The trigonometric representation shows the influence of the Earth's surface. The Earth plane surrounding radar antenna has a significant impact on the vertical polar diagram.
The combination of the direct and re-reflected ground echo changes the transmitting and receiving patterns of the antenna. This is substantial in the VHF(Very High Frequency) range and decreases with increasing frequency. For the detection of targets at low heights, a reflection at the Earth's surface is necessary. This is possible only if the ripples of the area within the first Fresnel zone do not exceed the value 0.001 R (i.e.: Within a radius of 1000 m no obstacle may be larger than 1 m!).

FRESNEL ZONE

In optics, is one of a series of confocal prolate ellipsoidal regions of space between and around a transmitter and a receiver.

Specialized Radars at lower VLF(Very Low Frequency) frequency band make use of the reflections at the Earth's surface and lobing to maximize cover at low levels. At higher frequencies, these reflections are more disturbing. The following picture shows the lobe structure caused by ground reflections. Normally this is highly undesirable as it introduces intermittent cover as aircraft fly through the lobes. The technique has been used in ATC ground mounted radars to extend the range but is only successful at low frequencies where the broad lobe structure permits adequate cover at higher elevations.

FREQUENCY SPECTRUM

The influence of the curvature of the Earth

Determining the height of an airplane is not that simple because:

the phenomenon of refraction occurs when electromagnetic waves pass through layers of the atmosphere with different densities
the surface of the Earth is curved

These two factors are taken into account in calculating altitude by radar systems, using a more complex formula.

Thus, the determination of the target height is not reduced to a simple trigonometric formula. If the curvature of the Earth is taken into account, the formula is modified as follows: