Sampling issues in using raindrop disdrometer observations to determine radar Kdp-Z and self-consistency relationships

Sampling issues are ubiquitous in using observations of raindrop size distributions to estimate bulk quantities such as rainfall rate R, radar reflectivity factor Z, specific differential phase K_dp or differential reflectivity Z_dr. Even if the drop size distributions are reasonably homogeneous over the sampled volumes of the atmosphere, samples comprising large numbers of drops are required to obtain good estimates of those quantities. However, the samples provided by available disdrometers are often not large enough, especially in light rainfall situations, to give satisfactory results.

Sampling variability problems range from skewness in the estimates of such quantities (most of the estimates are too low and a few are too high) to correlations among the estimated quantities that can mimic physical relationships among the variables. One example of the latter arises in efforts to determine relationships between K_dp and Z from drop-size data; such relationships are sometimes used in estimating rainfall rates. In qualitative terms, small samples from the typical long-tailed drop size distributions (exponential or gamma models are commonly used) often lack the large drops that produce high values of both K_dp and Z. Thus the sampling distributions comprise many examples with low values of K_dp and Z and some with high values of both. A series of samples (such as a time sequence) from a single distribution – as might be obtained during steady rain – will thus yield a K_dp – Z scatter plot very much like those that have been reported, even in the absence of any actual variation in either quantity. Actual variation in the rainfall itself would be superimposed upon such a scatter plot.

The nature of this sampling problem is illustrated by simulation of repetitive sampling from a gamma drop size distribution and plotting of the resulting values of K_dp and Z. Values of Z_dr can be added in a three-dimensional “self-consistency” plot. Understanding of such sampling issues is essential to proper interpretation of the reported relationships.