November 1, 2002
Field Strength Prediction in Irregular Terrain – the PTP Model
Author: Harry K. Wong
Abstract
This report describes a prediction technique for the calculation of the field strength of radio waves over irregular terrain paths. The concept of an "equivalent rounded obstacle" is ud to account for radio propagation loss over various possible irregular terrain shapes, including shapes which cannot easily be described geometrically. The technique replaces an arbitrary terrain profile with an equivalent rounded obstacle for which a value of path loss can be calculated using appropriate formulas.
Introduction
The technique prented here was first published in a report attached to a notice of propod rulemaking in 19981,2 and was promoted as a possible means of streamlining certain regulatory procedures ud to the coverage provided by broadcasting rvices. This update of that report incorporates improvements to the prediction model that overcome deficiencies pointed out by comment
s filed in that rule making proceeding. The improvements primarily involve accounting for effects of condary obstacles, i.e., tho obstacles located in the propagation path on either side of the primary obstacle. Finally, to fine tune this new technique, adjustments were made in model parameters to achieve clo agreement with actual measurement data collected over various propagation paths by the Television Allocations Study Organization (TASO).3
The technique was developed over a number of years in the cour of examining many hundreds of applications involving FM and TV broadcasting stations. In the applications, broadcast stations were proposing to move their transmitting antenna to a new location that, according to the standard propagation prediction technique, would not have provided an adequate signal over their community of licen. In the cas, most applicants were citing unusual terrain conditions that invalidate the prediction technique prescribed by FCC Rules, 47 C.F.R. §§ 73.333 1Notice of Propod Rule Making and Order, 1998 Biennial Regulatory Review – Streamlining of the Radio Technical Rules in Parts 73 and 74 of the Commission Rules, MM Docket No. 98-93, 13 FCC Rcd 14849 (1998).
2 The Second Report and Order, MM Docket No. 98-93, 15 FCC Rcd 21649 (2000) may be viewed at
v/Bureaus/Mass_Media/Orders/2000/fcc00368.pdf.
3 The measurement data ud for comparison with PTP predictions are the results of field strength surveys conducted by A.D. Ring & Associates for the Association of Maximum Service Telecasters, Inc., mostly in the years 1957-1960. The data were supplied to a panel of the Television Allocation Study Organization (TASO), and they were ud in development of the TV and FM broadcast curves which appear in FCC Rules as the standard method for predicting field strength contours. The data are available for independent study at
v/oet/fm/ptp/data/.
and 73.699.4 To verify the claims of adequate coverage prented in the applications, the
Commission needed a procedure or propagation model derived from theoretical considerations that could be verified by measurements. This procedure or propagation model needed to accommodate difficult terrain features which were not handled adequately by the propagation curves in the FCC Rules. The Point-to-Point (PTP) model fulfills the requirements, and in
addition, it is pictorially related to terrain elevation profiles in ways that provide insight into the cau of radio propagation loss in each particular ca. The PTP model’s implementation as a computer program is
uful as a first cut at
estimating the strength of
signals within about 100 miles of the transmitter.
Comparison with actual
propagation
measurements, and with
the results of other
prediction procedures, demonstrates that path loss values calculated by the
PTP model are relatively
accurate; and moreover
that the accuracy of the
PTP model is as good as
or better than that achieved by alternative procedures.5 The accompanying figures illustrate the relative accuracy of the PTP model, identified in the figure as the Wong curve. The ITM curve is the corresponding prediction of the Longley-Rice model.6 The fluctuations are due to terrain variations. Generally, the field is low when the receiving point is in a terrain depression. The standard procedure is to
u the curves found in FCC Rules, 47 C.F.R. §§
73.333 and 73.699. Notice in the figure that the FCC standard curves
match the data pretty well
but do not respond to
terrain effects like the
Wong and ITM curves.
The standard curves are
Springfield, Mass. 93.1 MHz, Station WHYN, 190°
Springfield, Mass terrain profile, 190° azimuth from station WHYN 4
47 C.F.R. §§ 73.333 and 73.699. 5 See v/Bureaus/Engineering_Technology/Documents/taso/graphs/ for study results. 6
NTIA Report 82-100, A Guide to the U of the ITS Irregular Terrain Model [ITM] in the Area Prediction Mode , authors G.A. Hufford, A.G. Longley and W.A. Kissick, U.S. Department of Commerce, April 1982. The computer program is described and can be downloaded from elbert.v/itm.html . ITS is the Institute for Telecommunications Sciences of the National Telecommunications and Information Administration (NTIA).
generally accepted as highly accurate on average, but they are of no u for evaluating the shadowi
ng effects of specific terrain elevation features between transmitter and receiver. The Longley-Rice model (ITM in the figure) makes its predictions from terrain profiles, but the Longley-Rice computer program was developed for application to a wide range of distances and phenomena including troposcatter propagation at relatively great distances. For reception points of 100 miles and less, the Longley-Rice computer program often makes anomalous predictions that are inconsistent with the procedures of Technical Note 101, the document on which it is bad.7 The PTP model tends to resolve the anomalies and is consistent with Technical
Note 101.
The PTP Model
To make its predictions, the PTP model incorporates the principal determinants of radio propagation over irregular terrain paths. The determinants are (1) the amount by which the direct ray clears terrain prominences or is blocked by them, (2) the position of terrain prominences or obstacles along the path, (3) the strong influence of the degree of roundness of the terrain features, and (4) the apparent earth flattening due to atmospheric refraction. Even in line-of-sight conditions when all terrain prominences lie below the direct ray, some may come clo enough to weaken the received fi
eld. This weakening effect is evaluated in terms of the degree to which a prominence penetrates certain geometrically defined zones, called Fresnel zones, around the direct ray. Determinant (2), position of the prominence or obstacle along the path, is important becau the football-shaped Fresnel zones are fatter and thus more deeply penetrated in the middle than at the transmitter and receiver ends.
The relative roundness of terrain features along the path is of special concern becau the radio field beyond a sharp obstacle is considerably greater than the field found beyond more rounded terrain features. The extremes are a knife-edge idealization in contrast to smooth earth with conquent differences in field strength of 20 dB or more. Applications to the FCC for broadcasting licen changes may claim strong or weak signals to some extent as the applicant wishes becau terrain elevation data from the U.S. Geological Survey is not of sufficient resolution for a preci determination of roundness. Some judgment is necessary that usually must be bad on the roughness of the terrain in the general area. Automating this judgment requirement, and thus streamlining the processing of applications that include engineering claims, was a principal motivation for developing the PTP model. The PTP model estimates an equivalent roundness in terms of the statistical variation of neighboring terrain elevations. If this statistical variation is small, t
he intermediate terrain is considered to have the effect of a relatively round obstacle. Sharpness thus corresponds to a large statistical variance.
1. DIFFRACTION LOSS CALCULATIONS
Diffraction loss for an ideal knife-edge obstruction can be calculated from the famous Fresnel integral. This integral originated in studies of optics by Augustin-Jean Fresnel in the early 19th 7 National Bureau of Standards Technical Note 101, Transmission Loss Predictions for Tropospheric Communication Circuits, authors P.L. Rice, A.G. Longley, K.A. Norton, and A.P. Barsis, January, 1967.
century. In application to radio propagation, formulas bad on this integral have frequently provided clo approximations to the diffraction effects of isolated mountain ridges.
In most situations however, the terrain does not at all remble a simple knife-edge, and to reprent obstructions in this simple way would underestimate the diffraction loss. Solutions for the diffraction loss over an isolated "rounded" obstacle have been given by Rice [1], Neugebauer and Bachynski [2][3], Wait and Conda [4]. In addition, Dougherty and Maloney [5] provide a readily evaluated formula for computing the diffraction loss over a rounded obstacle in terms of quantities υ and ρ, whe
re υ is the dimensionless parameter of the Fresnel-Kirchhoff diffraction formula and ρ is a mathematically convenient dimensionless index of curvature for the crest radius of the rounded obstacle. Diffraction loss is greater for broader obstacles of this type, increasing as the radius of curvature and ρ become larger.
The diffraction loss in every situation is somewhat less than would be calculated by replacing irregular terrain with a smooth spherical earth, the ultimate rounded obstacle. Methods of calculating the diffraction loss over a smooth spherical earth have been given by Burrows and Gray [6] and by Norton [7]. (The methods are difficult to apply, however, and here we resort to a formula obtained by fitting a curve in a CCIR graph as discusd in the next ction. ) Diffraction loss due to multiple knife-edges also lie somewhere in the range between tho for single knife-edge and smooth-earth terrain models. Deygout [8] provides easily implemented procedures for calculation when the terrain can be reprented this way. The technique described in this report does not involve multiple knife-edge considerations. However, we have found that the equivalent rounded obstacle approach gives results cloly approximating tho of other methods even in situations better described by multiple knife-edges.
2. GRAPH OF DIFFRACTION LOSS
CCIR [9] provides a graphical reprentation of knife-edge and smooth-sphere diffraction loss relative to that of free-space in terms of the ratio of path clearance to the radius of the first Fresnel zone. The figure below is the CCIR graph with the addition of the Dougherty-Maloney
diffraction adjustments for rounded obstacles. Note: the ratio of path clearance to first Fresnel radius, F/F1 in the figure, equals the Dougherty-Maloney parameter υ divided by the square root of 2.
It is found in the figure that the diffraction loss for ρ=1.0 is 0.6 of the way downward between the loss for knife-edge and smooth-sphere for all path clearance ratios, that is, for all values of F/F1. A similar proportion holds for the other values ρ, and hence we can characterize rounded obstacles by this proportion just as well as by the values of the Dougherty-Maloney parameter ρ. We denote this proportion by the symbol R, and call it the equivalent roundness factor. This graphical interpretation of the figure is the basis of the formulas ud in the equivalent rounded obstacle model. Knife-edge diffraction corresponds to R = 0.0; smooth-earth to R = 1.0.
The bounding curves in the figure, that is, tho for knife-edge and smooth earth, can be described by approximate formulas. Letting x = F/F1, the diffraction loss (relative to free-space) for a smooth-sphere diffraction is approximately
Smooth-sphere Loss = -38.68x + 21.66 dB,
and for a knife-edge
Knife-edge Loss = 1.377x2 - 11.31x + 6.0 dB for x > -0.5
= -50.4/(1.6 - x) + 36.0 dB for x < -.5.
Now when both F/F1 and R are given, path loss by the equivalent roundness model is be found by
Path Loss = Knife-edge Loss + R (Smooth-sphere Loss - Knife-edge Loss).
Section 3 describes how F/F1 is determined; ction 4 discuss the estimation of the equivalent roundness factor, R.
3. PATH CLEARANCE RATIO, F/F1
A major factor in determining diffraction loss is the clearance ratio, F/F1. The int diagram in the CCIR figure indicates how this quantity is defined. Consider a specific point-to-point path and the terrain elevations at all intermediate points from the transmitter. The height of the transmitter is presumed to be given, the receiver height is assumed to be 9.1 meters above the surface of the earth in FM radio rvice applications, and the heights determine a line of sight which may pass through or over obstacles. At a specific point along the path, the clearance F is the difference in height between the line of sight and the terrain elevation. At that same point we calculate the radius
F1 of the first Fresnel zone and form the ratio F/F1. The primary obstacle is at the point where this ratio is a minimum.
The first Fresnel radius in meters is given by
F==
1
