Notes on Longley-Rice Propagation

Notes on The Prediction of Tropospheric Radio Transmission Loss Over Irregular Terrain (the Longley-Rice Model)


This document 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Version 2.0, dated May 1970) uses "considerably modified diffraction calculations" and is "not now recommended and is no longer maintained by its developers."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.


The SoftWright implementation of the Longley-Rice model preserves the methods and calculations of the original Version 1.2.2 source code, and, as much as possible, integrates the model into the existing Terrain Analysis Package (TAP) software system. However, as described, below, certain constraints imposed by the Longley-Rice model require slight modifications in the use of the TAP system. These modifications are thoroughly discussed below.

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:

Longley-Rice Parameters

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

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


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


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.

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:


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:


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.


The original Longley-Rice programs include the following messages for the warnings:




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

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 .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 eff ant 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



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
GME is the effective earth curvature

2 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
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
HE(2) is the computed effective antenna height of the TX 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.


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).

Ordering Information For Longley-Rice Propagation Model Documentation

The following documents are available from National Technical Information Service (phone 1-800-553-6847, or 1-703-487-4656). The abbreviated titles refer to the notation used for the documents in the Terrain Analysis Package (TAP)™ Technical Reference Manual section on the Longley-Rice model.


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