Z-R Relationships

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 = AR^b

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 = 200R^1.6

Important Notes:

• The aforementioned Z-R relation will vary from place to place and in different precip settings (e.g., convective versus stratiform)
• So, A and b will vary