As with wavelength, the average power return from a target volume is inversely related to the square of its range from the radar. The 1/R2 acts to normalize the reflectivity values from different ranges. If normalization wasn't performed, storms close to the radar would always display higher reflectivity values than those farther away due to the greater power density at short ranges. If two storms have the same reflectivity, then the one closest to the radar will always return more power than the one farther away. For example, a target at a range of 10 nm would return 16 times as much power as it would if it was located 40 nm from the radar (i.e., for R = 10 nm, 102 = 100; for R = 40 nm, 402 = 1600).
For a more in depth discussion on the derivation of the Probert-Jones radar equation, see Rogers (1979) or Doviak and Zrnic (1984).