1
UK SG3
CP 66
Proposed revision of P.1546: Improved N correction
1
Introduction
The curves in Recommendation ITU-R P.1546 are based on measurements over terrestrial
paths made principally in Europe. They are considered applicable in temperate climates. The
variation of VHF and UHF field strengths with distance from the transmitter and with time is
to a large extent controlled by the vertical refractive-index gradient of the atmosphere.
Recommendation P.453 now incorporates a global database of N, the gradient in the lowest
65 m of the atmosphere in N-units/km, in electronic form. Five data files are available, giving
N values exceeded for 99, 90 50 10 and 1% of time, at intervals of 1.5 longitude and
latitude. It should be noted that P.453 gives values of dn/dz which, since refractivity
decreases with height, is negative. In this document the refractivity gradient is written as N
and interpreted as a positive number. Thus a large value of N indicated a steep gradient and
increased refraction over obstacles.
This document reports on an investigation into whether the P.453 N data can be used to
make adjustments to the P.1546 field-strength curves to adapt them for different radioclimatic regions of the world. The Annex to this document proposes a revision to the
Recommendation.
2
Delta-N data in temperate climates
Figure 1 illustrates all of the P.453 data from
45 to 60 N, and from -12 to 15 E. This
covers an area of N.W. Europe, including the
North Sea
The data exist only at the 50%, 10% and 1%
values of the abscissa. However, straight lines
join each set of three data to indicate that they
apply to the same geographical location.
It is clear that there are wide spreads of N
values over N.W. Europe. Moreover, it cannot
be assumed that a given location will have all 3
N values higher, or all 3 values lower, than a
different location. There are clear cases where
the joining lines in Figure 1 cross between
different values of % time.
2
Figure 2 shows N values for 36 to 48N and 69
to 111W (249 to 291E), covering a large area
of central and eastern U.S.A., part of the Great
Lakes and a significant area of the Atlantic,
selected as having roughly the same range of
weather as the N.W. Europe area illustrated in
Figure 1.
These data are broadly similar to Europe, with
a slightly lower spread of values.
These wide range of values presents a problem.
If the P.1546 curves are to be a reference from
which corrections for location can be made on
the basis of N, it is necessary to define
representative N values exceeded for 50%,
10% and 1% time from which to make the
correction.
Figure 3 shows N for the same area of Europe
as Figure 1, but including only locations over
land. This clearly shows a much smaller range
of values than Figure 1, indicating that P.453
data reflect the land/sea distinction.
Values of N for points over sea were similarly
found to be generally larger than for over land.
Thus consideration was given to using different
reference N values for land and sea curves.
This procedure was not adopted because the
land and sea curves already take into account
the differences between these path types. Also,
it would mean making smaller corrections for
sea curves than for land curves when correcting for a location with general higher refractivity
gradients, which if anything is the opposite of what would be expected.
It was thus concluded that a single set of reference N values should be adopted for all path
types, and the means for the 3 percentage times in Figure 3 were adopted, shown in Table 1.
Table 1: Mean European N values over land
% time
N N/km
50%
43.3
10%
141.9
1%
301.3
The value of 43.3 N/km for 50% time is sufficiently close to the round figure of 40 in P.1546
Annex 1 §14 for the above method for arriving at values to be viewed as reasonable. It was
decided to proceed with the investigation for land curves using these N values as applying to
the P.1546 land curves.
3
3
Maximum N differences arising from changes in location
The purpose of the proposed correction is to adjust the P.1546 curves for use in different
radioclimatic regions of the world, in each case for the same percentage time. This section
reports on the magnitude of the possible changes to N which may be required for this
purpose.
The 50%, 10% and 1% P.453 data files were searched for the lowest and highest values
anywhere in the world. Table2 gives these results.
Table 2: Lowest and highest N in P.453 data files
Percentage
time
Lowest
Highest
50
14.1
722.0
10
37.3
1371.0
1
58.3
1795.0
The differences between these values and the representative N values adopted in Section 2
(see Table 1) are given in Table 3. These represent the largest changes in N which will
occur when correcting curves for different radioclimatic regions.
Table 3: Largest changes to N
4
Percentage
time
Downwards
Upwards
50
-29.2
+678.7.1
10
-104.6.0
+1229.0
1
-242.8.0
+1494.0
Basis of the proposed method
It is wished to use available evidence to derive a process for modifying the existing P.1546
curves on the basis of N statistics. The evidence used in this document consists of the
relationship of differences between P.1546 curve families for 50%, and 10% and 1% time and
the corresponding N exceedances. In other words, if differences between N exceedances
for different percentage times can predict 10% and 1% curves from 50% curves for a given
location, then possibly differences between N exceedances for a given percentage time can
be used to adjust a curve for use in a different location.
It is accepted that this process may not be reliable. To confirm how valid it may be, and
possibly to adjust the method, if would be useful to compare the results with empirical fieldstrength curves developed in different regions of the world. It is particularly hoped that ABU
curves will be used for this purpose. At the time of writing these curves were not available in
electronic form suitable for comparison.
4
5
Differences between sets of P.1546 curves for different percentage times
The scaling factors used in the proposed method were based on the differences between
P.1546 curves for difference percentage times. In particular an attempt was made to
approximate to the distance-dependence of the increases in field strength for smaller
percentage times. Thus a review was made of these differences. Although it requires 18
figures, the complete set is reproduced here.
Figures 4 to 21 show the differences in dB equal to (E10 - E50 ) and (E1 - E50 ) for the 100
MHz, 600 MHz and 2 GHz land curves. The figure numbering is given in Table 4.
Table 4 - Figure numbers for differences between % time curves
Frequency
MHz
Land
Cold sea
Warm sea
10%
1%
10%
1%
10%
1%
100
4
5
6
7
8
9
600
10
11
12
13
14
15
2 000
16
17
18
19
20
21
For convenience in comparison Figures 4 to 21 are presented two per page, with the 10%
results at the top of the page and the 1% below.
They are best viewed in colour. However, if viewed without colour most families of
differences can be interpreted by noting that the only solid trace is for h1 = 10m, and that the
families change systematically as h1 increases. In colour, individual traces can be identified
by the legend on the left of the ordinate scale; the subscripts in the range 1 to 8 indicating
columns 1 to 8 in the P.1546 data tables, being the field strength values for h1 from 10 m to 1
200 m respectively.
5
6
7
8
9
10
11
12
13
14
The results shown in Figures 4 - 21 show generally systematic trends, although with sufficient
variation of form to suggest that they may not have been produced from a wholly consistent
process.
A particular observation is that some of the differences are negative, which is illogical. From
the definition of the curves, which represent field strengths exceeded for given percentage
times, curves for a given percentage time cannot be less than for a larger percentage time.
Such discrepancies are few and limited to a maximum of about 2 dB, but it is commented in
passing that some adjustment to the curves seems to be required.
There are clear dependencies on distance and h1. Both of these are to be expected since the
principal mechanism, at least down to about 5% time, is the effect of N on terrain
obstructions. It is evident that enhancements at smaller time percentages take effect for low
values of h1 at shorter distances than for higher h1 values. At longer distances, however, the
enhancement can be greater for larger values of h1. It is not obvious why this should be so,
and the effect is not systematic. Below about 5% time departures from an exponential
atmosphere play a larger role, particularly ducting, and this is reflected in the generally less
regular behaviour of the 1% results.
It is interesting to note that the maximum differences show little systematic frequency
dependency, being of the order of 10 dB and 20 dB for the 10% and 1% results respectively.
Attempts were initially made to find a function of distance and h1 to approximate to the form
of the results shown in Figures 4 to 9. It was found, however, that a better approximation
could not be found than a simple function of distance only. The function used for this
purpose is described in the following section.
15
6
Distance dependency of correction function
Initially an attempt was made to find a function of both distances and effective height to
correct curves for changes in N. This was frustrated by some irregularities in the source
curves leading to illogical or unrealistic derived curves
It was thus decided to propose a correction which varies with distance and not effective
height, but to apply the full correction only to the lowest of each family of curves, that is, for
h1 = 10 m. The correction for other curves will be scaled to maintain the same proportional
distances from the h1 = 10 m and maximum field strengths. This procedure maintains the
relative positions of the curves within each family.
The proposed distance function is given by:
F(d)
where:
d
=
=
{ 1 - exp ( -d / 50 ) } ( exp ( -d / 6000)
(1)
distance in km;
Equation 1 is illustrated in figure 22.
Note that it gives only distance
scaling. The actual correction also
depends on the change in N.
The final correction C in dB to be
applied to curve for h1 = 10 m is
given by:
C
=
K (N - No)  F(d )
(2)
where:
K
N
N0
and
=
=
=
Empirical scaling factor;
N at the required location;
Reference value of N;
F(d) is given by equation (1)
As stated above, the corrections applied to curves for other values of effective height are in
proportion to the attenuation below maximum field strength, thus maintaining the relative
positions of each family of curves.
16
7
Differences in dB between actual and generated 10% and 1% families
Figures 23 to 28 show the differences between the actual 10% and 1% time families and
curves generated from the 50% families using equation (2). These corrections were made at
the notional "temperate climate" point represented by the N values derived in Section 1,
namely:
50%
43.3 N/km
10%
141.9 N/km
1%
301.3 N/km
Thus in equation (2) the term given by (N - No) will be:
for 10% time (141.) - (943.3)
for 1% time (301.3) - (43.3)
=
=
98.6 N/km
258.0 N/km
The scaling factor 'K' in equation (2) was set empirically to 0.08. This results in errors which
are approximately equally distributed around zero.
Thus figures 23 to 28 illustrate the errors in applying the correction defined in Section 6
above. As before they are presented two to a page for ease in comparison. They are also
plotted with the same scales for convenience in comparing error amplitudes.
It is noted that the errors for the conversions to 10% curves are generally lower than for
conversion to 1% curves. As expected the differences between curve shapes is evident in
these results.
17
Figure 23: Comparison of generated and actual curves. VHF 10%
Figure 24: Comparison of generated and actual curves. VHF 1%
18
Figure 25: Comparison of generated and actual curves. UHF 10%
Figure 26: Comparison of generated and actual curves. UHF 1%
19
Figure 27: Comparison of generated and actual curves. 2 GHz 10%
Figure 28: Comparison of generated and actual curves. 2 GHz 1%
20
8
Adjustment to maximum field strength curves
In addition to adjusting the normal field strength curves for N, consideration must be given
to the maximum field strength curves. In the present P.1546 curve familes, maximum field
strength for land at all percentage times and for sea at 50% time is the free-space field
strength. For both cold and warm sea at 10% and 1% time, the maximum field strength is
greater than free-space by an enhancement given by:
Eh (d, t) = 2.38 (1 - exp (-d / 8.94)} (log (50 / t)
(3)
where:
d = distance in km;
t
= percentage time (1% or 10%).
Enhancements above free-space are attributable to ducting, in which electromagnetic energy
tends to expand in two dimensions as opposed to three. In an ideal duct the field strength
decays with distance according to 10.log(d). This can be viewed as an upper bound for signal
enhancement.
Increases to the maximum field strengths are given in P.1546 over sea since surface ducts
occur for large fractions of time over water, and tend to extend for longer distances without
interruption. It is proposed to maintain this distinction between land and sea curves.
The theoretical minimum value of refractivity gradient for ducting to occur is 157 N-units. It
is noted that the mean N value of 301.3 for European land derived in Section 1 (see Table 1)
is significantly above 157, thus confirming that the 1% curves are influenced by ducting, as
would be expected.
Ideally, a systematic enhancement to the maximum field strength curve should be made when
the value of N to which a family of curves is to be corrected is greater than 157. However,
since the existing P.1546 sea curves already have an enhancement serving the same purpose
for N = 301.3, further enhancements to both land and sea maximum curves must be
restricted to N greater than 301.3. The proposed additional enhancement was derived as
follows:
a) the distance dependency will be given by equation (1);
b) the amplitude will be proportional to (N - 301.3);
c) a scaling factor will be adjusted such that at the maximum N possible (1795, see Table
1) the maximum slope of the combined existing 1% sea and additional enhancements will
be just less than +10.log(d).
Since the underlying free-space maximum decays at 20.log(d), the result will be that under the
most extreme conditions possible the corrected maximum field strength will decay at slightly
more than 10.log(d) for a certain range of distances. In other words, the most extreme case
will almost reach the theoretical upper bound of signal enhancement.
The resulting enhancement added to maximum field strengths is given by:
Eemax
=
0.07 M {1 - exp ( -d/50)} (exp ( -d/6000)
where:
= N - 301.3
if ((N > 301.3)
= 0
otherwise
and the constant 0.07 has been selected to achieve the condition stated in c) above.
M
(4)
21
22
Equation (4) is illustrated in figure 29 for a 1% sea curve. It shows the existing 1% sea
enhancement, and the result of adding equation (4) for three N values up to the maximum of
1795, at which the maximum slope is just less than 10log(d). The dashed straight line at this
slope is purely for comparison.
9
Modification of main correction for large values of N
The empirical scaling factor 0.08 derived in Section 7 was based on comparisons between the
actual P.1546 10% and 1% time curves, and curves generated from the 50% curves. This
process involved N values up to no more than 301.3, with no changes to any maximum field
strength curves.
When a N correction is used move a given curve family to a different radio-climatic location
N values can go up to 1795. Using a simple scaling factor of the order of 0.08 over this
much larger range of N results in infeasible distortions to the curves, including large positive
values of slope, that is, of field strength increasing substantially with distance.
However, over the larger range of N part of the required correction can be accomplished by
the additional enhancement made to maximum field strengths. Thus the scaling factor K in
equation (2) is redefined as a parabolic function of (N - No) given by:
K
=
0.08 (N - No)
(N - No)  0
(5a)
=
14.94 - 6.693 (N - No)2
(N - No) > 0
(5b)
The scaling factor K now acts as before for changes to smaller values of N, but for changes
to larger values of N it progressively reduces in effect over the range of N values where
ducting will dominate, and where the increase in maximum field strengths will be most
effective.
23
10 Adjustment of P.1546 for different radio-climatic locations
On the basis of the above the following method can be used to adjust P.1546 curve families
for use in radio-climatic regions of the World having different values of N. For each
distance in the field strength tabulation, and in the following order:
a) If N is greater than 301.3 add the correction given by equation (4) to the maximum field
strength values for the family of curves.
b) Calculate the scaling factor K using equation (5), where No is the reference for the
percentage time given in Table 1.
c) Add the correction given by equation (2) to the lowest member of the curve family, that is,
for h1 = 10 m, noting that K must be the value given by equation (5). If necessary limit
the result either such that it does not exceed the maximum field strength. When and only
when the change in N is positive (N - No > 0), limit the result such that the new
difference in dB of the h1 = 10 m curve below its maximum field strength curve is not
greater than the original.
d) Calculate the field strengths for the remaining value of h1 to maintain the same relative
positions of the field strengths between E1 for h1 = 10 m and the maximum Emax using:
E'n
=
E'1 + (En - E1) (E'max - E'1) / (Emax - E1)
where the primes indicate corrected values.
Figures 30 to 38 show some sample results for extreme cases using the above method.
24
Figure 30 shows the most extreme increase in VHF 50% land field strengths given by the
largest value of N in P.453 exceeded for 50% time.
Figure 30: VHF Land 50% curves moved to N = 722.0 (maximum exceeded 50% time)
Figure 31 shows the corresponding UHF results.
Figure 31: UHF Land 50% curves moved to N = 722 (maximum exceeded 50% time)
25
Figure 32 shows the corresponding 2 GHz results.
Figure 32: 2GHz Land 50% curves moved to N = 722 (maximum exceeded 50% time)
Figures 33 to 35 show the same sequence for 10% curves, with N increased to the maximum
value of 1371.
Figure 33: VHF Land 10% curves moved to N = 1371 (maximum exceeded 10% time)
26
Figure 34: UHF Land 10% curves moved to N = 1371 (maximum exceeded 10% time)
Figure 35: 2GHz Land 10% curves moved to N = 1371 (maximum exceeded 10% time)
27
Figures 36 to 38 show the same sequence for 1% curves, with N increased to the maximum
value of 1795.
Figure 36: VHF Land 1% curves moved to N = 1795 (maximum exceeded 1% time)
Figure 37: UHF Land 1% curves moved to N = 1795 (maximum exceeded 1% time)
28
Figure 38: 2GHz Land 1% curves moved to N = 1795 (maximum exceeded 1% time)
Figures 30 to 38 show the most extreme cases of adjusting P.1546 land curves for higher
values of N. For all three percentage times the N value is the highest found in the P.453
data files. No test was conducted as to whether the corresponding locations were over sea or
land since the mixed-path method requires both land and sea field strength curves to be valid.
The curve families retain their general shape after the adjustments. It may be noted that in a
few cases the slope of an h1 = 10 m curve approaches zero at about 100 km. This is a limiting
condition in applying N corrections; it is not realistic to predict field strengths increasing
with distance.
No results are presented for reducing N. This process retains the general shape of a family
of curves and produces no artifacts.
Figures 39 and 40 (overleaf) show the most extreme enhancement for warm sea curves at
VHF and UHF respectively. In figure 39 there is an extended range of distance over which
the h1 = 10 m curve has zero slope, and in figure 40 there is a range of distances over which
the slope is positive. This is infeasible, but it is suggested that it can be accepted. It is
suspected that the restrictions which have had to be placed on the corrections made for higher
N values result in an under-estimate of signal enhancement. Allowing this minor anomaly is
better than making reductions in enhancements for all curves. The effect does not occur at 2
GHz, where all curves coincide with the maximum field strengths.
29
Figure 39: VHF Warm sea 1% curves moved to N = 1795
(maximum exceeded 1% time)
Figure 40: UHF Warm sea 1% curves moved to N = 1795
(maximum exceeded 1% time)
30
11 Proposed revision to P.1546
The proposed revision to P.1546 given in the Annex puts the adjustments to the curves in a
separate Annex of the Recommendation. This is suggested since the method for adjusting the
curves for different N values may well be subject to further revision, and it will be
convenient to keep it separate from the description of the main method.
This leaves the question of the present information given in Annex 1 of the Recommendation,
§14, where the correction for 50% time curves for distances beyond the horizon is defined as
0.5(N - 40). The constant 40 plays the same role as the mean 50% N in the new proposals
of 43.3 (see Table 1). These two values are sufficiently close not to constitute a problem.
The scaling factor of 0.5, however, is much larger than the value of 0.08 derived when
comparing actual and generated 10% and 1% curves in Section 7 above. As noted in Section
9 above, this simple scaling factor gives a reasonable match over the limited variation of N
concerned, but needs to be reduced for larger increases to N. This is even more true for the
scaling factor of 0.5. Simple calculations show that for diffraction over a single knife-edge in
the shadow boundary region, 0.5 dB/N-unit for small changes in refractivity gradient close to
40 is a reasonable approximation. But this is not true for larger values of N associated with
non-exponential atmospheres. For instance, the largest N value exceeded for 50% time is
722 (see Table 2). Using 0.5(N - 40) with this value gives a correction of 341 dB, which is
clearly wrong.
These raises the question as to whether the P.453 dn/dz data are defined differently to N in
§14, but no discrepancy seems to be apparent.
On this basis, therefore, the revision given in the Annex presents the new method as a
replacement for the 0.5(N - 40) correction.
The other correction in §14 based on mean values of surface refractivity is a different issue.
Mean values globally have maxima at about 400, and thus a maximum correction of about 20
dB will result from this method. Although the relevant parameter is vertical refractivity
gradient, not refractivity at a particular height, in view of the fact that some atmospheric
conditions resulting in anomalous propagation are known to correlate with high surface
refractivity, at least to some extent, and since some users of the Recommendation may not
have N data available, it can be argued that this correction should be retained. This position
has been adopted here, although with the availability of P.453 data it does not seem to be a
very strong argument.
12 Conclusions
The method discussed above is not based on data from different radio-climatic regions of the
world. For this reason it should not be viewed as completely reliable. It produces uniform
results with increases or decreases in field strengths as would be expected from changes to
N. It maintains the general form of the P.1546 curve families with only a few minor
anomalies.
The resulting proposed revision to P.1546 given in the following Annex is thus viewed as a
temporary method which can be used in preference to attempting to use the P.1546 curves as
they stand for any region of the world.
31
A limiting factor is that the P.1546 curves already incorporate a number of N-related effects,
and in particular the land and sea curves have fundamentally different forms, as would be
expected. It is possible that fundamentally different methods should be used to adjust field
strengths for land and sea curves. It would be difficult to do this and to ensure that the mixedpath method would still be valid.
A truly universal set of field-strength against distance curves would probably have to be based
on different principles in the first place. In the meanwhile the most urgent task is to compare
the present proposals against whatever data for different radio-climatic regions are available.
ANNEX - PROPOSED REVISION OF P.1546
1. In Annex 1, §14:
Delete the 3rd sentence "If the mean value of N .. to the curves." and replace by " Annex [X]
gives a method of adjusting the sets of curves given in Annexes 2, 3 and 4 for different
regions of the world where N values may be substantially different. The method is based on
vertical refractivity gradient data associated with Recommendation P.453. It should be noted
that the method should be viewed as provisional until further testing against measured data
can be carried out."
The paragraph now continues with the next sentence starting: "If N is not known, but ..."
2. New Annex:
Insert new annex [X] and arrange sequential equation numbering:
"The curves given in annexes 2, 3 and 4 are based largely on measurements in temperate
climates. Fields strengths in regions of the world where the vertical atmospheric refractivity
is significantly different will not, in general, be so accurately predicted.
The following method may be used to apply vertical refractivity gradient information from
Recommendation ITU-R P.453 to correct the curves in annexes 2, 3 and 4 for use anywhere in
the world. The P.453 data files give refractivity gradients in N-units/km in the lowest 1 km of
the atmosphere as negative values. However, refractivity gradient N is treated as though
positive in the following equations.
It should be noted that this method has not been tested against measured data.
Administrations are invited to make such comparisons.
Note that
The adjustments made to the curves are based on both the value of vertical refractivity
gradient at the location of interest, and the difference between this value and the refractivity
gradient represented by the curve. For this purpose the curves in annexes 2, 3 and 4 are
considered to represent reference values of vertical refractivity gradient No given by:
For fields exceeded for 50% time: No
For fields exceeded for 10% time: No
For fields exceeded for 1% time: No
=
=
=
43.3
141.9
301.3
N-units
N-units
N-units
(1a)
(1b)
(1c)
32
To adjust a family of field-strength curves for a different radio-climatic region of the world,
set N to the vertical refractivity gradient (as a positive number) exceeded for the time
percentage of interest obtained from P.453.
Calculate the change in vertical refractivity gradient N given by:
N
=
N - No
(2)
where No is the reference vertical refractivity gradient for the percentage time of the curve to
be adjusted given by equation (1).
For any distance, d km, if N is greater than 301.3, add an adjustment to the maximum field
strength given by:
Emax = 0.07 (N - 301.3) {1 - exp ( -d/50)} (exp ( -d/6000)
dB
(3)
Note that no change is made to maximum field strengths if N is less than or equal to 301.3.
Calculate the scaling factor K given by:
K = 14.94 - 6.693  10-6 (1494 - N)
= 0.08 N
For the h1 = 10 m field strength add an adjustment, E1 , given by:
E1
= K {1 - exp ( -d/50)} (exp ( -d/6000)
N > 0
N  0
(4a)
(4b)
dB
(5)
The value of E1 must be limited if necessary as follows:
a) E1 must be limited if necessary such that it does not exceed the adjusted maximum field
strength;
b) If N is greater than zero, E1 must be limited if necessary such that the difference
between the corrected maximum and h1 = 10 m field strengths is not greater than it is in
the unadjusted curves. Note that this condition must not be applied when N is less than
zero.
Adjust field strengths for other values of h1 such that they occupy the same proportional
position between the maximum and h1 = 10 m field strength as the corresponding field
strength in the unadjusted curves, using:
E'n
=
E'1 + (En - E1) (E'max - E'1) / (Emax - E1)
E1
=
field strength for h1 = 10 m
En
=
field strength for h1 values greater than 10 m
Emax
=
maximum field strength
where:
and primes indicate adjusted values.