Rates of Geomorphic Change - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 103

Fig. 9.1 The sand rose diagram popularized by Fryberger (1979) in
McKee's (1979a) A Study of Global Sand Seas. The thick bars denote
the integrated drift potentials from each direction, and the arrow
indicates the direction to which the resultant drift potential (RDP) will
move the sand—this switch in direction usually makes the diagrams
much clearer in near-unidirectional cases. The shape of the plot

indicates the type of dune that should result, and the length of the
arrow suggests how much sand should move over the course of
the year (or whatever period the diageam refers to). The length of all
the thick bars added together is the total dript potential (DP). Image
USGS

The flux is the volume of sand that crosses a span of unit
length in unit time: its units are thus m 3 per m per year,
sometimes written in the dimensionally-equivalent form of
m 2 /year. It is a simple matter of geometry to understand
that, for a given migration speed, a bigger dune implies a
larger sand flux. Thus for a given sand flux, a larger dune
will move more slowly than a small one.
Let us consider a flat plain with a small barchan, 20 m
across with a height of 1 m. We can approximate its volume as
that of a cone with these dimensions, and thus *100 m 3 .The
average cross-section of the dune (i.e., the volume divided by
its span) is 5 m 2 . Hence, if the sand flux is 5 m 3 /m/year,
then the 20 m span sees a flux of 100 m 3 in 1 year, and thus
the dune moves by 100/5 = 20 m.
The calculation is simpler for a transverse dune (or the
slipface of a megabarchan) where the cross-section does not
vary over the timescale considered. For the same sand
transport rate (which is that in the Rub' Al Khali desert) of
5m 3 /m/year, then a slipface 50 m tall will advance
5/50 = 0.1 m. A date palm that began growing in the clear
a few meters in front of a dune may become buried in a few
decades, as is seen in the Liwa Oasis (see Fig. 23.5 ; Lorenz
and Radebaugh, submitted).

Fig. 9.2 Quantitative regime diagram, originally due to Wasson and
Hyde (1983). Compare with Fig. 6.1

list and compare no less than seven mass flux equations and
compare with laboratory data. As noted in Chap. 3 , wind is
strongly intermittent, and sand transport even more so, so
that measurements (see Chap. 16 ) are challenging. Over
typical ranges of shear velocity (from one to a few times the
threshold) experimental data have a scatter of about a factor
of 4, and the various proposed expressions have similar
variation. One could stick, for convention's sake, with the
Lettau/Fryberger expression, or for accuracy one could
choose a Q*u *t (u * - u *t ) 2 form advocated by Kok et al.
(2012), or classicists may have affection for Bagnold's
original Q*u 3 expression. The results will not be dramat-
ically different (prefactors have been omitted for clarity
in this discussion, and the prefactors will be different for
different planets).
While we will devote the rest of this section to dis-
cussing the sand flux as manifested in dune and ripple
movement, we should of course note that the sand flux can
be measured directly with sand traps (see Chap. 16 ).

9.3 Observed Dune Migration Rates

Virtually all the published dune migration rates (e.g.,
Figs. 9.3 and 9.8 ) are for barchan dunes. This is because
they are easy to measure—they are the fastest-moving
dunes, and because they form in areas of poor sand supply,
the dune is usually easy to demarcate against a flat and
distinct plain. Although transverse dunes may have appre-
ciable movement, the shape of the dune is difficult to