### 15.3 Ground and Weather Radar

The analysis in section 15.1 assumes that we are looking for ‘small’ reflecting objects – i.e. targets whose cross-sectional size is small compared to the width of the radar beam. In some cases, however, we view an ‘extended’ target which essentially fills the field of view. The most common examples are situations where the radar is directed towards the ground (e.g. for a radar altitude measurements from an aircraft), or a large cloud (for meterology), as illustrated in figure 15.4

The significant feature of these sitatuations is that – ignoring any losses due to air attenuation or scattering – all of the radiated power strikes the ‘extended target’ in an area (or volume) which is within the field of view of the RADAR receiver. As a result, in these cases the power level striking the target does not fall with the square of the range. Nor does the power reaching the target depend upon the antenna’s gain or antenna angle, , provided that the target is large enough to fill the beam. In such situations we can treat the extended target as if it were re-radiating an amount, , where is the power transmitted by the radar, is an effective reflectivity value for the target surface, is the range, and is the air’s attenuation coefficient.

The manner in which power is re-radiated or scattered by the target object clearly depends a great deal on its nature and how it may be oriented with respect to the radar. For simplicity we can imagine it reradiating into a hemisphere which includes the direction of the radar and take any directional reflection/scattering properties into the appropriate value. On this basis we can say that the power level returned to the radar will be

where is the effective area of the radar’s antenna. At low frequencies we can often neglect the air loss and say this is equivalent to

This expression differs from equation 15.7 in two significant ways. Most importantly, the received power only falls as the square of the range – unlike the standard radar equation. This is because there is no ‘outward journey’ loss as effectively all the transmitted power strikes the target. Secondly, the received power only depends up rather than . This is because the transmit gain does not alter the power reaching the target, only how small a portion of the target area is illuminated and in view.

The above expressions are appropriate for targets which, like the ground, act as a large surface. The situation when using radar to observe tenuous objects (e.g. clouds) is slightly different as some of the illuminating power will penetrate the cloud. Some of this power may be transmitted right through, other portions may be reflected from various depths inside the cloud. (And some of this might be re-reflected away from the radar line of sight.) The reflected/scattered power may be radiated away over a complete sphere rather than the half-sphere of a surface reflection.

One of the most significant effects is that, when using a pulsed transmission, we may at any instant see reflections from a spread of ranges which come from earlier or later portions of each pulse. As a result, the reflected power may depend upon the pulse length as well as its power, etc. It may also depend on the thickness of the cloud. Despite this, we can still use expression 15.17 but with a ‘modifed’ value of h which takes into account these various effects.

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