So, if we assume a certain drop size distribution (e.g., Marshall Palmer):
then recall: Z = Z(RR, SD) , so now we have a direct relation between Z and RR
since SD is known. An empirical relation between Z and R has been found to be:
Z = ARb
where A and b are empirically-derived constants.
The most common form of this Z-R relation is for rain assuming a Marshal Palmer drop size distribution:
Z = 200R1.6