The theory of radar storm detection is derived. The power received from rainstorms varies inversely as the fourth power of the wavelength and the square of the range (assuming total interception of the beam by the rainstorm area), and directly as the summation of the sixth powers of the radii of the droplets effectively illuminated. Moderate rain has a greater reflectivity than clouds not associated with rain by a factor of about 106.
Absorption by oxygen and water vapor causes attenuation of the radar beam. In a tropical atmosphere the theoretical two-way attenuation for 3.2-cm radiation over a 100-km range is 48%. Absorption and scattering by rain causes more serious attenuation. For 3.2-cm radiation the experimental two-way attenuation through 10 km of the rain intensities chosen as light, moderate, and heavy are approximately 16%, 51%, and 83% respectively.
For most storm-detection purposes, radar utilizing wavelengths in the vicinity of 3 to 6 cm is more suitable than 9- to 12-cm equipment. Through appreciable distances of moderate or heavy rain the use of 10-cm radar gives greater return signal than 3-cm equipment.