**ITU-R Correspondence Group 3K-1.**

**Report from the UK:\
Bullington and 3-edge diffraction methods compared with measured
results**

CONTENTS

[1 Introduction 1](#introduction)

[2 General description of the data files
2](#general-description-of-the-data-files)

[3 The calculation method 3](#the-calculation-method)

[4 Validation test results 7](#validation-test-results)

[5 The Data 11](#the-data)

[6 Comparison of diffraction models for median results
14](#comparison-of-diffraction-models-for-median-results)

[7 Results for longer paths 20](#results-for-longer-paths)

[8 Conclusions 23](#conclusions)

[9 Appendix A: Reading data files 24](#appendix-a-reading-data-files)

[10 Appendix B: Maps showing the measurement paths
28](#appendix-b-maps-showing-the-measurement-paths)

[11 Appendix C. Min, mean and max of path characteristics
34](#appendix-c.-min-mean-and-max-of-path-characteristics)

[12 Appendix D: Inspection of path profiles
37](#appendix-d-inspection-of-path-profiles)

[13 Appendix E. Scatter Plots 42](#appendix-e.-scatter-plots)

# Introduction

CG 3K-1 is developing a deterministic propagation model for
point-to-area radio services. The diffraction model appearing in the
current draft, contained in document 3/95r1, is the same as in Rec.
P.526-9 §4.4.2, although described differently, and is based on the
Deygout construction limited to a maximum of three edges, with an
empirical correction. This will be referred to as the "3-edge" method.

It has been suggested in 3K/171 and elsewhere that other diffraction
models should be considered. In particular a method based on the
Bullington construction, with an empirical correction, was proposed in
3K/TEMP/91 as more suitable than the 3-edge model, at least for
mountainous paths. This method is generally referred to as the
"Bullington" method, abbreviated to "Bul" where appropriate.

CG 3K-1 has compiled the results of propagation measurements from
various sources into a systematic format. This facilitates comparisons
between models and measured results over a wide range of path types.

This document provides a detailed account of comparisons made between
the measured data and the DNR using alternatively the 3-edge and
Bullington diffraction methods.

# General description of the data files

CG-3K-1 has converted a number of measured datasets to a common format,
distributed in .csv files. Several releases of these files were received
to deal with various data issues.

A summary of the file format and the information used in the comparisons
is as follows:

## Geographic coordinates

The first part of each file contains information relevant to
measurements over a single path. The comparisons used the following, all
read by finding a keyword followed by the value:\
Tx latitude, deg\
Tx longitude, deg\
Rx latitude, deg\
Rx longitude, deg

The test software required these as mandatory fields. The coordinates of
the terminals were used to calculate the coordinates of each profile
point, using great-circle geometry, in order to interrogate IDWM to
obtain the land/sea classification. The average coordinates were used to
obtain the mean refractivity gradient in the lowest 1km, as required for
median effective earth-radius factor, and mean surface refractivity
which is required by the troposcatter part of the method.

## Meteorology

The format includes a section under which radio-meteorology parameters
can be provided, but no field appears to exist for the refractivity
gradient ∆*N*. This was obtained from a separate ∆N map for the average
geographic coordinates of the path.

## Profile

A sequence of data rows define the path profile. The format provides the
number of these rows. The given number of rows was then considered
mandatory.

Each row has the following fields:

a)  Mandatory distance from the transmitter, km, from zero upwards.

b)  Mandatory terrain height, m above sea level.

c)  Optional clutter code. At the time of the comparisons these codes
    were not identified.

d)  Optional clutter height, m above ground level.

## Measurement details

One or more data rows giving information and results for measurements
over the path characterised as above, with values contained in fields
(Excel columns) in each row. Not all fields were used in the
comparisons, and many are in any case vacant in the data files.

Annex A describes in detail the process used to read the data files.

# The calculation method

This section provides details of the calculation methods used for tests
and comparison with the measured data.

## The diffraction methods

The following sub-sections provide a few comments on the two diffraction
models.

### The 3-edge method

Although this method uses the Deygout construction to locate profile
points to represent obstructions, it is not based on the original
principle under which these edges should always represent separate
obstructions. The change was made for the following reasons:

a)  There will always be an arbitrary element to any criterion for
    selecting edges, because it must be applied to a profile defined by
    discrete points.

```{=html}
<!-- -->
```
a)  More importantly, the original Deygout concept was intended only for
    paths obstructed by terrain obstacles, i.e., hills, not for smooth
    paths. A single method applicable to any type of path was required,
    and it was found that permitting edges to be at adjacent profile
    points caused the model to approximate smooth paths sufficiently for
    most purpose.

Figure 3.1 illustrates point b). Letters M, T and R denote adjacent
profile points selected for the main edge and tx-side and rx-side
auxiliary edges, according to the present 3-edge method for completely
smooth, spherical-earth cases, LOS on the left and NLOS on the right. In
both cases, *h~m~* is the obstacle height, negative in the NLOS case.

![](media/image1.png){width="6.2972222222222225in"
height="1.1840277777777777in"}

**Figure 3.1. Intentional adjacent edge points for a smooth-earth path**

Were the construction limited to a single obstacle only the main edge
would be taken into consideration. Since a rounded obstacles produces
higher diffraction loss than a knife edge, this would under-predict
smooth-earth loss. Taking the adjacent auxiliary edges into account
initially adds about 12 dB, since the smooth-earth geometry ensures that
for both auxiliary edges, ν is close to zero and thus each edge loss
close to 6 dB. This is the basic mechanism which permits the 3-edge
model to approximate spherical-earth diffraction.

For LOS and near-LOS cases of the above, the auxiliary-edge losses are
reduced by a factor \[1 -- exp (-*L~m~*/6)\], where *L~m~* is the
main-edge loss in dB, such that the predicted loss decreases smoothly
with reducing obstruction and becomes zero at full Fresnel clearance.

For land paths the auxiliary edges may or may not represent separate
obstacles. Figure 3.2 shows, on the left, the type of path often used to
illustrate the Deygout construction, where the auxiliary edges have
selected separate obstacles. If the central hilltop has a larger radius
of curvature, or if the profile points are more closely spaced, the
auxiliary edges may well be close to the principal edge on the same
obstacle.

![](media/image2.png){width="6.292361111111111in"
height="1.1569444444444446in"}

**Figure 3.2. Obstructed path: auxiliary edges on separate obstacles or
the same obstacle**

When the change is due to the central hilltop having a larger radius of
curvature, it is possible that the right-hand side of figure 3.2 is the
better interpretation. The more rounded principal obstruction has a
larger diffraction loss and it may be more important to add about 12 dB
for this hill top than the separate but sub-path auxiliary hills.

On the other hand, when the change is due only to a difference in
profile-point spacing, the difference in predicted loss must be viewed
as arbitrary. In particular, it cannot be assumed that the closest
practical profile-point spacing will be the most accurate. The
availability of the CG measured data might be a suitable opportunity to
see whether an optimum criterion for the 3-edge profile spacing might be
identified, but this has not been attempted at this stage.

### The Bullington method

The Bullington construction avoids the issue of separating obstacles by
locating only one diffraction edge. It can also be argued that the
profile-point spacing cannot be too small, since the construction
consists mainly of locating the terminal horizon points accurately.
These are both advantages of the method.

However, an apparent problem is that the Bullington construction ignores
the presence or absence of obstacles between the horizons in cases where
the transmitter and receiver horizons are at different profile points.
This is illustrated in Figure 3.3. The horizons and the position of the
virtual edge are the same in both the left and right-hand drawing, and
the method will predict the same diffraction loss. But in practice it
must be assumed that the central obstacle on the left would add to the
overall loss.

On the other hand, the construction appears to be supported by the
somewhat anecdotal view that diffraction loss tends to be dominated by
the terminal horizons. This is in fact the basis of the negative-*h*~1~
and TCA corrections in Rec. P.1546.

It is possible that obstructions closer to the centre of a path have
less significance because less additional loss is incurred by going
around it on a non-great-circle path, for a given obstruction width. In
other words, a given obstruction width subtends a smaller azimuthal
angle when the obstacle is near the centre of a path than when forming
the terminal horizons.

![](media/image3.png){width="6.294444444444444in"
height="1.0506944444444444in"}

**Figure 3.3. Bullington construction with and without a central hill**

A further point about the Bullington method described in 3K/TEMP/91 §2.2
is that it may estimate less well for smooth paths. A comparison of the
3-edge and Bullington methods for smooth paths appears in
"3K-1_DiffMethods_DFB_XX.doc".

For a LOS path the Bullington method is defined as the loss due to the
intermediate profile point with the highest value of the diffraction
parameter ν. This will be the same point as the principal edge of the
3-edge method. Thus for a LOS path the Bullington method diffraction
calculation will never predict more loss, and will often predict a lower
loss, since no other edges will contribute losses.

However, as described in 3K/TEMP/91 §2.2 the Bullington method has an
unconditional empirical correction given by 10 + 0.02*d*, where *d* is
the path length in km. This means that it will predict a loss of 10 +
0.02*d* for a LOS path with full Fresnel clearance. It is not known
whether this is an intentional feature of the method designed to add
loss for paths with little obstruction. Since it seems unlikely that the
method should predict at least 10 dB diffraction loss when there is full
Fresnel clearance, two versions of the method were compared against the
measured results:

a)  'Bul': as described in 3K/TEMP/91 §2.2 ;

```{=html}
<!-- -->
```
b)  'Bul+taper': as 'Bul' but the empirical correction is
    \[1-exp(-*L~e~*/6)\](10 + 0.02*d*) where *L~e~* is the knife edge
    loss. This arranges that the empirical correction decreases smoothly
    to zero for full Fresnel clearance in a similar manner to the 3-edge
    method.

    A further characteristic of the Bullington method, which applies to
    its use with or without the foregoing taper correction, is that for
    long paths it tends to predicts lower losses than the troposcatter
    model, with much less dependence on horizon angles. This is
    illustrated in Figure 3.4 which shows basic transmission loss
    calculated by the troposcatter and Bullington methods at 100 MHz for
    smooth paths and horizon elevation angles at both ends of 0 deg and
    +2 deg, over the range 100 to 1000 km. The Bullington results
    converge to a small range of values, well below the troposcatter
    losses, as the path length increases towards 1,000 km.

    ![](media/image4.png){width="5.145833333333333in"
    height="2.2083333333333335in"}

    **Figure 3.4. Basic transmission losses for troposcatter and
    Bullington, long paths**

    This is significant in the context of the complete method, since the
    3-edge model, and diffraction models in general, usually predict
    losses increasing above troposcatter losses for long paths,
    resulting in troposcatter results dominating in the blending
    procedure.

## Overall calculation

For the comparisons presented in Section 6 below, the DNR model was used
to calculate only predicted median troposcatter and diffraction basic
transmission losses, as follows.

a)  Each path profile was read from its data file. No access was made to
    any other topographic database for terrain heights or clutter
    information. Where clutter heights are provided (profile 4^th^
    column) the clutter heights were added to the terrain heights for
    the intermediate points, that is, all profile points except the
    first and last, assumed to be the location of the terminals.

```{=html}
<!-- -->
```
a)  At each end of the path, if the antenna height above ground is less
    than the clutter height, the terminal height was adjusted to equal
    the clutter height for the purposes of the diffraction and
    troposcatter calculations.

b)  The geographic coordinates of each profile point was calculated, and
    the IDWM DLL used to obtain a land/sea classification in each case.
    This was used to calculate the fraction of each path over sea or
    large bodies of water purely for path classification. This
    information is not used to calculate the troposcatter and
    diffraction losses.

c)  Median effective earth curvature was calculated for each path using
    Doc. 3/95r1 eqs (7) and (8a), with the average refractivity gradient
    in the lowest 1 km read for the average of the terminal geographic
    coordinates from file 'dN.txt' available within file 'N.zip' on the
    3K-1 Web site. These ∆*N* values show clear signs of being compiled
    manually from a map, but the file is convenient as a reference point
    for comparison, even if they do not represent the best values
    available for the location of a set of measurements.

d)  Free-space basic transmission loss was calculated according to
    Doc. 3/95r1 §4.2.

e)  Median diffraction loss was calculated using three methods:\
    i) The 3-edge method, *L~d50A~* , according to Doc. 3/95r1 §4.3;\
    ii) The Bul method, *L~d50~*~B~ , according to Doc. 3K/TEMP/91 §2.2
    with corrections;\
    iii) The 'Bult' method, *L~d50~*~C~ , consisting of the Bul method
    with the empirical correction adjusted to zero at full Fresnel
    clearance as described in 3.1.2 b) above.

f)  Troposcatter basic transmission loss was calculated according to
    Doc. 3/95r1 §4.4.

g)  At each end of the path the additional losses due to shielding by
    clutter, *L~ct~* and *L~cr~* for the transmitter and receiver
    respectively, are calculated according to Doc. 3/95r1 §4.7. At the
    time these tests were made information on the clutter codes was not
    available, and thus clutter was always considered to be urban. The
    clutter losses *L~ct~* and *L~cr~* are non-zero only when the
    antenna height above ground is less than the clutter height at that
    point.

# Validation test results

The tests reported in this section do not compare the accuracy of the
diffraction models. They are intended to facilitate comparisons of
independent calculations in the interests of detecting implementation
errors.

Two types of calculation for this purpose were conducted using
synthesised profiles:

![](media/image5.png){width="2.9583333333333335in"
height="1.1875in"}**Validation using canonical cases**. A useful
canonical diffraction geometry consists of equi-spaced co-linear knife
edges, as illustrated in Figure 4.1. Diffraction loss in this case is
given by 20⋅log(*N*+1) dB where *N* is the number of edges.

**Figure 4.1. Canonical diffraction case**

**Validation using smooth paths**. Tests with smooth profiles are easy
to set up, and are useful in confirming that models function as
expected.

## Synthesised test profiles

Four test profiles were constructed for the validation tests, as
summarised in Table 4.1. All consisted of 121 points, indexed from 0 to
120, with points spaced at 0.1 km, and thus a total length of 12 km. No
clutter information was included.

All terrain heights are set to zero except for the points needed to make
equi-spaced edges, with no edges in profile 0, one in profile 1, two in
profile 2, and three in profile 3.

**Table 4.1: Terrain heights, m asl,** in test profiles

  -------------- -------------- -------------- -------------- --------------
                 Test profile                                 
                 number                                       

  Index          0              1              2              3

  0 - 29         0.00           0.00           0.00           0.00

  30             0.00           0.00           0.00           98.41

  31 - 39        0.00           0.00           0.00           0.00

  40             0.00           0.00           98.11          0.00

  41 - 59        0.00           0.00           0.00           0.00

  60             0.00           97.88          0.00           97.88

  61 - 79        0.00           0.00           0.00           0.00

  80             0.00           0.00           98.11          0.00

  81 - 89        0.00           0.00           0.00           0.00

  90             0.00           0.00           0.00           98.41

  91 - 120       0.00           0.00           0.00           0.00
  -------------- -------------- -------------- -------------- --------------

The terrain heights for these edges, in metres above sea level, were
selected such that for a refractivity gradient of -39 N-units/km, which
gives an effective earth-radius factor of 1.332, and for real earth
radius = 6371 km, the edges are co-linear with antennas at 100 m agl at
each end of the profile.

The main purpose of these tests is to provide simple means for different
implementations of the diffraction models to be compared. In view of
this the results below are quoted to somewhat higher precision than
would normally be justified by the expected accuracy of the models.

Canonical results are quoted, where available, for interest. This is not
intended to be a test as to which model comes closest to the canonical
cases.

## Results for equi-spaced co-linear edges

The frequency was set to 300 MHz, and the antenna heights to 100 m agl
at both ends of the path. Table 4.2 shows results from the 3-edge
diffraction for test profiles 1 to 3.

**Table 4.2: Canonical cases using the 3-edge method**

  ------ ------ -------- ------ -------- ------ -------- --------- -------- --------- --------
  Prof   n~m~   L~m~     n~t~   L~t~     n~r~   L~r~     L         T        L~d~      Canon

  1      60     6.0336   30     0.0000   90     0.0000   6.0336    0.6342   12.6798   6.021

  2      40     6.0323   20     0.0000   80     6.0325   12.0648   0.6341   16.5028   9.542

  3      60     6.0336   30     6.0331   90     6.0331   18.0998   0.6342   20.3319   12.041
  ------ ------ -------- ------ -------- ------ -------- --------- -------- --------- --------

Table 4.3 describes the columns of Table 4.2 and comments on their
contents.

**Table 4.3. Description of columns and remarks on results in Table
4.2**

  ----- ------- ----------------------------------------------------------
  Col   Head    Comment

  1     Prof    Profile number. Also number of edges

  2     n~m~    Profile index of principal edge. Arbitrarily selects 1^st^
                of 2 edges.

  3     L~m~    Loss due to principal edge, dB. All close to the ν = 0
                loss of \~6 dB.

  4     n~t~    Profile index of tx-side edge. At mid point where no edge
                exists.

  5     L~t~    Loss due to tx-side edge, dB. Zero where no edge exists

  6     n~r~    Profile index of rx-side edge. At mid point where no edge
                exists.

  7     L~r~    Loss due to tx-side edge, dB. Zero where no edge exists

  8     L       Sum of edge losses, dB

  9     T       Taper term: 1 -- exp (*L~m~*/6)

  10    L~d~    Final result: diffraction loss, dB.

  11    Canon   Canonical result, dB, for interest only
  ----- ------- ----------------------------------------------------------

Table 4.4 shows results from the Bullington methods, optionally with
taper as described in §3.1.2 b), for test profiles 1 to 3. For a
marginal LOS/NLOS path the predicted loss does not vary significantly
with number of edges, since only one edge is considered.

**Table 4.4: Canonical cases using the Bullington methods**

  ------ ------ ------ ------ ------ ------- ------- ------- ------- -------- -------- --------
  Prof   n~t~   n~r~   n~m~   D~e~   L~e~    T       C       C~t~    L~d~     L~dt~    Canon

  1      60     60            6.0    6.034   0.633   10.24   6.481   16.274   12.515   6.021

  2      120    0      40     4.0    6.032   0.633   10.24   6.481   16.272   12.513   9.542

  3      30     90            6.0    6.034   0.633   10.24   6.482   16.274   12.516   12.041
  ------ ------ ------ ------ ------ ------- ------- ------- ------- -------- -------- --------

Table 4.5 describes the columns of Table 4.4 and comments on their
contents.

In all cases the results in Tables 4.2 and 4,4 are as expected. This can
be confirmed by parallel calculations.

**Table 4.5. Description of columns and remarks on results in Table
4.5**

  ----- ------- ---------------------------------------------------------
  Col   Head    Comment

  1     Prof    Profile number. Also number of edges

  2     n~t~    Profile index of tx-side horizon point.\
                The receiver index, 120, is selected for a LOS path.

  3     n~r~    Profile index of rx-side horizon point.\
                The receiver index, 0, is selected for a LOS path.

  4     n~m~    Profile index of point causing highest sub-path
                obstruction.\
                Calculated only for LOS paths

  5     D~e~    Distance of real or virtual edge from tx, km.

  6     L~e~    Loss due to real or virtual edge, dB

  7     T       Taper term: 1 -- exp (*L~e~*/6)

  8     C       Empirical correction: 10 + 0.02*d*, dB

  9     C~t~    Empirical correction with taper applied

  10    L~d~    Final result: diffraction loss, dB, without taper.

  11    L~dt~   Final result: diffraction loss, dB, with taper.

  12    Canon   Canonical result, dB
  ----- ------- ---------------------------------------------------------

## Smooth paths

Test profile 0 was used for the smooth-path tests, changing antenna
heights to obtain different degrees of obstruction. In all cases the
same antenna height was used at both ends of the path. Although this
does not test the full functionality of the diffraction methods, the
resulting symmetry simplifies parallel calculations.

Table 4.6 gives the results of the smooth-path tests for the 3-edge
method at 300 MHz. These show that the path has full Fresnel clearance
for antenna heights of 40 m, and passes through the LOS/NLOS transition
between 5 and 2 m antenna heights. For non-zero diffraction losses the
three edges are adjacent at the centre of the path, except for 1 m
antenna heights.

**Table 4.6. Smooth-path tests using the 3-edge model**

  ------- ------- ------- ------- ------- ------- ------- ------- ------- --------
  H~tx~ m H~rx~ m n~m~    L~m~    n~t~    L~t~    n~r~    L~r~    T       L~d~

  40      40      60      0.000   0       0.000   0       0.000   0.000   0.000

  30      30      60      0.403   59      5.462   61      5.462   0.065   1.792

  20      20      60      2.248   59      5.666   61      5.666   0.312   9.063

  10      10      60      4.304   59      5.870   61      5.870   0.512   15.679

  5       5       60      5.394   59      5.973   61      5.973   0.593   18.693

  2       2       60      6.060   59      6.035   61      6.035   0.636   20.397

  1       1       60      6.284   48      6.088   72      6.088   0.649   20.990
  ------- ------- ------- ------- ------- ------- ------- ------- ------- --------

Table 4.7 gives the results of the smooth-path tests for the Bullington
method, optionally with taper as described in §3.1.2 b). For the LOS
paths the single edge loss is the same as the principal edge losses in
Table 7, as expected, but slightly higher for the virtual edges in NLOS
paths.

**Table 4.7. Smooth-path tests using the Bullington methods**

  ------- ------- ------ ------ ------ ------ -------- ------- -------- ------- -------- --------
  H~tx~ m H~rx~ m n~t~   n~r~   n~m~   D~e~   L~e~     T       C        Ct      L~d~     L~dt~

  40      40      120    0      60     6.0    0.000    0.000   10.240   0.000   10.240   0.000

  30      30      120    0      60     6.0    0.403    0.065   10.240   0.663   10.643   1.065

  20      20      120    0      60     6.0    2.248    0.312   10.240   3.191   12.488   5.439

  10      10      120    0      60     6.0    4.304    0.511   10.240   5.230   14.544   9.534

  5       5       120    0      60     6.0    5.394    0.592   10.240   6.060   15.634   11.454

  2       2       58     62            6.0    6.061    0.635   10.240   6.498   16.301   12.559

  1       1       41     79            6.0    6.331    0.651   10.240   6.662   16.571   12.993
  ------- ------- ------ ------ ------ ------ -------- ------- -------- ------- -------- --------

# The Data

The following sub-sections provide various descriptions of the datasets
assembled by\
CG 3K-1.

## Summaries of datasets

Appendix B shows maps giving the layout of the measurement paths, and
Appendix C shows graphs giving the minimums, means and maximums of
various path characteristics. These appendices are intended as
convenient summaries of the dataset characteristics.

## Dataset tables

The first two columns of Table 5.1 give indices and names for the
datasets. Names starting 'EBU' were supplied in the same zip file, but
within sub-directories with names given by the second part of each name.

The next two column gives the number of data files and the total number
of results in them for each dataset, counting the files and results read
via the process described in Appendix A. Each data file contains one or
more results. Thus some datasets have more results than files. The
significance of the numbers of files is that these give the number of
paths in each dataset over which measurements have been made. In
particular, US phase 2 contains 20,610 results, but obtained over only
410 paths.

**Table 5.1**. Summary of datasets

  ---------- ---------- -------- --------- ------------ -------- ----------- ------- -------------
  Dataset:              Number             Longitude,            Latitude,           
                        of:                deg                   deg                 

  index      name       files    results   min          max      min         max     Region

  0          ABU        35       210       74.3         104.03   1.12        31.7    Asia

  1          EBU_BBC    38       70        -6.33        4.27     51.05       54.17   UK

  2          EBU_BBCL   68       68        -0.23        0.08     51.25       51.48   UK

  3          EBU_BBCn   274      274       -2.1         0.2      51.27       54.97   UK

  4          EBU_ERT    36       36        23.05        24.05    37.17       38.4    Greece

  5          EBU_HOL    75       77        5.05         6.43     50.82       52.58   Holland

  6          EBU_IRT    598      598       8.02         10.53    47.55       48.57   Germany

  7          EBU_IRTL   156      156       7.8          11.73    48.03       48.63   Germany

  8          EBU_IRTs   11       63        10.13        13.22    47.55       49.25   Germany

  9          EBU_ORF    76       489       8.02         16.33    46.6        48.63   Austria

  10         EBU_RAI    87       87        8.9          9.78     44.78       45.15   Italy

  11         EBU_S      107      107       13.02        17.32    59.37       63.5    Sweden

  12         EBU_SUI    1,083    1,246     6.12         7.93     45.98       47.38   Switzerland

  13         EBU_TDF    68       72        -0.6         6.52     45.12       49.5    France

  14         EBU_YLE    100      100       23.32        24.92    60.18       60.43   Finland

  15         EBU_YLEs   17       68        22.33        29.25    59.47       62.95   Finland

  16         Swiss      435      435       6.13         9.34     46.43       48.57   Switzerland

  17         USPhase1   1,767    15,800    254.16       278.97   39.37       41.7    US

  18         USPhase2   410      20,610    253.73       282.01   36.17       40.79   US

             Totals     5,441    40,566                                              
  ---------- ---------- -------- --------- ------------ -------- ----------- ------- -------------

The next four columns give the minimum and maximum longitudes and
latitudes for paths in the dataset.

The last columns describes the general region. In several cases
measurements extend to neighbouring countries.

Table 5.2 gives the ranges of frequency and path lengths covered by each
dataset, duplicating information shown graphically in Appendix C. The
last four columns provide information on the extent to which measured
paths are over sea. The first of these gives the percentage of paths
which are more than 10% over sea. The last three columns give the
average percentage of the paths over sea, the highest sea percentage of
any path, and the percentage over sea of all paths in the dataset
aggregated. These show that only a small proportion of the measurements
involved paths crossing the sea or large bodies of water.

**Table 5.2: Summary of dataset characteristics (including
trop**oscatter paths)

  --------- ------- ----------- --------- -------- ------- --------- ------ ------ -------
  Dataset           Frequency             Path             \% paths  \%            
                    MHz                   length           \>10% sea sea:          
                                          km                                       

  Index     Name    Min         Max       Min      Max               Av     Max    Total

  0         ABU     92.9        107.5     6.8      218.8   20.0      5.6    40.7   1.1

  1         BBC     41.5        469.0     2.3      235.1   5.7       4.9    99.0   46.4

  2         BBCL    1,490.0     1,546.0   2.1      12.4    0.0       0.0    0.0    0.0

  3         BBCn    527.3       775.3     4.2      80.4    1.1       0.2    12.8   0.2

  4         ERT     203.2       217.2     11.7     72.5    33.3      7.5    56.1   9.3

  5         HOL     62.3        735.3     7.4      102.0   0.0       0.0    0.0    0.0

  6         IRT     93.8        652.8     3.5      98.4    0.0       0.0    0.0    0.0

  7         IRTL    1,463.0     1,500.0   1.1      20.2    0.0       0.0    0.0    0.0

  8         IRTs    88.0        101.9     30.7     150.5   0.0       0.0    0.0    0.0

  9         ORF     88.5        1,500.0   1.5      67.8    0.0       0.0    0.0    0.0

  10        RAI     97.4        583.3     12.3     40.8    0.0       0.0    0.0    0.0

  11        S       602.0       690.0     3.2      85.9    10.3      4.0    56.5   4.3

  12        SUI     88.0        107.7     0.8      78.1    0.0       0.0    0.0    0.0

  13        TDF     494.0       774.0     16.7     103.0   11.1      2.8    66.7   1.5

  14        YLE     105.0       105.0     5.3      73.4    0.0       0.0    0.0    0.0

  15        YLEs    88.2        623.3     47.7     287.2   11.8      6.9    56.4   6.7

  16        Swiss   200.0       855.3     6.0      158.3   0.0       0.0    0.0    0.0

  17        US1     20.0        101.8     1.0      80.8    0.0       0.0    1.2    0.0

  18        US2     76.0        9,190.0   0.4      124.9   0.0       0.0    0.0    0.0
  --------- ------- ----------- --------- -------- ------- --------- ------ ------ -------

The % sea values raise a few issues when compared with the maps in
Appendix B:

a)  The 40.7% sea path in the ABU results is 6.8 km long, partially over
    the straits between Malaysia and Singapore. It is just visible in
    Figure B2.

```{=html}
<!-- -->
```
a)  In BBCn it is not obvious in Figure B5, but two paths in the
    northern group pass over the sea at their south-eastern ends, giving
    a maximum of 12.8% over sea.

b)  The maximum of 56.1% sea for ERT is not consistent with Figure B6.
    Although the most southerly path passes over two islands and grazes
    a coast, it would appear to be rather more than 56.1% over the sea.
    This is confirmed by referring to a large-scale map. This is
    commented on below.

c)  The Swedish ('S') results show a path with 56.5% sea, even though
    all paths in Figure B13 are clearly inland. The "sea" proportion
    arises from the southerly group of paths where there are some large
    bodies of inland water.

d)  The TDF results show a path with 66.7% sea. This occurs in the
    northerly group in Figure B, some of which pass over the Seine
    estuary.

e)  The 56.4% sea value in row 15 comes from the path across the Gulf of
    Finland.

f)  The 1.2% sea path in the USphase1 results has not yet been found.
    However, less than 0.05% of the either US sets of aggregated paths
    are over sea.

## Suitability of the Terrain profiles

The accuracy of terrain profiles is a major issue when testing
diffraction models. In view of this the quality of the profiles provided
with the measured data was assessed in various way. Results appear in
Appendix D, where it is seen that quite a number of issues appear to
exist..

A summary of the conclusions is given in Table 5.3.

**Table 5.3: Qualitative assessment of supplied profiles**

  ----------- ------------ -----------------------------------------------
  Dataset     Usability    Comments

  ABU         Poor         Many profiles contain errors.

  EBU BBC     Good         Longer paths show quite good agreement with
                           SRTM, shorter paths less so, probably sue to
                           lat/long issue.

  EBU BBCL    Good         Profiles are a poor match to SRTM but this is
                           probably because the paths are short so
                           lat/long errors are important.

  EBU BBCn    Good         As above

  EBU ERT     Good         The area is mountainous so small lat/long
                           errors lead to large SD differences with SRTM
                           but the profiles look to be of high quality

  EBU HOL     Good, but    Most of the data is good. However all paths
              note the     that rise above 100m are incorrect. This being
              '100m'       Holland, there are very few of these. All the
              problem      Band3 files should be eliminated

  EBU IRT     Very good    Profiles and SRTM show good agreement.

  EBU IRTL    Good         Most paths are short and like the BBC paths the
                           lat/long uncertainty is the largest factor
                           causing differences between the supplied
                           profiles and SRTM

  EBU IRTs    Very good    This data set is good but there are only 11 of
                           them

  EBU ORF     Moderate     The agreement with SRTM is pretty poor, but it
                           might be explained if the fault is in the TX/RX
                           locations.

  EBU RAI     Good         The area is mountainous so small lat/long
                           errors lead to large SD differences with SRTM
                           but the profiles look to be of high quality

  EBU S       Very good    Considering the short paths and one minute
                           lat/long resolution, SRTM agreement is
                           remarkable. Could the profile data be based on
                           SRTM/Globe?

  EBU SUI     Good         There are mixtures of long and short paths with
                           the usual lat/long accuracy issues.

  EBU TDF     Moderate     Most profiles look OK but there is a case
                           (caenc3) where an entire 120m high hill appears
                           to be missing which can't really be just
                           lat/long resolution issue.

  EBU YLE     Good         The profile quality looks good, though it is
                           rather strange, looking quite like a database
                           including clutter. There are differences of
                           typically 10-20m with SRTM.

  EBU YLEs    Good         As above

  Swiss       Poor to      Some paths are very close to SRTM, some are
              excellent    completely different --e.g. a mean error of
                           500m over a plain. Inaccurate TX/RX locations
                           may be the cause.

  USPhase1    Good         There is a huge amount of data here and the
                           profiles appear good, similar to BBC.

  USPhase2    Good         As above -- What can you say about a 500m path
                           with a 1km uncertainty over TX/RX location?
  ----------- ------------ -----------------------------------------------

# Comparison of diffraction models for median results

The three diffraction models were tested for accuracy by comparison with
the measured results. Most of the measured results are for median
conditions, and the comparisons were thus conducted only for these
results.

For each data file the procedure described in Appendix A was followed to
extract valid median results. This means that only results for which
percentage time is given as 50, or those for which this field is empty
and which thus default to 50, were selected.

The troposcatter basic transmission loss for each path was calculated,
using the\
3K-1 DNR model. Results for which the predicted troposcatter basic
transmission loss was less than 6 dB greater than the measured basic
transmission loss were discarded.

The three diffraction models described in §3.1, namely '3-edge', 'Bul'
and 'Bult', were used to predict median diffraction losses and hence
median diffraction basic transmission loss for all paths, and the
discrepancies against the measured results were calculated as
predicted-minus-measured basic transmission loss. For these comparisons
the anomalous/ducting model and the final blending were not used, but
where clutter heights were available the intermediate profile points
were raised and the terminal clutter losses applied.

The calculation were performed using two computer programs produced
independently by different people. Results were compared to detect
errors and align the procedures as far as practicable, but computer code
was not shared. Tables 6.1 and 6.2 summarise the results.

**Table 6.1. Discrepancies: implementation 1**

  ------ --------- -------- ------ ------- ------ ------------ ------ ------- ------ ------------ ------ ------- ------
  Data   Num of\   3-edge                         Bullington                         Bullington                  
  set    results                                  (no taper)                         (+ taper)                   

                   min      max    mean    SD     min          max    mean    SD     min          max    mean    SD

  0      11        -19.0    15.2   -6.8    11.3   -16.7        14.0   -3.9    8.6    -21.7        13.6   -10.5   10.7

  1      55        -32.6    7.9    -13.7   8.6    -22.6        9.5    -10.3   7.5    -32.6        -0.7   -16.4   7.7

  2      67        -39.9    6.2    -22.0   9.6    -29.7        7.8    -14.2   8.6    -39.9        -2.3   -23.0   8.7

  3      267       -37.3    20.0   -8.1    10.0   -26.7        14.7   -8.5    7.5    -37.3        13.6   -12.5   8.8

  4      36        -36.1    21.8   -8.6    11.9   -41.1        12.3   -5.0    11.4   -41.2        11.8   -11.6   10.5

  5      66        -11.7    28.3   2.5     8.5    -13.0        28.6   0.1     9.9    -14.4        22.4   -3.6    9.2

  6      598       -31.0    34.4   1.9     8.4    -21.0        20.1   1.0     5.7    -31.0        16.9   -3.1    6.4

  7      156       -35.6    92.0   12.8    20.4   -26.1        41.3   13.3    13.6   -35.7        41.3   8.4     15.5

  8      18        -7.8     18.2   1.8     6.3    -11.4        9.0    -5.4    5.3    -14.7        8.8    -8.2    5.8

  9      489       -35.4    92.0   11.0    11.5   -28.0        39.1   1.2     10.4   -35.4        39.1   -0.1    10.5

  10     86        -17.0    16.4   0.0     6.6    -24.7        8.9    -3.3    7.6    -24.7        8.7    -5.4    7.0

  11     107       -35.9    47.3   -8.2    10.8   -25.9        22.0   -4.7    6.5    -35.9        22.0   -10.5   8.4

  12     1,185     -35.0    44.7   -5.2    10.8   -39.9        29.6   -3.4    9.0    -40.3        29.3   -8.9    9.1

  13     70        -26.7    50.5   6.8     13.9   -23.4        14.7   -3.7    8.8    -30.1        14.6   -5.9    9.2

  14     100       -11.6    31.0   7.2     8.9    -21.3        23.4   -0.2    8.9    -22.0        21.7   -1.6    8.7

  15     9         -22.9    0.0    -2.0    10.4   -27.8        6.7    -5.8    9.9    -28.0        4.6    -7.5    9.6

  16     319       -38.5    53.3   4.1     13.8   -27.9        15.3   -2.0    7.9    -38.5        14.8   -5.3    7.9

  17     6,864     -53.6    45.3   -8.2    11.8   -71.2        22.8   -17.7   11.2   -71.3        22.6   -19.2   10.9

  18     14,254    -48.5    68.5   1.6     10.7   -52.1        43.3   1.8     10.6   -52.2        43.2   -3.3    9.4
  ------ --------- -------- ------ ------- ------ ------------ ------ ------- ------ ------------ ------ ------- ------

**Table 6.2. Discrepancies:** implementation 2

  ------ --------- -------- ------ ------- ------ ------------ ------ ------- ------ ------------ ------ ------- ------
  Data   Num of    3-edge                         Bullington                         Bullington                  
  set    results                                  (no taper)                         (+ taper)                   

                   min      max    mean    SD     min          max    mean    SD     min          max    mean    SD

  0      8         -16.9    15.2   -5.8    10.5   -16.7        13.9   -3.2    10.0   -21.8        13.6   -9.2    11.6

  1      55        -32.7    7.9    -13.8   8.6    -22.6        9.4    -10.3   7.5    -32.7        -0.7   -16.4   7.7

  2      61        -40.0    6.1    -20.7   10.5   -29.8        7.7    -13.8   8.2    -40.0        -2.3   -22.1   8.9

  3      261       -37.4    20.0   -8.0    10.0   -26.7        14.6   -8.5    7.5    -37.4        13.6   -12.4   8.9

  4      13        -36.2    21.7   -9.9    14.6   -25.8        12.2   -3.6    9.8    -36.2        11.7   -12.0   11.8

  5      61        -11.8    22.2   2.1     7.2    -13.0        22.6   0.1     8.5    -14.4        16.3   -3.9    7.8

  6      598       -31.1    34.3   1.8     8.3    -21.0        18.5   0.8     5.7    -31.1        16.9   -3.2    6.4

  7      156       -35.7    85.9   8.7     19.4   -26.1        35.2   9.2     11.5   -35.7        35.2   4.4     14.0

  8      18        -7.9     18.2   1.7     6.3    -11.5        9.0    -5.5    5.3    -14.8        8.8    -8.2    5.8

  9      489       -35.4    85.9   10.9    11.1   -28.0        33.0   1.1     10.2   -35.4        33.0   -0.3    10.2

  10     86        -17.1    16.4   -1.7    6.6    -24.7        8.8    -3.4    7.6    -24.8        8.7    -5.4    7.0

  11     107       -36.0    47.3   -8.4    10.6   -25.9        22.0   -4.9    6.2    -36.0        22.0   -10.7   8.1

  12     1,185     -35.0    44.7   -5.2    10.8   -39.9        29.6   -3.5    9.0    -40.4        29.2   -8.9    9.1

  13     70        -26.8    50.4   6.7     13.9   -23.5        14.7   -3.7    8.8    -30.1        14.5   -6.0    9.2

  14     96        -11.6    24.9   5.7     7.5    -21.3        17.3   -1.9    7.3    -22.0        15.7   -3.2    7.2

  15     6         -12.4    10.2   1.4     7.2    -12.6        6.6    -1.7    6.1    -16.8        4.6    -4.1    6.8

  16     430       -38.9    53.2   2.4     14.4   -28.7        20.1   -2.1    7.9    -38.9        19.7   -6.2    8.4

  17     6,847     -53.7    45.2   -8.2    11.8   -71.3        22.7   -17.8   11.3   -71.3        22.6   -19.2   10.9

  18     13,963    -48.8    68.5   1.6     10.8   -52.1        43.2   1.6     10.7   -52.2        43.2   -3.4    9.5
  ------ --------- -------- ------ ------- ------ ------------ ------ ------- ------ ------------ ------ ------- ------

The results in Tables 6.1 and 6.2 are similar, but not in all cases
identical. In most cases differences in the discrepancies are thought to
be due to different sets of results being selected. It illustrates the
difficulty of defining and implementing a highly algorithmic procedure.

However, the statistical properties of both sets of results are very
similar. The mean discrepancies in Tables 6.1 and 6.2 are plotted in
Figures 6.1 and 6.2 respectively, and the standard deviations in Figures
6.3 and 6.4. Data exist only at the plotted symbols. The lines are only
to guide the eye in associating data for a given model.

It is clear from these graphs that the measured results contain
systematic errors, and different degrees of random errors. For both mean
and standard deviation of discrepancies there is a strong tendency for
the models to move in the same direction with change in dataset index.

A further point to note in the following graphs is that 85% of the
results are from the US measurements. However, particularly in the US2
dataset, there are many results from most paths, and thus each
individual result should not have the same weight as a single result
from a given path. This is a difficult situation to resolve rigorously.
It is thought most appropriate in this case to attempt to obtain a value
judgement between the diffraction models by inspection of the results
for each dataset.

## Mean discrepancies

Figures 6.1 and 6.2 show the mean discrepancies for each dataset plotted
for the three models, taking the results from Table 6.1 and 6.2
respectively. Both sets of independently-produced results show very
similar characteristics.

![](media/image6.png){width="5.635416666666667in" height="2.40625in"}

**Figure 6.1. Mean discrepancies from Table 6.1**

![](media/image7.png){width="5.635416666666667in"
height="2.3958333333333335in"}

**Figure 6.2. Mean discrepancies from Table 6.2**

In both Figures 6.1 and 6.2 the Bullington model without taper is
closest to zero for the largest number of datasets, followed by the
3-edge method, with Bullington+taper the least. Thus the Bullington
method without taper appears to give the lowest mean errors. However,
this method predicts at least 10 dB diffraction loss for a LOS path with
full Fresnel clearance, so it is not viewed as a practicable method as
it stands.

A further point about mean errors is that few datasets include many
clutter heights, and of these only sets 7 and 9 have many measurements
with terminal heights below clutter. If there is a general tendency to
under-predict basic transmission loss, this tends to happen for measured
results without clutter heights. The highest mean errors are mostly
positive, and are for datasets 7 and 9, which combine clutter heights
and low terminals.

## Standard deviation of discrepancies

Figures 6.3 and 6.4 show the standard deviation of discrepancies for
each dataset plotted for the three models, taking the results from Table
6.1 and 6.2 respectively. Both sets of independently-produced results
show very similar characteristics.

![](media/image8.png){width="5.59375in" height="2.3958333333333335in"}

**Figure 6.3. Standard deviation of discrepancies from Table 6.1**

![](media/image9.png){width="5.583333333333333in"
height="2.3854166666666665in"}

**Figure 6.4. Standard deviation of discrepancies from Table 6.2**

In both Figures 6.3 and 6.4 the Bullington model without taper produces
the lowest SD for the largest number of datasets, followed by
Bullington+taper, with the 3-edge method producing the highest in most
cases.

Thus the Bullington methods clearly correlate most closely with the
measured results.

It is noteworthy that the datasets with the clearest separation between
the 3-edge and Bullington methods, and where the two Bullington methods
differ little, implying high diffraction losses, are 6 (Germany), 12
(Switzerland), 13 (France) and 16 (Switzerland again).

## Scatter plots

Scatter plots of measured (or derived from measured) values of basic
transmission loss against the model predicted values help to identify
the reasons for some of the results given in Figures 6.1 to 6.4. A
complete set of scatter plots for each of the three models and each
dataset is given in Appendix E. A few examples follow, but the full set
of scatter plots contains further insight.

Dataset 18 (USPhase2) is the largest dataset, and all models show a low
mean and standard deviation of the model error. The scatter plot of
Figure 6.5 confirms this. It also shows a slight tendency for the 3-edge
method to overestimate, and Bullington to underestimate, the loss at the
higher loss values. These trends are seen in a number of the datasets.

![](media/image10.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image11.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

**Figure 6.5. 3-edge and Bullington models, dataset 18 (USPhase2)**

These trends were confirmed by plotting the model error against path
lengths for all datasets combined and fitting a linear regression line
to the data points. The trends are fairly weak and not easily seen by
eye in the plots (given in Appendix E), but the fits showed trends of
+0.12dB/km for the 3-edge model error, --0.02dB/km for the Bullington
model error, and +0.02dB/km for the Bullington+taper model error.

Dataset 7 (EBU_IRTL) is the dataset with the largest standard deviation.
Figure 6.6 shows that the range of measured path loss values is much
less than the models (both 3-edge and Bullington) predict. This suggests
that there is a problem with these measurements.

![](media/image12.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image13.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

**Figure 6.6. 3-edge and Bullington models, dataset 7 (EBU_IRTL)**

Dataset 9 (EBU_ORF) is a case where the 3-edge mean error is large and
positive, while Bullington has a low mean error. Figure 6.7 gives the
corresponding scatter plots. The behaviour of the two models is quite
different here, Bullington achieving the lower mean error by an
underprediction of a group of points at the higher loss values. This
deserves further investigation.

![](media/image14.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image15.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

**Figure 6.7. 3-edge and Bullington models, dataset 9 (EBU_ORF)**

More common is the occurrence of large negative prediction errors, such
as for datasets 2 (EBU_BBCL) and 17 (USPhase1). Dataset 17 is much
larger and therefore probably more significant. Figure 6.8 shows the
scatter plots. In this case the error is greater for Bullington (because
of the lower loss predictions at the higher loss values). From an
examination of the individual path profiles and loss values, it is clear
that the lack of clutter data in the data files must be the problem. On
some short paths, identified as line-of-sight by the Doc. 3/95r1
algorithm, the reported measured loss values could be as much as 30dB
greater than free space loss.

![](media/image16.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image17.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

**Figure 6.7. 3-edge and Bullington models, dataset 17 (USPhase1)**

# Results for longer paths

The effect of switching to the Bullington model in the complete DNR
method was noted in a third UK implementation. The following two
coverage maps are for 1 GHz, signal levels exceeded for 10% time, both
terminals heights 50 m agl, and terrain heights taken from GTOPO. The
colour coding is green = LOS with full clearance, mauve = LOS with
sub-path obstruction, blue = NLOS diffraction, red = troposcatter, and
yellow = anomalous. The maximum range is 300 km.

## Map calculated using the DNR with 3-edge method

Figure 7.1 was calculated using the 3-edge method, and shows
troposcatter dominating for long land distances, and ducting for long
sea distances.

![](media/image18.jpeg){width="6.2972222222222225in"
height="6.2972222222222225in"}

**Figure 7.1. Coverage map using the 3-edge method**

## Map calculated using the DNR with Bullington+taper method

Figure 7.2 was calculated with the same conditions as Figure 7.1 but
using the Bullington method with taper. It shows diffraction dominating
over a much wider area, at long land distances, and for some long sea
distances.

![](media/image19.jpeg){width="6.2972222222222225in"
height="6.2972222222222225in"}

**Figure 7.2. Coverage map using the Bullington+taper method**

## Comparison with P.1546

To confirm the drastic change between Figures 7.1 and 7.2 a separate
implementation of the complete DNR, with the three diffraction models
available as alternatives, was used to calculate basic transmission
losses for 10,000 randomly-selected paths around the British Isles. The
paths include all-land, mixed land/sea, and all-sea. These results,
analysed for which mechanism dominates, were compared with basic
transmission losses calculated from corresponding P.1546 VHF and UHF
land and sea field-strength curves.

Figures 7.3 and 7.4 show these results for 100 MHz and 600 MHz, 50%
time, with transmitter height 75 m agl and receiver height 10 m agl.

![](media/image20.png){width="6.295833333333333in"
height="2.1597222222222223in"}

**Figure 7.3. DNR compared with P.1546, VHF**

![](media/image21.png){width="6.295833333333333in"
height="2.1597222222222223in"}

**Figure 7.4. DNR compared with P.1546, UHF**

The P.1546 curves are viewed as an independent source of data in this
case. There does not appear to be a record of what measured results were
used to compile the original Rec.370 curves, but they probably exclude
most of the CG database. P.1546 modified the sea curves at short
distances, but otherwise the 50% time VHF and UHF curves are very
similar to the corresponding Rec.370 curves.

At both 100 MHz and 600 MHz the scatter of results from the full DNR
using the 3-edge method follow the P.1546 curves, with troposcatter
dominating diffraction for long paths.

The Bullington method shows a marked divergence below the P.1546 losses,
with diffraction always dominating, and with the tendency to converge to
a narrow range of losses at 1,000 km illustrated on a theoretical basis
in Figure 3.4.

The longest measured path in the CG database is 160 km. This is at the
distance where the effect in Figure 3.4 is starting to affect results
but is not large. It will thus have influenced some of the results
reported in Section 6, but probably without changing the main
conclusions. But the results in Figure 7.3 and 7.4 show that the DNR
with the Bullington method cannot be considered suitable for
coordination at distance beyond about 100 km.

# Conclusions

The results presented in Section 6 show that the Bullington method gives
generally lower standard deviations that the 3-edge method, particularly
for some datasets. The 3-edge method in most cases produces lower mean
errors. The taper of the Bullington empirical correction was improvised
for these tests. The calculation of mean error is influenced by whether
clutter heights are available.

The results presented in Section 7 show that using the Bullington method
results in a systematic under-prediction of loss for paths of 100 km or
longer. This makes a major difference for paths much beyond 100 km.

Thus although the Bullington method has the potential to improve
accuracy for shorter, and probably hillier, paths, a method must be
found to retain approximately the present prediction of loss for paths
beyond 100 km.

# Appendix A: Reading data files

The results of comparisons were found to depend, as would be expected,
on the exact selection of measured results. Due to a number of data
issues various tests needed to be applied when reading the data files.

The comparisons reported in the main body of this report used the
following procedures to select which results to use. In the following
description, "line" means a line of a CSV file, and "field" a
comma-separated sub-division of a line.

Note that the two independent implementations of Doc. 3/95r1 referred to
in Section 6 used slightly different strategies to deal with poor
quality data. Initially the "data filtering" was developed completely
independently, but comparisons showed large differences between the
models that were traced to the different levels of data filtering. The
results presented in Section 6 are from datasets filtered for the agreed
set of "errors" given below, but with slightly different approaches as
to how to deal with these errors.

## Filename

The first line gives the filename. This line is read and ignored.

## Geographic coordinates

Lines 2 to 5 contain keywords and values for:\
Tx latitude, deg\
Tx longitude, deg\
Rx latitude, deg\
Rx longitude, deg

An exact match to all four keywords is required. The values are read as
decimal numbers from the second field in each line. If the 2^nd^ field
in any line cannot be read as a floating-point number, the file is
discarded. The 4^th^ field in each line, giving the values in DMS, is
ignored.

## Tx/rx locations and start of profile

After reading the first 5 file lines as above, which must be in the
order given above, and before searching for the start of the profile, a
flag is set to indicate the default assumption that the transmitter is
at the start of the profile.

The start of the profile section is not expected to be at a fixed line
number. Lines are read until the first field matches
"{Begin of Profile}". If no such line is found the file is discarded.

During this search each line prior to finding the start of the profile
is tested for a first field matching "First Point Tx or Rx". If such a
line is found, and if the first non-space character in the 2^nd^ field
is 'R', then the above flag is set to indicate that the receiver is at
the start of the profile. If no such line is found, then the flag
remains at its default value indicating that the transmitter is at the
start of the profile.

## Number of profile points

The line giving the number of points in the profile is not expected to
be at a fixed position. After finding the start of the profile as above,
lines are read until a line is found for which the first field matches
"Number of Points:" If no such line is found the file is discarded.

If the line is found, the 2^nd^ field is read as an integer to give the
number of points in the profile. If the 2^nd^ field cannot be read as an
integer, the file is discarded.

## Profile points

It is now mandatory that the *N* lines immediately following the line
giving the value of *N*, where *N* is the number of profile points read
from the file, each provides information on the profile points, in order
of increasing distance from the start of the profile. Each of these *N*
lines must contain between 2 and 4 non-empty fields. These are read as
follows:

Field 1: Distance from start of profile in km. Mandatory.

Field 2: Height of terrain, m asl. Mandatory.

Field 3: Understood to be clutter-type code, but coding not available.
Ignored.

Field 4: Height of clutter above ground. Optional.

## Test for monotonic distances

It is essential that profile distances form a monotonic sequence. This
is tested as follows.

a)  The distance of the 1^st^ profile point should be zero. If it lies
    outside the range ± 1 m the file is discarded.

```{=html}
<!-- -->
```
g)  Starting with 2^nd^ profile point and proceeding in file order to
    the penultimate point, if the distance is less than 1 m more than
    the previous distance, the point is discarded.

h)  The distance for the last profile point in the file must at least 1
    m more than the previous distance. If this is not the case the file
    is discarded.

Although it is not essential, the above tests are conducted during the
process of reading and storing the profile information. When a profile
point is discarded due to having a non-monotonic distance, no profile
information is stored. When this happens the number of profile points
actually stored and used by the propagation model is thus fewer than
appear in the input file.

## Length of the path

The path length is taken as the distance of the last profile point in
the file. There is an earlier line which gives the path length
explicitly, but this is ignored.

## Distances copied to clutter heights

This test allows a known error in some files to be corrected without
discarding the file. The file itself is not modified.

The error consists of the distance from each point except the first
appearing as the clutter height of the previous point.

The test consists of counting the number of points, from the 2^nd^ point
to the last, for which the distance is within ± 0.1 of the clutter
height of the previous point. If this number is equal to or more than
half the number of profile points stored, the error is assumed to exist.
For the purpose of this test the number of points is divided by 2 using
integer division, which rounds the result down for an odd number of
paths.

If the error is detected, all clutter heights are set to zero.

## Profile reversal

If the receiver is flagged as being at the start of the profile, the
storage order of the profile points is reversed, during which process
each distances is recalculated.

(As a comment on implementation, this reversal is not essential. The
propagation model is symmetrical with respect to profile direction, and
the transmitter and receiver details can be associated with the
appropriate profile end-points. In practice this requires conditional
statements at several different points during subsequent processing. In
the software used for these tests it was considered cleaner to
physically reverse a profile, if necessary, such that the transmitter is
always at the first point.)

## End of profile

After reading and storing the *N* profile points, the first field of the
next line must match "{End of Profile}". If this is not the case the
file is discarded.

## Start of measurements

Lines are now read until a line is found in which the first field
matches "{Begin of Measurements". Note that the closing brace is
omitted, since in some files it does not appear. If no such line is
found the file is discarded.

## Measurement lines

The next line must contain results from a measurement. Optionally
additional measurement lines may follow. Each measurement line from
which valid data can be read is a result associated with the path
profile, and is compared with the propagation model.

## End of measurements

After reading each measurement line the following line is read. If the
first field matches "{End of Measurements}" it is assumed that there are
no further measurement lines. If this is not the case the line will be
treated as the next measurement.

A 'end of measurement' is not treated as essential. The measurement
lines are read, and the results compared with the propagation model, in
the order in which they appear in the file. This process stops when
either the 'end of measurement' line is found or the end of the file.

## Reading data from a measurement line

Table A1 lists the fields in each measurement line. The 'Comment' column
indicates the way in which they are used. Two cases are simple to
describe:

a)  'Mandatory': the measurement is discarded if the field is vacant.

```{=html}
<!-- -->
```
c)  'Not used': the field is never used in the comparisons.

The process of obtaining the measured basic transmission loss is more
complicated. It can be described in the order of steps followed by the
test software:

Step 1. If field 17 is available then the measured basic transmission
loss is obtained directly and none of the following steps are necessary.

Step 2. If field 17 is empty then field 16 must be available, otherwise
the result is discarded.

Step 3. It is now necessary to select an ERP value from one of fields 10
to 12. If field 4 is available then the matching ERP must be available,
otherwise the result is discarded. 'Matching' in this case means that if
polarisation = 1 (H), field 10 must be available, if polarisation = 2
(V), field 11 must be available, if polarisation = 3 (C), field 12 must
be available. If field 4 is not available then the ERP is taken from the
first field in which a value is available in order 11, 10, 12.

> If the above process produces an ERP, then the basic transmission loss
> is obtained using:
>
> $L_{b} = \text{169}\text{.}4 + \text{20} \cdot \text{log}(f) + W_{\text{erp}} - E$
> dB (1)
>
> where:
>
> *f* = frequency GHz
>
> *W~erp~* = ERP dB(W)
>
> *E* = field strength dB(μV/m)
>
> Otherwise the result is not used.

**Table A**1: Results fields in data files

  ------- -------- -------------------- -------- -----------------------------
  Index   Excel    Field name           Units    Comment
          col                                    

  0       A        Frequency            MHz      Mandatory

  1       B        Tx antenna height    m (agl)  Mandatory

  2       C        Tx antenna effective m        Not used
                   height                        

  3       D        Tx antenna height    m (agl)  Mandatory

  4       E        Polarisation         1/2/3\   Not used if field 17 has a
                                        H/V/C    value.\
                                                 Used if available and if
                                                 field 17 is empty and field
                                                 16 has a value

  5       F        Txdbm                dBm      Not used

  6       G        Max Lb               dB       Not used

  7       H        Txgn                 dBi      Not used

  8       I        Rxgn                 dBi      Not used

  9       J        Rx antenna           D/O      Not used

  10      K        ERP_max_horizontal   dBW      Not used if field 17 has a
                                                 value.\
                                                 Used as described if field 17
                                                 is empty and field 16 has a
                                                 value

  11      L        ERP_max_vert         dBW      

  12      M        ERP_max_total        dBW      

  13      N        HRP_red              dB       Not used

  14      O        Time percent         \%       Used if available, default to
                                                 50

  15      P        Losses relative to   dB       Not used
                   free space                    

  16      Q        Measured field       dBuV/m   Not used if field 17 has a
                   strength                      value.\
                                                 Mandatory if field 17 is
                                                 empty

  17      R        Basic transmission   dB       Used if available
                   loss                          
  ------- -------- -------------------- -------- -----------------------------

# Appendix B: Maps showing the measurement paths

The figures in this Appendix show maps of the measurement routes in each
dataset. The objective is to provide some indication of the location and
layout of the paths. Attention is particularly paid to path locations
relative to the sea or large bodies of water.

## Dataset 0: ABU

The Asian Broadcast Union results consist of two groups of measurements
with a large geographic separation. Figure B1 shows one set which is
wholly over land in an area north of Delhi, India.

The other measurements were made in Malaysia, as shown in Figure B2.
Although both paths are close to the sea, and the common terminal at the
south end is apparently on the coast, the paths appear to be wholly over
land.

![](media/image22.png){width="2.71875in" height="2.5in"}
![](media/image23.png){width="3.1354166666666665in" height="2.5625in"}

**Figure B1. ABU paths in India Figure B2. ABU paths in Malaysia**

## Dataset 1: BBC

Figure B3 shows all paths in the "BBC" data set. There are some fairly
shorts paths well inland, but there are several longer mainly-sea paths
between the UK and Ireland, and between the UK and Holland.

![](media/image24.png){width="4.645833333333333in"
height="2.5520833333333335in"}

**Figure B3. Set 1: BBC paths**

## Dataset 2: BBCL

Figure B4 shows these paths, which form groups based on two common
points between London and Gatwick.

## Dataset 3: BBCn

Figure B5 shows that although one group of measurements in this data set
are close to the sea, all paths appear to be over land.

![](media/image25.png){width="3.3958333333333335in"
height="2.5416666666666665in"} ![](media/image26.png){width="2.40625in"
height="2.5208333333333335in"}

**Figure B4. Set 2: BBCL paths Figure B5. Set 3: BBCn paths**

## Dataset 4: ERT

Figure B6 shows that these measurements in the vicinity of Athens
include several over-sea sections of path. One path appears to end over
the sea.

## Dataset 5: HOL

Figure B7 shows that the paths in Holland are well away from the sea,
and include areas where the land is significantly above sea level.
Although the climate might be coastal for some of these paths, none pass
over the sea.

![](media/image27.png){width="3.1041666666666665in"
height="2.5208333333333335in"} ![](media/image28.png){width="2.59375in"
height="2.53125in"}

**Figure B6. Set 4: ERT paths Figure B7. Set 5: HOL paths**

## Dataset 6: IRT

**Figure B8 shows the three groups of measurements in southern
Germany.**

![](media/image29.png){width="3.7708333333333335in" height="2.53125in"}

**Figure B8. Set 6: IRT paths**

## Dataset 7: IRTL

**Figure B9 shows the two groups of measurements, again in southern
Germany.**

![](media/image30.png){width="3.8229166666666665in" height="1.40625in"}

**Figure B9. Set 7: IRTL paths**

## Dataset 8: IRTs

**Figure B10 shows this groups of measurements in the extreme south-east
of Germany.**

![](media/image31.png){width="3.78125in" height="2.5104166666666665in"}

**Figure B10. Set 8: IRTs paths**

## Dataset 9: ORF

Figure B11 shows the ORF dataset, which includes paths in both Germany
and Austria.

## Dataset 10: RAI

Figure B12 shows the RAI paths. These are between Milan and the Gulf of
Genova, but well clear of the sea.

![](media/image32.png){width="3.3541666666666665in" height="1.59375in"}
![](media/image33.png){width="2.3541666666666665in"
height="1.6770833333333333in"}

**Figure B11. Set 9: ORF paths Figure B12. Set 10: RAI paths**

## Dataset 11: S

Figure B13 shows the two sets of paths measured in Sweden. Both are well
away from the coast, although with the large numbers of inland lakes
many paths will pass over a certain amount of water.

## Dataset 12: SUI

Figure B14 shows the dense network of measured paths in Switzerland.
Some paths pass over Lake Geneva.

![](media/image34.png){width="3.0729166666666665in"
height="2.5208333333333335in"} ![](media/image35.png){width="2.8125in"
height="2.53125in"}

**Figure B13. Set 11: S paths Figure B14. Set 12: SUI paths**

## Dataset 13: TDF

Figure B15 shows the two groups of French measurements in this dataset.
The N.W. group are around Le Havre, but do not pass over the sea. The
S.E. group are in the hilly area around Grenoble and are well away from
the sea.

## Dataset 14: YLE

Figure B16 shows the measurements made to the west of Helsinki. The
dashed line does not do justice to the coast of Finland, which contains
many inlets. The more easterly paths run approximately along the coast
and will pass over a certain amount of sea. Some of the westerly paths
will pass over lakes.

![](media/image36.png){width="3.5416666666666665in" height="2.53125in"}
![](media/image37.png){width="3.0104166666666665in"
height="1.5416666666666667in"}

**Figure B15. Set 13: TDF paths Figure B16. Set 14: YLE paths**

## Dataset 15: YLEs

Figure B17 shows a further generally longer set of paths in Finland. In
this case one of the paths crosses the Gulf of Finland into Estonia.

## Dataset 16: Swiss

Figure B18 shows a further set of Swiss paths covering a larger area of
the country, and with a few paths extending into France.

![](media/image38.png){width="3.3125in" height="2.53125in"}
![](media/image39.png){width="2.7083333333333335in"
height="2.5104166666666665in"}

**Figure B17. Set 15: YLEs paths Figure B18. Set 16: Swiss paths**

## Dataset 17: US phase 1

Figure B19 shows the two groups of paths in the USPhase1 dataset. Here
the geographic information consists of state borders. The SW corner of
Lake Erie is somewhat simplified. The measurements were made in Colorado
and Ohio, and are well away from the sea.

![](media/image40.png){width="4.197916666666667in" height="2.1875in"}

**Figure B19. Set 17: US phase 1 paths**

## Dataset 18: US phase 2

Figure B20 shows the two groups of paths in the USPhase2 dataset, with
groups of paths in Colorado again, and in Virginia. The East-Coast
seaboard is somewhat simplified.

![](media/image41.png){width="5.03125in" height="2.1875in"}

**Figure B20. Set 18: US phase 2 paths**

# Appendix C. Min, mean and max of path characteristics

Figures C1 to C7 give the ranges of various path characteristics within
each dataset. Each graph shows a vertical trace for each dataset. Each
trace has three symbols showing the minimum, mean and maximum values of
the characteristic.

The characteristic displayed in each case is given in the figure titles.

![](media/image42.png){width="4.875in" height="2.4583333333333335in"}

**Figure C1. Minimum, mean, maximum frequency in each dataset**

![](media/image43.png){width="4.875in" height="2.4791666666666665in"}

**Figure C2. Minimum, mean, maximum path length in each dataset**

![](media/image44.png){width="4.645833333333333in" height="2.4375in"}

**Figure C3. Minimum, mean, maximum Tx magl in each dataset**

![](media/image45.png){width="4.614583333333333in" height="2.4375in"}

**Figure C4. Minimum, mean, maximum Rx magl in each dataset**

![](media/image46.png){width="4.84375in" height="2.4583333333333335in"}

**Figure C5. Minimum, mean, maximum % points with clutter in each
dataset**

![](media/image47.png){width="4.822916666666667in" height="2.4375in"}

**Figure C6. Minimum, mean, maximum roughness factor in each dataset**

![](media/image48.png){width="4.84375in" height="2.46875in"}

**Figure C7. Minimum, mean, maximum sea fraction in each dataset**

# Appendix D: Inspection of path profiles

In view of the importance of the terrain profile to a diffraction model,
the profiles supplied with the measurement data were inspected in
various ways.

## Manual inspection

A manual inspection of the supplied profiles has shown several issues,
most notably non-monotonic range increments presumably caused by faults
somewhere in the data transfer. Data sets with non-monotonic profiles
should, strictly, be excluded from analysis as there is uncertainty over
the correct entry of the measurement data.

For example, in all original ABU data sets over 100km the range values
progress as shown in Table D1. There is obviously a leading digit
missing at 112.75 km. Errors like these are easy to spot and correct
manually in individual cases, but detailed inspection is hardly
practicable for all of the data. On the other hand, it is very difficult
to define automatic processing, of the kind described in Appendix A, and
to be certain that it detects all errors and makes appropriate
corrections.

Table D1 Error in ABU profile data

  ---------------------------------- ------------------------------------
  Distance, km                       Height, m asl

  112                                235

  112.25                             235

  112.5                              235

  12.75                              235

  113                                235

  113.25                             235

  113.5                              235
  ---------------------------------- ------------------------------------

The profiles themselves sometimes have low height resolution. This is
probably caused by extrapolation to 0.25km point spacing based on lower
resolution data. An example is shown in Figure D1 which demonstrates
this. While it may have no serious effect in this case, it is not
correct to assume the supplied data is accurate to the provided 0.25km
profile spacing.

![](media/image49.wmf){width="4.517361111111111in"
height="2.8430555555555554in"}

Figure D1 : Example of lower resolution data

Other anomalies exist in the height information. In Holland, a region
known not to be mountainous, some of the height data appears to have
been truncated. An example is given in Figure D2. Figure D3 shows this
data corrected manually.

![](media/image50.wmf){width="5.760416666666667in"
height="3.6256944444444446in"}

Figure D2. Example of truncated height data

![](media/image51.wmf){width="5.760416666666667in"
height="3.6256944444444446in"}

Figure D3. Truncated data corrected

## Comparison with SRTM 3 arc-second topographic database

Given these issues with some of the profiles, it was decided to make a
comparison against the 3 arc second SRTM topographic database available
from NASA. This data has a resolution of around 90m. An example of a
comparison in given in Figure D4 where the solid curve represents the
supplied profile and the line the SRTM derived profile. Each data point
represents a profile point from the original data file. It is clear that
this profile shows reasonable agreement, but it demonstrates a further
problem in the supplied data.

Close examination of Figure D4 shows height errors of 10-20m and some of
the peaks appear shifted. The profile was generated using the supplied
latitude and longitude data which is given in the files to many decimal
places. However, the actual geolocation data is only given to at best
the nearest minute. This represents an uncertainty of 1km in the
location of transmitter and receiver which explains the different
results from the SRTM data.

![](media/image52.png){width="5.615277777777778in"
height="2.9694444444444446in"}

Figure D4 : Comparison of SRTM and supplied profiles

Figure D5 demonstrates the effect of the uncertainty on two short paths.
These profiles would give completely different path loss predictions.
The inaccuracy in supplied latitude and longitude makes it impossible to
replace profiles of doubtful accuracy with SRTM derived profiles.

![](media/image53.png){width="2.6in" height="1.3868055555555556in"}
![](media/image54.png){width="2.6in" height="1.3868055555555556in"}

a b

Figure D5 : The effect of location uncertainty on short paths

Fortunately, it is still possible to use SRTM data to spot gross profile
errors. This is how the errors in the EBU Holland data were discovered
an example is given in Figure D6. Similarly, Figure D7 demonstrates that
the "Transmitter First" or "Receiver First" flags are not always
correctly implemented or have differing keywords.

![](media/image55.png){width="5.580555555555556in"
height="2.9784722222222224in"}

Figure D6. Comparison of profiles: significant error in the supplied
data

![](media/image56.png){width="5.7034722222222225in"
height="3.0194444444444444in"}

Figure D7. Example of a reversed profile

Unfortunately, the only way to reliably identify these errors has been
manual examination, which is not practicable for the larger data sets.
It is possible to generate an error variable based on the differences
but the latitude and longitude uncertainty tends to dominate over the
incorrect points, especially in mountainous regions.

## Land/sea issues

Referring to 5.2 c) in the main body of this report, although in general
the ERT profiles appear to be of good quality, a substantial discrepancy
was noted with land/sea classifications from IDWM for the file named
"g47". The path ends are at (decimal degrees) 23.117 E, 38.017 N and
23.750 E and 37.167 N. Figure 5.3 shows the profile plotted for a flat
earth. This is not consistent with Figure B6, nor with a larger-scale
map. The zero-height profile segments plotted in Figure 5.3 comprise
21.4% of the profile length. However, using the IDWM to identify sea
points gives 56.1% over the sea. As noted against the ERT data in Table
5.3, such discrepancies may well be due to the combination of
steep-sided hills at coasts and the resolution of geographic location.

![](media/image57.png){width="4.833333333333333in"
height="1.6666666666666667in"}

**Figure 5.3. Terrain profile for ERT results file "g47"**

A different point is that in file "g47" each zero-height segment of this
profile is recorded with only two point, at the segment's start and end.
This would produce an error if a zero-height section contained a horizon
point or diffraction edge It would be better if such profile segments
had zero-height profile points inserted at a spacing similar to the
spacing of non-zero heights.

# Appendix E. Scatter Plots

This Appendix contains scatter plots of measured (or derived from
measured) values of basic transmission loss and the model predicted
values.

There are four sets of graphs:

a)  3-edge model, separate plots for each of the 19 datasets, showing
    measured loss against model loss (2 pages)

```{=html}
<!-- -->
```
e)  Bullinton model, separate plots for each of the 19 datasets, showing
    measured loss against model loss (2 pages)

f)  Bullington + taper model, separate plots for each of the 19
    datasets, showing measured loss against model loss (2 pages)

g)  Plot of model error (model predicted loss minus measured loss)
    against path length. Here there is one graph for each model, the
    scatter plots including data points from all 19 models.

ABU BBC BBCL BBCn

![](media/image58.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image59.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image60.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image61.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

ERT HOL IRT IRTL

![](media/image62.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image63.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image64.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image12.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

IRTs ORF RAI S

![](media/image65.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image14.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image66.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image67.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

SUI TDF YLE YLEs

![](media/image68.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image69.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image70.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image71.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

Swiss US1 US2

![](media/image72.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image16.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image10.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

ABU BBC BBCL BBCn

![](media/image73.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image74.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image75.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image76.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

ERT HOL IRT IRTL

![](media/image77.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image78.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image79.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image13.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

IRTs ORF RAI S

![](media/image80.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image15.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image81.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image82.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

SUI TDF YLE YLEs

![](media/image83.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image84.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image85.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image86.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

Swiss US1 US2

![](media/image87.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image17.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image11.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

ABU BBC BBCL BBCn

![](media/image88.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image89.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image90.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image91.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

ERT HOL IRT IRTL

![](media/image92.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image93.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image94.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image95.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

IRTs ORF RAI S

![](media/image96.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image97.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image98.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image99.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

SUI TDF YLE YLEs

![](media/image100.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image101.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image102.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image103.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

Swiss US1 US2

![](media/image104.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image105.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image106.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

The scatter plots below show the model error (model predicted loss minus
measured loss) against path length. There is one graph for each model,
the scatter plots including data points from all 19 models.

The formula given under the graph is the best fit linear regression line
to the data where y is the model error and x is the path length. The
3-edge method shows a stronger trend than the Bullington model, and the
trends are in different directions.

3-edge Bullington Bullington + taper

![](media/image107.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image108.png){width="2.1666666666666665in"
height="2.1354166666666665in"}
![](media/image109.png){width="2.1666666666666665in"
height="2.1354166666666665in"}

y = --4.67 + 0.119 x y = --3.81 -- 0.020 x y = --8.78 + 0.021 x