# Marshall-palmer relation

From AMS Glossary

## Marshall–Palmer relation

The

*Z*–*R*relationship developed by J. S. Marshall and W. M. Palmer (1948) consistent with an exponential drop-size distribution.The relationship is

*Z*= 200*R*^{1.6}, where*Z*(mm^{6}m^{-3}) is the reflectivity factor and*R*(mm h^{-1}) is the rainfall rate. The relationship is sometimes generalized to the form*Z*=*aR*^{b}, where*a*and*b*are adjustable parameters.Marshall, J. S., and W. McK. Palmer, 1948: The distribution of raindrops with size.

*J. Meteor.*,**5**, 165–166.