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.

THE SURVIVORS

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.

DISSECTING THE FORMULAS

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.

IONOSPHERIC LAYERS

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.