On the Use of Tamir’s Model for Site-Specific Path

Loss Prediction of HF/VHF Systems in Forests

Marinho Alex Kamiroski Melo, José Carlos Araujo dos Santos, and Maurício Henrique Costa Dias
Electrical Engineering Department
Instituto Militar de Engenharia – IME
Rio de Janeiro, Brazil
maro.alex@hotmail.com, araujo@ime.eb.br, mhcdias@ime.eb.br

Abstract—One of the most referenced analytical methods to methodology impose general limits of validity for Tamir’s
calculate the HF and VHF radio propagation loss in forests is model: frequency band from 2 to 200 MHz and distances
Tamir’s model. Though it is very straightforward for point-area relative to the transmitter from 1 to 100 km. Thus, Tamir’s
radio coverage planning, its extension for site-specific predictions model represents a suitable approach for the planning of HF
is actually an open problem. In the present work, a heuristic and VHF terrestrial systems in forests.
approach is proposed to this matter, when digital terrain and
treetops heights models are available. Preliminary outcomes were Tamir’s model assumes a simplified geometry of the
computed by a Matlab code implementation of the adapted problem, in which both the ground and the canopy heights are
model. Coherent results were observed, with a “height gain” constant. The most obvious approach to applying the model to
typical of site-specific methods clearly standing out. a real scenario would consider the average heights of those two
layers. For a point-area (PA) prediction, this strategy is
Keywords-land mobile radio propagation factors; HF radio reasonable. However, when point-to-point (PP) prediction is
propagation; VHF radio propagation; vegetation. more convenient, Tamir’s model is not that straightforward to
be considered. PP or site-specific predictions often use digital
I. INTRODUCTION elevation models and other relevant morphological layers. In
One of the most striking features of the Amazon, the largest the case of wave propagation in forests on the HF and VHF
terrestrial biome in Brazil, is the presence of large extensions bands, it is necessary to know the height of the tree canopy, as
of dense forests. Over the past decades, the efforts of Brazilian well as the terrain height. Applying Tamir’s model considering
society in the preservation of this biome have been noticeable, the terrain and the treetops heights variations punctually is an
especially through the creation and conservation of parks and open problem in the literature.
reserves. However, the natural hostility and large extension of This work falls within the concerned scope and proposes a
such environment bring severe hardships for the logistics heuristic methodology for applying Tamir’s model to predict
viability of its protection and maintenance. site-specific coverage of HF/VHF systems in forests. To
The difficulty of establishing radio communications is one properly present the proposed technique, this article is
of the major problems faced by people who work in areas of structured as follows. Section II briefly outlines the reference
dense vegetation, such as park rangers, police officers, model considered in this study (Tamir). The methodology used
firefighters, army personnel and others. The forest environment to apply this model in algorithms that use digital terrain and
significantly attenuates the transmitted signal in the typical surface (tree canopy) bases is explained in section III. The next
bands of portable radios (UHF in particular), since radio waves section discusses preliminary results of the algorithm
are absorbed and scattered by trees. Moreover, the typical developed for HF/VHF terrestrial systems coverage prediction
range of portable radios used by them is already naturally in forests. Finally, section V concludes the paper.
limited by the need for low-power operation due to the use of
batteries. In this scenario, the operation on the HF and VHF II. TAMIR’S MODEL FOR PROPAGATION IN FORESTS
bands emerges as a viable alternative for links up to a few Tamir’s model starts from the flat earth assumption and
kilometers [1]-[2]. sees the forest as a lossy dielectric layer, i.e., with finite
The propagation mechanism that explains the higher range conductivity, interposed between ground and air [3]-[5]. It
observed in the HF and VHF bands is a surface wave that further assumes that the forest edges are sufficiently away from
propagates along the tree canopy, usually referred to as “lateral both radios (transmitter – Tx, and receiver – Rx), so that the
wave” [3]. Tamir was one of the first to evaluate this behavior, infinite length layer model holds as a good approximation.
by proposing a methodology for asymptotically estimating the Fig. 1 illustrates the model concept. The average height of the
field radiated by an infinitesimal dipole antenna inside a forest, tree canopy defines the layer height hf. In this paper, only the
modeled as a lossy homogeneous medium with refractive index situation in which both antennas are within the forest is
higher than that of air [3]-[5]. The assumptions taken in this considered, i.e., hT and hR < hf.

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 h
Air In the asymptotic field expressions of Tamir, it is
considered that the antennas are infinitesimal dipoles, with
Forest length l << λ0 (free space wavelength). Only vertical and
Rx horizontal linear polarizations are discussed in [3]. The model
hf Tx l assumes also that the transmitting and receiving antennas have
l
the same length and polarization. The present work deals only
hR with the vertical polarization case.
hT
It is important to emphasize that Tamir’s model points out
Ground the contribution of the lateral wave as the one that dominates
d
Figure 1. Forest model as a lossy dielectric layer between ground and air. the composition of the total received field. Thus, the portion
associated to the ionospheric refraction is neglected, as well as
Table I presents the electrical properties and heights of other contributions such as the direct path propagation, ground
forests, for three typical situations. The relative permittivity of reflections and forest-air interface reflections. The
the forest is given by εrf and its conductivity is represented by experimental validation of that model was the focus of some
σf. Forests from 1 to 3 are respectively characterized by Tamir studies, such as [7]-[8].
as thin, medium and dense [4]. The forest permeability is equal The field strength Elat received by a vertically polarized
to the air’s (μ0 =0.4π μΗ/m). infinitesimal dipole (in line with h axis of Fig. 1) is given by
[3]:
TABLE I. TYPICAL CONSTITUENT PARAMETERS OF FORESTS
− jk0 §¨ d + s n 2f −1 ·¸
Forest σf (mS/m) εrf hf (m) 60 Il e © ¹
1 0.03 1.03 5 E lat = − j (3)
2 0.1 1.1 10 n 2f − 1 d2
3 0.3 1.3 20-30
where I (A) is the input current at the transmitting antenna,
According to Tamir’s model [3], within the considered l (m) is the antenna length, k0 is the free space phase constant,
limits, the main propagation mechanism is a surface wave d (m) is the distance between the antennas, and hT,R (m) are the
which travels along the forest-air interface, originated from the the heights of the transmitting and receiving antennas,
refraction under incidence on the critical angle θc. Fig. 2 respectively. The other parameters in (3) are given by the
illustrates this concept. expressions [3]:

h dlat Air
s = 2h f − hT − h R (4)

θc Forest
n f = εˆ rf (5)
θc Rx
Tx hf l with nf being the forest refraction index.
l hR In this work, as in [4], the received power PR (W)
hT
x computation is based on the effective vector length concept to
determine the induced voltage VR (V) at the output terminals of
d Ground
the receiving antenna [9]. Therefore:
Figure 2. Tamir’s concept of lateral wave, with indication of the most
significant propagation path (dashed line). VR = Elat ⋅ l 2 (6)
From the boundary conditions on the forest-air interface 2 2
V R2 E lat l
and considering that the incidence occurs from a denser lossy PR = = (7)
medium (forest) to a less dense lossless medium (air), the R AR 4(RrR + RlR )
critical angle is given by [6]:
with Elat given by (3). RAR (Ω) is the receiving antenna
§ · resistance, which is equal to the sum of the radiation resistance
θ c = tan −1 ¨¨ ¸
1
(1) RrR (Ω) with the loss resistance RlR (Ω). The receiving antenna
Re{ εˆrf − 1} ¸ is assumed matched to the load.
© ¹
The transmitting antenna input current I can be expressed in
In (1), the complex relative permittivity is given by [6]: terms of the transmission power PT (W) by:
σf
εˆ rf = ε rf − j (2)
I=
ecd PT
ωε 0 RrT
(8)

in which ω (rad/s) is the angular frequency of the transmitted

in which ecd is the radiation efficiency and RrT (Ω) is the
signal and ε0 = 8.85 pF/m is the air permittivity.
radiation resistance of the transmitting antenna, assuming that

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the antenna is matched to the transmitter output (PT is the taken mainly in the s parameter of (4), since the real part of the
power effectively delivered to the antenna). The radiation exponential term in (3) is a function only of the stretch
efficiency is given by: propagated along the h axis before and after refraction on the
air-forest interface.
R rT
ecd = (9) Fig. 3 illustrates the application scenario of the proposed
RrT + RlT adjustment of Tamir’s model to be used with digital terrain and
vegetation heights models. It is noted that both the canopy and
where RlT (Ω) is the transmitting antenna loss resistance.
ground heights vary with the observation position along the
The radiation resistance is a function not only of the horizontal axis (x). Instead of a single canopy height hf, as in
antenna itself, but also of the surrounding medium. Fig. 2 and (3), two distinct heights shown in Fig. 3 must be
Nevertheless, the known expressions for free space condition considered: one taken at the refraction point close to the
were adopted in this work, since the effect of the ground and transmitter (hfT); the other at the refraction point near the
forest layer tend to be minimal on infinitesimal antennas, as receiver (hfR).
addressed in [4]. Thus, the radiation and loss resistances are dlat Air
given by [9]: h

2 θc
§ l · Forest
RrT , R = 80𠨨 ¸¸ (10) θc Rx
© λ0 ¹ Tx
hf T hf R
l

l d2 hR
l ωμ 0 hT
RlT , R = (11) d1 hg(x) x
2πa 2σ c
d Ground
In (11), a (m) is the antenna cross section radius and σc (S/m) Figure 3. Adaptation of Tamir’s concept of lateral wave for irregular terrain
is the metal conductivity from which the antenna is made. and canopy, with the most significant propagation path indicated (dashed
line).
III. TAMIR’S MODEL ADAPTATION FOR SITE-SPECIFIC
Thus, taking Fig. 3 geometry as reference, the electric field
PREDICTION
strength is now given by:
As illustrated by Fig. 1, Tamir’s model considers an
idealized uniform geometry of the forest layer, with no − jk0 §¨ d ′+ s′ n 2f −1 ·¸
variation of terrain and trees canopy heights. This approach is 60 Il e © ¹
appropriate for application in scenarios with inexpressive ′ =−j
E lat (12)
variation of these heights, particularly in PA predictions. It n 2f − 1 d ′2
suffices to take the average heights of the two strata as
where
references. On the other hand, in site-specific predictions, the
fluctuations of the received power as a function of variations in d ′ = d1 + d 2 + d lat (13)
heights along the analyzed pathways are expected to be
tracked. In this case, Tamir’s model cannot be straightforward s ′ = h f T − hT + h f R − hR (14)
applied in the form expressed in (3).
The distance dlat accounts for the total perimeter between the
In order to extend Tamir’s model application to PP points pointed out as air-canopy interface incidence and return
predictions, two fundamental aspects should be noted. Firstly, of the lateral wave to the forest, as indicated in Fig. 3. The
the dominant propagation mechanism is the lateral wave, a geometrical parameters d1, d2, hT and hR in (13) and (14) are
specific type of wave that travels along the concerned interface also pointed out in Fig. 3. The remaining variables in (12) are
(forest-air). The second important aspect regards the the same already defined in section II. It is also noteworthy that
application scenario. The idealized geometry of Fig. 1 is a mere all heights in (14) are referenced to h = 0 in Fig. 3.
abstraction of forests that have small terrain and treetops
altimetry variations, comparable to fractions or a few IV. PRELIMINARY TESTS
wavelengths of the radio signal. The dense rain forests,
abundantly present in the Amazon, are a typical example in the The proposed adjustment was implemented in a Matlab
Brazilian context. routine. The algorithm reads, initially, two arrays with terrain
and canopy altimetry data in the region of interest. These
Given the basic aspects of HF/VHF radio propagation in matrices are obtained from digital terrain models, such as
forests with almost regular terrains, this paper proposes a NASA SRTM project [10]. Fig. 4 shows a treetops heights
heuristic approach to adapt Tamir’s model for site-specific SRTM base (90 m horizontal resolution) of a 10.7 × 10.7 km2
predictions. To this end, two approaches are adopted. The first site at the surroundings of São Gabriel da Cachoeira (a
is to assume that the lateral wave follows the fluctuations in northwestern Brazilian Amazon town), downloaded from [11].
height of the trees, without significant additional losses, given
the small magnitude of these variations. The second is to The SRTM project has not raised enough data to enable the
consider that the main impact of fluctuations in terrain height is generation of digital terrain models of the Amazon forests. As a

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result, in order to test the numerical code with the adapted Figs. 6 and 7 illustrate the received power decay along the
Tamir’s model proposal, a hypothetical terrain heights matrix straight path between points T and R indicated in Fig. 4, for 15
had to be created (hg). To this end, an average forest height and 65 MHz, respectively. The point T represents a transmitter
hfm = 20 m was assumed as reference for the site depicted in located at coordinates (3510, 6750), and R a receiver at the end
Fig. 4. The created terrain altimetry array had the same canopy of the path, in (8460, 3600). Two models are represented: the
heights of the selected site (hf), minus that average height and a proposed one, which considers the actual altimetric data, and
Gaussian random variable with zero mean and adjustable the ideal or PA one, calculated for an average forest height of
standard deviation. Fig. 5 depicts a random base generated with 20 m and regular terrain (hg = 0 all the way). The difference
a 5 m standard deviation. between the canopy and terrain heights along the route is also
Canopy heights - hf (m) illustrated for ease of analysis.
110 Received power for f = 15 MHz
10000 -50
Tamir - hf = 20 m, hg = 0
9000 105 Adapted Tamir - actual heights

P r (dBm)
8000 -100

7000 100
T

6000 -150
y (m)

95 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
5000 d (m)
Altimetric differences
4000 30
R 90
3000 25

hf - hg (m)
2000 20
85
1000 15
0 80
0 2000 4000 6000 8000 10000 10
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
x (m)
d (m)
Figure 4. Canopy heights digital model of the seleted site. Figure 6. Received power and altimetric differences profile along the chosen
path, for f = 15 MHz.
Terrain heights - hg (m)
85 Received power for f = 65 MHz
-50
10000
Tamir - hf = 20 m, hg = 0
9000 Adapted Tamir - actual heights
80
P r (dBm)

8000 -100

7000 T 75
6000 -150
y (m)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
5000 d (m)
70
Altimetric differences
4000 30
R
3000 65 25
hf - hg (m)

2000 20

1000 60 15

0 10
0 2000 4000 6000 8000 10000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
x (m) d (m)
Figure 5. Terrain heights digital model of the seleted site. Figure 7. Received power and altimetric differences profile along the chosen
path, for f = 65 MHz.
In addition to the altimetric bases, the electrical properties
of the forest and the radio system parameters must be specified. In both Figs. 6 and 7 there is a clear presence of a “height
For this test, the dense forest values of Table I were taken. As gain” in the proposed model. Height differences greater than
for the radio system, short dipoles with l = λ0/50 were the average forest height (20 m) lead to increases in signal
considered, both vertically polarized at a 3 m height above the attenuation with respect to the ideal prediction, and vice versa.
terrain. Since mobile tactical systems were the envisioned In fact, the most significant variation expected was associated
application, a typical transmission power PT = 10 W was to the s´ parameter of (14), since d´ ≅ d in most of the cases
chosen. Path loss was calculated in two distinct carrier (when d >> max[hf - hg]). The results are consistent with
frequencies: one in the HF, other in the lower VHF band. expectations, and show significant variations (> 10 dB) that the
ideal model is not able to predict.

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 The algorithm is also able to perform a prediction for the for tactical HF/VHF radio systems in forests. From the
entire study area. Figs. 8 and 9 illustrate the signal coverage knowledge of the fundamental propagation mechanism in the
maps for the two scenarios previously considered. The results present scenario, a heuristic approach was proposed, inserting
are also consistent, showing a circular symmetry in the the point to point terrain and canopy heights variations into the
expected average signal decay with distance. Variations around electric field strength equation. The adapted model presents a
this behavior are due to the site-specific “height gain”, already site-specific behavior evidenced in the form of a “height gain”.
highlighted.
Preliminary tests confirmed the results coherence and the
Received power (dBm) x position higher potential to fully exploit altimetric databases for radio
-40
coverage predictions. This PP adaptation provides the ability to
10000
-50 indicate and quantify significant signal fluctuations in the
9000 analyzed scenario that the PA standard use of the original
8000 -60 model is unable to point out. Nevertheless, experimental
validation of the present proposal is still due.
7000 T -70

6000 ACKNOWLEDGMENT
-80
y (m)

5000 This work was partially supported by the Brazilian research

-90 promotion agencies FAPERJ (project 101.497/2010) and CNPq
4000
(PQ-2 grant to the 3rd author).
3000 -100

2000 -110
REFERENCES
1000
[1] M. S. Assis, “HF tactical communication in the Amazon region,” in
-120 Proc. of the International Conference on Communication Systems,
0 Singapore, vol. 2, pp. 1273–1277, 1990.
0 2000 4000 6000 8000 10000 [2] M. S. Assis, “Search and rescue in a forest environment,” in Proc. of the
x (m)
2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics
Figure 8. PP coverage pattern at the selected site, for f = 15 MHz. Conference (IMOC), Belém – Brazil, vol. 1, pp. 249-252, 3-6 Nov 2009.
[3] T. Tamir, “On radio-wave propagation in forest environments,” IEEE
Received power (dBm) x position Transactions on Antennas and Propagation, vol. AP-15, no. 6, pp. 806-
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817, Nov 1967.
10000 [4] D. Dence, T. Tamir, “Radio loss of lateral waves in forest
-50 environments,” Radio Science, vol. 4, no. 4, pp. 307-318, Apr 1969.
9000
[5] T. Tamir, “Radio wave propagation along mixed paths in forest
8000 -60 environments,” IEEE Transactions on Antennas and Propagation, vol.
AP-25, no. 4, pp. 471-477, Jul 1977.
7000 T -70 [6] C. A. Balanis, Advanced Engineering Electromagnetics, Wiley, 1989.
[7] J. C. R. Dal Bello, Propagação de Ondas Eletromagnéticas na Floresta
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– RJ, 1984 (in Portuguese).
[8] M. S. Assis, R. C. Pinto Filho, “Measurements of the electrical
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1000 [10] T. G. Farr, P. A. Rosen, E. Caro, R. Crippen, R. Duren, S. Hensley, M.
-120 Kobrick, M. Paller, E. Rodriguez, L. Roth, D. Seal, S. Shaffer, J.
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Figure 9. PP coverage pattern at the selected site, for f = 65 MHz. [11] Earth Science Data Interface (ESDI) at the Global Land Cover Facility,
in http://glcfapp.glcf.umd.edu:8080/esdi/index.jsp (last access
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V. CONCLUSION
An adaptation of Tamir’s model was proposed in this work,
to allow its full use in site-specific coverage prediction tools

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