Friday, November 24, 2023

Mediumwave Skywave Prediction #6 - Wrapping Things Up

Let's close up by defining a few of the terms used in the formulas from the last post, and finish by talking a bit about diurnal and seasonal effects.


Polarization coupling loss, sometimes depicted as Lp, is the fraction of incident power lost on entry into the ionosphere. Further polarization coupling loss occurs when the wave which emerges from the ionosphere induces a voltage in the receiving antenna. Polarization coupling loss depends to some extent on frequency and angle of incidence at the ionosphere. Polarization coupling losses are low in higher latitudes because the Earth's magnetic field is almost vertical. At the magnetic equator, however, the Earth's field is horizontal and polarization coupling losses on east-west paths are large.

Polarization coupling loss at MF is an important factor in skywave propagation. It arises because the Earth's natural gyromagnetic frequency lies within the frequency band being considered. The gyromagnetic frequency of the Earth's ionosphere varies between 800 kHz in the equatorial regions and 1600 kHz near the magnetic poles. When a linearly polarized mediumwave frequency radio wave enters the ionosphere, it gets split into two waves known as ordinary and extraordinary. At the gyromagnetic frequency the extraordinary wave is so greatly attenuated that it makes a negligible contribution to the received signal. As a consequence, the extraordinary wave can be disregarded within the mediumwave band. The propagation is therefore by the ordinary wave.

To explain further, conventional antennas at mediumwave radiate vertically-polarized waves. At MF, the wave which is accepted by the ionosphere and which will propagate back to Earth usually differs in polarization somewhat - hence the ionosphere may not be excited efficiently by the incident wave. We have decreased coupling efficiency, or polarization coupling loss. The wave which subsequently emerges from the ionosphere is in general elliptically-polarized and in-turn may not excite the receiving antenna efficiently because antennas near the ground are most sensitive to vertical polarization, resulting in additional loss.


For long distance paths (1000 to 6000 km or greater), when the path is over the sea and at least one end of the link is located on or near the sea coast, the phenomenon of sea gain can add from 3 to 10 dB to the predicted field strength. 

Gains peak at the usual single, double, and triple hop distances of 2000 km (8 dB), 4000 km (10 dB), and 6000 km (10 dB). Only about 3 dB is gained at the 1000 km distance. A dip in gain (to about 5 dB) occurs at about the 2500 and 5000 km distances.

A knowledge of the land-sea boundary information is necessary to assess the sea gain phenomena. Generally, in the skywave calculation, the sea gain correction is normally set to 0 dB without this knowledge. To take any advantage of sea gain, one of the terminals (transmitter or receiver) must be within about 10 km from the sea coast. Even at 10 km inland, the penalty is about -4 dB. At 4 km, about -2 dB. At 3 km, only about a -1 dB penalty.


Solar Cycle 25 is well on its way now, having started its general upward trend in sunspot count by late 2020. The daily sunspot count for August 30, 2023, for example, was 104.

Do sunspots effect nighttime skywave propagation at the medium waves? Yes they do, at a small but noticeable level. Here are the details.

Concerning medium wave, sunspots and the increasing solar flux are relevant to skywave field strength and are accounted for in most modern (nighttime) skywave prediction methods. In general, mediumwave skywave field strength is slightly better during low or zero sunspot periods, at the bottom of the solar cycle. The calculation of the additional path loss in dB is dependent on location.

Greater consideration is given to paths within North America and Europe (nearer to the north geomagnetic pole), and Australia (nearer to the south geomagnetic pole). The North American loss factor is 4 times that of Europe and Australia, and rises for all as we get to the higher latitudes. Longer paths, those between North America and Europe are usually interpolated.

The ITU skywave prediction method is one such method which incorporates these added loss factors due to sunspots and solar flux. Figures below have been extracted from that prediction method.

Below are increased single hop skywave loss factors in dB as the sunspot count goes up.

Paths within North America:

Sunspot count = 0 a net added loss of zero
Sunspot count = 7 an additional loss of 0.28 dB
Sunspot count = 25 an additional loss of 1 dB
Sunspot count = 50 an additional loss of 2 dB
Sunspot count = 100 an additional loss of 4 dB

Paths within Europe:

Sunspot count = 0 a net added loss of zero
Sunspot count = 7 an additional loss of 0.07 dB
Sunspot count = 25 an additional loss of 0.25 dB
Sunspot count = 50 an additional loss of 0.5 dB
Sunspot count = 100 an additional loss of 1 dB

Paths between North America and Europe:

Sunspot count = 0 a net added loss of zero
Sunspot count = 7 an additional loss of 0.175 dB
Sunspot count = 25 an additional loss of 0.625 dB
Sunspot count = 50 an additional loss of 1.25 dB
Sunspot count = 100 an additional loss of 2.5 dB

Admittedly, these extra losses are small but important enough that they are factored in for skywave calculations. Be aware that 3 or 4 dB can make a difference logging a station or not. A single S-unit is 6 dB.


The final determination which really completes our skywave field strength calculation must include three more tweaks:

1. Diurnal hourly losses/gains
2. Sunrise and sunset enhancements
3. Seasonally-driven losses/gains

The D-layer of the ionosphere is characterized as having a strong dependence on frequency, but this is present only during the daytime. The E-layer is the dominant contributor to LF and MF propagation at night and is only mildly dependent on frequency, so the effects of frequency of this layer can be neglected for most practical purposes.

Although daytime ionospheric propagation is relatively unimportant, it cannot be entirely disregarded at the upper end of the band, since ionospheric attenuation decreases with the square of the frequency. Nor can it be entirely disregarded at the lower end of the band, where partial reflection from the lower edge of the D region may occur, especially in winter at temperate latitudes.

The critical frequency of the normal E layer is about 1500 kHz at sunset, but it then falls rapidly as a result of electron-ion recombination and will assume a value of about 500 kHz late at night. Skywaves may be reflected from the E layer, or they may penetrate the E layer and be reflected from the F layer, depending on the frequency, path length, and time of night. Simultaneous reflection by both layers is also possible in some circumstances. 

Upper MW band diurnal (or daily) morning enhancement can show effect as late as 3 hours after sunrise. The start of the pre-sunset afternoon enhancement is delayed a little to about 2 hours before sunset, gradually building to sunset. The lower part of the band shows little of this effect, morning or night.

The diurnal enhancement described in the last paragraph is not to be confused with the short sunrise and sunset enhancements on extreme DX due to what is called "greyline effect", the signal traveling along, or partly along, the sunrise/sunset terminator.

Skywave propagation does indeed exist during the daytime hours, and its strength varies greatly, seasonally.

Daytime, noon-hour skywave is generally pegged at approximately 30 dB lower than the nighttime field-strength prediction, and this will vary considerably seasonally. An ionospheric transition period occurs immediately surrounding sunset and lasts till approximately four hours after sunset, and another occurs during the period from 2 hours before sunrise until sunrise where the field strength goes through this 30 dB change with a very steep slope. The shapes of the curves are not symmetrical for the transition from day-to-night and night-to-day.


In this series I have attempted to present to you first a little history skywave propagation analysis, who developed the formulas and how they are geographically dependent, and the formulas themselves. I hope it has brought some perspective to the process and you have enjoyed it.

Monday, September 11, 2023

Mediumwave Skywave Prediction #5 - Dissecting The Formulas

We'll get to the actual skywave prediction formulas shortly, but first let's talk about how to calculate the geomagnetic midpoint of our signal path. To get this, we'll need the latitude and longitude of both the transmitter and receiver sites. We'll also need the latitude and longitude of geomagnetic north, which moves by small increments each year. A nice chart can be found at:

The following geomagnetic north pole coordinates are accurate for 2023:

    dipoleN = 80.8° latitude (actual)
    dipoleW = 72.7° longitude (actual) -use a positive number in the final mid-point formula

Note: dipoleN and dipoleW are the geomagnetic north pole, NOT the magnetic north pole. There is a difference. To reiterate from the previous post, 'geomagnetic poles (dipole poles) are the intersections of the Earth's surface and the axis of a bar magnet hypothetically placed at the center the Earth by which we approximate the geomagnetic field. They differ greatly from the magnetic poles, which are the points at which magnetic needles become vertical. The magnetic poles are what has been "wandering", a subject in the news lately, but they drag the geomagnetic poles with them too, albeit at a lesser rate.'

First we'll calculate the actual geographic mid-point latitude and longitude between transmitter and receiver. The Movable-Type scripts website has our formula to do that:

Many websites have geographic mid-point calculators as well. Those familiar with Javascript can use the formula below or convert it to a different language if you wish to do the calculation yourself.

lat1 = transmitter latitude in degrees
lon1 = transmitter longitude in degrees
lat2 = receiver latitude in degrees
lon2 = receiver longitude in degrees

double dLon = Math.toRadians(lon2 - lon1);

    //convert to radians
    lat1 = Math.toRadians(lat1);
    lat2 = Math.toRadians(lat2);
    lon1 = Math.toRadians(lon1);

    double Bx = Math.cos(lat2) * Math.cos(dLon);
    double By = Math.cos(lat2) * Math.sin(dLon);
    double lat3 = Math.atan2(Math.sin(lat1) + Math.sin(lat2), Math.sqrt((Math.cos(lat1) + Bx) * (Math.cos(lat1) + Bx) + By * By));
    double lon3 = lon1 + Math.atan2(By, Math.cos(lat1) + Bx);

    //answer in degrees
    mid_lat = Math.toDegrees(lat3);
    mid_lon = Math.toDegrees(lon3);

mid_lat and mid_lon is the actual geographic mid-point of our path.

Now, we'll use a separate formula to translate the actual mid-point latitude-longitude to geomagnetic latitude:

    ThetaM(radians) = 
        Asin(Sin(mid_lat) * Sin(dipoleN) + Cos(mid_lat) * Cos(dipoleN) * Cos(dipoleW + mid_lon))

ThetaM will be in radians and must be converted to degrees. To do so:

    ThetaM(degrees) = (ThetaM(radians) * 180) / Pi

ThetaM is the geomagnetic latitude in degrees.

Let's dive right into the skywave prediction formulas. We know slant distance, geomagnetic latitude of the path mid-point, and we have everything we need to calculate Kr, the aggregated ionospheric losses. Take note that the skywave prediction normally is the prediction for the local midnight hour, equidistant between sunset and sunrise, commonly referred to as SS+6, or sunset + 6 hours.


The Wang method is the only method which offers good to excellent results for short and long paths alike at all frequencies in the LF/MF bands, at all latitudes, and in all regions. It has been demonstrated that the Wang method is the only method that can be considered a true worldwide method.

The Wang expression for field strength is:

Note: FS(dBu), is also known as dBµV/m.Where: FS(dBu) is the field strength in dBµV/m, V is the transmitter cymomotive force above the reference 300 mV in dB (better known as our effective radiated power (ERP) referenced to 1 KW in the direction of interest). ThetaM is the mid-point transmitter and receiver geomagnetic latitude, Dslant is the slant distance in km. Kr, or generalized ionospheric losses, are described below.

In the Wang method, the 107 (dB) factor is used for most of the world. New Zealand and Australia use 110 dB, giving that part of the world a 3 dB field strength improvement (half an S-unit).

To convert FS(dBu) back to millivolts per meter: mV/m = 10 ^ (FS(dBu) / 20) / 1000

The generalized ionospheric losses are found in Wang's Kr factor. Both Wang and the FCC method calculate Kr in this manner:

Kr is the loss factor in dB, to include ionospheric absorption, focusing and terminal losses, losses between hops, geomagnetic latitude influence, and basic polarization coupling loss.

Where: ThetaM is the geomagnetic latitude defined previously. Dslant, the slant distance, will modify Kr accordingly.

Wang recommends that the geomagnetic mid-point latitude, ThetaM, be between -60 (south) and +60 degrees (north). When compared to the ITU expression, Wang's expression is symmetrical about zero degrees latitude and is not dependent on frequency.

Let's do a Kr loss example for a 1500 km slant path and see what our ionospheric losses are.

Here are the results for a single hop, 1500 kilometer (932 miles) slant distance for various mid-point locations. Using this Wang formula, I've prepared a chart showing the additional losses, in dB, caused by geomagnetic latitude influence.

Basic Loss  Deviation  Geo-Lat Mid-Point (actual location of)
---------- ----------- ------- ------------------------------
7.854 dB      0          9.19   0°N, over the equator
8.347 dB     +0.493dB   18.15  10°N, over Venezuela
10.637 dB    +2.783dB   34.86  25°N, over south Florida
11.778 dB    +3.924dB   39.37  30°N, over north Florida
14.553 dB    +6.669dB   46.76  38°N, over Richmond VA
17.889 dB   +10.035dB   52.36  43°N, over Rochester NY
18.767 dB   +10.913dB   53.50  45°N, over Minneapolis MN
21.233 dB   +13.379dB   56.21  48°N, over Grand Forks ND

Basic Loss = the basic loss on this 1500 km path. The first entry has its mid-point (reflection point) over the equator.
Deviation = additional loss incurred as latitudes increase using the basic equator loss as the base.
Geo-Lat = the adjusted geomagnetic latitude of the reflection mid-point.
Mid-Point = the actual geographic location of the reflection midpoint.

As you can see, we have lost over 13 dB in field strength when the reflection point is at 48° actual latitude!

Here is an example of how geomagnetic positioning of the signal path affects the final field strength result. Reception of KFAB (1110 kHz), Omaha, Nebraska (41.23°N, 96.0°W) here in Rochester, NY, places the mid-point of our ionospheric reflection at a geomagnetic latitude of 51.355 degrees. The slant distance is 1548 km. An overall Kr loss of 17.45 dB gives an additional geomagnetic position penalty of some extra 9.596 dB over tropical paths!

Now, let's calculate an expected skywave field strength value for 50 KW KFAB-1110 here in Rochester, NY. From above, we already know our slant distance is 1548 km. Our Kr loss factor from the example above is 17.45 dB.

FS(dBu) = V(-18.739) + 107 - 20 * Log10(1548) - 17.45

FS(dBu) = 7.01

Converting to millivolts per meter:

mV/m = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m, or:

.00224 = 10 ^ (7.01 / 20) / 1000

.00224 mV/m is a weak signal indeed.

Why such a weak signal from a 50 KW powerhouse station at only ~1500 km? We are placed perfectly in KFAB's deep cardioid pattern notch at 76 degrees azimuth and a 4 degree takeoff angle. Facing us at those angles is a theoretical and nearly-microscopic 12.72 watts ERP. This is a primary lesson we learn from tower array pattern analysis, both skywave and groundwave. One will naturally think, "Well, it's a 50 KW station, and only a mere 960 miles distant. I should be getting a pretty good signal". Not necessarily so. If you are in a deep notch of a pattern, you may only be "seeing" a few watts facing you.

Take a look at the graphic below. You will see the deep cardioid notch of KFAB's nighttime pattern. Stations to the east suffer a great signal loss.

KFAB Nighttime Pattern. Click for larger image.

Where did the V(-18.739) figure come from, you ask? That is KFAB's facing 12.72 watts aimed at us, referenced to 1 KW, in dBW. It is 18.739 dB down from 1 KW. How did we get this and the 12.72 watts figure? The FCC has some rather serious formulas which will calculate power and mV/m levels delivered at any azimuth and elevation angle for any tower array. The FCC website for the station also provides a basic chart for each compass degree around the tower array, listing mV/m levels. This is the easiest to use, although it is calculated for 0 degrees takeoff elevation.


The FCC method has close resemblance to the Wang method. The FCC expression for field strength is:

Note: FS(dBu), is also known as dBµV/m (normalized to 100 mV/m, in dBµV/m per 100 mV/m).

Where: FS(dBu) is the field strength in dBµV/m, ThetaM is the mid-point transmitter and receiver geomagnetic latitude, Dslant is the slant distance in km. Kr, or generalized ionospheric losses, are described below.

The FCC formula would appear to not include any system gain, referred previously as "transmitter cymomotive force above the reference 300 mV in dB". The field strength predicted is normalized to 100 mV/m (in dBµV/m per 100 mV/m). We must convert this back to the actual mV/m value by multiplying by the number of 100 mV/m "portions" we have in the total mV/m measurement at 1 km. The total mV/m measurement is calculated and published by the FCC for each compass degree. This figure also contains our tower array gain - our effective radiated power (ERP) referenced to 1 KW from a quarterwave monopole.

Converting to millivolts per meter, again:

mV100 = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m

mV/m = mV100 * (measured_mVm@1km / 100) ...corrected to actual mV/m 

The FCC formula uses Wang's identical Kr factor. The generalized ionospheric losses are again found in it:

Refer to the previous discussion of Kr, above, in the Wang equation. Their usage is identical.

Wang again recommends that the geomagnetic mid-point latitude, ThetaM, be between -60 (south) and +60 degrees (north). It is not dependent on frequency.


The ITU expression for field strength is:

Note: FS(dBu), is also known as dBµV/m.

Where: FS(dBu) is the field strength in dBµV/m, V is the transmitter cymomotive force above (or below) the reference 300 mV in dB, Gs is the sea gain correction in dB, Lp is the excess polarization coupling loss in dB (defined graphically in ITU Recommendation 435-7), ThetaM is the mid-point transmitter and receiver geomagnetic latitude, Dslant is the slant distance in km. Kr, or generalized ionospheric losses, are described below.

Converting to millivolts per meter, again:

mV/m = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m

The ITU formula applies the basic path loss elements, the slant distance and the mid-point geomagnetic latitude influence. It also attempts to quantify some of the additional ionospheric losses I alluded to in an earlier post:

1. Sea gains (separately, as Gs)
2. Excess polarization coupling losses (separately, as Lp)
3. Sunspot influence (specified within Kr, as R)
4. Regional loss due to solar activity (calculated within Kr, as bsa * R)

The generalized ionospheric losses are found in the ITU's Kr factor:

Kr is the loss factor in dB, to include ionospheric absorption, focusing and terminal losses, and losses between hops, geomagnetic latitude factor, and basic polarization coupling loss. Unlike the Wang and FCC formulas, the ITU formula incorporates a sunspot factor and a frequency factor as well.

Where: f is the frequency in kHz, and ThetaM is the geomagnetic latitude defined previously. ThetaM must not exceed 60 degrees north or -60 degrees south. For paths shorter than 3000 km, the ITU suggests simply using the geographic mid-point between transmitter and receiver. Note: this, on average, skews results about 6 dB higher for North America.

Where: R is the twelve-month smoothed international relative sunspot number, bsa is the regional solar activity factor (bsa=0 for LF band; bsa=4 for MF band for North American paths, 1 for Europe and Australia, and 0 elsewhere). For paths where the terminals are in different regions we use the average value of bsa, for example: Europe to the USA, 2.5.

Note that we have a frequency correction, a geomagnetic latitude (ThetaM) correction, a regional correction in bsa (North America has the highest absorption), and a sunspot count correction.

The sharp analyst will notice that the ITU's frequency correction results in greater loss at higher frequencies, something perhaps theoretically sound, but not observed in North America (shown by measurements). The ITU suggests that for North America, a fixed frequency of 1000 kHz should be used.

Sea gain (Gs) is included in the ITU formula, but is usually set to zero and not accounted for since the transmitting or receiving station must be very close to a coastal point, generally within ten kilometers, and having a path length of thousands of kilometers. Lp, excess polarization coupling loss, is also included. This is an attempt to compensate for Lp differences in the generalized Kr part of the formula. We generally leave this at zero.


The modern day formula for the Cairo curve, adapted to Region 2, is presented for informational purposes. The resultant field strength should be further modified by subtracting ionospheric absorption losses (Kr), and adding any antenna gain.

The Cairo Curve, Revised for North America, Region 2

Where D is the overland great circle distance in kilometers between transmitter and receiver.

Again, we find our result in dBu per 100 mV/m (NTIA Report 99-368). It must be converted back to actual mV/m, as does the FCC formula.

mV100 = 10 ^ (FS(dBu) / 20) / 1000 ...convert dBu back to mV/m

mV/m = mV100 * (measured_mVm@1km / 100) ...corrected to actual mV/m

In the final part of this series on skywave prediction we will wrap up by discussing polarization coupling loss, sea gain, solar cycle losses, and diurnal and seasonal effects on mediumwave propagation.

Saturday, August 12, 2023

AM Radio In South America

I've been working on compiling a list of world AM broadcast radio (530-1700 kHz) still on the air. South America is essentially complete. The goal is a worldwide list of stations and locations.

Here is what is left of AM broadcast radio in South America as of this date, August 2023.

Click image for the larger view.

AM Broadcast Radio, 2023

Saturday, July 22, 2023

Mediumwave Skywave Prediction #4 - Slant Distance & Geomagnetic Latitude

We will define two important concepts in this article: Slant Distance and Geomagnetic Latitude, both critical to determining the base path loss factor. This is our first step in solving the mediumwave skywave prediction puzzle.

To review, here are our main formulas again.

The Wang Method:

The FCC Method:

The ITU Method:


The skywave field strength calculation process must compute a path loss factor between transmitter and receiver. Several parameters come into play here. The obvious one is the distance between transmitter and receiver. Greater distance incurs greater loss, plainly evident to the early experimenters. For many years the great circle overland distance was used in all formulas. It was eventually found that the actual distance traveled by the signal, the slant distance, was a better fit and produced better figures, as the signal must travel from transmitter to the reflection point high up in the ionosphere, then back down to the receiver. This, the preferred distance, is referred to as the Dslant distance in the formulas.

Slant distance is easily calculated for any signal path. From the FCC document 47 CFR 73.190:

' D is the overland great circle distance from transmitter to receiver.
' hr is the ionospheric layer height in kilometers. For mediumwave, usually set to 100.

Let's do a few examples. We will see that the higher the reflective layer height, the greater the slant distance. For added interest I've calculated TA, shown below, which is the signal takeoff angle from the antenna.

At 275 km overland distance, slant distance can deviate greatly. Takeoff angle is also large:

' 275 km distant station and a 100 km layer height, Dslant = ~340 km, TA=35°
' 275 km distant station and a 120 km layer height, Dslant = ~365 km, TA=40°
' 275 km distant station and a 150 km layer height, Dslant = ~407 km, TA=46°

At 1000 km overland distance, slant distance is only just a little greater. Takeoff angle has come way down:

' 1000 km distant station and a 100 km layer height, Dslant = ~1019 km, TA=9°
' 1000 km distant station and a 120 km layer height, Dslant = ~1028 km, TA=11°
' 1000 km distant station and a 150 km layer height, Dslant = ~1044 km, TA=14°

And slant distance is basically negligible at 2000 km. Takeoff angle is right at the horizon:

' 2000 km distant station and a 100 km layer height, Dslant = ~2009 km, TA=1°
' 2000 km distant station and a 120 km layer height, Dslant = ~2014 km, TA=2°
' 2000 km distant station and a 150 km layer height, Dslant = ~2022 km, TA=4°

Out past about 900 km or so, the slant distance is very close to the actual overland distance. As we get closer in from 900 km, the difference starts to accelerate. The Dslant distance value is dependent on the E-layer height and Dslant (in km) is always higher than the exact overland distance value. Slant distance is now commonly used in all modern skywave formulas.

This slant distance is used in two places in the formulas. It becomes part of the basic path loss factor, and part of the ionospheric loss adjustment (the Kr term). In the basic calculation, the larger the slant distance, the greater the basic path loss factor. Secondly, and since the ionospheric losses are subtracted from the basic path loss, the larger the slant distance, the greater the effect it has on ionospheric losses, Kr.

Ionospheric losses, Kr, will be explained in further detail in the next article.

Each formula uses the inverse square law in the basic path loss calculation. This will be in dB. This simply says that for every doubling of distance, the strength is one-fourth of what it was. For example, the strength at 1000 km is one-fourth the strength found at 500 km. This is realized through the formula snippet 20 * Log10(Dslant). 20x gives us the value needed in dBµV/m to subtract from our start value since we are dealing with field strength in voltage units.

Here are some path loss examples for a layer height of 100 km:

Dslant = 250 km = 48 dB (190 km overland distance)
Dslant = 500 km = 54 dB (458 km overland distance)
Dslant = 1000 km = 60 dB (980 km overland distance)
Dslant = 2000 km = 66 dB (1990 km overland distance)

Each doubling of distance increases the loss by another 6 dB, also one S-unit. The Dslant contribution to the basic path loss is subtracted from our start value of 106.6 dB (ITU), (107 dB, Wang), (97.5 dB, FCC).

In the ITU formula (- 0.001 * Kr * Dslant), Dslant again modifies the ionospheric losses, Kr. So, as you can see, the greater the slant distance, the greater its contribution to the ionospheric losses too.

Wang handles the ionospheric losses, Kr, a little differently (- Kr * Sqrt(Dslant / 1000). Dslant again modifies Kr. We can see again the greater the slant distance, the greater its contribution to ionospheric losses.

Wang's Kr value modification by Dslant is used the same way in the FCC formula.


Using the Dslant value has minimal effect on far stations, those out beyond 900 km or so, where Dslant is roughly equal to the exact distance value. An increasingly greater effect is evident on those stations as we narrow our distance to 250 km, and less.

A continuing problem still exists with accuracy for close in stations. Years ago, Wang suggested those stations less than 250 km distant should use a fixed E-layer height of 220 km, increasing the resultant Dslant value even more. That fixes the lowest slant distance at 506 km for any station closer than 250 km to the receiver. Consequently, 250 km becomes a hard "wall" which would make a station's calculated field strength at 251 km much stronger than one at 249 km. Nature undoubtedly has a proportional transition which must be accommodated.

It would be obvious that increasing the layer height also increases the transmitter signal's takeoff angle, generally resulting in a weaker facing signal to the receiver, resulting in the calculation further lowering the received field strength. By design, this was Wang's intent in raising the layer height to 220 km for stations closer than 250 km distance. It was not enough.


The remaining paragraphs in this, the Slant Distance section, are ideas outside of the current formulas, and are food for thought. In my program which creates the mediumwave pattern map set, RDMW (Radio Data MW), I wrote a sandbox mode which allows me to experiment with different skywave propagation ideas. These include varying layer heights, varying attenuation factors, seasonal effects, and sunrise/sunset enhancements. Tweaks can be modified by frequency also. It has revealed some interesting facts.

Part of the problem with the current worldwide formula set is that, given a database of stations like the FCC mediumwave database, it will produce an acceptable list of varying field strengths, but the field strength order, channel by channel, isn't always what is heard during actual band scanning. I tested this on all three formulas and found this curious.

Material written is very explicit indicating that the E-layer is well-defined and exists between about 100 km and 115 km. Mediumwave skywave is considered (by formula) to be reflected or refracted off the E-layer at 100 km exclusively. I do not believe this to be the case, and it is borne out by the inaccuracies in the formulas for close in stations, those about 900 km and closer.

Modifying the layer height has been experimented with extensively, generally by raising it incrementally as we get closer and closer to the transmitter, starting at about 900 km and modifying by the inverse cosine of the distance. Results were better, bringing field strengths more in line. Still, the resultant skywave calculations using this method did not quite match signal strengths by band scanning. Actual signals are always less for close in stations, except at the sunrise/sunset enhancement periods where they exhibit a temporary strengthening.

A gentle transition of E-layer reflectivity height from 100 km to 280 km (acknowledged, 280 km is outside of the E-layer) is suggested, starting at 100 km with station distances about 900 km and raising it as we get closer to zero distance using an inverted cosine method. However, a maximum layer height of 280 km does not fully correct the field strength inaccuracy. We must add in an additional decay factor as the station distance is decreased. I would advise against increasing maximum layer height beyond 280 km as I think it presents an increasingly inaccurate picture of conditions.

An inverted waveguide?

The Earth's natural waveguide effect is well known for extremely low frequencies (ELF), those below 3 kHz. What if, instead, we treat the ionosphere from 100 to 140 km as a sort of mediumwave inverted waveguide? That is, make our reflecting layer heights dynamic - the lower frequencies (starting at 530 kHz) reflecting at the lowest layer height, and higher frequencies (ending at 1700 kHz) reflecting at highest layer height? We could set a layer height range of 100 to 140 km to fully contain all reflections within the banded E-layer. Or, we might even experiment with a range of 100 to 300 km to allow higher frequency reflections at the F-layer. The first scenario was experimented with and seems most promising. It delivers surprisingly good field strength results verified by what is actually heard by band scanning.

Skip distance.

Many of you, when studying radio propagation, will see charts or graphics showing a single hop track up to the ionosphere and reflected back to Earth. Sometimes beneath it are printed the words, "Skip Distance". They are referring to a zone of dead signal, that is, an area where the signal is "skipping overhead", and not receivable in the skip zone. Take care to note this applies almost exclusively to shortwave frequencies, that of 3 MHz and above, and hardly at all to mediumwave. Mediumwave tends to "fill in" in the skip zone, at varying levels. Nighttime skip reflections are detectable and receivable at very short distances, even under 60 km.


For the curious, those wanting to calculate signal takeoff angle from a transmitter, this simple program will calculate it. Choose your layer height (hr) and your distance from receiver to transmitter (km).

Pi = 3.14159
hr = 100  'layer height, km
km = 900  'great circle distance, km
D = km / 40075 * 2 * Pi  '40075=circumference of earth, km
E = 6378 * Sin(D / 2)  '6378=radius of earth, km
F = E / Tan(Pi / 2 - D / 4)
G = Atn(F / E + hr / E) - D / 2
TA = G / Pi * 180  'TA in degrees

Takeoff angle is important. The ITU and Wang formulas include a basic gain/loss correction in dB referenced to 1 KW effective radiated power, ERP (the V cymomotive force parameter), but don't allude to any differences due to signal takeoff angle. The FCC formula accounts for the gain/loss correction in a different way, by normalizing its returned field strength value to 100 mV/m at 1 KW, still not alluding to any differences due to signal takeoff angle.

I'll show you an example of how ignoring takeoff angle can produce highly inaccurate results. We'll look at WBVP-1230 (1 KW) in Beaver Falls, PA. WBVP uses a single monopole tower at 0.64 wavelength tall. Their skywave signal takeoff angle from their antenna to Rochester, NY is 29.2 degrees, based on an E-layer height of 100 km, a substantial angle. If we ignore takeoff angle and assume to use their full 1 KW ERP (which we would only see at 0 degrees takeoff angle), we are calculating field strength at 1 KW "facing watts", that is, the ERP at the horizon, facing us. This isn't reality.

The reality is that our received signal is being delivered from the 29.2 degree angle, a very different effective radiated power than the angle at the horizon. At 29.2 degrees takeoff angle, with WBVP we only "see" 34 watts coming at us. WBVP will show up at very much less field strength on the dial than other stations because of this. Power differences because of elevated takeoff angle makes a huge difference in our calculation process and our resulting received field strength. It must be accounted for.

We move on to geomagnetic latitude and longitude.


Normal latitude and longitude is referenced to as the north (or south) geographic pole, an actual latitude of 90°, and respectively, -90°. Longitude at the poles is irrelevant as they all converge at this point. Geomagnetic latitude and longitude uses the geomagnetic poles as our north-south reference instead. Geomagnetic poles (dipole poles) are the intersections of the Earth's surface and the axis of a bar magnet hypothetically placed at the center the Earth by which we approximate the geomagnetic field. They differ greatly from the magnetic poles, which are the points at which magnetic needles become vertical. The magnetic poles are what has been "wandering", a subject in the news lately, but they drag the geomagnetic poles with them too, albeit at a lesser rate.

Imagine our Earth where the north pole was instead the geomagnetic north pole, currently (2023) in the extreme northwest corner of Greenland. The Earth's longitude lines would all emanate from that point, and it would be considered 90 degrees north latitude. The geomagnetic latitude of New York City, for example, would then be referenced to the geomagnetic north pole, not the actual north pole.

So, the result is this. Instead of New York City being at 40.75°N latitude actual, NYC is now at 49.95°N geomagnetic latitude. This makes a tremendous difference in our mediumwave skywave prediction. The geomagnetic north pole is where the auroral zone is centered in the northern hemisphere. The auroral zone greatly affects the mediumwave signal.

Geomagnetic location is sometimes called the geomagnetic dipole. Both the geomagnetic and magnetic poles have been wandering quite a bit over the last few years. In 1950 the geomagnetic pole was located at approximately 78.5°N and 68.8°W. Today, 2023, it has moved 4 degrees farther north and 2 degrees farther west. Here are the current and future predicted locations:

From website:

Geomagnetic dipole (Northern hemisphere):

2022   80.7°N  72.7°W
2023   80.8°N  72.7°W
2024   80.8°N  72.6°W
2025   80.9°N  72.6°W

So, in skywave analysis, first we must calculate the reflected signal's mid-path latitude and longitude and convert it to its geomagnetic reference. The mid-point latitude and longitude, before conversion, is generally half the distance between transmitter and receiver on a great circle line drawn between the two. We assume the geomagnetic north pole to be our new north pole at 90 degrees latitude. We first calculate the actual latitude and longitude of the path mid-point (the reflection point) between transmitter and receiver and reference its latitude (in degrees offset) to the geomagnetic north pole.

This mid-path latitude is then used in two places in the formulas. It becomes part of the basic path loss calculation, and part of the ionospheric losses (the Kr term). In the basic calculation, the higher the geomagnetic latitude, the greater the extra losses incurred. Secondly, and since the ionospheric losses are subtracted from the basic path loss, the higher the geomagnetic latitude, the greater the additional losses incurred.

In the ITU formula, the formula snippet 2 * Sin(ThetaM) establishes the basic geomagnetic loss relative to the path mid-point. At 40 degrees geomagnetic north latitude it is 1.28 dB, while at 60 degrees north it is 1.73 dB. So we see about a 0.5 dB difference (loss). Wang treats it differently, using Tan^2(ThetaM). In Wang's formula, and also the FCC formula, at 40 degrees geomagnetic north latitude the loss is 0.7 dB, where at 60 degrees north the loss is 3.0 dB. Wang is allowing greater compensation for North America as the mid-point approaches 60 degrees north.

In the next article we'll dive right into the formulas and put it all together.

Friday, July 14, 2023

Mediumwave Skywave Prediction #3 - Introduction To Formulas

Now that we've covered skywave prediction history in this series, let's look at a few actual formulas which are used to calculate skywave field strength. This will likely spill over into several articles as we describe the concepts and intricacies of skywave propagation.


By the turn of the millennium, three simplified formulas survived and are usable for worldwide mediumwave skywave field strength prediction. They each have viable options to consider.

They are:

The Wang Method:

The FCC Method:

The ITU Method:

Yes, they look cryptic at this point. Not to worry, we'll take these apart, item by item, and show you what they're attempting to do.

Where the ITU method attempts to provide a generalized worldwide formula, both the Wang and FCC methods are specialized for Region 2, the Americas, and specifically North America. It must be stressed that these are so-called "simplified formulas", though they do their job quite well. To wit, all have simplified the calculation process associated with hop loss, polarization coupling loss, and solar effects, boiling these down into a generalized expression, Kr. We will analyze Kr in due course.


Each of the these formulas can be sub-divided into three parts.

They are:

1. Calculate a base path loss factor which is based on the path distance. Dslant in the formulas.

2. Calculate the extra loss due to the path's geomagnetic mid-point relative to the geomagnetic north pole. ThetaM in the formulas.

3. Finally, factor in any additional losses/gains like frequency, sea gain, and basic values for ionospheric absorption, polarization coupling losses, focusing and terminal losses, and losses between hops, sunspot number and solar activity. Kr in the formulas.

These additional losses or gains (items 2 and 3), in dB, are subtracted from or added to the base path loss factor to arrive at a final overall path loss value. The final result of the above calculations then give us a ballpark field strength for the midnight hour, or what is usually called SS+6, or sunset+6 hours. This is directly translated into dBµV/m, or dB relative to 1 microvolt per meter, the predicted field strength available at the receiver.

We may or not choose to continue on with even more losses or gains, not shown in the formulas above. If we do, these extras can be:

• Diurnal hourly losses/gains (skywave prediction for the hour of the day). 

• Sunrise and sunset enhancements (skywave prediction at these critical hours).

• Seasonally-driven losses/gains (skywave prediction for winter versus summer).

So, let's gather all the pieces we need to solve the prediction puzzle. We will ignore the extras for now.

The Basics:

1. Calculate Dslant, the "slant distance" and use it to derive a basic path loss factor (a new term - we use slant distance instead of the great circle distance from transmitter to receiver).

2. Calculate ThetaM, the mid-point geomagnetic latitude, also part of the basic path loss factor.

The Ionospheric Tweaks (all but Sea Gain calculated within the Kr term):

3a. Choose the ionospheric layer height (usually 100 km).

3b. Account for Hop losses.

3c. Account for Sea Gain (usually ignored).

3d. Account for Polarization Coupling losses.

3e. Account for Sunspots & solar activity.

Let's first describe the ionosphere at mediumwave and how our signal is reflected or refracted back to Earth. Later on we'll define two important concepts: Slant Distance and Geomagnetic Latitude, both critical to determining the base path loss factor.


Nighttime mediumwave propagation has long been assumed to be reflected or refracted off the E-layer of the ionosphere. The ionosphere is layered as we go skyward, the layers being named the D, E, and F layers.

D-region 50-90 km (31-56 mi)

The D-region is a region of low electron density whose degree of ionization is determined primarily by solar photoionization. This region usually exists during the daytime, and it absorbs the energy of MF radio waves that pass through it. The MF sky wave is therefore highly attenuated as it enters the D-layer during the daytime. At night in the absence of the photo-ionization created by the sunlight, the ionization in the D-region is at a much lower level or is nonexistent, so the D-region no longer absorbs the energy from the MF sky wave passing through it.

Daytime skywave. Believe it or not, daytime skywave does exist and is present 24-7 in varying degrees depending on the season. In deep winter in the Northern Hemisphere (December, January), D-layer ionization during the day is strikingly less due to the lower solar position. Skywave signals, particularly at the upper end of the mediumwave band can pass right through it, and be reflected back to Earth off the E-layer at mid-day. Signals are weak, to be sure, but DX opportunities are abundant for those willing to dig for a signal. Deep winter D-layer absorption can be as much as 20-30 dB lower than at high summer (July, August).

The effect can be striking and unexpected in low-noise areas of the country where you are free from the extreme RF density of the east. I used to spend winters in southwestern Arizona. My custom was to do an annual Christmas trip to Denver, Colorado and I'd set my car radio on a frequency of one of the extremely distant powerhouse stations. I have received KFI-640, Los Angeles, in Trinidad, Colorado at the noon hour, a distance of 800 miles. At peak, the signal hovered right at or barely above the noise level, with long deep fades. Now, that to me is exciting DX.

Back at home in Arizona, I had a 25 ft. matched vertical, inductively-coupled to a variety of portable radios. Following is a sample of what was heard in deep winter during the middle part of the day.

Unusually good signals at noon:

KSL-1160 Salt Lake City, UT (506 miles) never went away at the noon hours. Week but very readable from 11:00-13:00 local, then back up to very nice strength again by 13:30.

KNBR-680 San Francisco, CA (524 miles)

KALL-700 N. Salt Lake City, UT (515 miles)

KCBS-740 San Francisco, CA (557 miles) with equal strength to two semi-locals KIDR-740 Phoenix and KBRT-740 Costa Mesa, CA.

KZNS-1280 Salt Lake City, UT (512 miles) was booming in with an outstanding signal at 12:30 local.

By 13:00 local:

KRVN-880 Lexington, NE appeared with decent strength. 944 miles.

KLTT-670, 50 KW Commerce City, Colorado (681 miles, suburban Denver) under stronger 198 mile groundwave 25 KW KMZQ-670, Las Vegas, NV

KNEU-1250 Roosevelt, UT at early afternoon. 515 miles but only a 5 KW station.

KGAK-1330 Gallup, NM 339 miles (another 5 KW).

E-region 90-140 km (56-87 mi)

During nighttime, the MF sky wave proceeds right on through the D-region to the E-region where it is refracted. The E-region ionization is from multiple sources that exist all of the time, so it is active during both the daytime and the nighttime. E-region ionization in the daytime is predominantly caused by solar ultraviolet and x-rays, while E-region ionization at night is caused predominantly by cosmic rays and meteors. The E-region is found at heights of 90 to 140 km, and it attains its maximum electron density near 100 km. This is the height within the E-region that is the predominant reflecting medium for MF propagation at night. The highly charged part of the E-region is a thin layer, roughly from 5 to 10 km (3 to 6 miles) thick.

Seasonal E-layer heights, as measured by ionosonde are:

Winter noon: 112 km, midnight: 118 km
Spring noon: 110 km, midnight: 108 km
Summer noon: 109 km, midnight: 104 km
Fall noon: 108 km, midnight: 111 km

These are actually measured sporadic-E heights, intense clouds of ionization within the E-layer itself, however evidence suggests that the reflective part of the E-layer may extend all the way to 140-150 km above the Earth. Though MF skywave calculations almost always fix the reflection layer at 100 km, it is evident that reflection or refraction of the MF signal surely does occur at varying altitudes, much dependent on time of day, frequency, and a host of other variables.

Critical frequency is a term used to describe the highest frequency above which radio waves penetrate the ionosphere and below which are reflected back. The critical frequency of the E-layer is mostly between 1.5 and 4 MHz, higher during a sunspot maximum than during a sunspot minimum.

This tells us two things. If our critical frequency has dropped to 1500 kHz or even lower (1.5 MHz, stated above), our MF signal may transit through the E-layer and be reflected back to us off the F-layer. Second, we may see this effect more during periods of lower solar activity. The F-layer, at night, settles in at about 250-300 km altitude. This can result in single hop distances upwards of 3000 km (1864 mi). Look to the upper range of the mediumwave band to sometimes provide unusual DX, particularly in the late night and early morning hours before sunrise.

The skywave/groundwave mixture. Skywaves and ground waves add vectorially. They can and do interfere with each other, the interference resulting in phase distortion in the audio you hear, and weakening (or strengthening) of the signal received at the receiver due to additive or subtractive combination. At night, at 500 kHz over average ground, the ground wave predominates over the skywave from the transmitter site out to distances of about 150 km, where the two signals are equal. The signals add as vectors, and destructive and constructive interference can occur. At 500 kHz at distances beyond 150 km, the sky wave is the predominant signal. At a signal frequency of 1500 kHz, the distance where the two signals are equal reduces to 45 km, because of the increased loss at the higher frequency.

F-region 250-400 km (155-250 mi)

The altitude of all the layers in the ionosphere vary considerably and the F-layer varies the most. During the daytime when radiation is being received from the sun, the F-region often splits into two: the lower and more insignificant one called the F1-region, and the higher and more significant one, the F2-region. Note also that the F1-region generally only exists in the summer. Typically the F1-layer is found at about an altitude of 300 km and the F2-layer at about 400 km.

At night, the two regions combine, and the combined F-layer then centers around 250 to 300 km. Like the D and E layers the level of ionization of the F-region varies over the course of the day, falling at night as the radiation from the sun disappears. However the level of ionization remains much higher than the lower regions.

The F-region is greatly affected by solar conditions. The maximum usable frequency, or MUF, is generally at least 15 MHz, but during the sunspot maximum period, the MUF may often exceed 50 MHz. The maximum usable frequency is the highest frequency that can be refracted off the ionosphere and returned to Earth (generally the F-region is implied).

Then we have what is called lowest usable frequency, or LUF. The sky would appear to be the limit here, but the problem we have is our signal must first transit through the D and E layers to get to the F-layer. This probably 
isn't going to happen during the day in the mediumwave frequency range due to the highly absorptive D-layer. So, during the daylight hours, the D-layer will limit the lowest frequency allowed to pass through. At night, it's a different story.

As we said in our description of the E-region, almost all MF signals will refract off the E-layer at night. But under certain conditions and at certain times of year, when the critical frequency of the E-layer drops to 1500 kHz or below, we have F-layer skywave in the AM broadcast band, a fascinating phenomena.

Let's summarize.

Practically, with all that said, our skywave prediction formula must choose a reflective layer height before we begin. The common choice is 100 km. Varied results will be found between 90 to 140 km, with the higher altitudes producing lower field strengths in general. The prediction experimenter might choose the higher altitudes for frequencies at the upper end of the mediumwave band, or they might even try forecasting for refraction off the F-layer at 250-300 km.

In the next articles, we'll discuss Slant Distance and Geomagnetic latitude. We'll also talk more about ionospheric layer heights, and how they affect the two.

Wednesday, July 5, 2023

Mediumwave Skywave Prediction #2 - A Formula History

The initial mediumwave measurement efforts of the 1930s resulted in graphs of expected field strengths, but only over certain tested paths. What was needed was a formula or formulas which would calculate strengths by plugging in actual transmitter and receiver locations. Scientists and engineers soon started work on this task. What they uncovered were yet more complications. The simple formulas they devised calculating path loss between two points, based on simple distance, didn't quite do it. There were other things going on high up in the ionosphere.

Questions arose:

"Why do field strengths suffer if the signal path is anywhere near (within 5000 km, or about 3000 mi) the geomagnetic poles?"

"How high is the reflective layer of the ionosphere for mediumwave at night? Does it vary?"

"What about multiple hops? Is there an additional loss penalty there?"

"Testing shows long paths over the sea result in increased strengths. Why is that?"

"Does the solar cycle have anything to do with mediumwave skywave propagation?"

And those weren't all.

Some mysterious thing was also going on at the signal reflection point high in the ionosphere. There were losses there which couldn't be accounted for.

Then there was the noticeable variability hour by hour throughout the day, every day. And certain peaks at the sunrise and sunset periods. Then someone noticed that signal strengths even varied by a few dB as the seasons progressed throughout the year.

The engineers and scientists had a mess on their hands to try to sort out. World War II ended, and work continued in earnest to quantify all the new data being accumulated. New ideas came forth. Throughout the latter half of the 20th century, formulas were either tweaked or abandoned.

The current plethera of formulas and tweaks available for mediumwave skywave field strength calculation is almost mind-boggling. Essentially, it all boils down to the overall path loss from transmitter to receiver. Once we have that, we can determine the expected received field strength. Luckily, we can attain high accuracy by breaking things down to basics, then tally the sum of the parts. The final path loss figure, in our familiar dB scale, is simply the addition and subtraction of the gains and losses of the individual pieces.


K.A. Norton and John C.H. Wang of the FCC are 20th Century heroes of the first order. Almost singlehandedly they led the charge in the quest to calculate expected field strengths in the longwave and mediumwave regions. Norton led the early efforts, and Wang the later.

John C.H. Wang 1934-2019

Let's talk about some of the formulas which emerged from all of this testing, and how they evolved. Or didn't!

Over the last half of the 20th Century, several countries and the ITU (International Telecommunication Union) contributed greatly to the basic formulas we use for skywave field strength prediction. This was years in the making. Each region of the earth has different requirements. North America, for instance, has its close proximity to the geomagnetic pole to deal with. Polarization coupling loss (the loss as the signal transitions the reflection point in the ionosphere) is more of a problem in the tropics but not at high latitudes. East Asia and Oceania seemingly have greater propagational signal strengths than other areas of the world. One basic formula would not suffice for all regions. It wasn't until the millennium that the dust had finally settled and it became clear which formulas worked best for which region.


The early Cairo curves of 1938 present field strength as a function of great circle distance only. The two Cairo curves and the FCC clear channel curve are similar for distances up to about 1400 km. At 3000 km the north-south curve is about 8 dB greater than the east-west curve. At 5000 km the difference is about 18 dB. The FCC clear channel curve falls between the two Cairo curves. The Cairo curves did not gain much recognition (in part, because of World War II) until 1975 when the LF/MF conference adopted the north-south curve for use in the Asian part of Region 3. The east-west curve, because it often underestimates field strength levels, has virtually been disregarded. The Cairo curves served their purpose well in the early years. Today it cannot be considered a candidate for worldwide applications.


The old Region 2 method started out as the FCC clear channel curves. It has a long history dating back to 1935. It presents field strength as a function of great circle distance only. It does not take into account effects of other factors such as latitude, frequency, sunspot numbers, etc.

North America has perhaps the most significant propagation anomalies to deal with. Increased positional geomagnetic loss (not auroral loss due to disturbed ionosphere) is strongest here in North America because of our closer proximity to the north geomagnetic pole than Europe at large. Wang, a long-time employee of the FCC, started to work on the skywave measurement problem by 1970. He soon was on the right track to a solution.

Wang, in 1985 and again in 1989, reported that the old Region 2 method offers reasonable accuracy when applied to temperate latitudes, but when applied to low-latitude areas (e.g., Puerto Rico), it displays a tendency to underestimate. However, when applied to high-latitude areas (e.g., northern United States and Canada), it displays a strong tendency to overestimate. Wang stated, "Clearly, this is due to the fact that it lacks a treatment of latitude. The [old] Region 2 method has served its purposes well and cannot handle today's heavy demands for frequencies. It is not a candidate for worldwide applications."

This antiquated method remained the recommendation of the ITU and the FCC for Region 2 well into the 1980s.


John C.H. Wang, the star engineer of the FCC, had a heavy influence in developing the FCC formula. The modernized FCC method of the 1990s combines Wang's ideas on absorption losses and geomagnetic influence of the signal path's mid-point with the old Region 2 method and the original Cairo curves. Elsewhere, Wang contributed greatly to the world's scientific community by offering and publishing his personal ideas and formulas outside of the realm of the FCC. Wang's FCC contribution as well as his personal formulas include an additional loss factor of 4.95 dB to attempt to compensate for sunspot activity and the extra North American geo-polar proximity absorption. Neither the FCC's nor Wang's formulas account for frequency. Finally, where Wang adds a factor for the antenna's array gain over a standard quarterwave monopole, the FCC formula does not. The two methods produce, perhaps unsurprisingly, nearly identical results. 


The USSR method, authored by Udaltsov and Shlyuger and proposed in 1972, appeared to be very promising at first. For one thing, it included a sound treatment of latitudes. A previous study by Wang, et al., in 1993, using data collected in Region 1 only, had mixed comments about this method. The findings were as follows [Wang]: "(1) When applied to single-hop paths within Europe, reasonably accurate results have been obtained. (2) When applied to long paths terminating in Region 1, calculated results are typically 10 to 20 dB lower than the measured values. The current study (late 1990s), which uses a much larger data bank, has strengthened these findings. Furthermore, the frequency term in this method indicates that the higher the frequency is, the lower the field strength is. Although this is theoretically sound, measured data from Brazil, New Zealand, and the United States, however, does not corroborate this." Wang also suggested that it was something short of a true worldwide method. For a number of years this method was included in the ITU's reccomendation for worldwide application at frequencies between 150 and 1600 kHz.


The 1974-1975 ITU Geneva conference adopted the USSR method for official use in Region 1 and in the southern part of Region 3 with modifications. P. Knight's 1975 sea gain formula and the J.G. Phillips-Knight 1965 polarization coupling loss term were also included. The ITU has adapted and modified this formula for general worldwide use to this day. It has some shortcomings for North America, as we will soon see.

The ITU method makes predictions that depend on both frequency and geomagnetic latitude. The field strength values are not symmetrical about the geomagnetic latitude equal to 0 degrees. The field strength expression also predicts lower field strength values as the frequency is increased in the MF band, but measurements performed in the United States show that the field strengths are higher at the higher frequencies in the MF band when compared to those measurements at the lower frequencies. Because of this discrepancy, the ITU method has not found wide acceptance as a worldwide prediction method. Curiously, their bandaid-approach is recommending a fixed frequency of 1000 kHz to represent the entire MF band.


The brilliant engineer John C.H. Wang started with the FCC in about 1970, and stayed for 40 years, continuing K.A. Norton's early work. Wang had made tremendous inroads by 1977, and after examining all of the available MF methods, developed a new MF skywave field strength prediction method for North America. Like the Udaltsov and Shlyuger method, the Wang method also contains a latitude term. The original FCC curves have a hump at roughly 100 km which Wang concluded was due to groundwave interference present in the 1935 data. The curves become smoother and better behaved after removal of these data points. Furthermore, this new method essentially linked the Cairo and the FCC clear channel curves together mathematically. The special case corresponding to a geomagnetic latitude of 35 degrees north in the Wang method is extremely close to the Cairo curve; the difference is within a fraction of a decibel. The special case corresponding to 45 degrees north is very similar to the old FCC curve. More importantly, it works well for long and short paths alike. Wang further improved on this method in 1979, modifying the ITU's basic loss factor (Kr) for North America and also tweaking the solar activity dependence factor (bsa). The formula was further tweaked again and published in 1985.

In 1986 the Region 2 conference which tackled the expanded band adopted Wang's method for calculating interregional interference. In 1990 this method became part of the FCC rules and regulations replacing the old clear channel curves (actually, the old Region 2 method) for domestic applications. In 1994 this method was adopted by the ITU for calculating field strengths between 1600 and 1700 kHz. This method has several other convenient features that should not be overlooked. It is simple and easy to use; a handheld calculator would suffice. The calculation procedures and required input information are similar to the Udaltsov and Shlyuger method, the method being used by Region 1 countries. Wang continued with improvements throughout the rest of the 1980s and into the millennium.


There are other prediction methods, some obscure or archaic. Namely, these are: the Norton Method (1965), the EBU Method (1962, reaching its final form in 1978), the Barghausen Method (1966), the E. Oliver Method (1971), and the P. Knight Method (1973). The Knight's method eventually was simplified, evolving into the UK Method.

The Cairo curves, the Norton, the EBU, and original ITU-sanctioned 1974 USSR methods still used actual overland great circle distances in their formulas. The modified USSR method (1978) uses the slant distance. Wang of the FCC was using slant distance by 1977.

In the next article we'll introduce the formulas.

Sunday, July 2, 2023

Mediumwave Skywave Prediction #1 - A Measurement History

Skywave propagation at mediumwave is a fascinating subject, both from a historical and technical standpoint. Radio itself has been around well more than 100 years, and broadcast radio since about 1920. As more and more stations entered the airwaves, nighttime spectral chaos ensued. How was it all sorted out? Who took charge of all this? How did we arrive at the calculations necessary to ensure that the thousands of radio stations transmitting didn't interfere with each other? What exactly goes into calculating a nighttime skywave signal strength for a distant medium wave station?

Let's try to answer these questions in this series. We'll cover the history in the first couple of articles, then dive into the technical in subsequent articles. Throughout this series, the LF and MF abbreviations, when used, refer to the longwave frequency (LF) and mediumwave frequency (MF) bands. Note that these articles discuss mediumwave skywave prediction only.


At the end of World War I, a fierce battle ensued between the US government and the Department of the Navy over control of the airwaves. The Department of Commerce eventually won and became master of the air and the regulatory agency for commercial radio here in the US. They started by establishing two broadcast frequencies: 833 kHz (360 meters) and 619 kHz (485 meters). The Federal Radio Commission took charge in 1926, lasting until 1934 when the current Federal Communications Commission was formed. By 1930, broadcast radio was on its way. Nighttime signals traversed the continent from coast to coast.

Throughout the early years of radio, interest mounted to quantitatively determine the service area of broadcast stations. Early mathematical efforts focused mainly on finding an accurate calculation for groundwave coverage. K.A. Norton of the FCC would play a major role worldwide in that effort. The intricacies of skywave would be unveiled later. You might be surprised to know that serious study of longwave and mediumwave skywave propagation didn't commence until some 12 years after the first commercial AM radio station went on the air.


The earliest worldwide concerted efforts to study longwave and mediumwave skywave propagation began in 1932. The International Radio Consultative Committee (CCIR), an arm of the ITU, formed a task force in that year to study propagation at frequencies between 150 and 2000 kHz. Three measurement campaigns were carried out between 1934 and 1937 on 23 long-range propagation paths between North America and Europe, North America and South America, and Europe and South America. Measurements on 10 short paths within South America were also carried out under the administration of Argentina. Two skywave propagation curves (skywave field strength graphs ordered by frequency and distance) were drawn based on the results of these measurements. One of the curves is for paths far away from Earth’s magnetic poles (north-south curve), while the other curve is for paths which approach Earth’s magnetic poles (east-west curve). The two curves were formally adopted at the 1938 International Radio Conference in Cairo and are known as the Cairo curves. They have survived, with modification in one form or another, to this day.

Click any image for the bigger picture.

The Cairo Curve Measurement Campaign

The Federal Communications Commission (FCC) of the United States carried out a skywave field strength measurement program in the spring of 1935 to derive a new set of curves for North America. At that time, there were eight clear channel stations. Nighttime signals of these stations were monitored at 11 receiving sites located in different parts of the United States. The curve corresponding to the annual median value (the signal level expected to be exceeded at least 50% of the time) was used to determine a station's coverage area, while the curve corresponding to the upper decile value (the signal level expected to be exceeded at least 10% of the time) was used to calculate the interference levels among co-channel stations. Characteristically, the 10% level is the higher signal level. These curves became part of the rules and regulations of the FCC and were adopted by the 1950 North American Regional Broadcasting Agreement (NARBA) for official use in the North American Region, which comprised the following areas: Bahama Islands, Canada, Cuba, Dominican Republic, Haiti, Jamaica, Mexico, and the United States. This method was eventually adopted with minor modifications for applications in all of ITU Region 2. It would not survive the millennium.

The FCC, knowing the clear channel curves had certain limitations (the curves do not take into consideration the effect of latitude and the proximity to the geomagnetic pole), initiated a long-term large-scale measurement program in 1939 to collect measurements from more than 40 propagation paths. The measurement program lasted for about one full sunspot cycle; in four cases it lasted for two cycles and ended in 1958. Frequencies of these paths ranged from 540 to 1530 kHz. Path lengths ranged from 322 to 4176 km. Mid-point geomagnetic latitudes (the signal reflection point between transmitter and receiver relative to geomagnetic north) ranged from 45 degrees to 56 degrees north, a narrow range of 11 degrees, although some paths from lower latitudes were later added. More about geomagnetic latitude later in the series.


I'll side-track for a minute and tell you about the ITU, the International Telecommunication Union, and how regions are defined. Today the ITU is a specialized agency of the United Nations responsible for many matters related to information and communication technologies. It was established on May 7, 1865 as the International Telegraph Union, making it the first international organization. The ITU has divided up the planet into three regions. Region 1 comprises Europe, Africa, the entire former USSR, Mongolia, and the Middle East west of the Persian Gulf, including Turkey and Iraq. Region 3 contains most of non-former USSR, Asia east of and including Iran, and most of Australasia. Region 2 covers the Americas including Greenland, and some of the eastern Pacific Islands.


Back to our history.

The Canadian Department of Transportation took path measurements in 1947, a year of maximum sunspot number and minimum field strengths.

The EBU, the European Broadcasting Union, carried out an extensive measurement campaign from from 1952 to 1960 for paths in western Europe. A controversial field strength prediction method was developed by Ebert in 1962. In this method, empirical relationships were derived for the effects of solar activity, the influence of magnetic field, frequency, and other factors. The Ebert method cannot be considered a success because it displayed a strong tendency to grossly underestimate field strength levels, sometimes by 30 dB. It was soon abandoned. Although the Ebert method was not a success, the importance of the EBU measurements cannot be overlooked. 

Three international organizations, the EBU among them, in 1963 and 1964 set up 7 receiving locations on the continent of Africa and did studies of propagation paths from two transmitters on Ascension Island. One phase of the project was to study polarization coupling loss and sea gain. Germany also conducted measurements at Tsumeb, southwest Africa. Altogether, the African measurement campaign involved 15 receiving sites, and data from 33 paths was documented. Frequencies ranged from 164 kHz to 1484 kHz. Distances ranged from 550 km to 7540 km. Mid-point geomagnetic latitudes ranged from 29 degrees south to 40.2 degrees north. Of these 33 paths, three were from Europe to Africa.

In the late 1960s and early 1970s a number of administrations and scientific organizations made valuable contributions. The EBU reactivated its efforts and collected data from more than 30 propagation paths; many of these are intercontinental paths. In Eastern Europe, the International Organization of Radio and Television (OIRT) contributed data from 12 short intra-European paths between 600 and 1400 km at frequencies between 164 and 1554 kHz. The former USSR also collected a significant amount of measurements. A summary of their results and a proposed new calculation method was published in 1972.


The big one, perhaps the biggest ever. The ITU's Regional Administrative LF/MF Broadcasting Conferences were held in Geneva, Switzerland for Regions 1 and 3. This was a major deal on several fronts. Channel spacing was to be decided on, worldwide. It was 1975!!! Also signal strength calculation standards were to be fixed and tailored by region and sub-region. Asian countries, particularly China, preferred the Cairo north-south curves. Australia and New Zealand believed neither method was adequate for their applications. They believed field strength levels in their part of the world are stronger than those observed in other places. Finally, a compromise was reached.

It was decided that the USSR method was to be used for Region 1. The Cairo north-south curve was to be used for the northern part of Region 3 (east Asia). For the southern part of Region 3 (Oceania) the modified USSR method was to be used with a correction factor of 2.7 dB added to the basic formula. Sea gain and polarization coupling loss terms were to be included whenever applicable. The propagation issue was a lesser concern compared to the channel-spacing issue. The conference was deadlocked for a number of weeks over two separate proposals: 8 kHz versus the traditional 10 kHz separation. Finally, a compromise of 9 kHz was adopted which became effective in November of 1978 for Regions 1 and 3.

In the meantime, the interference situation in South America was going from bad to worse, mainly because of the lack of any regional agreement, although some bilateral agreements were in existence. The situation in North America was somewhat better, thanks in part to the 1950 NARBA agreement.

After the ITU's LF/MF conference for Regions 1 and 3 was over, a number of administrations in South America petitioned the ITU to convene a regional conference involving all countries in ITU Region 2, the Americas. Consequently, two sessions took place. The first session dealt with technical matters and took place in 1980 in Buenos Aires. The second session dealt with the actual planning and took place in 1981 in Rio de Janeiro. The FCC clear channel curve was adopted for use in the entire region. It was also decided that sea gain and polarization coupling loss terms were not to be included in the calculations. At the first session, channel spacing was a very hot topic. The United States was in favor of 9 kHz (for all of South America), while Argentina and Canada were strongly against it. At the second session, the United States withdrew its proposal, and 10 kHz spacing was quickly agreed upon. It should be mentioned that in Region 2, longwave is not used for broadcasting. Therefore the 1980-1981 conference dealt with mediumwave only (535 kHz to 1605 kHz).


The CCIR Documents of the 1978 Kyoto Assembly further modified the 1974 sky-wave field strength prediction method for MF (150 to 1600 kHz) and recommended its provisional use worldwide. Several sky-wave field strength prediction methods proposed for various parts of the world also were described. 

They are:

1) Cairo North-South curve adopted for use in Asian part of Region 3 - mathematical approximation presented.

2) EBU method to be used in European Broadcasting Area with separate formula for distances less than 300 km.

3) USSR method - valid between 37° and 60° geomagnetic latitude for distances up to 6000 km and has no frequency dependence.

4) UK method - valid for all distances worldwide except for the auroral zones and has no frequency dependence.

5) Region 2 would use the FCC's method. The Wang 1977 method (Wang was a newly-hired and brilliant engineer at the FCC) was given as an alternative method for use in Region 2.

In 1979 Wang proposed a modification of the CCIR Kyoto 1978 worldwide method to improve accuracy in Region 2. Also in the same year, the Inter-American Conference on Telecommunications extended the FCC median signal level curve to distances beyond 4300 km using the Cairo North-South Curve and recommended its adoption for Region 2.

In response to Region 2 countries' request for more frequencies for broadcasting, the 1979 World Administrative Radio Conference (WARC-79, held in Geneva) of the ITU allocated the band 1605-1705 kHz for broadcasting in Region 2 only. Two sessions of regional conference took place in 1986 (Geneva) and 1988 (Rio de Janeiro) for the planning of the use of this expanded band in Region 2. It should be noted that this band is used by other services in Regions 1 and 3.

In preparation for the use of the expanded band and recognizing the need for additional data, particularly data from low and high latitude areas, the FCC initiated two separate projects in the early 1980s. In 1980, the FCC and the Institute for Telecommunication Sciences (ITS) of the Department of Commerce jointly began to collect low-latitude data at two receiving sites: Kingsville, Texas, and Cabo Rojo, Puerto Rico. The FCC-ITS efforts in low-latitude areas were supplemented by Brazil and Mexico; both administrations also collected a significant amount of data from low-latitude areas. In 1981, the FCC started a joint project with the Geophysical Institute, University of Alaska. The Alaskan project concentrated on high latitude data and lasted for five years, collecting data representing different levels of solar activity.

Administrations in the Region 3 area, Australasia, in cooperation with the Asian-Pacific Broadcasting Union, were equally active and productive in their path testing. In the northern part of this region, data from 84 paths had been documented by 1981. Australia and New Zealand jointly collected data from 85 paths. The Japanese administration had carried out a series of mobile experiments in the Pacific by 1987.

By the year 2000, measurements from more than 400 propagation paths had been documented. Great circle lengths of these paths ranged from 290 to 11,890 km. Signals of the few very short paths were verified to be skywaves. Frequencies ranged from 164 kHz to 1610 kHz. Control-point geomagnetic latitudes ranged from 46.2 south to 63.8 north geomagnetic latitude. A large amount of literature had been generated. By this time, largely the work of the ITU in setting standards and regulations for the longwave and mediumwave bands was finished. Fine tuning of the skywave calculation formulas was left to the scientists.

In the next part of this series, we'll wrap up the history and then go on to explore elementary skywave prediction and what is involved in solving it.

ITU Regions

Information for these articles has been gathered from the following resources:

An Objective Evaluation of Available LF/MF Skywave Propagation Models
John C.H. Wang
Radio Science, Volume 34, Number 3
May-June 1999

NTIA Report 99-368
Medium Frequency Propagation Prediction Techniques and Antenna Modeling 
for Intelligent Transportation Systems (ITS) Broadcast Applications
Nicholas DeMinco
August 1999

International Telecommunication Union Handbook
The Ionosphere and its Effects on Radiowave Propagation
Radio Communication Bureau 1998

Code of Federal Regulations Title 47
Radio Broadcast Services (FCC)
47 CFR Part 73

FCC Standard AM Broadcast Technical Standards
   ...notes and changes to 47 CFR Part 73
Broadcast Service Bureau
Filed January 20, 1987

Medium Frequency Propagation: a survey
P. Knight
BBC Research Department 1983/5
May 1983

Comparison of Available Methods for Predicting Medium Frequency 
Sky-Wave Field Strengths
Margo PoKempner
June 1980

LF AND MF SKY-WAVE PROPAGATION: the origin of the Cairo curves
P. Knight
BBC Research Department 1977/42
November 1977