53:119 Hydrology
Problem #6
Radar Reflectivity and Rainrates (Multiple Combination of Drops)

Determine the radar reflectivity factor (Z) and the radar-estimated rainfall rates for the three cases shown below. In each case, a small atmospheric sampling volume (1 m³) contains raindrops with a constant drop diameter.

Case	Number of Drops	Drop Diameter (mm)
A	8000	0.5
B	1000	1
C	8	5

For all three cases, compute the following:

1. The radar reflectivity factor (Z) (in mm⁶/m³).
2. The rainrate (in mm/hr) using the Marshall-Palmer Z-R relationship.
3. The rainrate (in mm/hr) using the Austin Z-R relationship.
4. The volume of water in the sampling volume (mm³).

The parameters for the Z-R relationship (Z=aR^b) are defined below:

Z-R Relationship	a	b
Marshall-Palmer	200	1.6
Austin	230	1.4

Note that Z has units of mm⁶/m³, and R has units of mm/hr for these parameters.