C.5 Path-averaged multiplier
This section describes a calculation which may be required a number of time for a given path.
For each rain-height hT given by equation (C.2.11), a path-averaged factor G is calculated based on the fractions of the radio path within 100-m slices of the melting layer. G is the weighted average of multiplier G given as a function of dh by equation (C.4.1) for all slices containing any fraction of the path, and if hlo < hT – 1200, a value of G = 1 for the part of the path in rain.
Figure C.5.1 shows an example of link path geometry in relation to the height-slices of the melting layer. hlo and hhi (masl) are the heights of the lower and higher antennas, respectively. It should be noted that this diagram is only an example, and does not cover all cases.
FIGURE C.5.1
Example of path geometry in relation to melting layer slices
The first step is to calculate the slices in which the two antennas lie. Let slo and shi denote the indices of the slices containing hlo and hhi respectively. These are given by:
(C.5.1a)
(C.5.1b)
Where the Floor(x) function returns the largest integer that is less than or equal to x.
In the special case where both antennas are in the same melting layer slice, that is slo = shi, including cases where hlo = hhi, G is calculated using:
(C.5.2)
Otherwise it is necessary to examine each slice with a slice index, s, between (a) the minimum of slo and 12 and (b) the maximum of shi and 1. For each of these slices, which is crossed by the path from hlo and hhi, calculate δh and Q according to the appropriate equations (C.5.3a) to (C.5.5b). 
is used to calculate the value of G for the slice using equation (C.4.1). As a separate operation, which should be considered once only, if slo > 12 (which means that hlo < hT − 1200), equations (C.5.6a) and (C.5.6b) will need to be evaluated. At the end of this process, the path-average multiplier can be calculated using equation (C.5.7).
For a slice fully-traversed by a section of the path:
(C.5.3a)
(C.5.3b)
For a slice containing the lower antenna, at hlo masl:
(C.5.4a)
(C.5.4b)
For a slice containing the higher antenna, at 
masl:
(C.5.5a)
(C.5.5b)
If hlo < hT − 1200:
(C.5.6a)
(C.5.6b)
Equations (C.5.3), (C.5.5) and (C.5.6) are represented in Fig. C.5.1, but not equation (C.5.4).
Note that all values from equations (C.5.3a) to (C.5.6a) should be negative.
For each value the corresponding G should be obtained from equation (C.4.1).
If S is the number of and Q values required for a given link path and layer height, the path-averaged factor G is now calculated using:
(C.5.7)
Appendix D
Anomalous/layer-reflection model
The basic transmission loss associated with anomalous propagation is calculated as described in the following sections.