*N*and

_{0}*Λ*have outlived their usefulness. These are

*graphical*parameters that arose when those investigators analyzed empirical DSD data by plotting them on semi-logarithmic scales (the use of semi-log scales now appears to be cast in a stone tablet). Those parameters lack any useful

*physical*connotation, and even lose their graphical meaning when the same notation is used in describing gamma DSDs. The “intercept parameter”

*N*has nothing to do with the intercept of a plotted gamma DSD function (whether on linear or semi-log scales), and the slope of the gamma DSD plot is not determined by the “slope parameter”

_{0}*Λ*alone.

The science is better served by reformulating the DSD functions in terms of physically meaningful parameters. For an exponential DSD function the parameters *N _{T}*, denoting the total drop number concentration, and

*D*, the mass-weighted mean drop diameter, serve nicely:

_{m} n(D) = N_{T }Λ exp(-ΛD) = (4N_{T }/D_{m}) exp(-4D/D_{m})

Statisticians recognize as the exponential probability density function (PDF), and would rarely if ever think of plotting it on semi-log scales. Use of the parameters *N _{T}* and

*D*allows for more meaningful analysis and discussion, as will be illustrated by a reinterpretation of Albert Waldvogel’s famous “

_{m}*N*jump” story and reformulation of an expression used in numerical cloud modeling.

_{0}For the case of a gamma DSD, a corresponding reformulation in terms of physically-meaningful parameters is

n(D) = N_{T }f(µ) D^{µ} (D_{m})^{µ+1} exp(-(µ+4)/D_{m})

This requires the gamma shape parameter *µ*, which in one sense is a graphical parameter but in physical terms is an index of the width of the distribution; the coefficient of variation is 1/(SQRT(1 + µ). The part of *n*(*D*) following *N _{T}* is the gamma PDF. The utility of this formulation will be illustrated by application to the question of finding relationships between

*µ*and

*Λ*, and to other expressions used in numerical cloud modeling.

To be sure, the expressions for *n*(*D*) become a bit more cumbersome with these parameterizations. However, the advantage gained in more meaningful analyses and discussions is well worth the small effort involved.