Z-R Relationship

J. S. Marshall and W. M. Palmer (1948) identified an exponential drop size distribution and derived the Marshall-Palmer relationship:

Z = 200 R ^1.6

While this relationship holds relatively well for stratiform rain common in high-latitude regions, it may not be fully applicable to rains and showers in tropical and sub-tropical regions. As such, some NMHS have derived and adopted their own a and b values in the Z-R relationships:

Z = a R ^b

The following table lists documented Z-R relationships:

Z-R relationships

Meteorological Service	a	b	Remark / Reference
HKO	58.53	1.56	The a & b values are also dynamically calibrated in operation. See also RSMC for Nowcasting
KMA (Stratiform)	32.03	1.41	Nam, J. C. (2003). Microsoft PowerPoint - NamTues2bRevised.ppt. Retrieved November 1, 2016 from Korea Meteorological Administration
KMA (Convective)	19.97	1.4677	Nam, J. C. (2003). Microsoft PowerPoint - NamTues2bRevised.ppt. Retrieved November 1, 2016 from Korea Meteorological Administration
MSS	61.75	1.61	Yeo, Jun Xiang, Yee Hui Lee, and J. T. Ong. Radar measured rain attenuation with proposed Z–R relationship at a tropical location. AEU-International Journal of Electronics and Communications 69.1 (2015): 458-461.
NOAA	250	1.2	Fournier, J. D. (1999). Reflectivity-rainfall rate relationships in operational meteorology. National Weather Service Technical Memo, National Weather Service, Tallahassee, FL.
TMD	300	1.4	Chantraket, P., Detyothin, C., Pankaew, S., & Kirtsaeng, S. (2016). An Operational Weather Radar-Based Calibration of ZR Relationship over Central Region of Thailand. International Journal of Engineering, 2016(2), 92-100.