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DETERMINING SEDIMENT BUDGETS AND COASTAL DEPOSITIONAL MORPHODYNAMICS BASED ON 3-DIMENSIONAL TERRAIN MODELLING USING GIS
(1) Colin D. Woodroffe, Bongkoch Samosorn, Ava D. Simms, (2) David M. Kennedy and John Marthick
(1) School of Geosciences, University of Wollongong (AU)
(2) School of Earth Sciences, Wellington (NZ)
Geographical Information Systems (GIS) offer potential to refine the estimation of sediment budgets and therefore provide insights into coastal morphodynamics, the co-adjustment of form and process as landforms evolve. Generally the pattern of sedimentation in coastal systems has been examined in 2 dimensions. Planimetric trajectories of change have been determined based on the superimposition of shoreline position from surveys or remote sensing at decadal time scales; whereas longer term evolution of coastal landforms has been based on cross-sectional stratigraphy and radiometric dating at century to millennial time scales. GIS enables the 3D or quasi-3D representation of coastal environments, and this paper explores the prospect of reconstructing mass budgets in three contrasting coastal settings, each of which appears to have experienced a relatively simple pattern of Holocene sediment accumulation. The three examples comprise a reef island on a coral reef platform (Warraber Island, Torres Strait), a coastal lagoon on an embayed coast (Lake Wollumboola, southern New South Wales), and a discrete coral reef and lagoon (Lord Howe Island, southwestern Pacific).
The topography of Warraber Island, perched on a platform reef in central Torres Strait, has been determined on the basis of photogrammetry, which reveals a pattern of progradation of successive ridges. The depositional history of the island is inferred on the basis of pits excavated across the island and radiocarbon dating on the skeletal sands recovered from those pits. Lake Wollumboola in southern New South Wales, is one of a series of coastal lagoons in southeastern Australia, each of which is at a different stage of infill. It has a small coastal catchment from which sediment loss has been estimated using a raster overlay procedure based on the revised Universal Soil Loss Equation. The mass budget of accumulated sediment in the lagoon was determined using 3D terrain modelling on the basis of shoreline surveys, bathymetric cross-sections, probes into the lake floor to point-of-refusal, and coring and radiocarbon dating of the Holocene muds. The fringing coral reef on Lord Howe Island occurs at, or near, the latitudinal limit to reef growth, and the reef that has developed during the Holocene along the western shore, and deposition of lagoonal sediments, have been discrete in both time and space. Extensive drilling, seismic reflection profiling and vibrocoring, together with a sequence of radiocarbon dates, offers the opportunity to reconstruct reef growth as well as the accumulation of associated sediments in detail.
Despite relatively good topographic and geochronological control on the pattern of accretion in each of these different settings, there are several constraints on the effectiveness with which a mass balance can be determined. The sensitivity of modelling of each of these coastal systems to these constraints is examined.
Introduction
The coastal zone is particularly dynamic. Waves and currents act to move sediment
and these short-term process regimes serve to continually adjust the shape
of coastal landforms in ways that can generally not be integrated over time
to forecast how the coast will evolve over longer time scales. Coastal morphodynamics,
the study of the mutual co-adjustment of process and form, can usefully be
considered at a series of spatial and temporal scales. The instantaneous response
of the substrate to incident wave or current processes, and the event-scale
adjustment of coastal landforms to extreme events such as storms are best
studied at short time scales (Cowell and Thom, 1994). These bear little similarity
to the long-term evolution of coastal geomorphology as revealed by stratigraphy
and radiometric dating of coastal sediments over geological time scales, particularly
over the Holocene. Coastal managers and planners need to operate at an intermediate
time scale, the engineering time scale, focused at decades to centuries (Woodroffe,
2003). Mass budgets, the calculation of the volume of sediments moved, may
enable some reconciliation of the behaviour of the coast at different time
scales.
It has been traditional to examine the coast in two dimensions. However, 2D representation of the shoreline is an oversimplification of the complex geo-phenomena that comprise the coast, collapsing it into a timeless planar space. The dynamic entities which contribute to the shoreline are frozen into 2D snapshots, and comparison between the form of the coast at different time periods is portrayed by this 'timeless boundary-drawing approach' (Raper, 2000, p. 128). Multidimensional Geographical Information Systems (GIS) provide a framework within which to simulate past adjustments to individual parts of the coast, and to predict possible future changes in response to environmental change. This may be possible where the traditional 2D GIS data sets comprising x and y components, can be expanded with a z component, the elevation (or depth).
The approach is not a truly 3D use of GIS, but involves a comparison of surfaces at different times to determine a first-order estimation of changes in sediment volume, and hence estimation of sediment fluxes. At the simplest level, termed spatial data modelling by Raper (2000), single-valued surfaces are mapped in 2D but visualised in 3D, and changes are assessed by the differences between these surfaces. More advanced 'process modelling' involves representation of fluxes incorporating time as a fourth dimension. There will need to be development of new data models before this fully multidimensional GIS can be implemented (Kucera, 1995). It is generally not possible to undertake full 3D modelling in commercially available GIS, and these are often regarded as 2.5D, representing an extension of cartographic modelling to compare the volume differences between surfaces (Tomlin, 1990). Nevertheless, multidimensional GIS already offer the prospect of more detailed monitoring and modelling of morphological adjustments along the coast (Raper, 2000; Raper et al., 2003). Interpolation can be achieved using various geostatistical approaches to represent topography by three-dimensional digital terrain models, either digital elevation models (DEMs) or triangulated irregular networks (TINs), and the assessment of volume changes represents a significant advance on the measurement of linear or planar changes and vertical or horizontal accretion or erosion rates.
In this paper, the usefulness of this multidimensional GIS approach is examined initially by using GIS techniques to examine the patterns of morphological change and simulate sediment budgets over geological (103 years) and engineering (101 years) time scales on Warraber Island, a small reef island towards the leeward of a elongated reef platform in Torres Strait. We describe efforts to integrate a disparate set of data and to simulate reef-flat topography and photogrammetrically-derived reef-island morphology, and then compare the apparent dynamism of this island at geological and engineering time scales. These results are then compared with sediment deposition within lagoons, first in the context of a coastal lagoon, Lake Wollumboola in southern New South Wales, and second in relation to sedimentation in the reef and lagoon at Lord Howe Island. It is shown that the determination of the full range of boundary conditions, and the time constraints placed by dating, limit the effectiveness with which the coast can be simulated in existing multidimensional GIS.
Reef and reef-island geomorphology
One of the most widespread constraints on Coastal GIS is the problem of closure,
also termed planar enforcement (Raper, 2000). In the application of GIS to
coastal topography it is often the case that the seaward, or the landward,
extent of or boundary to the coastal zone remains poorly defined. In an effort
to circumvent this problem a discrete reef containing a single reef-island
on the top of that reef in Torres Strait was selected. Torres Strait is a
shallow shelf separating northern Queensland and Papua New Guinea; it contains
a complex network of reefs. The Warraber reef platform, about 5 km long, is
the central of three linear reefs and Warraber Island is a small sandy cay,
about 1 km across, on the leeward margin of the central elongated reef platform.
Although the reef flat is extensive, water drains from it almost entirely
at low tide, and floods across it again as the tide rises. Tides in Torres
Strait are complex as a result of a gradient between the Coral Sea and the
Gulf of Carpentaria; tidal range is around 3.5 m at springs and there are
rapid tidal currents around the reef. The reef is dominated by southeasterly
winds and waves generally approach from the southeast, although wave focusing
ensures that waves break on all sides of the platform. A seasonal reversal
of winds means that summer (December) winds are experienced from the northwest.
The Holocene evolution of the reef platform on which Warraber sits is known in reasonable detail as a result of several shallow cores and radiocarbon dating of in situ coral microatolls exposed at lowest tides across the reef-flat surface (Woodroffe et al., 2000). The central core of the platform comprises reef flat that is emergent at all but high tide; this formed under conditions of slightly higher sea level around 5000 years BP. Younger and lower reef surrounds this, and the platform appears to have built out in a series of increments during the mid-late Holocene.
The topography of reefs is often poorly known; they are generally inhospitable for survey vessels, so whereas the principal shipping lanes may be intensively surveyed, other areas of reefs are known in insufficient detail to fully reconstruct topography. The broad morphology of the reef platform on which Warraber Island sits was determined by combining bathymetric data from existing charts, a sequence of laser airborne depth sounder (LADS) swaths for the area to the southeast of the reef, and estimates of reef-front morphology from diver-transects undertaken by CSIRO during lobster surveys (Skewes et al., 1997). These water depth data sets were reduced to a vertical datum of Lowest Astronomical Tide (LAT) and combined with dumpy level transects of the reef flat undertaken as part of ecological studies (Figure 1a). Reef-flat morphology was interpolated using kriging, but simulations were reassessed on the basis of the field experience of the geomorphologists and ecologists to better model the non-surveyed areas.

Figure 1a
It is possible, combining these various data, to determine the gross morphology of the reef morphology, producing a useful visualisation of the reef platform. However, the surveyed transects are too sparse to reconstruct the 3D topography of the reef flat precisely enough for modelling of wave refraction, input into hydrodynamic models, or determination of volumes of carbonate accreted during reef growth. For instance, the variations in reef-flat elevation are too subtle to be effectively interpolated between the surveyed transects; some improvements to the digital terrain model have been made based on ecological factors but much of the reef flat was not visited nor surveyed in detail.
In contrast, however, the reef island has been mapped in sufficient detail to determine volumes of sediment. Reef islands, the small, largely unconsolidated, islands on the margins of reefs, are often unstable, undergoing erosion and deposition. They usually occupy a small proportion of the surface area of reef platforms but appear particularly susceptible to environmental factors that may alter as a result of global environmental change. Clearer understanding of the morphodynamics of these islands would be of significance to indigenous communities living on them. Reef islands are composed entirely of carbonate, comprising the biogenic skeletal remains of the various organisms that live on the reefs (corals, molluscs, coralline algae and foraminifera).
The surface topography of Warraber Island was determined by photogrammetry, based on colour vertical aerial photographs taken in 1998 at a scale of 1:4000. The island has conglomerate along much of its northern shoreline which appears relatively stable, and the island appears to have prograded southwards with deposition of successive beach ridges (Rasmussen and Hopley, 1996). Spot heights and breaklines were converted from CAD into a detailed TIN of the surface of the reef island. After correcting for man-made features, former island extents were determined from the topography using kriging with adjusted anisotropy to conform to the trend of the progradational beach ridges.
The upper surface of the island is relatively flat, but the detailed photogrammetrically-derived topography indicates that overall elevation has decreased through time. The beach toe is an abrupt change of slope where the sandy beach meets the near-horizontal reef-flat surface and its former location was determined assuming that beach slope had remained similar to present. The TIN provides a particularly appropriate data model to reconstruct the past surfaces of the reef island because the beach slope can be realistically modelled by polygons whose z values represent the elevation of the reef flat and the former beach-ridge crest Conversion from TIN to a grid of 5m x 5m was undertaken using quintic interpolation to produce a smooth surface closely representing the actual topography. The point data of the grid of the island surface was then generated for final TIN construction. A buffer of 2.5 m on both sides of the beach crest was created to use as the mask for calculating the difference of z value between the beach crest and the reef flat at the same position.
A TIN of island topography was constructed for each of a series of time periods determined on the basis of the successive beach ridges (see Figure 1b). The volume of the island was calculated as the volume between the island surface and the reef flat. Using 3D Analyst, the successive increases in sediment volume could be calculated, although no account was taken of any erosional losses that might have occurred along the northern part of the island.

Figure 1b
This assessment of geomorphological change over century-millennial time scales was contrasted with apparent changes at decadal time scales based on a comparison of contact prints of aerial photographs taken in 1966, 1974, 1981, 1987, and 1998 (note: only a poorer quality xerographic copy of that taken in 1966 was available). The aerial photographs were georeferenced to minimise distortion and subsequent measurement error and ground control points were selected in consultation with Schlencker Mapping who had undertaken photogrammetric mapping of the island. In this study, the position of the beach toe was clearly visible and represents the intersection of the beach with the reef-flat surface whose elevation is known accurately from the surveys.
Comparing the digitised beach toes it was clear that the only
significant changes had occurred on the northeastern and southwestern ends
of the island where a cuspate beach has developed with an ephemeral sand spit
(Figure 1c). The volume changes were determined based on the planimetric differences
between time periods, presuming no changes to the surface whose elevation
is known from the 1998 photogrammetric survey. In fact, averaged z values
were used (4.8 m for the southwest spit and 4.6 m for the northeast spit,
respectively), and volume changes were calculated using TINs of the sand spits
at each time period.

Figure 1c
Estimates of volume changes between the stages in the geomorphological evolution of the reef island during the Holocene are, of course, dependent upon the accuracy of the estimation of total island volume. The total volume of sand within the reef island was reasonably accurately estimated on the basis of the photogrammetrically determined topography. The greatest unknown is the lower boundary between the island and the solid reef flat. A surface has been generated using kriging, but there remains doubt whether or not the gradually sloping surface generated is realistic, or whether a near-horizontal surface representing an extension of the emergent, near-horizontal reef-flat platform that lies to the southeast of the island, would be more realistic. There was limited probing; the presence of a coral dated to around 5000 years BP in a drill core undertaken as part of groundwater investigations lends some support to the latter idea, that the island is underlain by a horizontal platform of elevation of around 2 m AHD. This poorly-known lower boundary surface was the major source of potential error in the volume calculation for the entire island, which has a volume of 2,600,000 m3. The uncertainty of the shape of the reef platform beneath the island gives an error to the volume of sand accreted and this accounts for around 7% of the volume in the initial stages of island formation, but reduces to as little as 0.1% in the most recent phases of accretion.
Beach-ridge depositional chronology was initially based on radiocarbon dating of bulk sediment samples collected from backhoe pits, and appeared to support initial island deposition around 3500 years BP and gradual build out southeastwards until around 2300 years BP since which time it was inferred that little if any additional material was added to the island (Woodroffe, 2002). Bulk dates integrate the age of all of the skeletal material contributing to the sand. The reliability of bulk dates under these circumstances was questionable, since a conventional date on a bulk sediment sample from the modern reef flat also yielded an age of around 2300 years BP.
The rates of sediment addition are particularly influenced by the accuracy of the dating technique. A radiocarbon age does not indicate the time of deposition, but the time of death of the living organisms which contributed skeletal material to the sand. Nevertheless as sediment appears to be moved towards the island by the unidirectional wave patterns, and as there is relatively little sediment on the reef flat (although sediment thicknesses are generally less than 10 cm, they do reach 25-30 cm in places), the ages may only slightly predate time of deposition. Recent AMS radiocarbon dating of individual sand grains, concentrating on specific components, reveals that the bulk dates are biased by inclusion of some material that was contemporaneous with the 5000-year old fossil reef that forms the substrate (see foraminiferal ages in Figure 1b). The emergent reef flat is not a prolific producer of sediment, but gastropods do graze the surface, and these appear to be the contributor to the bulk sediment that consistently yields the youngest age, and is most likely to approximate time of deposition. Reassessment of island chronology based on AMS dating of the molluscs within the sediments suggests that the island has in fact accumulated at a more-or-less constant rate over the past 3000 years. The presence of small berms of gastropod shells along the modern beach, the recognition that shell sand is a resource that can be used as aggregate by the indigenous community, and a modern age determined for a gastropod in the active sediment on the reef flat, reinforce the suggestion that the island is still accumulating sediment and that molluscs are a major contributor to that new sediment production.
At the engineering time scale, intermittent adjustments to the island can be detected by comparison of aerial photographs (Figure 1c). Georeferencing of the aerial photographs, using ground control points, indicates a root mean square error (RMSE) generally less than 3 m. The location of beachrock outcrops along the southeast, southwest, west, and north of the island, visible in all photographs, agrees very well between the registered shorelines, with estimate error of <1 m. Changes apparent over the period of around 30 years covered by the photographs suggest that the distal ends of the island appear to have moved in a clockwise direction. On the northeastern end, the volume has increased continuously with decreasing rates from approximately 1000 m3/year between 1966-1974 to about 100 m3/year between 1987-1998. A different pattern of volume change has occurred on the southwestern sand spit, where the volume of the spit appears relatively constant.
If the reef island had accreted uniformly over the past 3000 years (assuming that the shell dates approximate the time of deposition), it would imply an average accumulation rate of 800-900 m3/year. The trend of volume change of the northeastern sand spit is similar to this rate averaged over the geological time scale but with a slightly smaller magnitude, whereas the rate of erosion of the southwestern spit between 1966 and 1974 is poorly known because of the poor resolution of the 1966 photographs. Further detailed study of alterations in environmental factors, such as wave, wind, and current conditions, over each period may clarify these adjustments.
Initial radiocarbon dating of other reef islands indicated that those in the northern Great Barrier Reef had been initiated at least 4000 years ago, and implied that they had accumulated during distinct phases of accretion (McLean and Stoddart, 1978, Hopley, 1982), in contrast to the relatively constant addition of coral clasts to shingle ridges dated on Lady Elliot Island in the southern Great Barrier Reef (Chivas et al., 1986) and on Curacao spit in the Palm Islands (Hayne and Chappell, 2001). Our studies indicate that the volumes of sediment are known much more accurately than the rate of addition. In future studies, patterns of change at these time scales will be compared with gross estimates of sediment production on the reef to give further insights into the evolution of the reef island, and its likely response to changes in environmental factors.
Sedimentation in lagoons
There are advantages in Coastal GIS in attempting to determine the volume
of sediments in coastal systems that exhibit some degree of closure. In this
section, the prospect of determining sediment budgets for discrete lagoons
is examined. Two examples are considered, a coastal lagoon in southern NSW,
Lake Wollumboola, and a reef lagoon, that is enclosed within the reef on the
western margin of Lord Howe island, the southernmost reef in the Pacific region.
Lake Wollumboola is a small, irregular coastal lagoon in southern New South Wales. It has a surface area of around 9 km2 and is fed by a catchment of area 35 km2 (Figure 2a). The objective of this study was to compare the 3D volume of sediment accumulated in the lake with the estimate of sediment loss from the catchment, using a variant of the revised Universal Soil Loss Equation (Simms et al., 2002). The sediment in the lake is derived largely from two sources. Marine sands are worked into a tidal delta and sand barrier that cuts the lake off from the sea; the resulting mud basin is then infilled with fine sediments derived from the catchment.
A mass budget of sediment accumulation in the lake was determined using the 3D terrain modelling functionality of ArcGIS. The topographic expression of the sediment surface within Lake Wollumboola has been modelled on the basis of shoreline surveys, echo sounding surveys and bathymetric cross-sections. The depth of Holocene sediment in the lake was determined from several transects of probes into the lake floor to point-of-refusal, and geostatistical interpolation was used to reconstruct the pre-Holocene topography. Vibrocores within the lake confirmed that point-of-refusal corresponds to the Holocene/Pleistocene contact and radiocarbon dating on shells within the muds provides chronological constraint on sediment accumulation (Figure 2b). Deposition of sediment in the lake can be estimated if the surface bounding the upper sediment - and the surface below can be compared. Both were created as TIN datasets.
Radiocarbon dates indicate relatively constant vertical accretion over the past 9000 years, but a complication in terms of calculating mass balance is the uncertainty of the exact location of the interface between the mud basin (derived from catchment) and the marine facies (derived from seaward). This was addressed by estimating two surface extents based on preliminary probing. In either case the interface was interpolated as a sloping surface, and this seems unlikely to realistically represent the processes by which tidal deltas and mud basins interact.
Further uncertainties relate to the unconfined nature of the lake shoreline. Despite good survey control of the shape of the lake shoreline, this cannot be easily translated into sediment volume. Former shore platforms fringe truncated cliffs at several sites along the western margin of the lake and are inadequately mapped to presently allow incorporation into the sediment volume of the lake. In other studies, these boundary conditions have been addressed by assigning dummy values, but these are rarely backed up by justifications. A further area where data are sparse relates to the true form of the underlying Pleistocene sediment surface. Although encountered in vibrocores and interpreted as the point-of-refusal at base of probes, there appears to be considerable variability in the shape of this surface.
Vertical rate of sediment accumulation has been estimated on the basis of radiocarbon dates on shells of Notospisula trigonella, a bivalve that is widespread through the lake muds. A surprisingly uniform rate of vertical accretion is indicated by the dates available from 3 cores within the lake. The manipulation of TIN surfaces was consistent with that used by Houlding (1994). The primary TIN surface (points-of-refusal with maximum depth of 5.0 m AHD) was kept constant and each reference plane (level between which the volumes were computed) varied according to the stratigraphy and the levels at which radiocarbon dates were available. The surface area of the lake increased as it infilled as those peripheral areas over which there are thinner sediments became flooded. The uncertainty associated with the true definition of the tidal delta becomes a more significant component of the volume estimate as the lake infills. It accounts for little variation in the initial stages of lake infill because our probing does not indicate that the lake is particularly deep beneath the tidal delta, although it may be that probes did not reach bedrock or the firmer Pleistocene sediment that underlies Holocene sediments. Although the lack of data on the underlying surface is a problem, this does not have a large impact on estimates of the volume of accretion through much of the Holocene, because the surface area at these times can vary only over a small percentage of the total surface area (Hoselmann and Streif, 1999). It must be noted, however, that sedimentation does not include that which was deposited on the alluvial plains associated with two major creeks that drain into the lake.
Similar problems are associated with the determination of sedimentation
rate in the lagoon at Lord Howe Island. The closure problem is especially
intractable because the shape of the reef boundary to seaward is poorly known
and the true geographical nature of the landward boundary is uncertain because
the coastal sediments are continuous with lagoonal sediments and some component
of the foreshore and backshore should probably also be considered lagoonal
at time of deposition (Figure 3a).
Although Lord Howe Island provides some advantages,
such as the fact that reefs are close to limit of coral reef growth and are
not very extensive, the problems involve the lower surface - known imprecisely
through coring and seismic profiling and subject to further errors as a result
of the interpolation algorithm used (Figures 3b, c and d). Further boundary
problems arise associated with the margins of the lagoon. The reef crest is
poorly known, as also is the transition onto the island and the transition
into coastal sediments. Radiocarbon dating indicates a relatively good agreement
between adjacent cores at the northern end of the lagoon, but uncertainities
associated with extrapolating that to the southern end of the lagoon cannot
be resolved (Kennedy and Woodroffe, 2000).
Discussion and Conclusions
GIS provides some advantages for the 3D simulation of coastal landform development
over different time scales. Whereas it has traditionally been used to determine
areal changes as a result of sedimentation and erosion, this study has explored
its use in 3D. In the case of the reef platform on which Warraber Island sits,
the details of the z value are generally not known with sufficient precision
to effectively reconstruct the platform with an accuracy sufficient to perform
modelling analyses. However, where the z value can be determined with sufficient
accuracy, as has been possible over Warraber Island itself, 3D topography,
and consequently sediment volumes, can be reconstructed. An advantage of using
3D is that topographic change can be depicted and perceived visually. However,
there remain boundary conditions which are difficult to resolve. Lower surfaces
must be interpolated and rarely is there sufficient data to differentiate
between competing hypotheses as to the real lower surface topography. On the
one hand, these may be relatively small in the overall budget calculation,
and perhaps more significantly, as in the case of Lake Wollumboola they may
effect only the earliest time period, early Holocene. Problems in the Lake
Wollumboola study include how accurately we know the lower surface; how effectively
we can determine details of sediment mapping around the shoreline and up the
alluvial valleys, and the uncertain transition from lake mud to marine sand
in the tidal delta.
Even if the total sediment volume can be estimated within relatively precise margins, radiocarbon dating remains a source of error, and limits the precision with which time periods can be discriminated, and the accuracy of dating must be assessed. The relatively good chronologies available in each of these cases offers scope for generating and testing hypotheses. For instance, it is possible to assess whether the reef island has accumulated more or less constantly or in discrete episodes, and whether recent patterns of change are occurring at similar rates to longer term geomorphological evolution. Dating provides a constraint on the possible interpretations; this is particularly effectively demonstrated in the case of the reef island sediments where the contamination through inclusion of older reworked material is clearly apparent.
Rates of accumulation of sediment can be calculated over the geological time scale if the ages can be translated into time of deposition. Estimates of periods or phases of deposition are affected by the outline of the shoreline identified at each time period. While much work remains to be done, there is, nevertheless, already potential to test hypotheses about whether accumulation rates have been more-or-less constant or have changed markedly.
It needs to be noted that the horizontal resolution, often based on grid cells of 5 x 5 m or similar is much less precise than the vertical resolution, where extremely precise z co-ordinates can be used. However, this contrasts markedly with the accuracy with which it is possible to determine the vertical component; depths are subject to the problems of compaction of cores, and variations in velocity of seismic waves by which seismic reflection profiling is interpreted. By far the largest errors remain, however, with the determination of the time dimension. The problems associated with radiocarbon dating have been amply demonstrated by the study of reef islands; even at the engineering time scale, it becomes unclear whether the shoreline has changed uniformly between aerial photograph snapshots, or whether these are just arbitrary points in time on a more complex trajectory of change.
Acknowledgements
Research in Torres Strait and Lord Howe Island was funded by the Australian
Research Council. Studies of Lake Wollumboola have been supported by Shoalhaven
City Council and the Department of Land and Water Conservation.
References