NTIA Report 86-203 

Ground-wave Analysis Model for 

MF Broadcast Systems 

N. DeMinco 

U.S. DEPARTMENT OF COMMERCE 

Malcolm Baldrige, Secretary 

Alfred C. Sikes, Assistant Secretary

for Communications and Information 

September 1986 

TABLE OF CONTENTS 

Page 

List of Figures iv 

List of Tables vii 

Abstract 1 

1. INTRODUCTION AND BACKGROUND 1 

2. THE SYSTEM PERFORMANCE PREDICTION PROGRAM GWVOA 3 

2.1 The System Interface Algorithm 4 

2.2 The Propagation Loss Prediction Methods 7 

 2.2.1 The Smooth-Earth Method 7 

2.2.2 The Smooth-Earth, Mixed-Path Method 10 

2.2.3 The Irregular-Earth, Mixed-Path Method 13 

2.3 The Noise Prediction Algorithm 15 

2.4 The Antenna Algorithm 18 

2.5 The Run Time and Accuracy Algorithms 26 

2.5.1 Time and Accuracy Tradeoffs 26 

2.5.2 Terrain and Frequency Effects on Accuracy 27 

 

3. A USER’S GUIDE TO PROGRAM GWVOA 41 

4. SAMPLE SESSIONS WITH PROGRAM GWVOA 58 

5. CONCLUSIONS 90 

6. ACKNOWLEDGMENT 90 

7. REFERENCES 91 

iii 
LIST OF FIGURES 

Figure Page

1. A three-section, mixed-path for the smooth- 11 

Earth, mixed-path method. 

2. Three-monopole array geometry. 23 

3. Four-monopole array geometry. 24 

4. Six-monopole array geometry. 25 

5. Path profile for Canyonlands, Utah 29 

 (rough terrain). 

6. Path profile for Santa Rita Mountains, 30 

Arizona (hilly terrain). 

7. Propagation loss predictions for the 31 

irregular-Earth method using 1 and 8 km 

terrain data spacing at .52 MHz over 

 rough terrain. 

8. Propagation loss predictions for the 31 

irregular-Earth method using 1 and 8 km 

terrain data spacing at 1.00 MHz over 

 rough terrain. 

9. Propagation loss predictions for the 32 

irregular-Earth method using 1 and 8 km 

terrain data spacing at 1.62 MHz 

over rough terrain. 

10. Propagation loss predictions for the 32 

irregular-Earth method using 1 and 8 km 

terrain data spacing at .52 MHz over 

 hilly terrain. 

11. Propagation loss predictions for the 33 

irregular-Earth method using 1 and 8 km 

terrain data spacing at 1.62 MHz 

over hilly terrain. 

12. Propagation loss predictions for the 33 

irregular-Earth method using 1 and 8 km 

terrain data spacing at 1.62 MHz 

over hilly terrain. 

13. Propagation loss prediction comparison for 35 

the irregular-Earth method using 1 – km 

terrain spacing versus the smoothEarth method at .52 MHz over rough terrain. 

iv 
List of Figures (cont.) Page

14. Propagation loss prediction comparison for 35 

the irregular-Earth method using 8 – km 

terrain spacing versus the smoothEarth method at .52 MHz over rough terrain. 

15. Propagation loss prediction comparison for 36 

the irregular-Earth method using 1 – km 

terrain spacing versus the smooth-Earth method 

at 1.00 MHz over rough terrain. 

16. Propagation loss prediction comparison for 35 

the irregular-Earth method using 8 – km 

terrain spacing versus the smoothEarth method at 1.00 MHz over rough terrain. 

17. Propagation loss prediction comparison for 37 

the irregular-Earth method using 1 – km 

terrain spacing versus the smooth-Earth 

method at 1.62 MHz over rough terrain. 

18. Propagation loss prediction comparison 37 

for the irregular-Earth method using 8 – km 

terrain spacing versus the smooth-Earth 

method at 1.62 MHz over rough terrain. 

19. Propagation loss prediction comparison for 38 

the irregular-Earth method using 1 – km 

terrain spacing versus the smooth-Earth, 

mixed-path method at .52 MHz over hilly 

 terrain. 

20. Propagation loss prediction comparison for 38 

the irregular-Earth method using 8 – km 

terrain spacing versus the smoothEarth, mixed-path method at .52 MHz over 

 hilly terrain. 

21. Propagation loss prediction comparison for 39 

the irregular-Earth method using 1 – km 

terrain spacing versus the smooth-Earth, 

mixed-path method at 1.00 MHz over hilly 

 terrain. 

22. Propagation loss prediction comparison for 39 

the irregular-Earth method using 8-km 

terrain spacing versus the smooth-Earth, 

mixed-path method at 1.00 MHz over hilly 

 terrain. 

v 
List of Figures (cont.) Page

23. Propagation loss prediction comparison for 40 

the irregular-Earth method using 1 – km 

terrain spacing versus the smooth-Earth, 

mixed-path method at 1.62 MHz over hilly 

 terrain. 

24. Propagation loss prediction comparison for 40 

the irregular-Earth method using 8 – km 

terrain spacing versus the smooth-Earth, 

mixed-path method at 1.62 MHz over hilly 

 terrain. 

vi 
LIST OF TABLES 

Table Page

1. Coefficients for Man-made Noise and 17 

 Galactic Noise. 

2. Signal-to-Noise Power Ratio and Achievable- 43 

Distance Prediction Questions, Their 

Meaning and Acceptable Range of Values. 

vii 

GROUND-WAVE ANALYSIS MODEL FOR 

MF BROADCAST SYSTEMS 

N. DeMinco∗

An automated analysis model is presented for the prediction of 

system performance of communications circuits that use the ground 

wave as the primary mode of propagation. The computer program Ground 

Wave for Voice of America (GWVOA) is a user-friendly program that can 

predict propagation loss, electric field strength, received power, 

noise, received signal-to-noise power ratio, and antenna factors over 

lossy Earth. The smooth-Earth and irregular-Earth propagation loss 

prediction methods can be used over either homogeneous or mixed paths. 

A special antenna algorithm is integrated into the computer program 

for rapid prediction of antenna performance as a function of antenna 

geometry, ground constants, frequency, and azimuthal direction for a 

variety of antennas. A description of the computer program GWVOA, a 

discussion of its capabilities, instructions for its use, and 

illustrative sample calculations are included in this report. 

Key words: ground-wave antenna model; ground-wave propagation; irregular 

terrain; lossy Earth; MF propagation; mixed path; smooth Earth; 

surface waves 

1. INTRODUCTION AND BACKGROUND 

For many years, the Institute for Telecommunication Sciences (ITS) has been 

involved in model development and analysis of ground-wave communications at high 

frequencies (3-30 MHz) and lower frequencies. In the past, ground-wave 

propagation prediction methods have been developed at ITS for both smooth and 

irregular Earth using elementary short dipole and monopole reference antennas. 

The ground-wave propagation loss prediction methods for smooth Earth include those 

reported by Berry and Herman (1971), L.A. Berry (OT Technical Memorandum 78-247, 

January 1978, limited distribution), and Stewart et al. (1983). Additional 

modifications were installed in 1984 by L.A. Berry (private communication, 1985). 

The ground wave prediction method for irregular-Earth terrain was developed by Ott 

(1971) and later extended by Hill (1982). These prediction methods have been 

compared with measured data by Ott et al. (1979) and Adams et al (1984). The 

 

∗

 The author is with the Institute for Telecommunication Sciences, National 

Telecommunications and Information Administration, U.S. Department of Commerce, 

Boulder, CO 80303.
measured data were taken using the same elementary antenna configurations that 

were used in the propagation loss prediction methods. 

The Voice of America (VOA) needed an analysis model that included the more 

complex antennas of typical communications and broadcast systems in the presence 

of lossy ground. This report describes the computer model Ground Wave for Voice 

of America (GWVOA) developed for VOA. The antenna algorithms developed for this 

computer program are valid for all ground constants and antenna geometries. A 

limited number of antenna types were incorporated into the algorithm. Additional 

types of antennas can be added. 

The main computer program GWVOA combines three propagation loss prediction 

methods for both smooth and irregular Earth, a system interface algorithm, a noise 

prediction algorithm, a reliability algorithm, and an antenna algorithm into one 

user-friendly analysis tool. 

The computer program can be used by individuals of moderate skill levels with 

little or no training for rapid analysis of many different communication systems 

in different geographic areas and under varied operating conditions. The computer 

program is a complete, user-friendly analysis tool for evaluating communications 

and broadcast circuits. It is written in standard ANSI FORTRAN 77. It is 

available through the Telecommunication Analysis Services on the ITS computer. 

The VOA will use the GWVOA model to predict VOA station coverage. Later in 

1986, an extended version of GWVOA, called MF-RESYDE, will become available. 

MF-RESYDE will include skywave and interference calculations, in addition to the 

GWVOA capabilities. 

Section 2 of this report describes the complete performance prediction model 

in program GWVOA. The subsections in this section will describe all of the 

constituent algorithms and methods contained within the main program. References 

will be given where necessary to provide more detail for the interested reader. 

Section 3 is a users' guide for the computer model GWVOA. A complete 

description of the questions asked by the program to request input data will be 

given with an explanation of what behavior will occur for different user 

responses. Tables of input variable range limits and default values will be given. 

An explanation of the limitations of the computer model in terms of input/output 

variables will also be contained in this section. Section 4 will include sample 

sessions with GWVOA to provide the user with illustrative examples and a means of 

checking program GWVOA for proper operation. 

2
In Section 5, conclusions will be presented regarding the overall accuracy 

and capabilities of computer program GWVOA. Recommendations for further work will 

also be put forth. 

2. THE SYSTEM PERFORMANCE PREDICTION PROGRAM GWVOA 

The performance of telecommunication systems that rely on ground-wave signals 

is dependent on transmitter power, signal frequency, transmitter and receiver 

antenna characteristics, ground constants, noise and interference environment, and 

the terrain contour between the transmitter and receiver. An accurate prediction 

of system performance depends on how well each of the dependent variables listed 

above is taken into account in the calculations. 

The computer program GWVOA combines three propagation loss prediction 

methods, a system interface algorithm, a noise prediction algorithm, and an 

antenna algorithm into a user-friendly analysis tool for system performance 

prediction. The propagation loss prediction methods, system interface algorithm, 

and noise prediction algorithm are valid from 10 kHz to 30 MHz. Collectively, the 

three propagation loss prediction methods can be used to predict propagation loss 

for the terrain that is either homogeneous or mixed path. The antenna algorithm 

for the single monopole antenna option, user gain input, and electric field 

strength are also valid from 10 kHz to 30 MHz. The ferrite loop antenna and the 

three monopole arrays are valid only from 0.5 MHz to 1.7 MHz. The antenna 

algorithm gives accurate representations of equivalent antenna gain to provide 

reasonably good predictions for engineering analysis. The accuracy of this 

algorithm will be discussed in a later section. The methodology of program GWVOA 

and its constituent algorithms and methods will be discussed separately in this 

section. 

The computer program GWVOA operates with three basic output options: 

received signal-to-noise power-ratio for a single frequency and direction, 

received signal-to-noise power-ratio for multiple frequencies and directions, and 

the maximum achievable distance for a user input signal-to-noise ratio and 

reliability at multiple frequencies and directions. 

In the received signal-to-noise power-ratio for a single frequency and 

direction option, the program predicts basic transmission loss, received electric 

field strength, received signal power, received signal-to-noise power-ratio for a 

particular reliability, noise level, and antenna factors over lossy Earth. The 

signal-to-noise power-ratio calculations can be made for multiple seasons and 

3
times. The user enters a desired reliability for the signal-to-noise power-ratio 

calculation. The transmission losses for this option are calculated with one of 

the user-selected propagation loss prediction methods: smooth homogeneous Earth 

(SE); smooth inhomogeneous (mixed path) Earth (SEMP); and irregular Earth, mixedpath (IEMP) with or without a slab representing forests, cities, etc. The terrain 

data base is automatically accessed by program (IEMP) or the user may manually 

enter terrain data. 

The received signal-to-noise power-ratio for multiple frequencies and 

directions option calculates everything that the first output option does for 

multiple frequencies and directions, but only the SE and SEMP propagation loss 

calculations are allowed. IEMP propagation loss computation times can be excessive 

for each path, resulting in prohibitively long run times. The user should exercise 

caution when selecting this propagation loss prediction method. 

The achievable distance option calculates the maximum distance from the 

transmitter at which the user input signal-to-noise power ratio and reliability 

are simultaneously achieved. The received power, noise level, and electric field 

strength are also computed. The calculations are performed for multiple 

frequencies, directions, seasons, and times of day. The propagation loss 

prediction methods using this option are also limited to the SE and SEMP loss 

prediction methods, because the repetitious calculations required with this output 

option would result in prohibitively long run times if the IEMP loss prediction 

method were used. 

Within these three basic program output options are many alternate paths the 

user can take depending on the user response to the input questions. This will be 

covered in detail in Section 3. 

2.1 The System Interface Algorithm 

The system interface algorithm is used to combine the propagation losses, 

antenna gains, and appropriate constants to calculate electric field strength and 

received power. It also combines the received power with a noise prediction 

for a desired reliability to determine signal-to-noise power-ratio for a given 

reliability. The achievable distance for a given input reliability and 

signal-to-noise power-ratio is also computed with the system interface algorithm. 

The standard equation used in GWVOA to relate the received power (dBW), 

transmitter power (dBkW), antenna gains (dBi), and basic transmission loss (dB) 

is: 

4
 Pr(dBW) = Pt(dBkW) + Gt(dBi) + Gr(dBi) - Loss(dB) + 30 (1) 

where 

 Pr(dBw) = the receiver power in decibels referenced to one watt 

 Pt(dBkW) = the transmitter power in decibels referenced to one kilowatt 

 Gt(dBi) = the transmitter antenna gain in decibels referenced to an 

isotropic radiator in free space 

 Gr(dBi) = the receiver antenna gain in decibels referenced to an isotropic 

radiator in free space 

Loss(dB) = basic transmission loss between two isotropic radiators computed 

from one of the three propagation models 

This equation is used to calculate the received power for all program 

computations requiring received power (signal-to-noise power-ratio, achievable 

distance, etc.). 

The equation used to calculate electric field strength, E in dBuV/m, from the 

transmitted power, transmitter antenna gain, frequency, and basic transmission 

loss is: 

E(dBuV/m)= 131.20 + 20 log f(MHz) + Pt(dBkW) + Gt(dBi) - Loss(dB) (2) 

where 

f(MHz) = the frequency in megahertz, and the remaining variables are as 

defined above for the received power calculation. 

This equation can be derived easily from an equation that originated in CCIR 

Report 112 (CCIR, 1959). The original equation in this document is an expression

for propagation loss Lp(dB): 

Lp(dB) = 135.97 - Gp(dBi ) + 20 log f(MHz) - E(dBuV/m) (3) 

where

5
Gp(dBi) is the path antenna gain in decibels, 

f(MHz) is the frequency in megahertz, and 

E(dBuV/m) is the electric field strength in dBuV/m for 1kW radiated power 

from a short, vertical electric dipole over perfectly conducting ground. 

The path antenna gain, Gp, for this transmitter antenna configuration is 

given as 4.77 dB in CCIR Report 112 (CCIR, 1959). If this is substituted into 

(3) and normalized to any arbitrary transmitter power Pt(dbkW) and transmitter 

antenna gain Gt(dBi), the resultant equation with E and PL transposed is (2). 

The received signal-to-noise power-ratio in decibels is the received power in 

dBW computed with (1) minus the noise power in dBW in a 1 Hz bandwidth, which is 

computed from the noise prediction algorithm for each time, season, frequency, and 

user-selected man-made noise level. 

Reliability is taken into account by a simplified algorithm that uses the 

median, upper decile, and lower decile of the total noise statistics. The total 

noise statistics are a combination of the median, upper decile, and lower decile 

of man-made, atmospheric, and galactic noise. This noise prediction algorithm is 

discussed in more detail in Section 2.3 and Spaulding and Washburn (1985). 

The reliability algorithm uses linear interpolation between the median and 

the upper decile value of the noise for reliabilities of obtaining a specific 

signal-to-noise power-ratio between 50 and 90 percent. Linear interpolation is 

performed between the median and the lower decile value of the noise for 

reliabilities of obtaining a specific signal-to-noise power ratio between 10 and 

50 percent. Linear extrapolation is used by extending the appropriate straight 

line segment beyond the upper or lower decile points to obtain signal-to-noise 

power ratio reliabilities greater than 90 or less than 10 percent. 

When the user enters a specific reliability in the single or multiple 

frequency and direction program mode, the noise level corresponding to that 

reliability is used for the signal-to-noise power ratio calculation. If the user 

is in the achievable-distance mode, then a signal-to-noise power-ratio and 

reliability are entered by the user. The program then uses the appropriate noise 

level corresponding to the input reliability and determines at what maximum 

distance the signal level is adequate to achieve the input signal-to-noise powerratio for the given input reliability. The result is the required received power. 

6
The system interface algorithm then calculates signal power versus distance from 

the transmitter until it gets to this required received power. The system 

interface algorithm then calculates signal power versus distance from the 

transmitter until it gets to this required received power. The distance is 

calculated as the maximum achievable distance corresponding to the user input 

signal-to-noise power-ratio and reliability. 

All three propagation loss prediction methods are permitted in the singlefrequency-and-direction signal-to-noise power ratio option. The use of the 

irregular-Earth propagation loss prediction method is prohibited in the multiple 

frequency and direction signal-to-noise power-ratio or achievable-distance 

options. 

2.2 The Propagation Loss Prediction Methods 

Program GWVOA contains three separate propagation loss prediction methods: a 

smooth-Earth (SE), a smooth-Earth, mixed-path (SEMP) and an irregular-Earth, 

mixed-path method that includes forested and built-up terrain over mixed paths 

(IEMP). The smooth-Earth and smooth-Earth, mixed-path methods are efficient 

programs with fast run times, but the irregular-Earth method is, in general, much 

slower in computation time due to the techniques used for the attenuation function 

calculation. The techniques used in IEMP are still the most efficient and fastest 

irregular-Earth computation procedures to date for general irregular-Earth terrain 

(Rotheram et al., 1985). The smooth-Earth methods calculate transmission loss for 

both vertical and horizontal polarization. The irregular-Earth method is limited 

to only vertical polarization. This section will briefly explain each of the 

three propagation methods used in GWVOA and point out the limitations of each. A 

description of computation times and relative accuracy of each model will be given 

in Section 2.5. 

2.2.1 The Smooth Earth Method 

The smooth-Earth method is that developed by L.A. Berry ("User's Guide to Low 

Frequency Radio Coverage Programs," OT Technical Memorandum 78-247, January 1978, 

limited distribution). It is also described in Berry and Herman (1971) and 

Stewart et al. (1983). Two additional computation techniques were implemented in 

the smooth-Earth method in 1984 by L.A. Berry (private communication, 1985). They 

will be described briefly in this section. The method is for computing 

ground-wave propagation loss over smooth homogeneous Earth. The ground wave 

7
includes the direct line-of-sight space wave, the ground-reflected wave, and the 

surface wave that diffracts around the curved Earth. The sky wave reflected from 

the ionosphere is not included in this calculation. 

The formulas used in the smooth-Earth model are adapted from Abramowitz and 

Stegun (1964), Wait (1964), Fock (1965), King (1969), and Hill and Wait (1980). 

The following six computation techniques are used: flat-Earth attenuation 

function, flat-Earth attenuation function with curvature correction (Hill and 

Wait, 1980), Hill and Wait's series for small Q (Hill and Wait 1980), the residue 

series calculation, geometric optics, and numerical integration of full wave 

theory. The flat-Earth attenuation function with curvature correction and Hill 

and Wait's series for small Q were added in 1984 by L.A. Berry (private 

communication, 1985). Antenna heights, path lengths, Earth geometries, ground 

constants, and frequency are used by the program to automatically select the 

appropriate computation technique. The losses calculated by the smooth-Earth 

method are in agreement with Norton's work (1941), where Norton's approximations 

are valid, and the CCIR Curves (CCIR, 1970). The smooth-Earth method is 

mathematically and numerically accurate for the ground-wave predictions for 

frequencies from 10 kHz to 100 MHz (L.A. Berry, OT Technical Memorandum 78-247, 

January, 1978, limited distribution). Above 30 MHz, the irregularities of the 

atmosphere make statistical methods more appropriate. Irregularities in the 

terrain have more of an effect at higher frequencies, so an irregular terrain 

model is more appropriate when terrain irregularities become appreciable in size 

with respect to a wavelength. 

The smooth-Earth method calculates field strength and converts this to 

propagation loss. The computation technique depends upon the relative geometry of 

the transmitter and receiver locations, the ground constants, and the radio 

frequency. The radio wave propagates as a surface wave when both the transmitter 

and receiver are near the Earth in wavelengths. If, in addition, the path lengths 

are short such that the Earth can be assumed to be flat, then the flat-Earth 

attenuation function (Wait, 1964) is valid. The equations are given in Stewart 

et al. (1983). 

When the transmitter and receiver are high enough such that an observer is 

well above the radio horizon when viewed from the other, the field strength 

involves the use of geometrical optics. The formulas are given in Stewart et 

al. (1983). When the receiving antenna is near the radio horizon of the 

transmitting antenna, the field depends upon diffraction effects in addition to

8
the direct wave. The computation technique is then by numerical integration of 

the full-wave theory integral (Stewart et al., 1983). 

For long path lengths, the Earth cannot be considered flat. If, in addition, 

the geometry is such that a straight line connecting the transmitter and receiver 

antennas intersects the curved Earth, then the full-wave theory integral must be 

evaluated using a residue series (Fock, 1965; Wait, 1964). 

For cases where the antennas are close to Earth but the distances are long 

enough such that Earth is not flat, the computation is performed using either a 

flat-Earth attenuation function with a small-Earth curvature expansion or a power 

series expansion. The addition of these two techniques is for the purpose of 

reducing the use of the numerical integration of the full-wave theory integral, 

since it is very time consuming. These two techniques bridge the gap for loss 

computation between the case where the Earth is flat (flat-Earth attenuation 

function) and that where the receiving antenna is near the radio horizon of the 

transmitting antenna. The computation technique is selected depending on whether 

the magnitude of a q factor is small or large (Hill and Wait, 1980). The q factor 

is given by: 

⎟ ∆ ⎠

⎞ ⎜

⎝

⎛ = − 3

1

2

Ka

q i (4) 

where 

 K = 2π/λ

λ = wavelength of radio wave (meters) 

a = radius of the Earth (meters) 

∆ = normalized surface impedance of the ground below the antenna 

 in question 

gc

gc

ε

ε −1 = for vertical polarization 

= −1 gc ε for horizontal polarization 

Ο

= +

ωε

σ

ε ε

i

g

gc g

9
εg = relative dielectric constant of the ground 

σg = conductivity of the ground in siemens per meter 

εΟ = permittivity of free space 8.85 x 10-12 farads per meter 

ω = 2πf. 

The surface impedance is a function of the ground constants of the Earth's 

surface. If the magnitude of q is small (<.1), then a power series expansion is 

used for the attenuation function (Bremmer, 1958; Wait, 1956, 1958). The 

attenuation function is the ratio between the electric field from a short dipole 

over the lossy Earth's surface to that field from the same short dipole located on 

a flat perfectly conducting surface. 

If the magnitude of q is large (≥.1) then a small curvature expansion is more 

appropriate for the attenuation function (Hill and Wait, 1980; Wait, 1956; 

Bremmer, 1958). The implementation of these two techniques reduces the need for 

the numerical integration technique and reduces computation time considerably. 

The smooth-Earth model is valid for all combinations of antenna heights, 

frequency, and dielectric constants by virtue of the six computation techniques 

contained within its structure. It should be used only out to the maximum ranges 

considered useful for ground-wave propagation at each frequency, since the sky 

wave would become significant from that distance to points beyond. This distance 

is roughly 300 km at low frequencies ≤ 0.5 MHz and depends on frequency in 

addition whether it is day or night. The ground-wave model is valid for path 

lengths ranging from 1 to 10,000 km (L.A. Berry, OT Technical Memorandum 78-247, 

January, 1978, limited distribution). 

2.2.2 The Smooth-Earth, Mixed-Path Method 

The smooth-Earth, mixed-path method is a specific sequence of smooth-Earth 

model runs over each of the segments that are then combined in a particular order 

as determined by the Millington algorithm (Millington, 1949). The antenna heights 

are set to zero for each run over each of the segments and combination of segments 

required by the algorithm. A height gain function is then applied to the 

transmitter and receiver antennas using the ground constants under each antenna 

and the user-supplied heights. The result is the propagation loss over a mixed 

path with compensation for antenna heights. The Millington algorithm implemented 

in the smooth-Earth, mixed-path technique will be discussed for the three section 

mixed path of Figure 1. Expansion to more sections is a straightforward process.

10
 

Figure 1. A three-section, mixed-path for the smoothEarth, mixed-path method. 

11
The first step involves the calculation of losses using the smooth-Earth model 

over single sections and combinations of sections using the different ground 

constants. With T as a source we first compute the loss Ltr in decibels (dB). 

 Ltr(dB) = L1(d1) - L2(d1) + L2(d1 + d2) - L3(d1 + d2) + L3(d1 + d2 + d3) (5) 

where 

 L1(d1) = loss in dB over distance d1 using σ1 ε1 

 L2(d1) = loss in dB over distance d1 using σ2 ε2 

 L2(d1 + d2) = loss in dB over distance d1 + d2 using σ2 ε2 

 L3(d1 + d2) = loss in dB over distance d1 + d2 using σ3 ε3 

 L3(d1 + d2 + d3) = loss in dB over distance d1 + d2 + d3 using σ3 ε3 

With R as a source compute the loss Lrt in decibels 

 Lrt(dB) = L3(d3) - L2(d3) + L2(d3 + d2) - L1(d3 + d2) + L1(d3 + d2 + d1) (6) 

where 

 L3(d3) = loss in dB over distance d3 using σ3 ε3 

 L2(d3) = loss in dB over distance d3 using σ2 ε2

 L2(d3+ d2) = loss in dB over distance d3 + d2 using σ2 ε2

 L1(d3 + d2) = loss in dB over distance d3 + d2 using σ1 ε1 

 L1(d3 + d2 + d1) = loss in dB over distance d3 + d2 + d1 using σ1 ε1

The total loss Lt(dB) is then computed: 

20log[ ( ) ( ) 2

( )

2

( ) ( ) t r

tr rt

t G Z G Z

L dB L dB

L dB = + − ] (7) 

 G(Zt) and G(Zr) are the height-gain functions for the transmitter and 

receiver antennas respectively. 

G (Z) = 1 + iKZ ∆ (8) 

where 

12
Z = the transmitter antenna height, Zt or receiver antenna height, Zr, in 

meters 

K = 2 π/λ and λ = wavelength in meters of radio wave 

∆ = normalized surface impedance of the ground below the antenna in question 

as defined in (4) previously. 

This smooth-Earth, mixed-path method will calculate the propagation loss over 

a mixed path with as many as 50 segments. The main program will request the 

ground constants and distances for each of the segments. It is valid for the same 

frequency and distance ranges as in the smooth-Earth method. 

2.2.3 The Irregular-Earth, Mixed-Path Method 

The irregular-Earth, mixed-path (IEMP) method uses an integral equation 

(Hill, 1982; Ott, 1971) to compute the propagation loss of a vertically polarized 

electromagnetic wave over irregular terrain that is covered with forests, 

buildings, or snow. WAGSLAB (Hill, 1982) is an extension of program WAGNER (Ott, 

1971) to model a slab representing the terrain cover. The irregular-Earth, mixedpath (IEMP) method in GWVOA is a modified version of program WAGSLAB (Hill, 1982). 

The terrain cover is modeled as a slab of user-specified thickness, length, 

conductivity, and dielectric constant. Antenna heights of the transmitter and 

receiver antennas without a slab are taken into account within the program using 

the height-gain functions discussed previously for the smooth-Earth, mixed-path 

method. When a slab is included, a special height-gain function (Hill, 1982) is 

used for antennas within or above the slab. The program can handle up to 50 

different segments over a mixed path. 

The modifications for the IEMP method of program GWVOA include a user 

friendly input/output interface, an automatic computation of distance increment 

select based on terrain roughness and frequency, an automated capability to sample 

terrain height at any interval, manual terrain input capability, and an algorithm 

to reduce the overall run time and simultaneously maintain computation accuracy of 

results. In addition, GWVOA includes the antenna gains for user-selected antennas. 

The original WAGSLAB used only a standard dipole transmitter antenna, and no 

provision was made for a receiver antenna. 

The integral equation approach in program IEMP is a point-to-point prediction 

method valid for frequencies between 10 kHz and 30 MHz. At higher frequencies, 

other techniques must be used that take into account the large variability of the 

13
groundwave in time and space. The analytical details of the integral equation 

are described in the references for WAGSLAB (Hill, 1982) and WAGNER (Ott, 1971). 

In both of these references, good agreement is found between this calculation 

method and other analytical computation methods. Comparisons of calculations with 

measurements have also been made (Ott et al., 1979; and Adams et al., 1984). 

One problem with the original WAGNER and WAGSLAB is the excessive computation 

time required. The computation time is proportional to the square of the number of 

points at which the computation is made along the path. The number of points 

required is related to the terrain roughness, frequency, and the path length. The 

accuracy is dependent on the number of points. The larger the number of points for 

a given distance, the more accurate is the calculation, but too many points may 

result in excessive computation time. 

The IEMP method contains modifications that reduce the overall computation 

time. A trade-off is made by the subroutine that controls the irregular-Earth 

calculation points of program GWVOA. It performs a tradeoff between the number of 

calculation points and propagation loss prediction accuracy. The terrain is 

examined for the path in question and a terrain roughness factor is calculated 

using a newly developed procedure. The frequency and path length are also used by 

the procedure. An increment size is then calculated based on these three factors. 

Using the path length and increment size, the number of points is determined. 

The increment selection procedure actually uses a window that slides along 

the path, so that an interval size is selected for different sections along the 

path. This added factor accounts for a path that has mixed sections of relatively 

smooth, hilly, and rough terrain over the entire path, so a path section will 

contain more calculation points if the terrain is rough or hilly than it would if 

the terrain were relatively smooth. This calculation of increment size as a 

function of terrain roughness is based on an extensive study of irregular-Earth 

propagation loss prediction accuracy for different terrain roughnesses over the 

frequencies of 0.5 MHz to 30 MHz. The increment size selection procedure minimizes 

the IEMP method computation time and maximizes accuracy over a path consisting of 

smooth, hilly, and rough terrain sections. This is transparent to the user, since 

everything is done within the program with no user interaction or awareness of the 

complexity of the calculation. 

Another subroutine within the procedure analyzes and interpolates between the 

results of the calculations within the IEMP method and determines what the losses 

14
are at the specific points where the user wishes to see the calculations. The user 

specifies the initial, incremental, and final distances during the input data 

questions so that the output has computation results where the user desires them. 

The IEMP method calculates losses at all the points necessary to maintain accuracy 

and reduce computation time. The user sees only the points that are specified to 

be output. 

Even though the IEMP method is valid from 10 kHz to 30 MHz, it is not 

recommended for rough terrain at the higher (20-30 MHz) frequencies, because even 

with the speed up algorithm the IEMP method computation time can be too excessive 

in certain cases. These frequencies do not propagate well over rough terrain. 

Sky-wave propagation may be more suitable for communications. 

At the other end of the frequency band (10 kHz to 1.7 MHz) the smooth-Earth 

method or smooth-Earth, mixed-path method may give comparable accuracy to the 

irregular-Earth, mixed-path method, so it may be more efficient to use one of 

these smooth-Earth models. The relative accuracy of these methods will be 

discussed later in Section 2.5. 

2.3 The Noise Prediction Algorithm 

The noise prediction algorithm in program GWVOA is an updated version of the 

noise prediction method used in the Ionospheric Communications Analysis and 

Prediction Program (IONCAP) (Teters et. al., 1983). The new version contains 

improved noise data (Spaulding and Washburn, 1985). 

The total noise statistics are a combination of the median, upper decile, and 

lower decile of man-made, atmospheric, and galactic noise. The noise in a 1 – Hz 

bandwidth is computed in the noise program for each 1-hour/3-month-season, 

frequency, geographic location and user-selected, man-made noise level. The 

median (MED) for the total noise power is the average value of the total noise 

power in decibels with respect to one watt (dBW) exceeded for 50 percent of the 

hours within a 1-hour/3-month-season. 

The upper decile value of noise (MED + DU) is the average noise power in 

decibels with respect to 1 W exceeded for 10 percent of the hours within 1-hour/ 

3-month-season. The lower decile value of noise (MED - DL) is the average noise 

power in decibels with respect to 1 W exceeded for 90 percent of the hours within 

a 1-hour/3-month-season. 

The noise level is then below MED + DU for 90 percent of the hours within a 

1-hour/3-month-season, and below MED - DL for 10 percent of the time in a l-hour/ 

15
3-month-season. These percentages correspond to the reliabilities of attaining a 

particular signal-to-noise power-ratio assuming a deterministic signal. If MED + 

DU is used in a signal-to-noise power-ratio calculation, the actual 

signal-to-noise power-ratio will be greater than that signal-to-noise power ratio 

90 percent of the time in a 1-hour/3-month-season. It follows that if MED - DL is 

used in a signal-to-noise power-ratio calculation, the resultant signal-to-noise 

power-ratio will be greater than that signal-to-noise power-ratio for 10 percent 

of the time in a 1-hour/3-month-season. Linear interpolation is used between the 

upper decile and median noise levels to obtain reliabilities of achieving a 

specific signal-to-noise power-ratio between 50 and 90 percent and between the 

lower decile and median noise level to obtain reliabilities of achieving a 

specific signal-to-noise power-ratio between 10 and 50 percent. 

Linear extrapolation is used by extending the appropriate straight-line 

segment beyond the upper or lower decile points to obtain signal-to-noise 

power-ratio reliabilities greater than 90 or less than 10 percent. 

The total noise statistics are computed from the statistics of the 

atmospheric, galactic, and man-made noise using the following expressions: 

MED = 10 log10 (10ATNOS/10 + 10GNOS/10 + 10MMNOS/10) (9) 

DU = |10 log10(10(ATNOS + DUA)/10 + 10(MMNOS + DUM)/10 + 10(GNOS + DUG)/10)) - MED| (10) 

DL = |10 log10(10(ATNOS + DLA)/10 + 10(GNOS + DLG)/10 + 10(MMNOS + DLM)/10) - MED| (11) 

where 

ATNOS = median atmospheric noise in dBW 

GNOS = median galactic noise in dBW 

MMNOS = median man-made noise in dBW 

DUA = difference in decibels between upper decile and median value of 

 atmospheric noise 

DLA = difference in decibels between median and lower decile value of 

 atmospheric noise. 

16
DUG = difference in decibels between upper decile and median value of 

 galactic noise 

DLG = difference in decibels between median and lower decile value of 

 galactic noise 

DUM = difference in decibels between upper decile and median value of 

 man-made noise 

DLM = difference in decibels between median and lower decile value of 

 man-made noise 

MED = median total noise in dBW 

DU = difference in decibels between upper decile and median value of 

 total noise 

DL = difference in decibels between median and lower decile value of 

 total noise 

All statistical parameters above are for a 1-hour/3-month-season time period. 

The statistics for atmospheric noise are determined from a computer subroutine 

called GNOIS using the latest noise coefficients as described in Spaulding and 

Washburn (1985). The man-made noise and galactic noise are determined using the 

expression (CCIR, 1982): 

 GNOS 

or = C – Dlogf – 204 (12) 

 MMNOS 

where C and D are described in Table 1, and f equals frequency in megahertz. 

Table 1. Manmade and Galactic Noise Coefficients

Environmental Category C D

Business 76.8 27.7

Residential 72.5 27.7

Rural 67.2 27.7

Quiet Rural 53.6 28.6 

Galactic 52.0 23.0

The user chooses the environmental category for man-made noise. The galactic 

and man-made noise values are always calculated using the coefficients of Table 1.

The upper and lower decile values of galactic and man-made noise are fixed within 

17
the noise prediction algorithm and are assigned the following values: DUM = 9, 

DLM = 7, DUG = 2, and DLG = 2. The noise value for the signal-to-noise 

calculation for single or multiple frequency and direction, and achievable 

distance is the noise value associated with the user entered reliability. 

2.4 The Antenna Algorithm 

The performance of antennas near or on the surface of the Earth can be very 

dependent on the interaction with the lossy Earth and surface-wave propagation. 

The effects of the lossy Earth for different antenna types and ground constants 

are in general difficult to predict. A quantitative estimate of performance in 

terms of an "equivalent gain" or "enhancement factor" also is difficult to obtain 

directly in general formulas for different practical antenna types. Presently 

available techniques with computer algorithms are very time consuming and require 

conversion or normalization for use in system computations. An antenna model was 

developed at ITS to provide an "equivalent gain" for use in communication systems 

analysis. The model quickly provides a number for "equivalent gain" and is 

normalized properly for systems calculations. 

The antenna algorithm is used to compute the equivalent gain of several 

antenna types as a function of the independent variables: antenna geometry, 

ground conductivity, ground dielectric constant, frequency, and azimuth. The 

equivalent gain calculated represents the effectiveness of the antenna in 

launching or receiving the ground wave. In general, this gain is not the same as 

the conventional antenna gain used in communication systems analysis. The antenna 

algorithm uses look-up tables and simple algebraic equations to determine the 

equivalent gain. The look-up tables and equations were derived from behavior 

analysis of extensive method-of-moments calculations using the computer program 

Numerical Electromagnetics Code, version 3 (NEC-3) (Burke and Poggio, 1977; Burke 

and Miller, 1983). The antenna algorithm allows fast prediction of equivalent 

gain since all time consuming calculations have been previously performed 

"off-line." 

The gain required for systems analysis calculations is usually with respect 

to an isotropic radiator in free space or some other reference antenna. 

Conventional methods for a gain calculation could not be used due to the close 

proximity of the antennas with respect to a lossy Earth. The gain calculation 

method used for deriving the antenna algorithm within GWVOA results in an 

equivalent gain with respect to an isotropic radiator in free space. 

18
A short dipole was selected as a reference antenna due to its simplicity for 

analysis and convenience in measurement. Many loss calculations in ground-wave 

analysis are referenced to short dipoles or monopoles. The computer program NEC-3 

is used to determine the equivalent gain of a short dipole over lossy Earth with 

respect to an isotropic radiator in free space for all ground conductivities, 

ground dielectric constants, and frequencies. The relative performance of the 

subject antenna with respect to the short dipole is then determined using the 

program NEC-3. These two factors are then combined to obtain the equivalent gain 

with respect to an isotropic radiator in free space. 

The gain of a short dipole antenna at the surface of a lossy Earth referenced 

to an isotropic radiator in free space can be derived from some basic 

relationships. The field intensity or power density in free space due to an 

isotropic radiator in free space is given by Norton (1959): 

2

2

4 D

e Pr

η π = (13) 

where 

e(V/m) = the electric field strength in volts per meter 

η(ohms) = the impedance of free space in ohms = 120 π

D(m) = the distance from the antenna in meters 

 Pr(W) = the radiated power in watts 

Taking the square root of both sides and rearranging terms, the primary 

electric field strength from an isotropic antenna is: 

( )

30Pr( ) ( / ) D mW

e V m = . (14) 

The primary electric field strength from an isotropic antenna in free space 

is: 

( )

30 ( ) ( / ) D mP W g

e V m = (15) 

where g is the equivalent antenna gain ratio referenced to an isotropic radiator 

in free space and P is the transmitter input power in watts. If the units are 

changed, the above equation becomes:

19
( )

173 ( ) ( / ) d kmP kW g

e mV m = (16) 

where 

e(mV/m) = the electric field strength in millivolts per meter 

P(kW) = the transmitter power in kilowatts 

d(km) = the distance in kilometers 

If the antenna is a short vertical element (g=3) at the surface of a 

perfectly conducting Earth, then 

( )

300 ( ) ( / ) d kmP kW

e mV m = (17) 

and this is the familiar 300 mV/m at 1 km for a 1 kW input over perfectly 

conducting Earth. 

The electric field strength for a lossy Earth and arbitrary gain g is given 

by Terman (1955) as: 

( )

173 ( ) ( / ) d kmA P kW g

e mV M = (18) 

where A is the Norton approximation (Norton, 1941) to the Sommerfeld attenuation 

function (Sommerfield, 1909). If this expression is rearranged to solve for g and 

the logarithm of both sides is taken, the gain of a short dipole antenna at the 

surface of a lossy Earth referenced to an isotropic radiator in free space is 

2 2

2 2

(173) ( )

( / ) ( ) ( ) 10log P kW A

e mV m d km Gd dB = (19) 

The effectiveness of an antenna in launching a surface wave "equivalent gain" is 

then determined by first calculating a ratio called the relative communication 

efficiency for each subject antenna as a function of the ground constants, 

frequency, antenna geometry, and azimuthal direction. The relative communication 

efficiency in decibels (dB) is then added to the reference dipole gain. The 

relative communication efficiency (RCE) (Fenwick and Weeks, 1963) of a subject 

antenna is defined by: 

20
r t

t r

E P

E P

RCE dB 2

2

( ) = 10log (20) 

where 

 Er(V/m) = electric field strength predicted by NEC-3 at reference 

distance d and input power Pr for a short dipole 

 Pr(W) = dipole antenna input power from NEC-3 used to compute Er 

 Et(V/m) = electric field strength predicted by NEC-3 at reference distance d 

and input power Pt for the subject antenna 

 Pt(W) = subject antenna input power from NEC-3 used to compute Et. 

The "equivalent gain" Ga (dBi) of the subject antenna over lossy Earth 

referenced to an isotropic radiator in free space is given by: 

 Ga (dBi) = Gd (dBi) + RCE (dB) (21) 

where Gd and RCE are as defined above. The "equivalent gain" referenced to an 

isotropic radiator in free space can now be used for communications system 

analysis. 

The antenna types modeled for VOA include: a monopole on a ground stake or 

ground screen; a 3-, 4-, or 6-monopole array on a ground screen; and a ferriteloaded loop. An electric field strength option and a user gain option have also 

been included. The user is asked to select an antenna type or one of the two 

options for the transmitter and receiver antennas. After the antenna type or one 

of the two options has been selected, the user is then asked certain questions 

whose answers describe the antenna. This information, the frequency and ground 

constants are used to determine the "equivalent gain" of the antenna from the 

look-up tables and algorithms. The "equivalent gain" numbers are then added to 

the signal level calculations of the systems interface algorithm for determination 

of signal-to-noise power-ratio. 

Although the questions that request the antenna input parameters are 

relatively straightforward and easy to understand, each of the antenna types 

modeled requires some explanation for an appreciation as to its limitations and 

general capability. 

21
The monopole antenna is valid for all frequencies from 0.01 MHz to 30 MHz. 

The valid range for lengths depends on the wavelength of the radio frequency. The 

smallest monopole length is .01 wavelength at the lowest frequency and the largest 

length is 0.7 wavelength at the highest frequency. The user can elect to use a 

radial-wire ground screen with a user specified radius from .01 wavelength at the 

lowest frequency to any finite number of wavelengths, and with 5-360 radials. The 

maximum ground screen radius actually used in the calculations is 0.6 wavelengths, 

since any increase in ground-screen size beyond this radius has a negligible 

effect on antenna performance. The user must also specify the efficiency of the 

monopole antenna. 

If the user does specify a ground screen, then the calculations are performed 

for the monopole on a ground stake. The ground stake is assumed to be between 

0.04 and 0.1 free space wavelengths in length and 10-4 wavelengths in radius. 

Over this range, the relative communication efficiency is insensitive to changes 

in the ground-stake length. 

The monopole length-to-radius ratio is assumed to be greater than or equal to 

25. This is a thin monopole assumption. 

The 3-, 4-, and 6-monopole array geometries and azimuth radiation patterns 

are fixed designs used by the Voice of America. The user is only required to 

specify the boresight bearing for the array. The boresight bearing is the angle 

measured from the transmitter in degrees east of true north (clockwise from north) 

of the antenna beam center. The default value in the program is the angle of the 

receiver measured from the transmitter in degrees east of true north. This allows 

the user to line up the antenna main beam with the receiver, if desired. The 

3-, 4-, and 6-monopole array geometries and azimuth radiation patterns are shown 

in Figures 2,3, and 4 respectively. All monopoles are 0.625 wavelengths in length. 

The valid frequency range is from 0.5 MHz to 1.7 MHz. 

The ferrite-loaded loop antenna simulates the conventional antenna found in 

commercial AM broadcast band receivers. The user can specify cylindrical loop 

sizes up to 25.4 cm in length and 2.54 cm in diameter. This antenna option is 

only valid from 0.5 MHz to 1.7 MHz. It is a very inefficient antenna and 

recommended use is for receive only applications. "Equivalent gain" values range 

from approximately -40 dBi to -80 dBi for the ferrite-loaded loop antenna. 

The electric field strength option will calculate the "equivalent gain" of 

any antenna if the electric field strength at a reference distance with a 

reference input power is known. This information can be obtained easily from the 

22
Figure 2. Three-monopole array geometry. 

23
Figure 3. Four-monopole array geometry. 

24
Figure 4. Six-monopole array geometry. 

25
NEC-3 program as output for any antenna the user chooses to model; however, any 

other means of obtaining these three parameters may be used. This model is valid 

from .01 to 30 MHz. 

The user gain option allows the user to specify gains at all input 

frequencies. This gain is any gain the user desires between -100 dBi and +100 dBi 

and allows parameterizing calculations with gain. 

2.5 Run Time And Accuracy Algorithm 

A set of time and accuracy algorithms has been developed to help the user 

decide whether to use a smooth-Earth propagation loss prediction method or an 

irregular-Earth loss prediction method. The irregular-Earth loss prediction method 

in most cases gives a more accurate prediction than a smooth-Earth method, but 

usually has a longer run time. The set of equations predicts run time and 

approximate accuracy with respect to measured data and run time for each of the 

three propagation methods. 

The accuracy of the irregular-Earth propagation loss method also depends upon 

the terrain data available for use by the method. Some areas of the world have 

sparse data if any at all. In other areas, only coarse terrain data is available 

with spacings of approximately 8 km. The ITS terrain data file contains data 

every 30 seconds in latitude and longitude (approximately 1 km at the Equator) 

Spies and Paulson (1981). This is available for most of the United States. 

The accuracy equations in GWVOA take terrain data file spacing into account 

when predicting propagation method accuracy. In many cases at lower frequencies 

(below 1.6 MHz) the equations indicate that a smooth-Earth propagation method can 

achieve similar results when compared to an irregular-terrain method. The user is 

cautioned that time and accuracy estimates are approximate. The purpose of these 

estimates is to give the user some insight into selecting one propagation loss 

prediction method over another. This is described in the next subsection. 

2.5.1 Time And Accuracy Tradeoffs 

The run times of the irregular-Earth method can be excessive in many 

communications analyses. The program GWVOA incorporates a feature that allows the 

user to obtain approximate run times and propagation model prediction accuracy for 

the runs being made. The accuracy was calculated with a limited amount of 

measured data. The time models were developed empirically from many runs of each 

of the three propagation methods. The time and accuracy prediction is not 

26
absolute, but it allows the user to gain an appreciation for the program run time 

and accuracy of each of the three propagation methods: smooth Earth, smooth Earth 

mixed path, and irregular Earth. The run time prediction allows the user to terminate a computer run if the time is excessive or to change computation methods. 

The accuracy prediction provides the user the same options if a similar accuracy 

can be obtained using a propagation loss prediction method that runs faster. 

The user enters all of the input data at the start of a GWVOA run. If the 

user chooses a smooth-Earth (SE) or smooth-Earth, mixed-path (SEMP) method, the 

run time or accuracy will not be given since the irregular-Earth method is not 

involved. The run times of SE and SEMP are too short to be concerned about. 

If the user chooses the irregular-Earth propagation loss prediction method, 

the GWVOA program will print out a table with the run times and accuracies of all 

three propagation models. The run times are in seconds. The accuracies are the 

mean and standard deviations in decibels of the approximate relative error in 

electric field strength with respect to measured data. If the mean is positive, 

then the propagation method prediction will result in a higher field strength than 

that of the measured data. If the mean is negative, then the prediction is below 

the measured data. It is emphasized here that both time and accuracy are 

approximate. They are provided only to give the user comparisons between the 

respective propagation loss prediction methods and a limited amount of measured 

data. The user is then given the option of deciding to process, modify or 

terminate the pending GWVOA run. The user can change the propagation loss 

prediction method if the irregular-Earth method run time is excessive. Comparable 

accuracy may be obtained by using one of the smooth-Earth methods, usually in a 

much shorter run time. Or the user can terminate the run if run times are 

excessive. 

2.5.2 Terrain And Frequency Effects On Accuracy 

The frequency and terrain roughness can profoundly affect the accuracy of 

propagation loss predictions. When the average terrain roughness (difference in 

height between adjacent terrain samples) is large with respect to a wavelength, 

the irregular Earth method will produce better predictions than the smooth Earth 

method. The accuracy is also a function of the terrain sample spacings of the 

terrain data base. The standard terrain file on the ITS Telecommunications 

Analysis Services computer contains data every 30 s of arc in latitude and 

longitude, which is a terrain data spacing of approximately 1 km at the equator. 

27
These data are available for most of the United States. Another terrain file 

contains data every 5 min of arc which is approximately every 8 km at the Equator. 

An irregular-Earth propagation loss prediction obviously will not be as accurate 

as using the coarse terrain as with the standard terrain file. There are areas 

where only coarse terrain data is available. The advantages of using an 

irregular-Earth method for better prediction accuracy when limited to a coarse 

terrain data set will be fewer for lower frequencies. The smooth-Earth method may 

be as accurate as an irregular-Earth method with coarse terrain. 

The accuracy algorithm described previously takes into account whether the 

terrain data is coarse or standard. 

In the AM broadcast band of 0.5 MHz to 1.6 MHz the user may indeed find the 

smooth-Earth propagation loss prediction methods adequate for communications 

performance predictions. A study was performed over this frequency range to 

investigate the relative accuracies between the smooth-Earth and irregular-Earth 

methods. It was found that if terrain data is available only every 8 km, 

then the smooth-Earth prediction is as good or better than an irregular-Earth 

method of prediction for the total path over rough terrain at frequencies between 

0.5 MHz and 1.6 MHz. If terrain data is available every 1 km, then the 

irregular-Earth method prediction better follows the terrain details, but 

on the average is similar to the 8 km predictions over the total path. Where the 

path starts also determines where the 8 km samples are taken. Many of the coarse 

features of rough terrain could in effect be smoothed out by such a sampling. 

Precautions were taken during the generation of this data, so that this would not 

occur. The 8-km irregular-Earth prediction and the smooth-Earth prediction have 

fairly good agreement over the 0.52 MHz to 1.62 MHz band for rough terrain. 

Figure 5 is an example of homogeneous rough terrain (Canyonlands), and Figure 

6 is an example of mixed-path, hilly terrain (Santa Rita Mountains). Figures 7 

through 9 compare irregular-Earth method loss predictions with 1 and 8 km terrain 

spacing for rough terrain from Figure 5 at the lower, middle, and upper 

frequencies in the band. The differences in loss prediction between 1 and 8 km 

terrain spacing increases as frequency is increased. Figures 10 through 12 

compare the irregular-Earth method loss predictions for a hilly path from Figure 6 

with 1 and 8 km terrain spacing. The difference in loss predictions again 

increases with increasing frequency, but the difference is less than for rough 

terrain over the total path. The loss predictions would be identical for smooth 

terrain when comparing 1 and 8 km terrain spacing. 

28
Figure 5. Path profile for Canyonlands, Utah 

 (rough terrain). 

29
Figure 6. Path profile for Santa Rita Mountains, 

 Arizona (hilly terrain). 

30
31
32
33
Figures 13 through 18 compare the rough-terrain, loss predictions of the 

irregular-Earth method for both 1 and 8 km terrain spacing with the smooth-Earth 

method. The 8 km irregular-Earth method loss prediction agrees quite favorably 

with the smooth-Earth method loss predictions over the AM broadcast band. 

Figures 19 through 24 made the same comparison in loss predictions for a 

hilly mixed path. The 1 and 8 km irregular-Earth method loss predictions both 

follow the smooth-Earth, mixed-path method loss predictions reasonably well. The 

comparison of the 1 and 8 km terrain spacing using the irregular-Earth method 

prediction over a smooth path would be identical to the smooth-Earth, mixed-path 

prediction. 

The curves of Figures 7 through 24 are intended to give the user some idea of 

the relative accuracies obtained when comparing the irregular-Earth method with 

the smooth-Earth method propagation loss predictions. The accuracy algorithm 

within GWVOA will provide a statistical description of the approximate relative 

accuracy in electric field strength with respect to measured data for the actual 

terrain path being considered in the analysis. This will further serve to guide 

the user in making a decision between a smooth-Earth and irregular-Earth method 

for loss prediction. The accuracy algorithm automatically takes terrain data file 

spacing into account when predicting the relative accuracy. In this process, the 

model examines the spacing of the terrain data points and also calculates the 

terrain roughness factor. For the AM broadcast band, there is little improvement 

in relative loss prediction accuracy when using the 8 km irregular-Earth method 

over a smooth-Earth method prediction, but the user can make the final decision 

based on the particular application. 

34
35
36
37
38
39
40
3. A USER'S GUIDE TO PROGRAM GWVOA 

The computer program GWVOA is written in ANSI Fortran 77 and is presently 

available on the ITS Boulder Laboratories Telecommunications Analysis Services (TA 

Services). Instructions for obtaining access to programs on TA Services are 

contained in Sections 1 through 4 of the Telecommunications Analysis Services 

Reference Guide published in 1985 by the Institute for Telecommunication Sciences, 

National Telecommunications and Information Administration, U.S. Department of 

Commerce. A general discussion on terminal operation and log-on procedures, etc. 

is contained in this guide. This section will describe the specific operation of 

program GWVOA. 

The computer program GWVOA will operate with three basic options: received 

signal-to-noise power-ratio for a single frequency and direction, received signalto-noise power-ratio for multiple frequencies and directions, and the achievable 

distance for a user input signal-to-noise power-ratio and reliability at multiple 

frequencies and directions. 

The option to compute received signal-to-noise power ratio for a single 

frequency and direction predicts basic transmission loss, received electric field 

strength, received signal power, received signal-to-noise power-ratio, noise 

level, and antenna factors over lossy Earth. The signal-to-noise power-ratio 

calculations can be made for several seasons and times. The user also specifies a 

desired reliability for the signal-to-noise power-ratio. The reliability is 

defined as the percent of time the signal-to-noise power-ratio is achieved or 

exceeded in a 1-hour/3-month-season time period for a given frequency and 

geographic location. The transmission losses for this option are calculated with 

one of the user selected propagation loss prediction methods: smooth homogeneous 

Earth (SE), smooth inhomogeneous (mixed path) Earth (SEMP), and irregular 

homogeneous or inhomogeneous Earth (IEMP) with or without a slab representing 

forests, cities, etc. The terrain data base is automatically accessed by program 

IEMP or the user may enter manual terrain data. 

The option for received signal-to-noise power-ratio for multiple frequencies 

and directions calculates everything that the single frequency and direction mode 

does, but only the SE and SEMP propagation loss prediction methods are permitted. 

IEMP is locked out since its computation times can be too excessive for each path, 

resulting in prohibitively long total run times. 

The achievable-distance output option calculates the maximum distance from 

the transmitter at which the user specified signal-to-noise power-ratio and 

41
reliability are simultaneously achieved. The received power, noise level, and 

electric field strength are also computed at this distance. The calculations are 

performed for multiple frequencies, directions, seasons, and time of day. The 

propagation loss prediction methods using this option are also limited to the SE 

and SEMP propagation loss prediction methods, because the repetitious calculations 

required with this option would result in prohibitively long run times if program 

IEMP were used. 

Within these three basic output options are many alternate paths the user can 

take depending on the user response to the input questions. The remainder of this 

section will describe the questions that are asked by program GWVOA to obtain the 

necessary input parameters from the user. Input parameters are self-explanatory; 

however, to provide additional assistance in understanding the input questions, 

Table 2 lists the signal-to-noise power-ratio and achievable-distance prediction 

questions. The meaning of each question, the acceptable range of user input 

responses, and the default values are also given in Table 2. The acceptable range 

of values appears before the numbered line of each question. The default value 

appears on the numbered line in parentheses after each question. 

After logging on to TA services, the user is asked to type in a valid 

command, and a list of valid commands is presented. The user must type in "GWVO" 

to access program GWVOA. GWVOA can also be typed in, but only the first four 

characters are necessary. The user is then presented with a menu where the user 

may get help, view a program description, and choose between a concise or verbose 

dialogue for the questions. Verbose dialogue is recommended until the user 

becomes familiar with program operation. The user is then presented with a choice 

between the three basic output options: received signal-to-noise power-ratio for 

single frequency and direction, received signal-to-noise power-ratio for multiple 

frequency and direction, or achievable distance with multiple input. 

42
The question session starts and the user is asked to supply input answers in 

response to the questions described in Table 2. 

Table 2. Signal-to-Noise Power-Ratio 

and Achievable-Distance Prediction Questions, 

Their Meaning, and Acceptable Range of Values 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____

 

Meaning

RF frequency .01 to 30.00 MHz 

1) RF frequency (5.00 MHz)>? 

Frequency at which prediction is to be made. 

Acceptable value range is .01 to 30.00 MHz. 

The default value is 5.00 MHz. This format 

for the frequency question is only used in 

single frequency and direction signal-tonoise power-ratio predictions. 

1) Frequency (MHz) 

Up to 7 values. 999 indicates 

end of list 

 Frequency No.1> 

 Frequency No.2> 

 Frequency No.3> 

This format for the frequency question is 

used in the signal-to-noise power-ratio 

prediction for multiple frequencies and 

directions, and the achievable-distance 

option. The user is asked to enter up to 

seven different frequencies at which a 

prediction is to be made. Three nines 

(999) input by the user indicate the end of 

the frequency list. The user must enter at 

least one frequency. Acceptable value 

range is .01 to 30.00 MHz. There is no 

default value. 

Transmitter antenna height 0.0 to 

 12000.0 m 

2) Transmitter antenna 

 height (2.0m.)>? 

The antenna height is the actual height of 

the antenna feed point above the 

surrounding terrain. It is not necessarily 

the height of the structure. Acceptable 

value range is 0.0 to 12,000.0 meters. The 

default value is 2.0 meters. 

Receiver antenna height 0.0 to 

 12000.0 m. 

3) Receiver antenna height 

 (2.0m.)>? 

The antenna height is the actual height of 

the antenna feed point above the 

surrounding terrain. It is not necessarily 

the height of the structure. Acceptable 

value range is 0.0 to 12,000.0 meters. The 

default value is 2.0 meters. 

43
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

1 - Lats and longs of both antennas 

2 - Lat & long of transmitter, 

 bearing and distance to 

 receiver 

4) Antenna range options (1)>? 

The user may choose how the transmitter and 

receiver locations will be input to the 

program. The locations may be input by 

either the latitudes or longitudes of both 

the receiver and transmitter, or the 

latitude and longitude of the transmitter 

with bearing and distance to the receiver. 

The default is option 1. 

Distance between antennas 1.00 to 

 21000.00 km. 

Distance between antennas 

5) (100.00 km.)>? 

If option 2 of question 4 is elected, the 

user is asked to input the distance between 

the transmitter and receiver antennas. 

Acceptable value range is 1.0 to 

21,000.0 km. The default is 100 km. 

Transmitter latitude -90.00 to 

 90.00 

Inputs of the form X, Y, Z imply 

 degrees, minutes, seconds 

Inputs of the form X.Y imply 

 decimal degrees 

6) Transmitter latitude (40.03)>? 

If either option 1 or 2 of question 4 is 

elected, the user is asked to input the 

latitude of the transmitter location. 

Acceptable value range is -90.00 to +90.00 

deg. Positive degrees are north of the 

equator. Negative degrees are south of the 

equator. The default value is 40.03 

deg. 

Transmitter Longitude -180.00 to 

 180.00 

7) Transmitter longitude 

 (-105.30)>? 

If either option 1 or 2 of question 4 is 

elected, the user is asked to input the 

longitude of the transmitter location. 

Acceptable value range is -180.00 to 

+180.00 deg. Positive degrees are east of 

the prime meridian. Negative degrees are 

west of the prime meridian. The default 

value is -105.30 deg. 

Receiver latitude -89.99 to 89.99 

8) Receiver latitude (30.59)>? 

If option 1 of question 4 is elected, the 

user is asked to input the latitude of the 

receiver location. Acceptable value range 

is -89.99 to +89.99 deg. Positive degrees 

are north of the equator. Negative degrees 

are south of the equator. The default 

value is 39.59 deg. 

Receiver longitude -180.00 to 

 180.00 

9) Receiver longitude (-104.50)>? 

If option 1 of question 4 is elected, the 

user is asked to input the longitude of the 

receiver location. Acceptable value range 

is -180.00 to +180.00 degrees. Positive 

degrees are east of the prime meridian. 

Negative degrees are west of the prime 

44
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____

 

Meaning

meridian. The default value is -104.50 

degrees. 

Bearing 0.00 to 360.00 

10) Bearing (10.00)>? 

If option 2 of question 4 is elected, the 

user is asked to input the bearing angle 

measured from the transmitter to the 

receiver in degrees clockwise from true 

north. Acceptable value range is 0.00 to 

360.00 deg. The default is 10.00 deg. 

This format forbearing is used for the 

signal to noise power ratio prediction with 

single frequency and direction. Multiple 

directions are covered in questions 11 

through 13. 

Initial bearing 0.00 to 360.00 

11) Initial bearing (10.00)>? 

If the user elected the signal to noise 

power ratio or achievable distance option 

with multiple frequencies and directions, 

this question will ask for the initial 

bearing angle in degrees clockwise from 

north at which the user desires to begin 

computation (i.e., North=0 deg., East=90 

deg., South=180 deg., and West=270 deg.). 

The acceptable value range is 0.00 to 

360.00 deg. The default value is 10.00 

deg. 

Bearing increment .00 to 360.00 

12) Bearing increment (10.00)>? 

If the user elected the signal-to-noise 

power-ratio or achievable-distance option 

with multiple frequencies and directions, 

this question will ask for the amount the 

user desires to increment from the initial 

bearing angle in degrees. Computations 

will be performed at each incremental 

bearing determined by adding the bearing 

increment to the initial bearing or 

previous bearing until the final bearing is 

reached. The acceptable value range is 

0.00 to 360.00 deg. The default value is 

10.00 deg. 

Final bearing 0.00 to 360.00 

13) final bearing (100.00)>? 

If the user elected the signal-to-noise 

power-ratio or achievable-distance option 

with multiple frequencies and directions, 

this question will ask for the final 

bearing at which the user wishes to perform 

the computation. Computation is performed 

at each incremental bearing until the final 

45
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

bearing is reached. If the final bearing 

is made equal to the initial bearing, the 

computation is only performed at the 

initial bearing. This allows the user to 

make computations at many frequencies for 

one bearing. The acceptable value range is 

0.00 to 360.00 deg. The default value is 

100.00 deg. 

1) - Vertical (V) 

2) - Horizontal (H) 

14) Antenna Polarization (1)>? 

The user is asked to input the polarization 

of the transmit and receive antennas. The 

acceptable input values are either 1, 2, V, 

or H. The default is 1 for vertical 

polarization. 

1 - Vertical Monopole (VM) 

2 - 3 Monopole Array (3M) 

3 - 4 Monopole Array (4M) 

4 - 6 Monopole Array (6M) 

5 - Ferrite Loop (FL) 

6 - Field strength Option (FS) 

7 - User Gain Input (UG) 

15) Transmitter Antenna Type (1)>? 

The user is asked to select the transmitter 

antenna type from this list. The 

acceptable input values are number 1, 2, 3, 

4, 5, 6, and 7 or VM, 3M, 4M, 6M, FL, FS, 

and UG opposite each of the antenna types 

in the list. The default is 1 or VM for 

the vertical monopole. After selection of 

an antenna type, the user will be asked 

additional information about the antenna 

selected. 

The following questions depend on 

which antenna was selected in 

answer to question 15. 

Monopole Antenna

Transmitter Monopole Length 

 .01λ to .7λ

Transmitter Monopole Length 

 (.01λ)>? 

The user is asked to input the length of 

the monopole antenna in the units of length 

previously chosen at the start of the 

program runs (meters or feet). The range 

of acceptable values depends on wavelength, 

but will be displayed with the question in 

the length units previously chosen by the 

user (meters or feet). The shortest 

monopole length permitted is 0.01 

wavelengths at the lowest frequency that 

was input to question 1. The longest 

acceptable value for monopole length 

permitted is 0.7 wavelength at the highest 

frequency that was input to question 1. If 

the program GWVOA is being run at a single 

frequency, the lengths are based on that 

46
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____

 

Meaning

single frequency. The default value is 

0.01 wavelength at the lowest frequency or 

single frequency. 

1 - YES (Y) 

2 - NO (N) 

Do you want a ground screen (1)>? 

The user is asked if the monopole antenna 

has a ground screen in the Earth beneath it. 

If the response is yes the user will be 

asked for the radius of this radial-wire 

ground screen and the number of radial 

wires. (The ground screen is a standard 

circular, radial-wire, ground screen.) If 

the response is no, the monopole is assumed 

to be used with a ground stake. Acceptable 

responses are 1 for Y for yes, and 2 or N 

for no. The default value is 1 for yes. 

Transmitter ground screen radius 

 0.01λ to any finite number 

Transmitter ground screen radius 

 (.01λ)>? 

The user is asked to input the radius of 

the radial wire ground screen in the units 

of length previously chosen at the start of 

the program run (meters or feet). The 

range of acceptable values depends on 

wavelength. The smallest ground screen 

radius permitted is 0.01 wavelengths at the 

lowest frequency. The largest radius 

permitted is any finite number. The 

default is 0.01 wavelengths at the lowest 

frequency. 

Transmitter number of radials 

 5. to 360. 

Transmitter number of radials 

 (5. )>? 

The user is asked to input the number of 

radial wires in the ground screen. The 

acceptable range is from 5 to 360 radials. 

The default is 5 radials. 

Transmitter Monopole Efficiency 

 1 - 100 Percent 

Transmitter Monopole Efficiency 

 (100%)>? 

The user is asked to input the overall 

efficiency of the monopole antenna in 

percent. The acceptable range of values is 

1 to 100 percent. The default value is 100 

percent. 

3 Monopole Array

Transmitter boresight angle 

0.00 to 360.00 (angle to 

 receiver)>? 

The user is asked to input the angle in 

degrees east of north (clockwise from true 

North) that the antenna beam points. The 

reference angles are: North = 0 deg., East 

= 90 deg., South = 180 deg., and West = 270 

deg. The acceptable value ranges are 0.00 

to 360.00 deg. The default is the 

clockwise angle to the receiver measured 

47
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

from the transmitter for a single bearing. 

For a multiple bearing case, the initial 

bearing to the receiver is taken as the 

default. 

4 Monopole Array

This is identical to the 

3 monopole array. 

6 Monopole Array

This is identical to the 

3 and 4 monopole array. 

Ferrite-Loaded Loop Antenna

Transmitter length of rod 

 (cm) 1.00 to 25.40 cm 

Transmi tter length of rod 

 (cm) (25.40 cm)>? 

The user is asked to enter the length in 

centimeters of the ferrite-loaded loop 

antenna used for the transmitter antenna. 

The ferrite-loaded loop antenna is a 

cylindrical rod shape. The acceptable 

range of values is from 1 cm to 25.4 cm. 

The default is 25.4 cm. 

Transmitter diameter of rod 

 (cm) 0.10 to 2.54 cm 

Transmitter diameter of rod 

 (cm) (2.54 cm)>? 

The user is asked to input the diameter in 

centimeters of the ferrite-loaded loop 

antenna used for the transmitter antenna. 

The ferrite loaded loop antenna is a 

cylindrical rod shape. The acceptable 

range of values is from 0.1 cm to 2.54 cm. 

The default value is 2.54 cm. 

Field Strength Option

Transmitter field intensity at 

 ref. point, .0001 to lxl08

 mV/m 

Transmitter field intensity at 

 ref. point, (300 mV/m)>? 

The field strength option can compute the 

equivalent gain of an antenna if the user 

supplies the electric field strength at a 

reference distance with a given reference 

input power. The field intensity at a 

reference point is the first input asked 

for when this option is elected. The 

acceptable range of values is from .0001 to 

lxl08

 mV/m. The default value is 300 mV/m. 

Transmitter input reference power, 

 .001 to 10,000 kw 

Transmitter input reference power, 

The user is asked to enter the transmitter 

input reference power required to produce 

the field strength at the reference 

48
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

(1.0 kw)>? 

distance. The acceptable range of values 

is .001 to 10,000 kw. The default value is 

1 kw. This is not effective radiated power. 

It is transmitter input power to the 

antenna terminals. 

Transmitter reference distance, 

 λ to 1000 km 

Transmitter reference distance, 

 (the greater of λ or 1 km)>? 

The user is asked to enter the reference 

distance at which the transmitter field 

intensity is produced with the transmitter 

reference power. The acceptable range of 

values is 1 wavelength to 1,000 km. The 

default is 1 km or 1 wavelength, whichever 

is greater. 

User Gain Input

Transmitter gain -100.00 to 100.00 

 Transmitter gain (0.00)>? 

The user is asked to input a gain for the 

transmitter antenna in decibels referenced 

to an isotropic radiator. The acceptable 

value range is -100.00 to 100.00 dB. The 

default value is 0.00 dB. 

1 - Vertical Monopole (VM) 

2 - 3 Monopole Array (3M) 

3 - 4 Monopole Array (4M) 

4 - 6 Monopole Array (6M) 

5 - Ferrite Loop (FL) 

6 - Field Strength Option (FS) 

7 - User Gain Input (UG) 

16) Receiver Antenna Type (1)>? 

The user is asked to supply the receiver 

antenna type from the list given. The 

acceptable input value is 1 or VM for the 

vertical monopole. After selection of an 

antenna type, the user will be asked 

additional information about the antenna 

selected in a manner identical to that 

described for the transmit antenna. The 

word transmitter will be replaced by 

receiver in all of the questions. 

Actual transmitter input power 

 .0001 to 100000.00 kw 

18) Actual transmitter input power 

 (1.00 kw)>? 

This question asks for the value of 

transmitter input power. The acceptable 

value range is .0001 to 10,000 kw. 

The default value is 1.00 kw. 

21) Local time of day (format HHMM) 

 Up to 24 values. 999 indicates 

 end of list. 

Time No.1> 

Time No.2> 

Time No.3> 

etc. 

The user is asked for the times of day in 

local time at the transmitter site at which 

the prediction is to be made. The format 

is four digits. The first two digits are 

the hour on a 24 hour clock and the last 

two digits are minutes. (For example, 1200 

is 12 o'clock noon, 1830 is 6:30 pm.) The 

acceptable value range is 0000 to 2400. 

There is no default. The user must input 

at least one time and a 999 to indicate an 

49
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

end of list. The user can input up to 24 

times. A 999 must be supplied immediately 

after the last time on the next line if 

less than 24 times are submitted. 

22) Seasons 

 Up to 4 values, 999 indicates 

 end of list. 

1 - Dec, Jan, Feb (DJF) 

2 - Mar, Apr, May (MAM) 

3 - Jun, Jul, Aug (JJA) 

4 - Sept, Oct, Nov (SON) 

Season No. 1> 

Season No. 2> 

The user is asked to input the seasons at 

which the prediction is to be made. The 

user may input up to four seasons. The 

acceptable value range for each season is 

one of the digits 1 thru 4 or DJF, MAM, 

JJA, SON. The user must input at least one 

season, and a 999 to indicate an end of 

list. A 999 must be supplied immediately 

after the last season on the next line if 

less than four seasons are submitted. 

There is no default option. 

Required reliability 0 to 100.00% 

23) Required reliability (90.00%)>? 

The user is asked to input the required 

reliability of attaining the computed 

signal-to-noise power-ratio. A 90 percent 

reliability implies that the computed 

signal-to-noise power-ratio for a 

signal-to-noise power-ratio prediction, or 

the required signal-to-noise power-ratio 

for an achievable-distance calculation will 

be achieved 90 percent of the time in a 

1-hour/3-month-season time block for the 

season, local time of day, and frequency. 

The acceptable value range is zero to 

100 percent. The default value is 90 

percent. 

1 - 127.2 Business 

2 - 131.5 Residential 

3 - 136.8 Rural 

4 - 150.4 Quiet Rural 

24) Man-made noise (-dBW) at 

 1 MHz (1) >? 

This is the manmade noise level input by 

the user. The numerical values given are 

in decibels below 1 W at 1 MHz. Four 

options are given ranging from a "noisy" 

business level to a "quiet" rural level. 

The computer program calculates the noise 

level for the frequencies at which the 

predictions are made. Acceptable value 

range is one of the four digits 1 through 

4. The default value is a 1 for business 

(-127.2 dBW). 

Required signal/noise ratio 

 1.00 to 200.00 dB. 

25) Required signal/noise ratio 

 (2.00 dB)>? 

This is the required signal to noise power 

ratio that the user wishes to obtain in the 

achievable distance computation. this 

question is only asked for the achievable 

50
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

distance option. The acceptable value 

range is 1.00 to 200.00 dB. The default 

value is 2.00 dB. 

1 - Smooth Earth (SE) 

2 - Smooth Earth, Mixed Path (SEMP) 

3 - Irregular Earth, Mixed Path 

 (IEMP) 

26) Processing Method (1)>? 

The user must select the propagation model 

to be used in the computation. All three 

propagation models are available only in 

the single frequency and direction 

signal-to-noise power ratio prediction. If 

the multiple frequency and direction 

signal-to-noise power ratio prediction or 

the achievable distance prediction were 

elected at the beginning of the program, 

then only options 1 and 2 of this question 

would be presented. Acceptable value 

ranges are 1, 2, or 3 and SE, SEMP, and 

IEMP, except as explained above. IEMP is 

the irregular-terrain propagation model. 

The default is 1 for the smooth-Earth 

propagation model. 

Earth radius ratio .500 to 3.000 

27) Earth radius ratio (1.333)>? 

The user may select the effective Earth 

radius ratio to account for standard 

refraction of the atmosphere. It is the 

ratio between the effective Earth radius 

and the actual Earth radius. Acceptable 

value range is .500 to 3.000. The default 

value is 1.333 (4/3). 

1 - Single calculation at the 

 receiver 

2 - Incremental calculations 

 between xmitter and receiver 

28) Type of output (1)>? 

This question is asked only for the single 

and multiple frequency and direction 

signal-to-noise power-ratio predictions. 

The user may select between a single 

calculation at the receiver location (1) or 

incremental calculations between the 

transmitter and receiver at user-selected 

points along the path (2). The acceptable 

responses are a 1 or a 2. The default is a 

1 for a single calculation at the receiver. 

If option 2 is selected, then questions 29, 

30, and 31 are asked to define computed 

output locations. 

Field calculations will be 

performed according to the 

following parameters. 

This message is printed if option 2 of 

question 28 is selected. 

51
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

Meaning

Minimum distance for xmitter 

 λ Km to receiver distance 

29) Minimum distance for xmitter 

 (receiver distance)>? 

This is the minimum distance at which the 

user desires to make the first computation 

between the transmitter and receiver. The 

acceptable value range is (a wavelength at 

the lowest frequency) in kilometers or 

miles to the receiver distance in 

kilometers or miles. The default value is 

the receiver distance. The acceptable 

value range will be printed for each case 

with the question. 

Incremental distance .0001 to 

 receiver distance km. 

30) Incremental distance 

 (1.00000 km.)>? 

This is the increment size at which the 

user desires to make each successive 

computation. This increment is added 

repeatedly to the distance input for the 

minimum distance of question 29 until the 

maximum distance is reached. The 

acceptable value range is .0001 km to the 

receiver distance in kilometers. The 

default value is 1.0 km. The acceptable 

value range will be printed for each case 

with the question. 

Maximum distance from xmitter 

 R29 to receiver distance km. 

31) Maximum distance from xmitter 

 (receiver distance)>? 

This is the maximum distance from the 

transmitter along the transmitter to 

receiver path at which the user wants the 

computation made. It does not have to be 

at the receiver distance. The acceptable 

value range is R29 kilometers to the 

receiver distance. R29 is the user 

response to question 29. The default value 

is the receiver distance. The acceptable 

value range will be printed for each case. 

32) Ground Constants 

Sigma = Conductivity (.00001-100. 

 siemens/meter) 

Epsilon=Relative permittivity (1-100) 

Sigma .0000001 to 100.0000000 

Sigma ( .1000000)>? 

Epsilon 1.000 to 100.000 

Epsilon (1.000)>? 

If the smooth-Earth option is elected, the 

required inputs are the conductivity and 

relative permittivity of the ground along 

the path that are required. the acceptable 

range for conductivity is .00001 to 100 

siemens per meter. The acceptable range 

for relative permittivity is 1 to 100. The 

default value for conductivity (sigma) is 

0.1 siemens per meter. The default value 

for the relative permittivity is 1. 

32) Ground constants 

You may specify up to 50 ground 

 segments. 

If the smooth-Earth, mixed-path option is 

elected, the required inputs are the 

conductivity and relative permittivity of 

52
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

Meaning

Your total distance is the 

 receiver distance in km. 

Sigma = conductivity (.00001-100. 

 siemens/meter) 

Epsilon = relative permittivity 

 (1-100) 

Segment No.1 

Sigma .0000001 to 100.0000000 

Sigma .1000000)>? 

Epsilon 1.000 to 100.000 

Epsilon (1.000)>? 

Segment length 0.000 to 1000000.00km 

Segment length (1.000 km.)>? 

distance remaining is the receiver 

distance minus the length of 

segment No. 1 in kilometers. 

Segment No. 2 

Sigma .0000001 to 100.0 

Sigma (.1000000)>? 

Epsilon 1.000 to 100.000 

Epsilon (1.000)>? 

Segment length 0.000 to 

 1,000,000.000 km 

Segment length (1.000 km)>? 

each segment along the path and the segment 

length. The user may specify up to 50 

segments. The program will ask for the 

ground constant of each segment in order 

from the transmitter to the receiver. The 

program keeps track of the segment length 

and informs the user of the path length 

remaining to the receiver location. 

Acceptable value ranges for the ground 

constants are identical to those for a 

homogeneous path. Default values are also 

the same. The segment length acceptable 

value range is any nonzero value less than 

or equal to the transmitter-to-receiver 

distance. There is no default value. 

32) Ground constants 

You may specify up to 50 ground 

 segments 

1 - Yes (Y) 

2 - No (N) 

Will you want to define a slab on 

 any of the ground segments? (2)>? 

Your total distance is the receiver 

 distance in km. 

Sigma = conductivity (.00001 - 100. 

 siemens/meter) 

Epsilon = relative permittivity 

 (1-100) 

Segment No.1 

If the irregular-terrain model is elected, 

the user can input ground constants and 

segment lengths for up to 50 segments. The 

acceptable value range and defaults are 

identical for smooth-Earth, mixed-path. In 

addition, a slab can be placed on each 

segment of ground with a conductivity and 

relative permittivity and slab thickness. 

The ground constants for the slab have the 

same acceptable ranges and defaults as the 

ground constants of the ground. The 

acceptable value range for slab thickness 

is 0 to 700 m. The default is 1 m. The 

program keeps track of the segment lengths 

and informs the user of the distance 

remaining. 

53
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

Meaning

Sigma .0000001 to 100.0000000 

Sigma (.1000000)>? 

Epsilon 1.000 to 100.000 

Epsilon (1.000)>? 

Segment length 0.000 to 1000000.000 km 

Segment length (1.000 km.)>? 

 1 - Yes (Y) 

 2 - No (N) 

Do you want a slab on this 

segment? (0) >?1 

Slab input 

Sigma .000010 to 100.00000 

Sigma (1.000000)>? 

Epsilon 1.000 to 100.000 

Epsilon (1.000)>? 

Slab thickness 0.000 to 700.000 M. 

Slab thickness (1.000 M.)>? 

Distance remaining is receiver 

distance - length of segment 1 in km. 

Segment No. 2 

Sigma .0000001 to 100.0000000 

Sigma (.1000000)>? 

Epsilon 1.000 to 100.000 

Epsilon (1.000)>? 

Segment length 0.000 to 1000000.000 km. 

Segment length (1.000 km.)>? 

 1 - Yes (Y) 

 2 - No (N) 

Do you want a slab on this segment (1)>?2 

Distance remaining is the receiver 

 distance minus the lengths of 

 segments No. 1 and 2 in kilometers. 

Menu (Summary)? At this point in the program run, the user 

 has entered all of the input data. The 

 user may obtain a summary of all input data 

 by using a carriage return or may edit the 

 data by entering an E. If a P is entered, 

54
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

two events can occur depending on whether 

or not the user elected the irregular-Earth 

terrain model in question 26. If the user 

did not elect the irregular-Earth terrain 

model, then the next question is "Do you 

wish to process this data set (1)>?," to 

which the user responds 1 for yes and 2 for 

no. If the user elected the irregular-Earth 

terrain model, then the terrain data 

management question follows to ask the user 

what terrain data to use. 

1 - Obtain terrain data from file 

2 - Input terrain data manually 

Terrain data management (1)>? 

This question occurs only if the user 

elects to use the irregular-Earth terrain 

model. If the user responds with a 1, then 

the terrain data is obtained from the 

terrain data base using the LAT LONG user 

inputs that were asked for previously in 

questions 5 through 13. After a carriage 

return, the user must also enter a 5 and a 

carriage return to exit from terrain data 

management. 

The following series of questions result if the user elects to input terrain data 

manually (Option 2). 

Interval size .01 km to receiver 

 distance 

Interval size (1 km)> 

If the response to the manual terrain input 

question is yes, the user is asked for the 

spacing between terrain points. The 

acceptable range of input values is 0.1 km 

to the receiver distance. The default 

value is 1 km. 

1) Altitude at 0.00 km 

 from xmitter (0.00 m)? 

2) Altitude at 1 km from 

 xmitter (0.00 m)? 

3) Altitude at 2 km from 

 xmitter (0.00)? etc. 

After the user specified the interval size 

above, the user will be asked to supply 

terrain heights along the path at each 

interval until the receiver is reached. 

The computer will ask for the specific 

terrain height at each interval. The 

acceptable value range is any height from 

0.00 to any finite height in units 

previously input by the user. 

1 - Obtain terrain data from file 

2 - Input terrain data manually 

3 - Summary of terrain data 

4 - Edit terrain data 

5 - All done 

If the user elected option 2, input 

terrain data manually, and completes the 

above questions by entering the terrain 

data, the user is given the remaining 

options of summarizing the data (3), 

55
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

 

Meaning

Terrain data management (1)>? 

editing the terrain data (4), or All done 

(5). Option 5 allows the user to proceed 

with the program and exit the terrain data 

management. The table, with run times and 

accuracies, is then presented. 

 Approx. Rel. Error 

 (field strength) 

 WRT Meas. Data 

 Run time Mean Stnd.Dev. 

 (sec) (dB) (dB) 

IEMP 57.2 9.2 1.3 

SEMP 10.6 10.2 1.5 

SE 4.6 10.2 1.5 

If the irregular-terrain model IEMP was 

elected for question 26, a table is 

presented with the run times and accuracies 

for each propagation model listed. The 

user can decide if using the irregular 

terrain model is worth the extra run time. 

The run time is in seconds and the errors 

are in decibels. 

 1 - Yes (Y) 

 2 - No (N) 

Do you wish to process this 

 data set (1)>? 

The user can elect to run this data or not 

based on a decision made from the 

information in the above table. Acceptable 

values are a 1 or Y for yes or a 2 or N for 

no. If the response is yes, the data is 

processed. If the response is no, the user 

is returned to the main menu to edit data, 

input new data, or quit. 

Question number 32 is the last question needed to supply input parameters. If the 

user elected either the signal-to-noise power-ratio prediction for multiple 

frequencies and direction or the achievable distance prediction, the question 

number 32 would be repeated for each bearing. The program does the computation 

after the ground constants are input for each bearing and then asks for the ground 

constants of the next bearing. 

The remaining questions are program control related. 

Menu (summary)? A carriage return will output a summary of 

the input data, since the default value is 

summary. Any of the main menu commands are 

acceptable input. "E" for edit will permit 

user to edit the data input file. 

A "P" will cause the program to proceed to 

the data process question. 

1 - Yes (Y) 2 - No (N) Do you 

wish to process this 

 data set (1) >? 

The user is asked if the input data set is 

to be processed. Acceptable responses are 

1 or Y for Yes or 2 or N for no. The 

default is 1 for yes. 

Input Title, 1 to 80 characters If the user elects option 1, the program 

asks for a title from 1 to 80 characters. 

56
Table 2 (Cont.) 

Question Descriptions, Acceptable 

Value Ranges, Default Values_____ 

Meaning

The user must input at least one character 

and then a carriage return. 

Calculation in progress This response informs the user that 

calculation is being performed. 

Choose proceed to input new data set 

Edit to modify data 

H = Help 

D = Program Description 

C = Concise Dialog 

V = Verbose dialog 

E = Edit data 

S = Summary of Data 

P = Proceed 

Q = Quit 

Menu (Proceed)? 

If user elects option 2 to not process 

this data, this response appears and the 

main menu is presented. The user can 

respond with any menu item as an 

acceptable response. The default is 

"proceed." This allows the user to edit 

the data set, input a new data set, or 

abort the run with a QUIT command. 

After a data set has been processed, the output is displayed on the screen. 

 1 - Yes (Y) 

 2 - No (N) 

Do you wish to process another 

 set (1)>? 

Choose proceed to input a new 

 data set 

Edit to modify data 

Program GWVOA completed 

The user is given the option of processing 

another data set. The acceptable responses 

are 1 or Y for a yes and 2 or N for a no. 

The default is 1 for yes. If the user 

responds with a yes, the main menu appears 

again and a new data set may be entered or 

the present one edited. If the user elects 

proceed "P" to input a new data set, the 

default values for the questions will be 

those of the previous data set. If the 

user responds with a no, the program 

terminates. Control is passed to the TA 

Services commands. 

57
































5. CONCLUSIONS 

Program GWVOA is a versatile and user-friendly analysis model for systems 

performance prediction of communications circuits that use the ground wave as the 

primary mode of propagation. It provides computation results with reasonable 

accuracy for engineering analysis. 

One primary feature of this computer program is its ability to accurately 

predict antenna performance for certain antenna types over lossy Earth. Other 

antenna types can be added to the antenna algorithm. The gains of most antennas 

can vary radically over a lossy Earth depending on the antenna height, geometry, 

and ground constants. The antenna algorithm within GWVOA is believed to be 

accurate to within 1-2 dB depending on the actual antenna type. This accuracy is 

with respect to actual computations performed with NEC-3. The antenna algorithm 

does not agree with program NEC-3 exactly, because a certain degree of data 

smoothing was performed to represent the antenna behavior with simple algebraic 

equations and look-up tables. The model could be improved to reduce this error by 

further refinement of the look-up tables and equations. An antenna measurement 

program to verify the antenna algorithm is needed that would determine its 

relative accuracy with respect to measured data. 

A second feature of this program is that it combines a smooth-Earth and 

irregular-Earth propagation loss prediction capability for homogeneous and 

inhomogeneous Earth into one unified and user-friendly analysis tool. Electric 

field strength and received signal-to-noise power-ratio are also available as 

outputs. A reliability prediction is available in the signal-to-noise power ratio 

computation. The achievable distance output option is a convenient tool for 

obtaining coverage contours for different signal-to-noise power ratios and 

reliabilities. 

Recommendations for future work include the following: expanding the antenna 

algorithm to include other practical antenna types, verifying the antenna 

algorithm with measured data and using this data to refine the algorithm, and 

investigating further methods of speeding up the irregular-Earth propagation loss 

prediction method without sacrificing loss prediction accuracy. 

6. ACKNOWLEDGMENT 

The Voice of America provided partial funding for the development of the 

computer program GWVOA. Discussions with Mr. Leslie A. Berry, Dr. George A. 

Hufford, Dr. A. Donald Spaulding, all of the Institute for Telecommunication 

90
Sciences, and Dr. David A. Hill of the National Bureau of Standards provided 

invaluable advice during the development of program GWVOA. Mrs. Janet Geikas of 

the Institute for Telecommunication Sciences provided invaluable computer 

programming assistance. 

The author wishes to express appreciation to the many individuals who have 

previously developed the ground wave propagation loss prediction techniques, at 

the Institute for Telecommunication Sciences, which have been integrated into the 

computer program GWVOA. 

The author also wishes to express appreciation to Mr. Gerald J. Burke of the 

Lawrence Livermore Laboratory for his invaluable suggestions in the use of the 

Numerical Electromagnetics Code (NEC-3) computer program to analyze the antennas. 

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93