Meteorology

Calibrating intensity of return

Because the targets are not unique in each volume, the radar equation has to be developed beyond the basic one[7]:

where \,P_r is received power, \,P_t is transmitted power, \,G_t is the gain of the transmitting antenna, \,\lambda is radar wavelength, \,\sigma is the radar cross section of the target and \,R is the distance from transmitter to target.

In this case, we have to add the cross sections of all the targets:
where \,c is the light speed, \,\tau is temporal duration of a pulse and \,\theta is the beam width in radians.

In combining the two equations :


Which leads to:
Notice that the return now varies inversely to \, R^2 instead of \,R^4. In order to compare the data coming from different distances from the radar, one has to normalize them with this ratio.