Rates of Geomorphic Change - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 102

9

Rates of Geomorphic Change

In this section, we discuss the net transport and what it
means in terms of bedform construction and migration. Had
we written this section only 2 years ago, it could have
confined itself to the Earth, but dune and ripple movement
on Mars has now been directly observed and quantified.

resultant sand transport: in the case of a near-unidirectional
wind regime, this has the convenient effect of avoiding the
close superposition of the resultant vector on top of the
larger wind lines. Figure 9.1 shows some examples.
The RDP divided by the DP is a measure of the wind
unidirectionality. If the quantity approaches unity, the wind
is unidirectional, whereas a smaller ratio indicates winds
that are variable in direction. This gives a quantitative
metric against which to compare resultant morphologies.
Figure 9.2 shows this mapping. It should be noted, though it
is rarely stated, that the magnitudes of the individual DPs,
and thus both the magnitude and direction of the resultant,
are explicitly dependent on the choice of ut. The method-
ology for computing the sand flux in Fryberger (1979) is
arranged somewhat archaically towards hand computation
via tables of binned windspeeds and display with a plotter,
now it is straightforward to simply add the east and west
components of sand transport vectors in a script or
spreadsheet and compute the results from a wind mea-
surement time series directly. Some care must be taken,
however (Bullard 1987) in using units: Fryberger's meth-
odology somewhat implicitly assumes the use of knots
throughout.

9.1 The Sand Rose

The systematic formalization of the variability and strength
of wind at a site was introduced by Fryberger (1978), and his
convention is widely used today. For wind blowing in a
given direction at speed U, the sand flux Q will be
Q = U 2 (U - u t )f, (an expression derived from Lettau and
Lettau (1969)) where u t is the threshold windspeed, and f is
the fraction of time (usually expressed as a percentage) that
this wind persists: if U \ ut, then Q = 0. To calculate the net
sand transport in a given direction, Q is calculated for all the
windspeeds encountered. Because of the near-cubic depen-
dence on windspeed, it may be that relatively infrequent
winds may dominate the transport: if u t = 5, and U = 20
occurs only 1 % of the time while U = 10 occurs 10 % of
the time, the U = 20 contribution will be larger than that of
U = 10. The sum of these contributions is a vector in the
wind direction, and is referred to as a Drift Potential (DP). It
can be plotted as a line, and the set of DPs ('arms')—usually
for the 16 points of the compass—plotted together (follow-
ing meteorological convention, with a line defining the
direction from which the wind came) is called a sand rose.
The magnitudes of all the DPs added together is also
referred to as the Drift Potential, and is essentially a non-
linear measure of the windiness of a place. However, of
most interest for overall transport is the resultant when the
DPs are added vectorially, such that an East drift cancels
out a West drift, etc. This vector sum has a magnitude (the
Resultant Drift Potential, RDP) and a direction (Resultant
Drift Direction). This vector is displayed on the sand rose as
an arrow with a head to discriminate it from the contributing
DP lines. The vector is shown in the direction of the

9.2 Sand Fluxes

Fryberger suggests three broad categories of transport
environments, based on the magnitude (in 'vector units' or
VU) of the RDP: low energy (\200 VU), intermediate
(200-399 VU) and high ([400 VU).
The sand transport rate relates directly to the RDP
(Fryberger shows a plot, using the transport relation of
Lettau and Lettau (1969)), with a constant of proportionality
of *0.07 m 3 /m/year per VU (the constant depends slightly
on wind threshold, and on sediment density). In other
words, a low/intermediate environment with DRP = 200
would see a sand flux of about 14 m 3 /m/year. Note that this
transport relation is only one of several—Kok et al. (2012)