Reflectivity/Rainfall Relationship

Reflectivity Z ↔ Rainfall Rate R

Reflectivity Z is related to the sizes of all raindrops in a pulse volume

The rain rate R is related to the sizes of all raindrops in a pulse volume and their fallspeeds

A very rough relation between the two is: Z = 200R1.6

 

 

So how do we infer rainfall rate?

Because the radar provides a relatively large areal coverage, with a spatial and temporal resolution that is not achievable by other means, and can also provide an estimate of the reflectivity factor for the precipitation target, much research has been done on rainfall measurements. In practice the size distribution and phase of the precipitation is not known. Consequently the relationship between radar reflectivity and rainfall are based on empirical studies, where rainfall rate is measured at the surface while the effective reflectivity factor is simultaneously estimated by radar at some standard height above the rain gauge (Figure 4).

 

Empirical studies of the relationship between effective reflectivity and rainfall involve measuring the rainfall at the surface and the effective radar reflectivity at some standard level above the surface.

Rayleigh scattering theory:

For a collection of i particles in a sampled volume

  • Z =weighted sum of cross sections of individual particles per unit volume
  • Z = Σni(D)Di6 /unit volume (mm6/m3) where ni(D)= number of droplets with diameters between Di and Di+ΔD

Empirical studies have yielded many relationships between radar reflectivity and rainfall rate, for different precipitation types, geographic regions and seasons. These relationships generally take the form

Z ≈ a Rb

where Z is the radar reflectivity in mm6/m3 and R is the rainfall rate in mm/hr. Such relationships are known as “Reflectivity/Rainfall” (Z/R) equations.

Reflectivity/Rainfall equations

Empirically derived relationships between radar reflectivity (Z) and rainfall rate (R) for various precipitation types and synoptic situations.

For example, many services use the standard Marshall-Palmer relationship for estimating rainfall rates from radar reflectivity.

Z = 200R1.6

From this it can be shown that: R = 10(log R)

Other Z/R relationships reported by Battan (1973) include:

  • For orographic rain Z = 31R1.71 (Blanchard 1953)
  • For thunderstorms Z = 486R1.38 (Jones 1956)

Experimental Z/R relationships plotted on a Z and R space.

Curves for these equations are shown in Figure 5 together with the Marshall-Palmer equation. It is evident that rainfall rate measurements made with radar will only be approximate unless specific studies are made at a given location. This is thus an “rough as guts” approximation, but that’s how its done!

iDevice icon Reflection

Danger of using fixed Z-R relationships

 

 

In both cases the measured reflectivity is mm3/m3 → 29 dBZ

What is the rainfall rate in these two cases using the very rough relation above?