Examples of Propagation

In the first example, a weak offshore flow of $\sim 5$ms$^{-1}$ from the Arabian deserts produced a surface-based temperature inversion of about 100m over the Gulf. Moisture trapping beneath that inversion resulted in a radar duct, as seen in Figure 3b. In Figure 3a we show the radar coverage a few hundred kilometres downstream of the coastline, where the refractive conditions are almost uniform with range.

Figure 3. Propagation over the Gulf waters, within a modelled surface duct $\sim 100$m deep.

The next example differs from the first in that a signal is sent from a land-based antenna looking out towards the sea (the coastline is at a range of 30km). Ducting does not occur during the overland part of the path. Over the sea, a marine internal boundary layer (and hence also a radar duct) grows with increasing distance from the coastline. Only that part of the signal which reaches the marine boundary layer can become trapped. Thus, the trapped signal strength is much weaker than in the first example.

Figure 4. Propagation from land to sea (the coast is at 30km) in the mid-afternoon. A surface duct develops with increasing distance from the coast, reaching a depth of $\sim 100$m.

For the third example, we consider the same configuration as the second, but now we look at the situation a few hours later: in the early evening, rather than the mid-afternoon. At this time, the formation of a sea-breeze has caused low-level marine air to be advected inland. This produces ducting conditions over land, albeit with a shallower duct than is found over the sea. Since the radar antenna is located with the duct itself, the trapping at this time is much stronger.

Figure 5. Propagation from land to sea (the coast is at 30km) in the early evening. A sea-breeze has produced ducting conditions over land.

Let us now consider a higher offshore wind speed, $\sim 15$ms$^{-1}$. In this case marine conditions are characterised by deeper boundary layer. There is an elevated temperature inversion that results in a region of negative $\partial M / \partial z$ between about 300 and 400m, with positive gradients above and below. Such a configuration (Figure 6b) is known as an S-shaped duct. Figure 6a shows the radar coverage for such a duct, the antenna being a few hundred kilometres downstream of the coastline, where the refractive conditions are almost uniform with range. At short ranges, we see signal trapping in the region of negative $\partial M / \partial z$. At longer ranges, we then find that there is appreciable radar energy in the lower portion of the S, the signal having been refracted back down towards the surface.

Figure 6. Mid-afternoon propagation over the Gulf waters, within a modelled S-shape duct $\sim 350$m deep.

Now consider this same strong-wind case during the night, when the land-sea temperature contrast is weaker. The inversion strength at the top of the MIBL also becomes weaker. When emitted from a ship-based antenna, the radar signal is initially refracted away from the earth's surface. Once it reaches a region of negative $\partial M / \partial z$ aloft, the signal is redirected towards the horizontal, and, if the ducting region were deep enough and strong enough, the signal would be refracted downwards. In this example however, with only a weak, elevated duct, there is significant distortion of the radar propagation but little actual trapping of the signal.

Figure 7. Night-time propagation over the Gulf waters, within a weak, elevated duct.

The final coverage diagram has a rich structure. A signal is sent in the mid-afternoon from a ship-based antenna 170km out to sea and is directed towards land. A strong offshore wind is blowing from the desert land surface. At a range of about 50km and a height of 300m, the signal is refracted down towards the surface due to the presence of an elevated inversion at the top of the MIBL. This inversion has formed an S-shaped duct over the sea. The radar signal is reflected back upwards from the sea surface at a range of about 100km. Close to the coast, note that the MIBL consists of a surface-based rather an elevated temperature inversion, and so the S-shaped duct is replaced by a surface-based duct. Approaching closer to land, the duct becomes shallower and weaker. Towards the end of the range shown, there is no temperature inversion and therefore no duct above the land surface. The radar signal is able to escape from the decaying duct as the coast is approached. The pattern of signal trapping and release in this example gives rise to a ``radar hole'' at a range of about 100km and a height of about 320m. Communication between the ship and an aircraft located within the hole would be disrupted. However, a prediction of the hole may give the radar operator some chance of affecting useful countermeasures.

Figure 8. Propagation from a ship-based antenna pointing towards land, in conditions of strong offshore flow from a warm land surface.