Longley-Rice Considers The Entire Environment

The original method of determining propagation of these new signals required some refinement
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In the golden age of our industry, when AM was king, and FM was the new twerp on the block, the realization came about that the original method of determining propagation of these new signals required some refinement.

The original propagation curves were developed in the late 1940s, based on studies performed at that time. Nearly 20 years later, in the mid- to latter-1960s, the new curves were released. These are a refinement of the original models and were developed through additional studies.

Since the effects of terrain on the propagated signal had been empirically observed, a terrain roughness factor was introduced into the model. This factor was intended to correct for additional deviations that would tend to occur in mountainous regions, but its use has more or less been on the fringes of engineering for the last half-century or so. The curves were intended to be representative of average terrain, which was pegged with a delta-h value of 50 m. Delta-h is defined in a distance range of 10 to 50 km (6-31) miles from the transmitter, and is the difference between 10 percent below the highest elevation and 90 percent below the highest elevation in this slice.

While the standard contour method has worked reasonably well for the last 50 years, the more a particular case diverges from the standard assumptions, the greater the observable spread is in observed behavior versus predicted behavior. Simply put, the contour model works fairly well in the Midwest, but the further you get from fly-over country, the more problematic it becomes.

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One of the major shortcomings of the contour model is the fact that it bases its distance to particular field strength on the average terrain in a limited slice along an azimuth. For FM, that slice exists in a zone from 3 to 16 km (2 to 10 miles) from the transmitter site. All other locations are ignored. Thus, for example, if I had a Class A station with an ERP of 6 kW and an average terrain in the 3-16 kilometer slice from the transmitter along a given azimuth of 100 m, the standard contour model would predict a distance to the 60 dBu contour of 28.3 km along this azimuth. Then suppose I constructed an infinitely tall granite wall at 17 km from the site. The contour model would continue to show 60 dBu at a distance of 28.3 km from the site, even though we all intuitively know the wall would stop the signal. Similarly, what happens with the terrain closer to the site than 3 km is also ignored.

Enter the terrain dependent models, the most famous of which is Longley-Rice.


Around the time that the current curves were under development, the Longley-Rice or Irregular Terrain Model was also being developed. The genesis of the model creation was due largely to the needs of television frequency planning. Since significant computing horsepower is required to make predictions with this model, its use for many years was restricted, for economic reasons, to those with very deep pockets. The proliferation of huge desktop computing power has allowed the model to become more widespread in its use. Indeed, there is hardly a day that goes by that I do not run several such maps from the comfort of my office, and I wager the same is true for many of you.

The relevancy of the Longley-Rice model is due to the fact that it does not look at just a sample of the terrain, but looks at all of the terrain along a given path length. Additionally, other factors, such as atmospheric properties, free-space, localized ground cover and receive antenna characteristics, are considered. The result is a fairly accurate representation of how a propagated signal behaves in a given environment. Recently, in an attempt to verify observed problems in coverage with a particular facility, I performed field strength measurements against Longley-Rice modeled coverage. In nearly all cases, the measured deviation was less than approximately 1 dB between measured and modeled. That's pretty darn close.

In determining field strength values, the model uses free-space attenuation, and then applies statistical estimates to adjust the value accordingly. The variables utilized are a situational variability, time variability and location variability. The received signal level is therefore the signal attenuated by free-space losses further attenuated by the sum of these attenuation variables. Because of the number of variables available, some of which can be tweaked by the person performing the study, there can be swings in predicted field strengths.

For example, calculating predicted field strength in a continental temperate climate zone would yield different results than if the same path were calculated in a desert or tropical environment. Similarly, due to scattering, urban areas will result in a greater attenuation of the signal than over open land. Ground conductivity also plays a role in the model, with its effects more pronounced at lower frequencies.

To get results that are more accurate with Longley-Rice, the sample sizes can be changed. For instance, one commercially available software package allows cell size to vary from 0.1 to 4 km. Forterrain samples, this package also allows terrain to be sampled at several defined intervals from 30m to 1 km. The result is that very fine or coarse resolution maps may be created. Of course, the finer the resolution, the longer the time the calculations take to complete.

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Since Longley-Rice provides output on a cell or pixel basis, contours are not native to the model. The Federal Communications Commission tends to prefer contours, and so many of the available packages will allow you to derive a contour from the results. Typically, a contour may be derived for a first, mean or last occurrence of a particular field strength. If the terrain is irregular in a particular region, this can sometimes have strange effects. Wild variations in the terrain up or down along a given path can result in the contour location on a given azimuth being at a significantly different location than an adjacent radial. This can pose problems for city of license coverage studies, as the derived contour may fall short of serving the community, while inspection of the individual cells shows there is more than adequate signal.

Although the commission accepts Longley-Rice for both coverage and interference studies for television facilities, its use by FM stations is typically limited to city of license coverage and main studio location studies.


Until a decision in 2010 colloquially known as Skytower, the commission typically limited the use of Longley-Rice to cases where the delta-h value along paths in question was less than 20 m or greater than 100 m, and required at least a 10 percent variance in the coverage predictions between the curves and Longley-Rice. The delta-h provision has been removed, and now anytime there is a variance of at least 10 percent between the models, Longley-Rice may be used.

It is important to note, however, that Skytower does not authorize a blanket use of Longley-Rice in all instances. Its applicability is limited to cases where the 70 dBu (city grade) field strength is of interest, such as demonstrating city of license coverage at the application stage for "commercial" channels, or in showing that a particular main studio location is rule compliant. All other uses such as allocation exhibits, contour overlap, interference studies and city of license coverage for "non-commercial" channels still must rely on the applicable contour derived from the standard FCC contour.

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Finally, Longley-Rice allows the receive antenna height and gain to be factored into the signal calculations, whereas the FCC contours are based on a dipole antenna with a receive height 30 feet above ground. Adjusting the gain and height of a receive antenna with Longley-Rice can allow more illustrative examples of coverage, especially in urban areas when combined with localized groundcover effects. While such illustrations are beneficial for understanding the coverage of a particular facility, submissions to the commission using Longley-Rice will still need to be based on a dipole at the standard height.


To wrap up this month, an illustration of the result Longley-Rice provides is informative. The first map illustrates the predicted coverage of one of the stations in my area by this model. The prediction assumes the impact of local ground conditions, and a dipole antenna at the reference height. On the first map, the Longley-Rice coverage is overlaid with three FCC contours. The variations in terrain caused by the River tend to increase the coverage in certain directions, especially to the north.

In the second map (at left), a comparison is drawn between the 60 dBu contour by the FCC standard method, and the mean occurrence 60 dBu contour derived from Longley-Rice. On average, the FCC contour and the Longley-Rice contour are actually similar to each other. The delta-h in this region is reasonably close to 50 m, on which the FCC contours are derived. As a result, a correlation between the two models should be expected.

Last, but not least, the third map (above) compares the first occurrence, mean occurrence and last occurrence 60 dBu contours for the facility as derived from Longley-Rice. Even with the relatively flat terrain in the region, there is a wide spread between the locations of the first and last time on each radial where the 60 dBu field strength is calculated.

In the end, Longley-Rice is a huge step forward in predicting facility coverage. Consideration of the entire environment in which a station operates allows for a more accurate picture of what is transpiring. Armed with that information, both management and engineering are better equipped to make necessary decisions.

Ruck is the principal engineer of Jeremy Ruck and Associates, Canton, Ill.