Rainfall Estimation - Introduction

From the radar equation, we can get Z, the radar reflectivity factor. Recall that:

	(1)

Z depends on the rainfall rate (RR) and the size distribution (SD) of the drops.

So Z = Z(RR,SD)	(2)

Since Z is known, but RR and SD are unknown, (2) shows that we have one equation, but two unknowns.

Solution to problem:

Let's assume a specific form of the size distribution - the Marshal Palmer Drop Size Distribution:

	 (3)

Where D is the drop diameter (mm)

N₀ is just a constant = 8000/m³mm

l can be expressed in terms of the rainfall rate:

l = 4.1R^-0.21 (for rain)

where R is the rainfall rate in mm/hr.

So (3) becomes:

		(4)

Hence, we can use (4) with a known rainfall rate (R) to calculate the number of drops (N_d) at a given diameter, (D). (see graph above)