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 :sup:`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 :sup:`b` The following table lists documented Z-R relationships: .. csv-table:: Z-R relationships :header: "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, 392ā€“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, 1669ā€“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 Zā€“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. `_"