Z-R Relationship

Previously, the climatological Z-R for Kwajalein was derived from a historical drop size distribution data set made with a drop camera at Majuro Atoll. The new climatological Z-R is based on drop size data collected by a Joss-Waldvogel disdrometer at Kwajalein in the wet seasons of 1999 and 2000. The error was minimized over many samples to calculate the Z-R most appropriate for monthly rain accumulation. The best fit Z-R obtained from 891 10 min samples totaling 869 mm of rain is:

Z=175R1.5

No differentiation is made between convective and stratiform Z-R's at this time.

There are many factors that affect the relation between measured radar reflectivity and surface precipitation. First and foremost is that the radar's lowest beam increases in height above the surface the farther it gets from the radar due to the earth's curvature. Thus, variations in drop-size distribution, enhancement by hail, diminution by downdraft, low level growth in fog or stratus and low level evaporation in dry air (Austin MWR May 87, pp. 1053-71) can act within the distance between the lowest radar beam and surface to change the amount of precipitation measured.

A comparison of radar reflectivity over a network of rain gauges at the surface can help define the bias created by the factors mentioned above. There are temporal and spatial drawbacks to comparing rain gauge data and radar reflectivity. A rain gauge network consists of a number of point-source continuous measurements, while a ground radar covers a much larger area but has a typical resolution of 2 km x 2 km and only samples roughly every 10 minutes. However, these drawbacks are accepted due to the greater factor of uncertainty of deriving surface precipitation from radar reflectivities measured sometimes kilometers above the ground.

Various methods are used to adjust the radar surface precipitation estimate with rain gauges through the use of a corrected Z-R relationship. The most general method is to calculate the monthly amount of rain at each gauge and at the radar pixel above each gauge (using a standard Z-R relation to convert reflectivity into rain rate). Then the average monthly accumulation ratio of all the gauges is used to adjust the Z-R relation (assuming the gauges to be ground truth). However, this method has not been viable at Kwajalein because of the limited number of locations for gauges and the difficulty in maintaining a gauge network in such remote conditions.