOACAP predictions are still better, and some applications even rely on real-time ionospheric soundings.

Note by LX4SKY. Today, among the best (I mean accurate and flexible) propagation prediction programs available name WinCAP Wizard 3, GeoAlert-Extreme Wizard and DXAtlas, all three VOACAP-based running under Windows 32-bit and providing additional features (e.g. beacon monitoring, auroral oval, long-term statistical data, etc).

The ultimate test of paths is found in ray-tracing, and the PropLab Pro program from Solar Terrestrial Dispatch is the only one that is presently available. The program not only traces propagation paths but also provides details on the distribution of electrons, globally or vertically, and gives a foundation for all ionospheric work. Myself, I would be absolutely LOST without PropLab Pro.

Ionization of the E and F regions

Now we have to get down to cases, dealing with the ionosphere above the D- and E-regions. But the transition is a smooth one, going from a well-mixed region largely made up of molecules and molecular ions to a region where collisions are less frequent, atoms become more abundant and constituents start to be sorted out by their chemical weight. We'll never really get up to the case where hydrogen is the dominant constituent but that is the idea, gravitational separation, in the upper reaches above us.

The ionization in the E-region is under solar control and was shown by the critical frequency depending on solar zenith angle (Z). Now, in going higher, toward the F-region peak, solar control does continue, up to the F1-region at about 200 km altitude. So the critical frequency foF1 during daytime is expressed similarly:

foF1 (MHz) = [4.3 + 0.01 x SSN].[cos(Z)]0.2

Peak and valley in the E-region.

As shown earlier, the electron density in the F1 region is greater than the E-region and the same is true of the critical frequency. And constant frequency contours will be centered about the sub-solar point. But at large zenith angles, the algorithm is less reliable and at night, the ionization in the F1-region decreases to low values. It does not go to down to a vanishing level but, instead, there is a "valley" in the electron density above the night-time E-region, as shown at right.

The origin of the valley is complex, related to the change from molecular ions of oxygen and nitrogen down low to the appearance of atomic oxygen and the ion-atom interchange above 90 km that produces the molecular ion of nitric oxice (NO). Again, the ionization in darkness has the same origin as the E-region.

Whether day or night, the ionization in the D-region is just not great enough to significantly bend or refract HF signals. On the other hand, during the day, ionization in the E-region can cut off signals from reaching the F-region. In short, signals like that go off on low-angle, shorter E-hops during the day.

At night, HF signals will just pass through the weak ionization that remains in the E-region, shown above, just as if it were not there. That's another way of saying that the night-time value for foE is very low, even less than 0.5 MHz, and the region is no impediment to the advance of HF signals. On the other hand, that's NOT the case for signals in the 160 meter band. That will be VERY interesting but let's do some other things first.

Variation of the plasma frequency with the sunspot number.

For example, let's look at how critical frequencies vary with sunspot number so we can put effects of the various ionospheric regions in perspective. For one thing, with the different heights for the regions, E-region around 100 km while the F1-region is around 200 km and the F2-peak up around 300 km, the frequency data will show how signals penetrate into the ionization overhead. That has a bearing on the lengths of the hops that result or, in more meaningful terms, on our ability to work DX on the various bands. So let's look at a crude representation of some mid-latitude critical frequency data for daytime conditions.

This graphic requires that you use your mind's eye to make connections between data points but the results is pretty clear: the lower E- and F1-regions which are under solar control show only modest changes in critical frequency or electron density as the sunspot number increases with solar activity.

The F-region, on the other hand, shows large changes in critical frequency and is not under solar control, without any simple algorithm involving the solar zenith angle like the E- and F1-regions.

 The best way to illustrate the difference between solar control of the E-region and the situation with the F-region is through the use of maps showing the iso-frequency contours for the two regions.

E-region iso-frequency contours at fall equinox at 0600 UTC.

So the map displayed at right and generated with HFProp illustrates the situation for 0600 UTC on the fall equinox. Of course, the sun is on the equator and at this time, it is located at 90° E longitude. The iso-frequency contours are centered on the sub-solar point (but distorted by the Mercator projection). 

Accordingly, the left side of the figure is in darkness, and the right side is in the sunlit portion of the earth, and the terminator, the grayline, consists of two straight lines at 0° E and 180° E longitude.

As noted above, the situation is similar for the F1-region (or F2) except that the critical frequencies are somewhat higher as shows very well the map displayed below right. 

But the idea of solar control is clear from the E map at right; the ionization is where the sun shines and essentially nothing in darkness!

Now as far as the F-region is concerned, its peak is up around the 300 km level and depends on the season, time of day and sunspot number. But at those heights, the electron collision frequency is low and the recombination rate of electrons with the positive ions (O2+ and NO+) is quite low. So as shows very well the maps displayed below, ionization continues to exist after sunset; the geomagnetic control of the ionosphere is shown by the fact that the F-region map for critical frequency foF2 is organized better by geomagnetic coordinates rather than the usual geographical coordinates.  

The map below left conveys how the shape of geomagnetic dip equator compares with the iso-frequency contour of the F2-region at low latitudes displayed at right. The sunlit and dark hemispheres are the same as before but it is seen that F-region continues after sunset, particularly at low latitudes and along the direction of the geomagnetic dip equator.  

At lef dip of the geomagnetic equator at fall equinox at 0600 UTC predicted by DXAtlas. At right the F2-critical frequency in the same conditions. To compare with the E-region critical frequency (cf above right). Note than on the side plunge into darkness (left half) the propagation is still open for DX activities, mainly on low bands. The propagation is controlled (in quiet time) by the horizontal component of the geomagnetic field and in a much lesser extent by the sun ionization.

Such critical frequency maps demonstrate that the ionosphere is controlled by the geomagnetic field at great heights but down lower, the distribution of ionization is under solar control. The transition occurs in going up through the F1-region. As for DX propagation, it is controlled in quiet times by the geomagnetic field but it doesn't take much imagination to think that any sort of disturbance of the field would upset DXing. More later!

Reference Notes

Critical frequency maps of the E- and F-regions can be seen in my book The Little Pistol's Guide to HF Propagation. In addition, they will be found in books Radio Amateurs Guide to the Ionosphere by McNamara, and Ionospheric Radio (IEE Electromagnetic Waves Series, Vol. 31). by K.Davies.

Excellent critical frequency maps are obtained from the PropLab Pro program. In fact, that program gives a full complement of ionospheric maps and in several projections.

Next chapter

Down-Sizing of the Ionosphere

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