Last Updated on July 5, 2026 by John Berry
If we draw a path profile with an effective Earth radius of 4/3, we can draw a straight line between stations and this will be the state, or better, for 50% of the time. We can then term the resulting loss over this path with this geometry as the median loss. Path losses, and corresponding signal strengths received, are then normally distributed in time about this median. When the signal falls below the median, we term this a fade.
Many of the pages here discuss incidence of k-factor fading – slow fading about the median caused by changes in the refractivity of the troposphere. In a fade, the signal level falls and is unusable. k-factor fading is governed by the troposphere’s refractivity, or strictly, the troposphere’s refractivity gradient. Typically, in UK and western Europe, the refractivity gradient, dN/dh (∆N), is -40 N/km. N is in units of refractivity. A dN/dh of -40 corresponds to an Earth radius factor, k, of 4/3 and an effective radius of 8500km. For reference, the actual Earth radius is 6731km.
Just as a fade is a reduction in signal below the median, so it’s possible to have an enhancement in signal level. Radio amateurs refer to this as a lift. Literally, the signal level is lifted above the median.
k exceeded
Professionals talk of ‘k exceeded’ for 50% of the time, and indeed some design systems for the ninety-percentile – k exceeded for 90% of time. The signal received will be the corresponding (high) level or better.
Mostly however, k-factor fading is an issue of interference. If k rises, and the Earth flattens, interference might be incident from distant stations that would not normally be heard. Interference degrades wanted services. This is the core of frequency planning – ensuring that interference will only be experienced for small percentages of time.
But radio amateurs want to know the value of k for low percentages of time – perhaps at the five percentile, the value exceeded for 5% of the time or less.
So, Recommendation ITU-R P.453-14 gives the month median value of ∆N at around -40. Rec. P.453 also gives values for 1% (-300), 5% (-100), 90% (-20) and 99% (+30) of time, allowing the frequency distribution below to be assembled. Simply, the bigger the k, the better.
Then ke, k effective in the diffraction nomograph, can be calculated from the formula, ke = 157/(157-∆N). As noted in Recommendation ITU-R P.452-16, ∆N is a positive quantity in this formula (otherwise the result is nonsense).
Application
ke can be used in the calculation of diffraction losses and distance estimated in the nomograph in the page on Diffraction.
At VHF and above, this flattened Earth as a result of change in tropospheric refractivity is exciting because it leads to DX working. For 50% of time, the distance achievable might only be 50km. For 5% of time this range might increase to 300km, and for 1% of time it might be 1,000km. To work stations beyond the normal requires radio amateurs to watch the weather and get on the radio when conditions suggest a lift.
These ideas are applied in other pages. If the path loss for 5% of the time is to be estimated for example, the corrected frequency is f/ke2 or about 16MHz for a 144MHz operational frequency. This gives a diffraction loss over Free Space Loss of about 65dB. For reference, the diffraction loss over Free Space Loss for 50% of the time is around 130dB. A loss of 65dB will allow a 300km path to work. At 130dB it won’t work.
In summary then, a lift occurs when k, the Earth radius factor rises above 4/3, to values like 3. At that point, on that day and time, the path loss drops and stations can be worked hundreds or even thousands of kilometres away. This state seldom occurs – perhaps only on 5% of days in a year.
This is not to be confused with ducting. Ducting and tropospheric lifts are different.