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offer spectacular exposures (Guo & Riding 1998;
Hammer et al. 2007), demonstrating general
increase in scale and steepness with time (upwards
coarsening), higher precipitation rates at rims and
terrace walls, and upstream or usually downstream
migration (Fig. 7).
Several authors have mapped travertine precipi-
tation rates in natural terraced systems (Liu et al.
1995; Lu et al. 2000; Bono et al. 2001; Hammer
et al. 2005). These studies demonstrate substantially
higher precipitation rates in areas of high flow vel-
ocity near terrace rims and walls, causing relative
upwards and outwards growth of the rims.
The most spectacular method for the study of tra-
vertine terrace dynamics is time lapse photography.
Veysey & Goldenfeld (2008) produced a movie
based on a year-long data series from the
Mammoth Hot Spring complex in Yellowstone
National Park, showing progressive coarsening by
pond inundation where the rim of a pool grows
faster than the rim of the upstream pool, causing
drowning of the upstream pool and the formation
of a single large pool. Their movie also shows
downstream migration of terraces.
The formation and expansion of downstream-
pointing lobes is seen both in time lapse movies
and in simulations. Hammer et al. (2007) attempted
to explain this 'fingering instability' by observing
that the regional, underlying terrain slope implies
a higher and steeper terrace wall at the downslope
tip of the lobe than at the sides. As discussed
below, this leads to faster precipitation rates at the
tip of the lobe and therefore differential downslope
migration rates of the rim, causing a downslope
stretching of the pool.
It is commonly observed that terrace systems are
partly dry (Fig. 6a). This is not always due primarily
to reduction in overall flux. As a result of travertine
build-up, water continuously finds new routes. Old
pathways may be abandoned and dry up, but
become active again at a later date (Chafetz &
Folk 1984).
Fig. 4. Dried-up microterracettes at the Troll
hydrothermal springs, Spitsbergen. Lens cap for scale.
The almost constant height of terracettes implies larger
pool areas in regions of small slope. (a) Oblique view.
(b) Horizontal view from the same position.
tension loses importance and unit steps are not
observed.
Travertine terraces owe some of their beauty to
the almost perfectly horizontal orientation of the
rims. Any artificially added protuberance will
reduce water flow and precipitation locally, allow-
ing the surrounding rim to catch up, while any
incised notch will increase flow locally but divert
flow away from the rest of the rim, causing rela-
tively faster precipitation in the notch. Clearly, a
flat rim will have a tendency to 'self-repair', restor-
ing to a stable horizontal line after perturbation. In
fact, water flow over the rim is rarely uniform, but
localized to a number of narrow sites (Fig. 6).
Clearly, these sites are continuously repositioned,
producing a statistically uniform growth rate along
the rim over time.
Pattern formation mechanisms
Travertine terracing is a self-organizing pattern
formation process involving a number of coupled
physical processes. Several authors have recently
modeled the process at different levels of abstrac-
tion, highlighting different aspects of the problem.
At the purely geometric level, it is clear that a
simple relationship between slope steepness and
growth rate is sufficient to produce a terraced
pattern. Starting from a rough slope with small
random perturbations, Jettestuen et al. (2006) used
such a growth rule to computer simulate the emer-
gence and coarsening of steps. Interestingly, the
Terrace dynamics
The emergence and dynamics of travertine terraces
can be studied with a number of techniques. Cross
sections of travertines allow direct observation of
relative growth rates and depositional sequences.
The travertine quarries of Rapolano Terme in Italy
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