What are the underlying calculations, parameters, and assumptions for the Longley-Rice (ITM) propagation model?

Overview

This FAQ describes the assumptions and methods used in SoftWright’s implementation of the “Longley-Rice” point-to-point model for radio propagation in the Terrain Analysis Package (TAP).

The Longley-Rice model predicts long-term median transmission loss over irregular terrain relative to free-space transmission loss. The model was designed for frequencies between 20 MHz and 40 GHz and for path lengths between 1 km and 2000 km.

Note that SoftWright has implemented the “point-to-point” mode rather than the “area” mode because required path-specific parameters can be determined from detailed terrain path profiles available in TAP. The point-to-point mode implemented by SoftWright uses detailed terrain profiles to determine the distances to radio horizons, the horizon elevation angles and effective antenna heights needed by the model. As with other SoftWright propagation models, coverage studies of large areas are accomplished using a large number of individual path studies to multiple points along multiple radials from the central transmitting site.

This implementation is based on Version 1.2.2 of the model, dated September 1984. A later series (beginning with Version 2.0, dated May 1970) uses “considerably modified diffraction calculations” and is “not now recommended and is no longer maintained by its developers.” (“A Guide to the Use of the ITS Irregular Terrain Model in the Area Prediction Mode”, NTIA Report 82-100, page 17). Note also that the version 1.2.2 implemented by SoftWright does not utilize several other corrections to the model proposed since the method was first published (see A. G. Longley, “Radio propagation in urban areas,” OT Rep. 78-144, Apr. 1978; and A. G. Longley, “Local variability of transmission loss- land mobile and broadcast systems,” OT Rep., May 1976).

Technical Foundation

TAP users should consult the following technical publications for a detailed discussion of the theoretical and empirical bases of the model:

“Tech Note 101”: P. L. Rice, A. G. Longley, K. A. Norton, and A. P. Barsis, “Transmission loss predictions for tropospheric communication circuits,” U.S. Government Printing Office, Washington, DC, NBS Tech. Note 101, issued May 1965; revised May 1966 and Jan. 1967.

“Longley-Rice”: A. G. Longley and P. L. Rice, “Prediction of Tropospheric radio transmission over irregular terrain, A Computer method-1968.” ESSA Tech. Rep. ERL 79-ITS 67, U.S. Government Printing Office, Washington, DC, July 1968.

“NTIA Report”: G. A. Hufford, A. G. Longley, and W. A. Kissick, “A guide to the use of the ITS irregular terrain model in the area prediction mode,” NTIA Rep. 82-100, Apr. 1982.

“ITS Report”: “Telecommunications Analysis Services Reference Guide”, Institute for Telecommunications Services, Spectrum Division, Dec 7, 1983.

A brief but helpful overview of the model, as well as a comparison to other models, is found in IEEE publication “Coverage Prediction for Mobile Radio Systems Operating in the 800/900 MHz Frequency Range,” IEEE Trans. Vehicular. Technology, vol. VT-37, p. 21, 27-35, 1988.

General Parameters

Like the other models available in the TAP system (e.g., Carey, Bullington, Okumura) the Longley-Rice model requires the input of certain general parameters to set up the program for propagation calculations:

  • Frequency The nominal frequency range for the Longley-Rice model is listed as 20 MHz to 40 GHz in the original paper. The upper limit is modified to 20 GHz in some later documentation.
  • ERP Effective Radiated Power is entered in the units set by the user in the System Configuration Screen (mW, W, kW, dBm, dBW, dBk).
  • Antenna Omni-directional transmitter operation is assumed unless a directional antenna is specified.
  • Heights Antenna heights above ground for transmit and receive facilities are entered in the user-specified units (feet or meters). The program will compute the effective heights needed for Longley-Rice calculations.

Longley-Rice Parameters

The nature of the Longley-Rice model requires certain additional parameters:

  • Polarization: Either horizontal or vertical polarization must be specified. The Longley-Rice model assumes that both antennas have the same polarization, either vertical or horizontal.
  • Refractivity: The refractivity of the atmosphere determines the amount of “bending” of the radio waves. In other TAP models, the effect of refractivity is entered as effective earth curvature, typically “4/3 earth” (1.333). In the Longley-Rice model, there are three ways of specifying refractivity:
  1. You can enter the “Surface Refractivity” value directly, typically in the range of 250 to 400 N-units (corresponding to earth curvature values from 1.232 to 1.767). An effective earth curvature of 4/3 (=1.333) corresponds to a surface refractivity value of approximately 301 N-units. Longley and Rice recommend an Ns equal to 301 N-units for average atmospheric conditions.
  2. You can enter the refractivity referenced to sea level No and the surface refractivity Ns will be computed based on the elevation of the path. Values of No can be read from maps, such as Figure 1 on page 5 of the 1968 Longley-Rice paper.
  3. You can enter the effective earth curvature value K (such as 1.333 for 4/3 earth) and the surface refractivity Ns will be computed from:
  • Permittivity: The relative permittivity (e ) or dielectric constant of the ground. Typical values are shown below.
  • Conductivity The soil conductivity (in Siemens per meter) of the ground. Typical values are shown below.
Relative Permittivity Conductivity (Siemens per meter)
Average ground 15 0.005
Poor ground 4 0.001
Good ground 25 0.020
Fresh water 81 0.010
Sea water 81 5.000
  • Seven climate codes are categorized in the Longley-Rice model as shown:
1 Equatorial (Congo)
2 Continental Subtropical (Sudan)
3 Maritime Subtropical (West coast of Africa)
4 Desert (Sahara)
5 Continental Temperate
6 Maritime Temperate, over land (United Kingdom and continental west coasts)
7 Maritime Temperate, over sea

According to Longley & Rice, “The Continental Temperate climate is common to large land masses in the temperate zone. It is characterized by extremes of temperature and pronounced diurnal and seasonal changes in propagation. In mid-latitude coastal areas where prevailing winds carry moist maritime air inland, a Maritime Temperate climate prevails. This situation is typical of the United Kingdom and of the west coasts of the United States and Europe. For paths that are less than 100 km long, there is little difference between the Continental and Maritime Temperate climates, but for longer paths the greater occurrence of super refraction and ducting in maritime areas may result in much higher fields for periods of 10 percent or less of the year.” (see NTIA Report)

Variability

Longley-Rice defines four modes of variability. The mode selected determines the meaning of the reliability and confidence values used in the model. The mode of variability can be considered the “point of view” for considering the meaning of “reliability” and “confidence” in the calculations.

The modes of variability defined by Longley-Rice are: Single message mode, Individual mode, Mobile mode, and Broadcast mode. These modes are defined in more detail in NTIA, p. 37.

In earlier versions of the SoftWright implementation (up to and including TAP 4.0) all calculations use the point-to-point mode of Longley-Rice to compute the field at individual locations (multiple points along multiple radials from a transmitter site). Therefore, the mode of variability was fixed as “Individual” mode (called “Accidental” mode in some of the literature). Furthermore, since we are exactly defining the receive location for each calculation, the program did not consider location variability. Beginning with TAP 4.1, both the mode of variability and the option for location variability can be selected by the user. The default values for these parameters are “Individual” and “Ignore Location Variability” for compatibility with the earlier versions of TAP.

The types of variability described in Longley-Rice are time, location, and situation variability. These three “dimensions of variability” were developed to account for and categorize variations in measured median signal levels (see NTIA Report, pp. 28-31): (Note that short term variability of the type associated with multipath propagation is not covered by the model.)

Time variability accounts for variations of hourly median values of attenuation due to, for example, slow changes in atmospheric refraction or in the intensity of atmospheric turbulence. The computed field strength value is an hourly median value; the actual field strength at the receiver location would be expected to be above that value during half of each hour and below that value for half of each hour. Time variability describes the effects of these changes over time. The time variability for the calculation is expressed as a percentage from 0.1% to 99.9%. This value gives the fraction of time during which actual received field strength is expected to be equal to or higher than the hourly median field computed by the program. This variable allows you to specify how you want to deal with the time variability of changing atmospheric (and other) effects as described above. Entering higher percentage reliability values effectively reduces the variability resulting from these factors. The resulting field strength predicted by the program will be lower, but with increased reliability that the actual field that could be measured would equal or exceed the computed value at any given time.

Location variability accounts for variations in long-term statistics that occur from path to path due to, for example, differences in the terrain profiles or environmental differences between the paths. The location variability for the calculation is expressed as a percentage from 0.1% to 99.9%. This value gives the fraction of locations where actual received field strength is expected to be equal to or higher than the median field computed by the program. This variable allows you to specify how you want to deal with the location variability. Entering higher percentage reliability values effectively reduces the variability resulting from these factors. The resulting field strength predicted by the program will be lower, but with increased reliability that the actual field that could be measured would equal or exceed the computed value at any given time.

Situation variability accounts for variations between “like appearing” (NTIA, p. 30) systems with the same system parameters and environmental conditions, including differences in the ability of individuals to accurately take field strength readings. “It is at this point that ‘hidden variables’ enter, variables whose effects we do not understand or which we simply have not chosen to control. The values of these variables are at the whim of nature and differ between what would otherwise be identical situations. The effects of these differences produce the changes in observed statistics” (NTIA, p.30). Situation variability describes the effects of the changing conditions resulting from these “hidden variables.” The situation variability for the calculation is expressed as a percentage from 0.1% to 99.9%. This value gives the fraction of “identical” paths on which actual received field strength is expected to be equal to or higher than the field computed by the program. This variable allows you to specify how you want to deal with the “hidden variables” that are “at the whim of nature” as described above. Entering higher percentage confidence values effectively reduces the variability resulting from these factors. The resulting field strength predicted by the program will be lower, but with increased confidence that the actual field that could be measured would equal or exceed the computed value.

In the default settings of the SoftWright implementation of Longley-Rice, these dimensions of variability are expressed in terms of “reliability” and “confidence”. The terms are introduced in the NTIA Report at 36. According to this report, reliability refers to a measure of the variability that a radio system will observe during its use. Confidence refers to the variability that remains after specifying reliability, measurable in the aggregate of a large number of radio systems.

Terrain Profile Characteristics

The Longley-Rice model, as implemented by SoftWright, uses the elevation values to create a detailed profile of a path for analysis by the program. In the case of the Longley-Rice program, the elevation values are read from the TAP elevation data base. As with other propagation models in the TAP system, the file can contain multiple radials and path studies can be performed for multiple points along each radial.

Note that the model as it was originally designed expects terrain profile information at equal increments along a specific path. Although other propagation models available in the TAP system permit unequal elevation point spacing (such as when a radial elevation data file is edited to insert a particular peak or ridge), such files pose a potential problem for the Longley-Rice program. Elevation data extraction parameters that are specified for use with the Longley-Rice field calculation program are first read to determine compliance with the uniform spacing requirement. (The spacing of elevation points on different radials does not have to be the same, but the spacing between points on any given radial must be uniform.) The spacing between points is assumed to be the distance from the site to the first elevation point on the radial. Any intermediate points (i.e., successive points spaced at less than that distance from the preceding point) that are found are ignored. If the spacing between successive points is greater than the determined uniform spacing any remaining elevation data on the radial cannot be processed by the model and that portion of the radial is skipped. The program will compute field strength values out to the last uniformly spaced point on the radial.

Path Parameter Calculations

1. Effective Antenna Heights: Effective antenna height is defined as the height of the antenna above the “effective reflecting plane” (see IEEE at 28). The model first determines a “range of interest” based upon above ground elevation and the horizon distance of each antenna, and then uses one of two methods to determine the effective heights from the ground levels and least squares elevation values.

2. Horizon Distances and Elevation Angles: The horizon elevation angle refers to the angle by which the horizon rays are elevated or depressed relative to the horizontal at each antenna (see Longley-Rice at 3-1). Using detailed terrain profile information, the model calculates horizon elevation angles as a function of antenna heights above sea level, the effective earth’s radius and the great circle distances from each antenna to its horizon.

3. Terrain Irregularity: The model first uses linear interpolation to fit a straight line within the range of interest and then determines an interdecile range D h(d) above and below this line (see IEEE at 28). The terrain irregularity parameter D h is then computed.

4. Reference Attenuation: The horizon elevations and distances generated by the model are used to calculate transmission loss relative to free space. The model divides total transmission loss into “free-space basic transmission loss” and reference attenuation relative to free space. The free-space basic transmission loss is calculated as a function of frequency and distance. The net received field at any point is computed from the free-space field reduced by the computed reference attenuation relative to free space. One of three prediction methods described in Annex 3 of Longley-Rice is used to calculate the reference attenuation based upon the distance from the transmitting antenna.

    • Line of Sight Attenuation: Within radio line of sight, attenuation relative to free space is calculated using two-ray optics formulas.
    • Diffraction Attenuation: A diffraction method is used just beyond line of sight that computes a weighted average of estimates of diffraction attenuation over a double knife edge and over irregular terrain.
    • Forward Scatter Attenuation: Forward scatter attenuation is computed when the path length and/or the angular distance exceeds certain limits determined by the model.

 Parameter Checking

The Longley-Rice programs described in NTIA and other literature include validation of various parameters. The warnings are categorized into four “levels” according to the severity of the error:

Level Description (NTIA, p. 70)
1 Caution, parameters are close to limits
2 Impossible parameters; default values have been substituted
3 Internal calculations show parameters out of range
4 Parameters out of range

The level recorded by the program is cumulative in the sense that if both a level 1 error and a level 3 error are encountered, the error reported is level 3.

Examples of the warnings detected in the Longley-Rice model help to illustrate these levels:

Level Example of the warning
1 A specified frequency below 40MHz is “close to limits” of stated Longley-Rice range of 20 – 40GHz.
2 A climate code of -1 is an “impossible parameter” since the range is 1-7. A default value of 5 (“continental temperate”) will be substituted.
3 Internal calculations based on the path elevation data can show that a horizon elevation angle is beyond the range considered valid for the Longley-Rice calculations.
4 A specified frequency below 20MHz is “out of range” since the stated Longley-Rice range is 20 – 40GHz.

These rather brief and general messages represent a number of different conditions. The SoftWright implementation of the Longley-Rice model expands these messages to include more information about the specific condition that resulted in the warning level set by the program. If more than one warning or error was encountered, all messages will be recorded as described later in this section. The SoftWright messages are listed below.

Detailed Message Level
Horizon distance(s) may be too short.1 3
Horizon distance(s) may be too long.2 3
Horizon elevation angle greater than 11.5 degrees.3 3
Frequency below 40 MHz. 1
Frequency above 10 GHz. 1
Antenna height(s) less than 1 meter AGL. 1
Antenna height(s) greater than 1000 meters AGL. 1
Surface refractivity below 250. 4
Surface refractivity above 400. 4
Earth curvature less than 75e-9. 4
Earth curvature greater than 250e-9. 4
Real surface transfer impedance less than imaginary part. 4
Frequency below 20 MHz. 4
Frequency above 20 GHz. 4
Antenna height(s) less than 0.5 meter AGL. 4
Antenna height(s) greater than 3000 meters AGL. 4
Distance for calculation is greater than 1000 km. 1
Distance less than 5x difference between effective antenna heights.4 3
Distance for calculation is less than 1 km. 4
Distance for calculation is greater than 2000 km. 4
Invalid climate code; climate code set to 5. 2
Invalid variability mode; mode set to 0. 2
Time probability set less than 0.1%. 1
Location probability set less than 0.1%. 1
Situation probability set less than 0.1%. 1

Notes:

1. This condition occurs in Longley-Rice if the computed horizon distance is less than:

where HE is the computed effective antenna height of the antenna and GME is the effective earth curvature.

2. This condition occurs in Longley-Rice if the computed horizon distance is greater than:

where HE is the computed effective antenna height of the antenna and GME is the effective earth curvature.

3. This condition occurs in Longley-Rice if the computed horizon elevation angle is greater than 0.2 radians (11.5°).

4. This condition occurs in Longley-Rice if the distance for the computed field strength is less than:

where HE(1) is the computed effective antenna height of the TX antenna and HE(2) is the computed effective antenna height of the RX antenna

Whenever the Longley-Rice program encounters any of these conditions the warning(s) are recorded in the TAP Results Data Base file for the study.

Conclusions

The discussion in this article is intended to be a cursory overview of the model’s treatment of the parameters and statistics of radio propagation as treated by the Longley-Rice model. You are encouraged to refer to the literature to develop your own understanding and interpretation of the Longley-Rice concepts.

Given your system parameters and statistical choices that you have supplied in TAP’s Longley-Rice module, our implementation of the model will generate a file of field strength values computed from the long-term median transmission losses at each increment and along each radial you have selected. This file can then be used just as other TAP field strength files with TAP’s graphical features (such as the threshold plotting).