# How to understand the dBZ scale for weather radar and the reference (1 mm^6 per m^3)? Where does the 6 come from?

I was watching Typhoon Gaemi's strange path and shape using the Taiwan Central Weather Bureau radar data, and noticed that the intensity scale is in dBZ units. It's a decibel unit so every increase of 10 (say 30 to 40) is a factor of ten increase.

Based on the linked Wikipedia article, I think that a concentration of one 1 mm diameter droplet per cubic meter corresponds to dBZ value of 0.

The signal is expected to be linear with droplet density - if we double the density from one droplet per cubic meter to two, we should expect a factor of 2 increase in the signal, or about 3 dB.

However, from what I understand so far, if each of those droplets instead doubled in size to 2 mm diameter, the signal would increase by a factor of $$2^6$$ or 18 dB.

Question(s):

1. Have I got all of that right? Am I understanding correctly so far?
2. Where does the exponent of 6 come from?
3. Is this why groups of migrating birds and even butterflies show up so well in weather radar?

• Quick comment regarding 2.: If I remember correctly for radar observations you assume $\lambda \gg D$, $\lambda$ being wavelength and $D$ being diameter, and hence we are in the Rayleigh limit as far as scattering is concerned. The (Rayleigh) scattering cross section scales with $D^6$. I believe that is why there is a power of 6 in the radar reflectivity. Commented Jul 25 at 10:51