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"

   "HKO", "58.53", "1.56", "The a & b values are also dynamically calibrated in operation. See also `RSMC for Nowcasting <https://rsmc.hko.gov.hk/nowcast/calibrationZRRelationship.html>`_"
   "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. <https://dr.ntu.edu.sg/handle/10220/25894>`_"
   "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. <https://www.weather.gov/tae/research-zrpaper>`_"
   "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. <https://www.researchgate.net/publication/305319190_An_Operational_Weather_Radar-Based_Calibration_of_Z-R_Relationship_over_Central_Region_of_Thailand>`_"