Geology Reference
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falls in sea-level, transitions between facies were
modifi ed thus allowing preferential changes into
facies that might be better adapted to the new
environment, defi ned by water depth. Figure 14
outlines the directions of anticipated changes
and the fi xed-point vectors of the modifi ed TPM
(Figs 14b and c and 15), allowing to predict
future distribution of facies. To generate the
model, the sum of all loop-values (probabilities
of self-transition) was kept constant. Then the
loop values of those vertices (facies) that were
assumed to shrink in the changed environment
were rounded down to the next integer decade
(10, 20, 30, etc.). The amount that had been gained
by rounding-down the loops was then redistrib-
uted over those vertices (facies) that were to be at
an advantage in the changed environment caus-
ing stronger retention in these facies. Transitions
between facies were adjusted to respect the con-
straint of row summability to unity. Depending
on the environmental change desired, the tran-
sition probabilities into either the neighbouring
shallower or deeper facies was increased, while
transitions into facies at the same depth were kept
at equal weight. This had the effect that either the
facies at the shallow extreme (emergent sand) or
deep extreme (dense coral) became more refl ect-
ing (in the sense that the chain would not transit
frequently into and remain long at the extremes,
thus their frequency in the FPV would be
decreased) or more absorbing (in the sense that
the extremes would be more frequently transited
into and the chain would remain longer in them,
increasing their frequency in the FPV). Thus it was
possible to let facies adjust in frequency at the cost
of each other, depending on how sea-level would
position them on the gently changing depth ramp
and whether they encountered their preferred
depth range. Since the system was bounded at
the shallow and the deep ends due to the nature of
the analysis (masking of pixels deeper than dense
corals) and limited space was available on the
banks for changes in facies composition, no new
facies could be generated.
In the rising sea-level scenario (facies transit
preferentially into a neighbouring deeper-water
facies, shown in Fig. 14 by bold arrows), the shal-
low facies (emergent sand, submerged sand, sparse
seagrass-algae) were made to retreat strongly
(Fig. 15) and the facies typically found on the
bank-edges (corals, dense algae) increased due
to better availability of habitat in their preferred
depth range. This is plausible since little space
exists for a landward retreat of shallow facies
(a)
D
D
D
S
E
(b)
Fig. 13.
(a) Spatial transition probability matrix obtained
from pixel counting the classifi ed Landsat image of the
Murawwah study area. From eight available classes, two
(masked pixels in the ocean and on land) were excluded
to concentrate on subtidal shallow facies. (b) The weighted
digraph corresponding to the matrix in (a). Where rows
do not sum to zero, this is a result of rounding error
that did not occur in analyses, where more positions behind
the decimal point were used.
events on decadal scales lead to higher transition
probabilities from corals to dense algae than any
other facies. Similarly directed temporal transi-
tions would occur between dense seagrass-algae
and sparse seagrass-algae whenever conditions are
unfavourable (extreme hot or cold events, changes
in sea-level) and between the latter and bare
sand sheets.
How the distribution of facies might change
was examined by changing transition likelihoods
in the temporal TPM, and basic predictions were
made about effects of a changed environment, in
this case sea-level rise and fall of 1.5 - 2 m. This
gentle oscillation remained within the relatively
narrow depth range over which facies were evalu-
ated on the Landsat image (0-8 m). Sea-level was
treated implicitly and the bathymetric informa-
tion did not enter into any calculation - water
became 'shallower' or 'deeper'. So if sea-level was
considered to rise, a transition into a deeper facies
could be expected in previously shallow areas.
Thus the transition probability shallow-to-deep-
facies had to be increased. To simulate rises or
