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
FMI 223 1.53 Leinonen, J., Moisseev, D., Leskinen, M., and Petersen, W. A.: A Climatology of Disdrometer Measurements of Rainfall in Finland over Five Years with Implications for Global Radar Observations, Journal of Applied Meteorology and Climatology, 51, 392–404, 2012.
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
MeteoSwiss 316 1.5 Germann, U., Galli, G., Boscacci, M., and Bolliger, M.: Radar precipitation measurement in a mountainous region, Q. J. R. Meteorol. Soc., 132, 1669–1692, https://doi.org/10.1256/qj.05.190, 2006a.
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.