3.1 Limited percentage times

The percentage of an average year for which the predicted loss is not exceed, T_pc in Table 2.2.1, is allowed to vary from 0% to 100%. The percentage times used for calculation are limited such that they remain in the range 0.00001% to 99.99999%.

Percentage time basic transmission loss not exceeded:

                % (3.1.1)

Percentage time basic transmission loss is exceeded:

                % (3.1.2)

3.2 Path length, intermediate points, and fraction over sea

The path length in km is given by the last distance in the terrain profile, d_n, as described in § 2.1. It is convenient to give this distance an un-subscripted symbol:

                km (3.2.1)

Calculate the longitude and latitude of the mid-point of the path, _me and _mn, from the transmitter and receiver longitudes and latitudes, as given in Table 2.2.1, using the great circle path method of Appendix H by setting d_pnt = 0.5 d in equation (H.3.1). Several climatic parameters are required for this location, as described below.

Set the fraction of the path over sea, . This fraction may be obtained from the ITU digitized world map (IDWM). If array z, described in § 2.1, has been coded according to the zones described in Appendix D, Table D.1, where adjacent z values have different codes, the boundary between the two zones should be assumed to occur half-way between the corresponding profile points.

3.3 Antenna altitudes and path inclination

The transmitter and receiver heights above sea level are calculated from the first and last terrain heights from the profile and the input heights above ground given in Table 3.1:

                masl (3.3.1a)

                masl (3.3.1b)

Assign the higher and lower antenna heights above sea level:

                masl (3.3.2a)

                masl (3.3.2b)

The higher and lower antennas heights can be the same if h_ts = h_rs.

Calculate the positive value of path inclination given by:

                mrad (3.3.3)

3.4 Climatic parameters

Measured values of the following climatic parameters applicable to the region concerned can be used if available. If suitable measurements are not available, the parameters can be obtained for the longitude and latitude of the mid-point of the path from data files as described in the following subsections. The files are organized as arrays of values at a fixed spacing in longitude and latitude. The first row starts at 90N and contains a full set of latitude values from 0E to 360E, even though all of these are at the North Pole. Following lines are at the point spacing further south until the South Pole is reached. The files have different point spacings, but in all cases it is sufficiently accurate to use bilinear interpolation from the four nearest data to the point required. All of these data files have associated longitude and latitude files which define the location of every point.

3.4.1 Refractivity in the lowest 1 km

The parameters N_d1km50 and N_d1kmp give the change in refractivity, in N-units, from the surface to 1 km above the surface of the Earth, not exceeded for 50% and p% of an average year respectively. These are used to account for ray bending in diffraction calculations via the concept of effective Earth radius or curvature. They can be viewed as the spatially-averaged refractivity gradient in the lowest 1 km of the atmosphere.

N_d1km50 is numerically equal to N, defined in Recommendations ITU‑R P.452 and ITU‑R P.1812, but of opposite sign. N is everywhere positive, and thus N_d1km50 is everywhere negative.

N_d1kmp can be negative or positive, depending on location and the value of p. It can fall below −157 N-units, the value at which effective Earth radius becomes infinite.

The change in sign convention adopted here is to align with a conceptually similar parameter, N_d65m1, used for clear-air multipath fading and enhancements, obtained as described in § 3.4.2 below.

N_d1km50 and N_d1kmp are available from files “DN_Median.txt”, “DN_SubSlope.txt” and “DN_SupSlope.txt”.

Obtain N_d1km50 as:

                N-units (3.4.1.1)

where S_dN is the value interpolated from file “DN_Median.txt” for the path mid-point at _me, _mn.

Obtain N_d1kmp as:

   N-units     p < 50 (3.4.1.2a)

   N-units     p  50 (3.4.1.2b)

where:

S_Nsup is the value read from file “DN_SupSlope.txt” for the mid-point of the path;

S_Nsub is the value read from file “DN_SubSlope.txt” for the mid-point of the path.