INTERNATIONAL TELECOMMUNICATION UNION
RADIOCOMMUNICATION
STUDY GROUPS
UK SG6
CP67rev3
Document 3M/UK10-E
Document 3J/UK8-E
7 May 2002
English only
Received:
Subject:
United Kingdom
INFORMATION PAPER
Development towards a model for combined rain and sleet attenuation
1
Introduction
Attenuation in the melting layer has been identified in the UK as the probable cause of
anomalous attenuation to fixed services during precipitation in the north of the country. This
paper provides information on progress within the UK on developing an extension of the rain
attenuation method in P.530 to include the effect of sleet, based on melting-particle modeling
performed at Essex University.
The method described here is viewed as incomplete, but is presented at this stage for
comment.
2
Physical basis of the method
The right-hand side of figure 1 shows the geometry of a melting layer. Dry (non-melting) ice
crystals above the layer are considered to cause negligible attenuation. Ice particles fall into
the top of the melting layer and emerge from the bottom as rain. As particles fall through the
melting layer their size, shape and wetness vary. Specific attenuation rises relatively rapidly
to a value higher than for the equivalent rain, and then falls back until it reaches the rain value
at the bottom of the layer where all melting is complete.
Figure 1: Gamma factor giving variation of specific attenuation in the melting layer
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The left-hand side of figure 1 shows the variation of specific attenuation with height as a
multiplier of the specific attenuation for the rain rate existing below the layer. This multiplier
is termed the 'gamma factor'.
3
Choice of gamma-factor function
The work at Essex showed that the form of the gamma-factor function is sensitive to the
nature of the ice particles falling into the layer. At present there is insufficient measured data
to provide a definitive function. Moreover, it is probable that various types of ice particles
exist under different conditions.
The gamma-factor function (h) shown in figure 1 is typical of the Essex results, and is
given by:
(h)
=
1(h) / [ 1 + 2(h){ 4 1(h) - 1} ]
1(h)
=
{ 1 - exp ( -h / 70)}2
(1a)
2(h)
=
{ 1 - exp [ -(h / 600)2 }2
(1b)
(1)
where:
and h gives position in the layer as height relative to the zero-degree isotherm.
4
Height of melting layer in relation to the radio link
The height of a melting layer is characterised by the position of the 0C isotherm, written here
as h0. This can be viewed as the top of the melting layer.
The mean height of the melting layer varies with latitude, in addition to which there are other
time variations, including seasonal.
In the proposed rain/sleet model the mean value of h0 , as a height above sea level, will be
calculated using Recommendation ITU-R P.839.
Seasonal and other time variations of h0 will be modeled by the distribution given in P.452 for
mode(2). Using the data points of this distribution gives results showing marked
discontinuities. Thus the P.452 distribution is sliced into 100-m divisions, which results in
small but acceptable steps.
5
Thickness of the melting layer
For the results presented in this paper the melting layer was assumed to have a depth of
1200 m.
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6
Statistics of variable melting layer height
In order to handle any
distribution of layerheight variability a
numerical method is
used. The range of the
height distribution is
divided into equi-size
'bins'. (Note that the
term 'bin' is used here
for convenience, even
though they are not
histogram bins.) A bin
size of 100 metres has
been found a reasonable
compromise between
obtaining smooth results
and minimising
computation. Figure 2
illustrates this method
for a Gaussian
distribution
Figure 2: Height distribution divided into 'bins'
Note that a Gaussian distribution has been used in figure 2 purely for ease of plotting. As
mentioned in Section 4 above, the height distribution in P.452 is used in the actual method.
Each bin of the height distribution has an associated probability (Pn for the nth bin) that the
melting-layer height will fall within it. The sum of the probabilities for all bins must, of
course, be unity.
7
Time-dependent attenuation function
The present method in P.530 calculates the rain attenuation exceeded for 0.01% time and then
applies a fixed time dependency to the attenuation for other percentage times. The time
dependency of the attenuation ratio Ra is given as a function of percentage time p by:
Ra(p)
=
0.12 p -{0.546 + 0.043 log(p)}
(2)
There are two issues here. The first is that in the method described below the percentage time
for a given fade ratio is needed, i.e., equation (2) needs to be solved for p, as given by:
Tr(r)
=
1011.628[-0.546 + {0.298 + 0.172 log (0.12 / r) } ]
%
(3)
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The second is that time dependency is needed for smaller times than the lower limit of
0.001% given in P.530. The general form of equation (2) over a wide time range is shown in
figure 3.
Figure 3: Time-dependency of rain attenuation ratio given in P.530
The time-dependency of the attenuation ratio reaches a maximum of about 6.5 at about
510-7 % time, and then decreases for smaller times. This is, of course, well below the
minimum time of 0.001% given in P.530. However, in the present method it is desirable to be
able to obtain attenuation ratio down to such small percentage times, even though the overall
result is not sensitive to the high attenuation ratios which result. (The same issue arises when
implementing combined clear-air and rain attenuation using the P.530 methods.)
Thus the time-dependent function for attenuation ratio is extended for small percentage times
by a straight line fitted to the point of inflection in figure 3. This is given as an extended
function Re(p) as:
Re(p)
=
-3.5 - 1.8 log (p)
(4)
The change-over between equations (2) and (4) occurs at p = 210-5 at which the attenuation
ratio is 4.9585. The two functions are illustrated in figure 4, with the extension shown
dashed.
Figure 4: Normal and extended attenuation-ratio time dependency
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As in the case of equation (2), equation (4) needs to be solved for p, given by:
Te(r)
=
10 (r + 3.5) / -1.8
(5)
Thus the complete function required by the following method to give the percentage time a
given fade ratio r is exceeded is:
T(r)
=
=
8
1011.628[-0.546 + {0.298 + 0.172 log (0.12 / r) } ]
10
(r + 3.5) / -1.8
r < 4.9585
(6a)
r >= 4.9585
(6b)
Calculation of combined rain and sleet attenuation
The calculation follows the following steps.
8.1
Rain-only attenuation exceeded for 0.01% time
The method of P.530 is followed in the normal way to calculate A01, the rain attenuation
exceeded for 0.01% time. This includes obtaining the rain rate exceeded for 0.01% time for
the location of interest from P.837, obtaining the corresponding specific attenuation from
P.838 taking frequency, polarisation and path slope into account, and calculating the effective
path length.
8.2
Mean melting-layer height
The value of h0 is obtained from P.839 according to the latitude of the path centre.
8.3
Path mid-point height
The height above sea level of the mid-point of the radio path is calculated.
8.4
Probabilities and gammas for rain and sleet attenuation
An accumulator Pr is initialised to zero to hold the aggregated probability that the path centre
will be in rain below the melting layer during precipitation. Each bin of the height
distribution is then considered in turn:
a)
The height of the zero-degree isotherm hn is calculated as ho plus the bin-centre height
offset, where n represents the nth bin.
b)
Taking hn as the top of the melting layer, the height of the mid-path point in relation to
the layer is calculated. There are then 3 cases, according to whether this point is below,
inside, or above the layer:
i) If below the melting layer, the path is considered to be affected by rain attenuation
only. Accumulate the bin probability Pn into Pr. Flag the bin as irrelevant.
ii) If inside the melting layer, the path is considered to be affected by sleet attenuation.
Flag this bin as relevant, and calculate the gamma factor for this bin Fn using equation (1).
iii) Otherwise (the path is above the layer), flag the bin as irrelevant.
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8.5
Iterate fade for required composite percentage time
Having followed the procedure given in 8.4 above for all layer-height bins, there will in
general be a number of rain/sleet attenuation vs % time functions given by the rain fade model
in P.530 §2.4, distinguished by different values of gamma factor, made up as follows:
a) If Pr is non-zero, there will the rain-only function, for which the gamma factor is unity;
b) If one or more bins are relevant, there will be same number of functions each with the
associated gamma factor .
Let it be assumed that, however composed, there are one or more such functions, each with an
associated probability Pk and gamma factor Fk, where k indicates the kth function.
Figure 5 illustrates the procedure whereby a trial fade value Ai is adjusted to steer the
composite percentage time Pc to the target outage, where Pc is given by:
Pc
=
k [ Pk T (Ai / A01 Fk ) ]
Figure 5: Iterating attenuation ratio for composite rain/sleet
The iteration can assume monotonic functions, and the rain-only value for the path is an
appropriate starting point for the trial attenuation.
(7)
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9
Sample results
Figure 6 shows the predicted rain/sleet attenuation exceeded for 0.01% time for a 10 km
zero-inclination path at 14 GHz and horizontal polarisation plotted against latitude from 50 N
to the North Pole. The rain rate exceeded for 0.01% time is constant at 30 mm/hr.
Figure 6: Sample results. Paths at sea level and 500 m asl
The two traces are for paths at sea level and at 500 m asl. As the paths are notionally moved
to higher latitudes the upper is influenced by the melting layer first, as expected. By the time
the pole is reached this upper path is above the layer for a sufficiently large proportion of the
total time for the attenuation to have fallen again to the rain-only level.
The results for the lower path are a duplicate of those for the upper path, moved to higher
latitudes. This is again as expected, since the same layer geometry is used at all latitudes.
Figure 7 shows the same details at sea level for fades exceeded for 0.01 and 0.001 % time.
Figure 7: Sample results. Fades exceeded for 0.01 and 0.001 % time
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The 0.001 % results are an amplified version of the 0.01% results, as expected. They are
perhaps not realistic figures for a practicable radio system, but illustrate the method.
10 Results for the UK
The sample results in Section 9 cover latitudes from the English Channel to the North Pole.
Figure 8 shows results between 58 and 60N, roughly the extend of the UK mainland, for paths
at 0, 300 and 600 m asl. The percentage time is 0.01%; all other details are as before.
Figure 8: Rain fades exceeded for 0.01% time, 30 mm/hr, 14 GHz, 10 km path
Figure 8 shows that for a sea-level path the sleet allowance would start at 56N, the latitude of
Edinburgh. For a path at 300 m asl the additional fade starts at 52N, just north of London.
And for a path at 600 m asl, were one to exist, from the South Coast.
11 Conclusions
The method described above appears to have the potential for a combined rain/sleet
attenuation model. The results shown in Figure 8 are at least feasible. However, it must be
noted that the model is based on two estimates. The gamma factor function described in
Section 2, and the depth of the layer, are assumptions. The gamma function can be adjusted
for the amount of additional loss due to sleet, and the layer thickness can be adjusted to
control the latitude at which the sleet allowance starts. However, neither at present is based
on experimental evidence.
In addition, there are a number of points where refinements to the method would be desirable:
a) It would be an advantage to avoid the necessity to extend the attenuation-ratio timedependency function for small percentage times, or if this is not practicable, to consider
whether a revised extension should be used. It would seem certain that rain attenuation
does not increase by a fixed amount for each decade of smaller time, but logically the
function cannot change slope. As noted above the point may not be critical since when
percentage time is small the corresponding attenuation is large and has little effect on the
composite attenuation.
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b) Since the same time-dependency applies for all gamma factors it would seem that it
should not be necessary to iterate a trial fade, as illustrated in figure 5. It would be useful
to solve equation (7) for Ai.
c) Rather than calculate results in the layer only for the path mid point, it would be better to
integrate along the path in order to take account of height variation in the case of a sloping
path.
The UK would like to discuss with other administrations what techniques they use to counter
the effects of sleet and snow (where these meteorological conditions are a source of difficulty)
and to consider the possible extension of the rain attenuation model for terrestrial paths in
P.530 to include other forms of precipitation.