*R*, radar reflectivity factor

*Z*, specific differential phase

*K*or differential reflectivity

_{dp}*Z*. 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.

_{dr}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*and

_{dp}*Z*. Thus the sampling distributions comprise many examples with low values of

*K*and

_{dp}*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*can be added in a three-dimensional self-consistency plot. Understanding of such sampling issues is essential to proper interpretation of the reported relationships.

_{dr}