# The implications of oceanographic chaos for coastal management.

Eric Wolanski1, Brian King1 and Simon Spagnol1

1

Australian Institute of Marine Science, PMB No. 3, Townsville M.C. Qld. 4810, Australia

### Abstract

Classical oceanography advocates a concept of continuous spatial and temporal distributions in physical, biological and chemical properties. Thus, when dealing with human environmental impacts, the classical management approach is to superimpose upon a continuous natural distribution the likely mean changes due to man, thereby defining the impacted zone.

On the basis of field data and analysis with mathematical models of coastal processes, it would seem that chaotic distributions of current fields prevail in topographically complex environments. As a result distributions of physical, chemical and biological properties, natural and anthropogenic, also demonstrate chaotic, patchy or random structures. It becomes meaningless to discuss mean distributions.

Risk assessment modeling, which measures variability using stochastic techniques, may be an appropriate methodology to better assess environmental impacts of coastal developments along a rugged coast. Chaos needs to be incorporated in environmental impact studies in the coastal environment in order to arrive at meaningful predictions especially if they extend to biological processes. Chaos also needs to be considered when collecting field data.

### Graphics

The graphics on the CD can be accessed using a web browser such as Netscape Navigator or Microsoft's Internet Explorer. To start open the file 'index.htm' on the CD-ROM. All animations on the CD are stored in AVI format using Cinepak compression. If your browser has trouble viewing these animations visit the homepage (http://home.netscape.com or http://www.microsoft.com) to download the appropriate plugin.

### Introduction

Water currents are usually the first thing measured in environmental impact assessment studies in the ocean. To predict the impact of a pollutant discharge the speed and direction of the currents are used in a model to calculate the trajectory of contaminants. To characterise a non-conservative material carried by the water currents, the usual practice is to incorporate in the model sink and source terms. In the model turbulence is usually parameterised, often using an eddy diffusion approach, or explicitly calculated using a turbulence closure assumption. This modelling technique is successful in reproducing simple ecological and biogeochemical processes in the open ocean (e.g. Nihoul, 1993 and references therein).

This technique is also routinely applied in the coastal engineering community to determine environmental impacts from human activities such as structures, dredging and dumping of contaminants (eg oil, sewage and dredge spoil). Usually the predicted contaminant plumes are smooth. These plumes are then superimposed on an atlas of marine resources to determine likely environmental impacts.

In practice, post-construction verification of models is the exception rather than the rule. Thus, if the structure works within expectations in an engineering way, i.e. the wave field is within predicted range, then the environmental impact from engineering structures is also assumed to have been predicted correctly.

Wave models, the principal tool of coastal engineers, have nothing to do with models related to environmental issues. Ecosystem or pollution models are seldom verified. Sewage plumes are an example. Discharges from sewage outfalls are predicted to be continuous, smoothly varying pollutant plumes. In practice however, these plumes are extremely patchy (Wu et al., 1994; Pritchard et al., 1996). This patchiness applies to other contaminants also. For instance, oil slicks commonly break up into patches that the models do not reproduce (Dean et al., 1990). This patchiness has important implications for a coastal manager because an oil spill at sea along a rugged coast can oil one beach while the adjoining one remains untouched (Hayes et al, 1990).

At the ecosystem level patches are known to exist at all scales in all environments, and patches have been recognised as important natural processes (Engbert and Drepper, 1994; Hamner, 1988; Hassel et al., 1991; Pickett and White, 1985; Steele, 1978). Surprisingly, this knowledge has largely been ignored in environmental engineering models for coastal management.

Our study sites are topographically complex coastal environments. They include estuaries (Fig. 1), islands and coral reefs (Fig. 2) and mangroves (Fig. 3). We demonstrate that patches are the common rule and not the exception. We argue that engineers, scientists and marine resources managers need to take this process into account. Specifically they must learn to deal with variability and unpredictability and not with static or quasi-steady, rigid models. When dealing with particularly sensitive areas, more caution is needed to deal with the unpredictability of the system.

### Water currents

Eddies behind islands and headlands are commonly observed in coastal waters (Fig. 4; see also Wolanski, 1994). They generate patchiness and variability along the coast, but this process has remained largely unstudied. Oceanographers have largely ignored them, as recently as 1983 Robinson’s book on eddies in marine science does not even mention them.

Water currents are usually one of the primary parameters measured in the field, this is best done from oceanographic moorings with current meters suspended under a subsurface buoy on a taut wire or, in shallow waters, within a frame (Anim.1). In topographically complex systems, such as around a headland or an island, eddies are a common feature (Fig. 4). Many current meters are needed to characterise the flow field. For instance 26 current meters were necessary (Wolanski, 1994) to measure the eddy behind Rattray Island, a 1500 m wide island in 20-30 m depth of water (Anim 2.). All 26 current meters were needed because currents in the eddy region varied rapidly, both temporally and spatially (Anim 3.). If only a few current meters had been used, as is common practice in most environmental impact assessment studies, an unrealistically simple (and incorrect) picture of the flow field would have emerged. The flow field at Rattray Island develops an eddy, a patch of water which varies in size throughout the tidal cycle; with currents inside the eddy lagging that of the undisturbed tidal current outside the eddy (Anim 3.). Other measuring techniques are possible, e.g. the use of an acoustic Doppler current profiler mounted on a ship crisscrossing the area (Geyer and Signell, 1990; Signell and Geyer, 1991). This improves spatial resolution but diminishes temporal resolution.

It was only after the Rattray Island data set became available that it was possible to test if 3-D models were able to reproduce complex coastal flows and to compare the performance of the models against the observations from the 26 current meters (Galloway et al., 1996). The only other comparison between 3-D models in the literature was the MOMP numerical experiment for which no field data were available (Roed et al., 1995). Four models compared by Galloway et al. (1996) were NOAA’s Mecca model, the Princeton ocean model POM, the Hamburg oceanography model HAMSOM, and the AIMS-GHER model. Initially none of the models performed satisfactorily because they all under-estimated by 30 to 90% the size and strength of the observed eddy (Galloway et al., 1996). For reliable predictions it was necessary to introduce other processes previously not incorporated in these models, such as the high turbulence in the free shear layer shed at the flow separation points (Wolanski et al., 1996). The final simulation, shown in Anim 4., reproduces within 80% the size and intensity of the observed eddy.

The Rattray Island study demonstrates that the flow behind a single island leads to patchiness at horizontal scales varying in time. There is no unique length scale of the island wake because it is continuously changing. Over a few tidal cycles the processes are even more complex. Indeed, models predict that small eddies merge into large eddies and that these large eddies can recirculate back and forth around the island and merge in a process apparently akin to that of strange attractors (see Anim 5.) that results from the model of Furukawa and Wolanski, 1998). This leads to a chaotic distribution of vorticity.

Topographically generated patchiness in the flow field does not require that the obstacle emerges from the water, it also forms in a system of shoals and channels such as the Dutch Wadden Sea (Riddenrikhof, 1995). In its simple form this circulation consists of periodic tidal currents superimposed on a lattice of residual eddies the size of the chaotic region. This simple representation, valid for the Dutch Wadden Sea, breaks down when widespread chaotic advection occurs, which happens when the bathymetry varies significantly within a tidal excursion length (typically a few km). This occurs commonly throughout the Great Barrier Reef as well as in many rugged coastlines with headlands and islands. For such rugged systems the flows are fully chaotic. This is shown in Anim 6., generated from the model of King and Wolanski (1996) for the tide- and wind-driven flows through the Great Barrier Reef. The flow field resembles an ever-changing mosaic of eddies, jets and stagnation zones. Model verification is only possible in open waters far from obstacles, where the flows vary smoothly. In the presence of topographic complexity it is not realistic to ensemble-average to obtain mean currents or mean flushing rates for large areas; every area has its own dynamics.

Chaotic circulation leads to patchiness in the distribution of passive tracers. Shown in Anim 7. is the result of two plume releases, one in the open water and the other one in the reef matrix. It can be seen that the open water plume remains coherent and that its width increases in time as mixing progresses in all directions. This behaviour is to be expected from mixing models based on a fairly uniform flow field (Fischer et al., 1979). However the reef matrix plume rapidly becomes chaotic.

To cope with this patchiness, the classical engineering technique would be to use ensemble-averaging. This would be counterproductive for the users of such models, e.g. biologists, because chaotic water circulation drives the chaotic distribution of the biology. Indeed, Hamner and Hauri (1977) noted that water in an headland eddy over a coral reef contained a different population of zooplankton than did the free stream water flowing over a sandy bottom. In a process sketched in Anim.5, the eddy was ejected back into the free stream when the tides reversed and became a patch of reef water rich in zooplankton surrounded by plankton-poor shelf waters. The patch retained its reef zooplankton for as long as it was tracked it (a few hours). When many reefs are present, such as on the Great Barrier Reef and near a rugged coastline, the coastal sea becomes a mosaic of patches. This chaos is apparent in biological properties (e.g., chlorophyll) measured from ships and satellite (Wolanski, 1994).

Ensemble-averaging this chaos to produce simple statistics such as a mean value and a standard deviation for various parameters (e.g. nutrients and chlorophyll) is not useful because each patch has its own ecosystem dynamics (Hassel et al., 1991; McCook, 1994).

Ensemble-averaging is also questionable even in much simpler systems, such as a branched estuary. A case in point is the Fly River estuary in Papua New Guinea (Fig. 1). The estuary is about 60 km long, is shallow (typically only a few meters deep at low tide) and has three major channels. The dominant forcing is the tide, the freshwater inflow and the wind (Wolanski et al., 1997b). Current data of 2 – 8 week’s duration at ten sites were available to verify the model. The model explained at least 90% of the variance at the mooring sites (King and Wolanski, 1996a), so it can be used to explore the dynamics of the system. The flow field is very complex and its understanding requires computer visualisation (Anim 8.). This animation illustrates clearly the tides propagating from the sea to be dissipated over the shallow bottom. It shows the tides propagating at different speeds and with a different flood-ebb tide asymmetry in each channel. In each channel there are strong lateral and along-channel variations, with zones of extremely strong flushing next to zones of much weaker currents leading to stagnation zones. The currents are strongly steered by the topography of channels meandering through shoals. At the apex of the delta where the three channels meet, each channel injects momentum and vorticity at different times in the tidal cycle and at different locations. The resulting currents in this area are chaotic with horizontal quasi-turbulent motions at the scale of the channel width.

### Suspended sediment and plankton

Visual observations in the muddy coastal zone (Fig. 5) show the presence of patches of turbid waters in blue waters. These patches can be a few meters to a few hundreds of meters in diameter, with no clear pattern of distribution. To quantify the dynamics of the fine sediments, there are a number of field techniques that rely on deploying automated sediment samplers in an oceanographic mooring or on ship-born measurements.

Because of the high costs of automated samplers, an oceanographer can seldom deploy more than a few samplers at sea, usually obtaining temporal but not spatial data. Automated samplers are usually very bulky and necessitate large ships for most deployment and recovery (Anim. 9). Even 40 km offshore from the mouth of Fly River in Papua New Guinea, in shelf water deep enough that resuspension of bottom sediment does not occur, suspended sediment distribution is extremely patchy. This can be seen from the factor of 10 difference between daily catches of sediment (Fig. 6 ).

Suspended sediment concentration can also be measured using optical sensors such as nephelometers and transmissometers, though marine fouling can limit their use. Used in turbid topographically complex estuaries, these instruments also record enormous temporal and spatial variability (Wolanski et al. ,1998). As a result of this variability even 24 nephelometers as they used may have been insufficient to measure the net flux of sediment at the mouth of the Fly River.

In very muddy coastal environments a convenient ship-borne sampler is a high-frequency echo-sounder. The data show enormous patchiness, with fluid mud entrained in suspension in patches at scales of centimetres to meters in an apparent chaotic manner (Fig. 7).

Another shipboard technique is direct observation of suspended sediment and the plankton in suspension, using an underwater video camera equipped with a macro-lens (Fig. 8). This technique is the preferred option because it minimises disturbances to the suspended matter (Eisma et al., 1990). However it has limitations because of four reasons. First, it necessitates a lot of power to illuminate the field of view, and this requires an electric cable to the main research vessel or a small boat (Fig. 9). Secondly, in rough weather waves introduce rapid and violent instrument motions that blur the images. Third, it is impractical in very turbid systems (usually the cut-off point is about 100-200 mg/l) when the concentration is so high that excessive floc overlap occurs on the images. Finally, strong currents cause floc breakage around the camera housing’s optical port. In these environments an alternative sampling technique for suspended sediment is to sample the water using a wide Niskin bottle with no rubber cord inside the tube. This minimises floc breakup. The suspended matter settles onto a microscope slide with a well (Anim. 10). Using an externally operated piston, the well slide is then capped with another slide without disturbing the sample, which can then be examined with an inverted microscope.

All these techniques reveal an enormous amount of patchiness at all scales. Duplicate casts can yield widely different estimates of sediment concentration.

In clear waters, without mud, nonmotile and asexual zooplankton commonly occur in patches up to 20 cm wide and most oceanic plankton in patches up to 5 m wide (Davis et al., 1992). Patchiness in this case is generated by the plankton aggregating by swimming. In muddy waters the instruments reveal that the marine snow is sticky and traps small flocs of suspended sediment to generate microaggregates typically 500-2000 m m in diameter (see examples in Fig. 10, Fig. 11 and Fig. 12 ). These microaggregates have settling speeds 10-100 times faster than those of the original small mud flocs. This settlement process constitutes a biological filter at the mouth of turbid tropical estuaries that trap the sediment in patches in the coastal zone (Ayukai and Wolanski, 1997).

There is a dynamic feedback in these patches between the physics and the biology. Previously the common belief was that the main effect of mud was to decrease light and hence primary production. It was also thought that that bacterial activity was extensive on mud (Alongi, 1998). Mud obviously affects both light and bacterial activity, but our observations reveal that plankton are also strongly affected. Frequently we found plankton grazing on the surface of the flocs (Anim. 11). At other times we found plankton actually being killed by the flocs. For instance, plankton can become glued by a string to a floc and cannot escape even after swimming madly in circles around the floc, like a dog on a leash (Anim. 12). Plankton can also become trapped in a floc by its hooks and be unable to escape (Anim. 13). Plankton can also become buried in a stringy mud floc and trapped like a fly in a spider web (Anim. 14). Because of this apparent direct interaction between plankton and mud, one suspects that patchiness in mud distribution would introduce patchiness in the plankton distribution, which in turn would introduce patchiness into the entire food chain. This requires further investigation.

### Turbidity and seagrass

Mangrove-fringed Hinchinbrook Channel in tropical Australia (Fig.13) is shallow, with a series of sand banks, a muddy coast and a number of natural channels several meters deep (Anim. 15). Strong tidal currents prevail. At spring tides the waters inundate the fringing mangroves near high tide. The currents vary smoothly spatially and temporally (Anim. 16), calculated from the model of Wolanski et al. (1990). The complex topography and the location of distinct sand patches and mud patches result in suspended sediment distribution that is also highly patchy temporally and spatially (Anim. 17). Further patchiness is introduced by the wind because some areas are sheltered by sand banks while other areas are exposed to wind and waves (Anim. 18). In turn this patchiness is reflected in a patchy distribution of sedimentation zones in the fringing mangroves. Presumably this patchy suspended sediment concentration is reflected in patchiness of the plankton abundant in this channel. Seagrass forms rich meadows along the shallow mangrove-fringed coast and somehow they survive repeated events of high turbidity and sedimentation (Wolanski et al., 1997c). If high concentrations of suspended sediment concentration (1,000-5,000 ppm) were prolonged, the meadows would not survive (Onuf, 1994; Schoellhamer, 1996). The response of seagrass to chaotic events of high sedimentation and turbidity is unknown.

### Coral, fish and prawn larvae

On the Great Barrier Reef most hard corals spawn once a year in a synchronised event called mass spawning. Mass spawning can release millions of eggs that float around a single reef, such as Bowden Reef on the Great Barrier Reef (Fig.14). Yet as this cloud of eggs is advected and mixed by the currents, the egg plume is extremely patchy (Anim. 19), with no apparent correlation spatially (from site to site) or temporally (at a given site from daily samples). The distribution is chaotic, with the standard deviation from the triplicate samples having the same magnitude as the mean at a given site. In such cases the mean values are probably meaningless. Patchiness develops quickly after the release of eggs into the water (Fig.15). These patches usually take the form of slicks a few meters in width and several hundreds of meters to a few kilometres in length (Wolanski and Hamner, 1988). Clearly the distribution the concentration of eggs is chaotic.

The distribution of coral fish larvae is also patchy. At Bowden Reef, for example, fish larvae occur in patches for a few days. Patches of weakly motile larvae are located generally downstream of the reef (Anim. 20) and patches of highly mobile fish upstream of the reef (Anim. 21) (Wolanski et al., 1997a). There is thus no smooth distribution.

The distribution of prawn larvae in shallow, mangrove-fringed waters is also patchy and highly variable from species to species. This is shown in Anim. 22 for the case of Klang Strait on the west coast of Malaysia. No spatial or temporal correlation exists.

Scientists cope with such spatial and temporal patchiness by calculating the mean over triplicate samples and the ensemble-average of the data (e.g. Oliver et al., 1992 for coral eggs and Chong et al., 1996 for prawn larvae). With this technique the only parameter retained to characterise patchiness is the standard deviation. However, in these chaotic flows the standard deviation has a magnitude comparable to the mean (e.g. Anim. 19). This makes the mean and standard deviations meaningless. These parameters indicate only that there are either plenty of larvae or there are none; no useful statistics remain.

It is only recently that modellers have tried to understand this patchiness at a scale of tens to hundreds of meters (Wolanski and Sarsenski, 1997). The verification of these models is extremely difficult because the biological data are collected at different times at different sites in a tidal cycle; hence a synoptic picture of the distribution in the field is unavailable. For the case of coral eggs spawned at Bowden Reef, the model predicts the formation of a plume entraining eggs away from the reef (Oliver et al., 1992). As can be seen in Anim. 23, the predicted plume is extremely patchy, if not chaotic. Model verification was carried out by comparing, at a given instant of time, observed and predicted concentrations. In some cases, such as in Fig.16, where biological data were available simultaneously at different points (the exception rather than the rule because it requires several small boats operating simultaneously), the comparison is pleasing. However, when all the data over several days and at about twenty sites are used, no significant correlation is found between observed mean concentrations (calculated from triplicate samples) and the instantaneous predicted concentrations (Oliver et al, 1992). It is not clear if this model failure is due to the model underestimating the patchiness due to sub-grid scale aggregating processes (Wolanski and Hamner, 1988) or to the patchiness being so large that triplicate samples are not enough to reliably estimate the mean values.

For prawn larvae, modellers did not attempt to reproduce patchiness. They focused instead on the process of recruitment into the mangroves. The adult prawns spawn at sea and the larvae find a refuge in mangroves where they mature. The modellers used the observed prawn larvae concentrations at sea to seed advection-diffusion models and predicted the fate of the larvae over the subsequent two weeks (Anim. 24). The distribution is chaotic. The only available information to verify the models was the relative distribution of prawns in the mangroves, and comparison with predictions was favourable.

For coral fish larvae, the field data suggest that the bulk of the recruits immigrate from reefs further upstream (Wolanski et al., 1997a). Advection-diffusion models of the fate of a cloud of larvae carried passively by the prevailing currents and coming into contact with a reef are unable to reproduce the patchiness (Anim. 25). Indeed, the model predicts that most of the larvae are simply deflected around the reef and do not aggregate. This prediction is contrary to the observations shown in Anims 20 and 21. However, if larval swimming behaviour is included in the model, the model predicts the formation of patches in agreement with the observations (Anim. 26). Because the larval fish patches are not static but move around the reef, the distribution is chaotic.

The longevity and size of these patches depend on larval swimming speed. The predicted location of recruitment zones agrees with observations if the larvae swim at about 0.05 m s-1 (aggregation is downstream) to 0.15 m s-1 (aggregation is upstream). These swimming speeds are realistic, based on visual observations (Leis et al., 1996). The predictions are also sensitive to the distance to the reef that fish larvae are "aware" of the reef and swim toward it. Direct observations suggest this distance is at least 1 km (Leis et al., 1996). In the model a distance of 2-3 km gave the best match of the predictions to the observations.

Chaos is also observed in the horizontal distribution of sprat larvae even in a much simpler topography, e.g. the German Bight (Bartsch and Knust, 1994). Their attempt to model this was unsuccessful, maybe because the larvae were assumed not to swim horizontally.

### Water quality

Typically water quality may involve nutrients and faecal coliforms from sewage discharges and heavy metals from mining and industries. In tropical waters nutrients are rapidly consumed and predictions of the directly impacted zone can be limited to the first few days of residence after discharge. Over longer periods the impact is on benthic communities. Distinguishing natural from pollution-related environmental changes in the benthos is very difficult (Boesch et al., 1990), yet this is a key to coastal management because of the confounding effects of natural and pollution variability (Ferraro et al., 1991).

Nevertheless, the first impact to be studied is the spatial extent of the water-borne pollutant plume. Simple analytical plume models (e.g. Fischer et al., 1979) are elegant but unrealistic along a rugged coastline. A typical example is Malakal harbour, Palau (Fig.17). It has a deep water harbour surrounded by shallow waters and a coral reef to the east. The currents were studied by Hamner et al. (1997). They are primarily tidal and are complex because channelled by the topography (Anim. 27). As a result the impacted zone from a sewage discharge varies enormously with small changes (100 m only) in the discharge point. For instance (Anim. 28), if the discharge is located just offshore of a small headland, as is actually the situation in the harbour, the plume spreads over much of the outer harbour and the southern shipping channel while the inner harbour remains relatively uncontaminated. The sewage plume is patchy and intermittent over the coral reef and since it is 2 days old by the time it reaches the reef its impact on the coral reef is thus likely to be small (Hamner et al., 1997). If the discharge occurred just inside the headland (Anim. 29), the inner harbour and the northern shipping channel would be contaminated. In both cases the plume breaks up in patches in the outer harbour. Occasional water quality sampling at a few scattered points in the harbour without synchronising the sampling with the expected location of the plume as a function of the tide, as is the usual practice, is clearly meaningless.

In turbid estuaries mud is a major sink for pollutants such as heavy metals. Predictions of the fate of these pollutants necessitate understanding not only the dynamics of water and fine sediment but also the chemistry of the heavy metals in the estuary (Salomons and Forstner, 1984). In particular, different forms of particulate metals may exist and the metals may be exchanged between the particulate and the diffused states and between different forms of particulate states (Fig.18). These reaction rates are a priori unknown but may be derived from laboratory experiments. The results are generally very difficult to interpret because several parameters are important, including salinity, suspended sediment concentration, pH, POC and DOC. Nevertheless, for practical applications it may be necessary to simplify these relations to incorporate only the dominant parameters. For instance, a decay model could be used to parameterise the transformation of releasable metal into exchangeable metal, and a Kd model could be used for the reaction between particulate and dissolved metals. The estuarine mobile mud can be assumed to be ultimately saturated with metal at steady state. With all these simplifying assumptions the resulting distribution of predicted dissolved (Anim. 30) and particulate (Anim. 31) metals can be predicted. Further modelling shows that the zones of maximum concentrations vary continuously with varying tidal amplitudes and with the wind. The size of the impacted zones, the maximum concentration, and the duration of these high concentration events are predicted to be highly variable temporally and spatially. A mean and a standard deviation at target points are insufficient to characterise the impact because essentially the situation is chaotic.

### River Plumes

River plumes are often very patchy, especially when the coast is rugged and the freshwater discharge unsteady. An example is the Burdekin River, Queensland, Australia. The plume is extremely patchy (Fig.19). Oceanographers are able to successfully model this plume (King et al., 1998). The results, shown in Anim. 32, show the plume forming as the river discharge increases. It turns left at the mouth, a result of the Coriolis force, and flows northward along a rugged coast around numerous headlands and islands. The model suggests that the patches are due to the unsteadiness of the wind and to the freshwater discharge, and to the complex currents at the headlands. The patchiness in the salinity field was also enhanced by discharges from neighbouring rivers and by tidal interactions with headlands along the coast. The model underestimates by a factor of about 2 the observed patchiness at the reef (Wolanski, 1994), patchiness in this case being the amplitude of the salinity variability at times scales of 2-5 days.

The main influences on the size of the river plume, and thus on which reefs are impacted, are the discharge volume of the river and the local wind forcing. These vary annually, so one would expect different reefs to be impacted differently each year. Given that the fate of the plume is highly variable and patchy, a risk assessment analysis from a hindcast of the floods for the last couple of decades is needed to quantify the impact of river floods on the Great Barrier Reef. This is achieved by simulating many years of floods and by quantifying the recurrence and duration of freshwater impact on given reefs.

This modelling capability provides a tool to assess physical impacts to reefs from riverine material (e.g. fine sediment and nutrients) produced as a result of various land management policies in the catchment area. Although the physical impact is chaotic, it can be quantified statistically although the model underestimates the patchiness. The resulting ecological impact probably cannot be predicted yet. Research on the biological response of reefs to such transient forcing clearly is warranted because riverine material affects the biology of coastal waters and its quality and quantity are both greatly affected by human land use.

### Discussions

Topographically complex environments include rugged coastlines comprising headlands and islands, coral reefs and mangrove-fringed coastal waters. While our examples refer to tropical environments, the conclusions probably apply also to temperate systems with a rugged coast with headlands, shoals and salt marshes. Such environments are common in the world, yet they have been little studied compared to topographically simple systems such as the North Sea, where there are continental shelves with comparatively straight coastlines. Physical, biological and chemical data from those areas with complex topography reveal extremely complex, if not chaotic, distributions. Standard measurements in biology and chemistry, e.g. triplicate samples at a number of sites, are meaningless, as we have shown for the case of coral eggs and fine sediment concentration.

How then to use the scientific information from field data and computer models to help coastal management? This question remains unresolved. However engineering experience in dealing with oil spill predictions provides a clue to a likely new approach. In such man-made crises modellers use a wide range of current predictions for different scenarios of winds and tides to calculate the probability of an impact and the severity of an impact should one occur. An example of risk assessment modeling using chaotic inputs to the model is shown in figure 20. This shows the predicted region ‘at risk’ from an oil spill in Surat Thani harbour in the Gulf of Thailand, when strong and dominant winds from the southwest are blowing. Under these conditions, it is suggested that about 150 km of coastline are at some risk of impact. The most probable fate of an oil spill under these conditions is shown in black which will see the oil slick at sea for many days allowing time for weathering and dilution of the oil. These data are then superimposed on a map of coastal resources, such as ports, seagrass, mangroves, beaches and rocky shores, to predict probabilities of environmental impacts at various locations along the coast. Managers can use this information to develop a statistically-driven strategy to cope with an oil spill. The situation is relatively simple because the original environment essentially has zero background oil.

A similar strategy could be applied to faecal coliforms from sewage discharges because they are naturally absent from the environment.

It is much more difficult to predict environmental impacts in a complex topography from other human activities such as dredging, structure engineering, spoil dumping and nutrient discharges. One reason for this is that, contrary to purely anthropogenic wastes such as oil, a topographically complex environment naturally exhibits high variability in parameters that man can influence, such as currents, suspended sediment, nutrients and metals. At our study sites chaos or random environmental fluctuations dominate the system and this variability is under-estimated by numerical models. The status of modelling environmental impacts in a complex topography is insufficient to reliably predict the response of a naturally chaotic environment to additional disturbances from man.

The risk assessment approach is promising. So far it has mainly been applied to quantify physical effects from waste discharges from man. Present marine eutrophication models (eg Gray, 1996) and deterministic management models that are derived from them (eg Done et al., 1997), neglect the oceanographic and biological chaos and may generate misleading answers. Indeed, ecological processes are known (eg McCook, 1994) to be influenced by a very large number of factors, both physical (eg oceanography and climate) and biological (eg recruitment and interaction between species or species assemblages). Many of these processes vary chaotically, so that ecological outcomes may be largely unique to a particular set of circumstances (eg Underwood and Denley, 1984; Foster, 1990; McCook and Chapman, 1997). This in turn means that prediction of a biological impact is intrinsically uncertain, aside from any difficulties with detection rationales.

This does not mean that modelling is not useful. It is helpful because it can predict the concentration of substances (e.g. mud, metals, nutrients and larvae) under various scenarios, though it under-predicts the patchiness. These predictions, particularly if they extend to biological processes, may not be helpful to management if they do not successfully incorporate also natural patterns of variability. Because the biological response is often the key criterion in environment impact studies, modelling is usually seen as having failed management. Solving this problem is not trivial because attempts to incorporate chaos and patchiness in ecosystem models are still very much at the research stage (eg Hassel et al., 1991; Engbert and Drepper, 1994; McCook, 1994).

More often than not, the natural variability appears chaotic to environmental engineers, they usually characterise it by computing means and standard deviations. Simplifying the system by these simple statistics destroys any chance to characterise topographically complex coastlines and lead to unreliable predictions for important applications. Practical such cases include responses of seagrass and corals to short-term events of high turbidity, both natural and anthropogenic. Other cases include algae in coastal waters responding to pulses of nutrients, both natural and anthropogenic. Other practical applications include changes in recruitment patterns for fish and crustaceans in the presence of engineering structures and dredged channels. There has been no attempt yet to quantify how a marine ecosystem already subjected to chaotic forcings will respond to an increase or a variation in this forcing from anthropogenic effects, present state-of-the-art practice (eg, Gray, 1996) largely ignores the natural chaos. For environmental impact modelling to reach the desks of coastal resources managers as practical tools in the decision-making process, these pitfalls need to be addressed as a matter of priority.

### Conclusions

Chaos is largely ignored in environmental impact studies in the coastal environment, this may lead to meaningless predictions especially if the predictions extend to biological processes. Also, chaos needs to be better taken into account when collecting field data. In particular in most environmental impact assessment studies for coastal developments, only the mean and standard deviation of a number of parameters are measured occasionally at a few points. Our studies demonstrate that in a topographically complex coastal environment much more data are required in view of the chaos in the flow, chemical and biological distributions.

### Acknowledgments

This study results from 19 years of field work and modelling in the Great Barrier Reef of Australia. This research was supported by the Australian Institute of Marine Science, the IBM International Foundation, CRC-Reef Research, Ok Tedi Mining Limited, Kansai Electric Power Co., Japan’s Port and Harbour Research Institute and others. Special thanks are due to Takeshi Asaeda, Tenshi Ayukai, Joe Baker, Danny Brooks, Ving Chin Chong, Robert Cusumano, John Bunt, Eric Deleersnijder, Peter Doherty, Murray Eagle, Keita Furukawa, Duncan Galloway, Bill Hamner, Keita Furukawa, Ian Gardner, Eng Bin Lim, Ray McAllister, Laurence McCook, Jamie Oliver, Russell Reichelt, Joe Sarsenski, Kris Summerhayes and Ian Wood.

### References

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