Sand - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 18

Fig. 2.2 Histograms of sand size: amount (in weight %) against the
logarithm of particle size (expressed as the f number in Table 2.1 ).
Note the differentiation between the base and crest of the dunes; the

sharp peaks indicate strong sorting of the particles. Note also the
generally broader sizes in the interdune areas. These data from

Ahlbrandt (1979), USGS image

the distribution droop vertically. But Bagnold's sand num-
bers looked at this way were startlingly different: the points
fell on two inclined straight lines, indicating two power
laws. Such a functional form likely says something about
the probabilities of moving a particle, or the process by
which grains are broken down (Gaussian processes result
from random additions, but successive fracturing, for
example, leads to a power law). More generally, logarithmic
plots avoid suppressing attention to the extremes of the
distribution—we highlight the importance of this aspect in
Chap. 3 : Wind. In addition to logarithmic axes, sometimes
data of this sort are plotted with 'probability' axes (essen-
tially a way of stretching the plot under the assumption it is
Gaussian); such approaches have been used in dune pattern
analysis, although they seem less general and no better than
logarithmic ones.

Note that much of the literature on sand sizes considers
the statistical moments of the distribution—not only the
mean size and the standard deviation, but also the skewness
(how much one tail is fat relative to the other) and kurtosis
(how spread the tails are). Sometimes these statistical mea-
sures are plotted for collections of sand samples in an effort to
draw conclusions about the sand's provenance. Such con-
clusions may or may not be terribly robust (Figs. 2.2 and 2.3 ).
While the Udden-Wentworth scale is essentially con-
figured by the measurement tool (sieves) it should be noted
there are other ways to measure particle size. One is to
observe the terminal velocity, to infer how long material
takes to fall out of the air (or out of liquid suspension).
Laboratory particle-sizers can use this technique, and the
longevity of impact-raised dust clouds was used to constrain
surface particle size at Venus and Titan. But electronic