Numerical Models - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 229

19

Numerical Models

The last 1-2 decades have seen a transformation in dune
studies due to our growing ability to simulate using
numerical models on computers the wind-driven processes
that shape dunes. The transformative aspect is that, due to
computer power, these simulations can now study the pro-
cesses in a time- and spatially-resolved way (and not just in
the bulk-averaged manner considered by Bagnold and oth-
ers). These models are able to reproduce the wide range of
observed morphologies and behaviors, bringing a new level
of understanding to dune studies. A deep hierarchy of
modeling approaches now exist, pertaining to dunes them-
selves as entities, to the transport of individual particles, or
to the wind, or some combination of these. We will discuss
these in approximate order of maturity.

be of the order of 10^4-10^5, depending on the number of
layers in the model vertically. These equations must be
solved in short enough timesteps that the solution is
numerically stable, such that thousands of iterations a day
may be needed. Thus GCMs can be very computationally
demanding, and indeed are a major application of super-
computers and large computer clusters.
While the Navier-Stokes equations are universal, the
way in which other physical processes are represented in
GCMs is not. In particular, how friction with the ground is
handled, how sunlight and thermal infrared radiation is
absorbed, scattered and emitted in the atmosphere (the
radiative transfer scheme), and how convection, clouds and
precipitation are modeled, are aspects that see a wide
variety of approaches. It is simply not feasible to model all
the features of these processes at a fine enough level
explicitly—consider the spatial variability of clouds on
Earth—and so at the chosen grid scale, these processes must
be 'parameterized' (i.e., approximated by some computa-
tionally convenient fudge). Each planet has its own pecu-
liarities: Mars has dust storms and sublimating polar caps,
Titan a thick haze and a methane hydrology, etc. There is
also an intrinsic difficulty in modeling the dynamics of a
more massive atmosphere: not only does the model take
longer (in computational time as well as simulated time) to
'spin up' to a steady state, but the larger inertial effects in a
thicker atmosphere give it more 'hidden variables'—in
essence, more potential for chaotic unpredictability. In this
respect, the Martian atmosphere (Fig. 19.1 ) is rather easy to
predict, in that it responds quickly and directly to solar
heating (although the distribution of surface dust provides
the system with some year-to-year 'memory').
Global models are useful to estimate regional environ-
ments, for example the overall ('trade wind') patterns of
airflow, which latitudes may be systematically dry and
which may see much rainfall, and so on. An extensive
comparison between the pattern of dunes and measured
winds were made in the landmark volume by McKee et al.
(1979a), but only a few studies have explored simulated

19.1 Modeling the Wind

Applying numerical models of global or regional airflow to
dune studies is perhaps more highly developed for other
planets than for Earth, in that measurements of wind are
very limited and thus to put the presence or pattern of dunes
in a meteorological context requires numerical simulation
of the wind environment.
At the global level, this is simulated by a Global Cir-
culation Model (GCM, sometimes also a General Circula-
tion Model), which is the same sort of computer program
used to forecast our weather. Essentially, the atmosphere is
divided up into a 3-dimensional grid (which on a sphere
entails some tricks) and the equations of force and motion
(the Navier-Stokes equations) are solved for each cell in the
grid to work out any pressure changes and how fast the
flows are in and out in each direction. Where global scale
flows are considered (as in Global Circulation Models),
some major factors are the variation of pressure with alti-
tude and the effect of planetary rotation which affects
dynamics via the Coriolis effect. GCMs typically have grid
cells of a few degrees, such that the total number of cells,
tens or hundreds of km across (the model resolution), may