Whilst it might appear that the gradients in radio refractive index (RRI) in the middle and upper troposphere are too small to achieve much, in fact scatter theory does not need any more than those observed. To give you an idea just how small the gradients need be, radio acoustic sounding systems (RASS) rely on backscatter generated by RRI gradients generated by acoustic waves. These allow estimation of vertical temperature profiles. MST radar systems also illustrate how significant natural backscatter can result from RRI gradients in the troposphere, and thus allow estimation of vertical wind profiles.
Refractive effects can also significantly enhance scatter volume. The following examples, again computed using the US Navy's AREPS 1.01 software, show some interesting points.
Demonstration of the common volume available for scattering, stations 500 nautical miles apart, separated by sea, with a standard gradient in RRI.
For simplicity, losses for the second station at 500 miles are not plotted quantitatively. It is often said that the lowest part of the common volume results in the majority of the scattered signal; in fact, the situation is more complex, as the minimum common loss is higher up within the common volume.
Demonstration of the common volume available for scattering, stations 500 nautical miles apart, separated by sea, with a surface duct present at 1000 feet above the ground.
Losses for the station at 500 miles are not shown here, but it is very clear how the surface duct reduces losses at elevation, and thus increases signal strengths in the common volume.
The common volume available for scattering, stations 500 nautical miles apart, separated by sea, with a surface duct present at 1000 feet above the ground.
This time, losses are shown for both stations, to illustrate the very complex nature of signal strengths within the common volume, and the much greater common volume. Naive concepts of a wedge-shaped common volume are clearly inadequate when RRI gradients are not 'standard', i.e. refractive effects can enhance scatter by increasing signal strengths within the common volume, and greatly enlarging the common volume.
So even if your path may not actually use a duct, the presence of a duct somewhere along the path may greatly assist forward scatter. Watch this page for some more modelling work soon, intended to look more specifically at forward scatter.
The Inner Sanctum page contains a bibliography, several volumes of which provide a lot of detail on scattering theory. There are (at least) three papers which you will also find worth studying:
Richards, E G (1958) The estimation of transmission loss in the trans-horizon region. IEE Symposium on Long-Distance Propagation above 30 Mc/s, 28 Jan 1958. Pp. 177-183.
Norton, K A, Rice, P L, & Vogler, L E (1955) The use of angular distance in estimating transmission loss and fading range for propagation through a turbulent atmosphere over irregular terrain. Proc IRE October 1955, 1488-1526.
Johnson, M A (1958) A review of tropospheric scatter propagation theory and its application to experiment. IEE Symposium on Long-Distance Propagation above 30 Mc/s, 28 Jan 1958. Pp. 165-176.
Last updated 27 Dec 1998
Howard Oakley
Mail howard@quercus.demon.co.uk