Z-R Relations from raindrop disdrometers: Sensitivity to regression methods and DSD data refinements

In recent studies, a number of researchers have noted that empirical Z-R relations of the form Z = aRb are affected by the specific manner in which the (Z,R) data points regressions are obtained and that these method-dependent differences may be similar in magnitude to the Z-R equation contrasts observed for physically different precipitation processes. In this study we examine some of these method dependencies, including the choice of dependent variable (R or Z), choice of lower cut-off threshold value (for example, excluding all points with R < 1 mm/h), choice of regression type (linear fit to log-R vs log-Z data or power law fit directly to R vs Z data), and combinations of these. The test datasets were obtained with the same Joss-Waldvogel drop momentum-sensing raindrop disdrometer for primarily convective precipitation in Colorado and for shallow, stratiform periods of winter storms on the coastline of northern California.

We also investigated how the Z-R regressions are affected by various refinements to the raw drop size distribution (DSD) data recorded by the disdrometer. These include accounting for instrument dead-time corrections, using the factory's instrument-specific diameter/channel calibration instead of the nominal calibration used in the raw data files, accounting for the effects of site altitude on the drop fall speeds and diameter/momentum relations, increasing the sampling integration time from the usual 1 minute increments, and adjusting the raw file Z values for the non-Rayleigh conditions appropriate for observations with X-band wavelengths.

Differences among the Z-R equations resulting from the various regression method details and the DSD refinements, as applied to exactly the same dataset, have been quantified with a root mean squared difference statistic for the values of R derived from the population of observed Z values. These method and refinement differences are then compared with the corresponding difference between the two location rainfall types. It will be shown that several of the method and refinement choices had very little effect, but others had surprisingly large effects on the values of (a) and (b).