Predicting characteristics of dune bedforms using PSO-LSSVM

Dunes have a large influence on hydraulic roughness, and, thereby, on water levels which could affect the navigability of rivers and performance of hydraulic structures. The present study investigated the variation of geometric and topographic characteristics of dune bedforms and flow features as measured in laboratory studies(data sets from laboratory experiments) to estimate the roughness coefficient and characteristics of dune height. The Least Squares Support Vector Machine(LSSVM), which was optimized using Particle Swarm Optimization(PSO), was used as the Meta model approach to predict the values of interest. Developed models were separated into three categories: modeling using flow characteristics,modeling of flow and bedform characteristics, and modeling by using flow and sediment characteristics.It was found that for estimation of the roughness coefficient in open channels with dune bedforms,models developed based on flow and sediment characteristics performed more successfully. The model with input parameters of flow and grain Reynolds numbers(Re and R_b, respectively) and the ratio of the hydraulic radius(R) to the median grain diameter(D_(50)) yields a squared correlation coefficient(R2) of0.8609, a coefficient of determination(DC) of 0.7361,and a root mean square error(RMSE) of 0.0034 for a test series of Manning's roughness coefficient which was the most accurate model. Results proved the key role of flow Reynolds number(Re) values as an input feature for all models predicting the roughness coefficient. Accordingly, classic approaches led to poor results in comparison. On the other hand, results obtained for estimated values of relative dune height led to moderate prediction quality, which albeit,outperformed classic approaches.     

The effect of asymmetric dune roughness on tidal asymmetry in the Weser estuary

The bed of estuaries is often characterized by ripples and dunes of varying size. Whereas smaller bedforms adapt their morphological shape to the oscillating tidal currents, large compound dunes (here: asymmetric tidal dunes) remain stable for periods longer than a tidal cycle. Bedforms constitute a form roughness, that is, hydraulic flow resistance, which has a large-scale effect on tidal asymmetry and, hence, on hydrodynamics, sediment transport, and morphodynamics of estuaries and coastal seas. Flow separation behind the dune crest and recirculation on the steep downstream side result in turbulence and energy loss. Since the energy dissipation can be related to the dune lee slope angle, asymmetric dune shapes induce variable flow resistance during ebb and flood phases. Here, a noncalibrated numerical model has been applied to analyze the large-scale effect of symmetric and asymmetric dune shapes on estuarine tidal asymmetry evaluated by residual bed load sediment transport at the Weser estuary, Germany. Scenario simulations were performed with parameterized bed roughness of symmetric and asymmetric dune shapes and without dune roughness. The spatiotemporal interaction of distinct dune shapes with the main drivers of estuarine sediment and morphodynamics, that is, river discharge and tidal energy, is shown to be complex but substantial. The contrasting effects of flood- and ebb-oriented asymmetric dunes on residual bed load transport rates and directions are estimated to be of a similar importance as the controls of seasonal changes of discharge on these net sediment fluxes at the Lower Weser estuary. This corroborates the need to consider dune-induced directional bed roughness in numerical models of estuarine and tidal environments.     

Influence of compound bedforms on hydraulic roughness in a tidal environment

The effect exerted by the seabed morphology on the flow is commonly expressed by the hydraulic roughness, a fundamental parameter in the understanding and simulation of hydro- and sediment dynamics in coastal areas. This study quantifies the hydraulic roughness of large compound bedforms throughout a tidal cycle and investigates its relationship to averaged bedform dimensions. Consecutive measurements with an acoustic Doppler current profiler and a multibeam echosounder were carried out in the Jade tidal channel (North Sea, Germany) along large compound bedforms comprising ebb-oriented primary bedforms with superimposed smaller secondary bedforms. Spatially averaged velocity profiles produced log-linear relationships which were used to calculate roughness lengths. During the flood phase, the velocity profiles were best described by a single log-linear fit related to the roughness created by the secondary bedforms. During the ebb phase, the velocity profiles were segmented, showing the existence of at least two boundary layers: a lower one scaling with the superimposed secondary bedforms and an upper one scaling with the ebb-oriented primary bedforms. The drag induced by the primary bedform during the ebb phase is suggested to be related to flow expansion, separation, and recirculation on the downstream side of the bedform. Three existing formulas were tested to predict roughness lengths from the local bedform dimensions. All three predicted the right order of magnitude for the average roughness length but failed to predict its variation over the tidal cycle.     

Structure of flow over alluvial bedforms: an experiment on linking field and laboratory methods

This paper presents results of a field study designed to examine the structure of flow over mobile and fixed bedforms in a natural stream and to compare the results with findings of previous laboratory studies within the framework of double time–space averaging approach. Measurements of turbulence were obtained in a small river in Illinois, USA, over a fine spatial grid of sampling points above a mobile sandy bedform and its artificially moulded replica. Flow structure over the artificial bedform is similar to that observed in laboratory studies, but is markedly different from the flow structure over natural bedforms. These differences are most pronounced in the roughness sublayer, whereas flow in the logarithmic layer over natural and artificial sand waves is fairly similar and exhibits spatial uniformity. The double time–space averaged distributions of turbulence statistics conform to the multilayer model of flow structure over bedforms. Mean velocity distributions indicate neither classical flow recirculation nor substantial reduction of velocities in the lee of bedform crests. However, vertical patterns of turbulence statistics over depth suggest that stacked wakes similar to those observed in laboratory studies exist above the bedforms. Thus, despite the absence of flow separation, wake development seems to be induced by the systematic influence of upstream bedforms on the vertical structure of turbulence. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling river dune development and dune transition to upper stage plane bed

Large asymmetric bedforms known as dunes commonly dominate the bed of sand rivers. Due to the turbulence generation over their stoss and lee sides, dunes are of central importance in predicting hydraulic roughness and water levels. During floods in steep alluvial rivers, dunes are observed to grow rapidly as flow strength increases, undergoing an unstable transition regime, after which they are washed out in what is called upper stage plane bed. This transition of dunes to upper stage plane bed is associated with high transport of bed sediment in suspension and large decrease in bedform roughness. In the present study, we aim to improve the prediction of dune development and dune transition to upper stage plane bed by introducing the transport of suspended sediment in an existing dune evolution model. In addition, flume experiments are carried out to investigate dune development under bed load and suspended load dominated transport regimes, and to get insight in the time scales related to the transition of dunes to upper stage plane bed. Simulations with the extended model including the transport of suspended sediment show significant improvement in the prediction of equilibrium dune parameters (e.g. dune height, dune length, dune steepness, dune migration rate, dune lee side slope) both under bed load dominant and suspended load dominant transport regimes. The chosen modeling approach also allows us to model the transition of dunes to upper stage plane bed which was not possible with the original dune evolution model. The extended model predicts change in the dune shapes as was observed in the flume experiments with decreasing dune heights and dune lee slopes. Furthermore, the time scale of dune transition to upper stage plane bed was quite well predicted by the extended model. Copyright © 2015 John Wiley & Sons, Ltd.     

The influence of dunes on mixing in a migrating salt‐wedge: Fraser River estuary,Canada

Dune bedforms and salt‐wedge intrusions are common features in many estuaries with sand beds, and yet little is known about the interactions between the two. Flow visualization with an echosounder and velocity measurements with an acoustic Doppler current profiler over areas of flat‐bed and sand dunes in the highly‐stratified Fraser River estuary, Canada, were used to examine the effect of dunes on interfacial mixing. As the salt‐wedge migrates upstream over the flat‐bed, mixing is restricted to the lower portion of the water column. However, as the salt‐wedge migrates into the dune field from the flat bed, there is a dramatic change in the flow, and large internal in‐phase waves develop over each of the larger dunes, with water from the salt‐wedge reaching the surface of the estuary. The friction Richardson number shows that bed friction is more important in interfacial mixing over the dunes than over the flat‐bed, and a plot of internal Froude Number versus obstacle (dune) height shows that the salt‐wedge flow over the dunes is mainly supercritical. Such bedforms can be expected to cause similar effects in interfacial mixing in other estuaries and sediment‐laden density currents, and may thus be influential in fluid mixing and sediment transport. Copyright © 2010 John Wiley & Sons, Ltd.     

A probabilistic model for sediment entrainment:The role of bed irregularity

A generalized probabilistic model is developed in this study to predict sediment entrainment under the incipient motion, rolling, and pickup modes. A novelty of the proposed model is that it incorporates in its formulation the probability density function of the bed shear stress, instead of the near-bed velocity fluctuations, to account for the effects of both flow turbulence and bed surface irregularity on sediment entrainment. The proposed model incorporates in its formulation the collective effects of three para-meters describing bed surface irregularity, namely the relative roughness, the volumetric fraction and relative position of sediment particles within the active layer. Another key feature of the model is that it provides a criterion for estimating the lift and drag coefficients jointly based on the recognition that lift and drag forces acting on sediment particles are interdependent and vary with particle protrusion and packing density. The model was validated using laboratory data of both fine and coarse sediment and was compared with previously published models. The study results show that all the examined models perform adequately for the fine sediment data, where the sediment particles have more uniform gra-dation and relative roughness is not a factor. The proposed model was particularly suited for the coarse sediment data, where the increased bed irregularity was captured by the new parameters introduced in the model formulation. As a result, the proposed model yielded smaller prediction errors and physically acceptable values for the lift coefficient compared to the other models in case of the coarse sediment data.     

Sand settling through bedform-generated turbulence in rivers

Fluvial bedforms generate a turbulent wake that can impact suspended-sediment settling in the passing flow. This impact has implications for local suspended-sediment transport, bedform stability, and channel evolution; however, it is typically not well-considered in geomorphologic models. Our study uses a three-dimensional OpenFOAM hydrodynamic and particle-tracking model to investigate how turbulence generated from bedforms and the channel bed influences medium sand-sized particle settling, in terms of the distribution of suspended particles within the flow field and particle-settling velocities. The model resolved the effect of an engineered bedform, which altered the flow field in a manner similar to a natural dune. The modelling scenarios alternated bed morphology and the simulation of turbulence, using detached eddy simulation (DES), to differentiate the influence of bedform-generated turbulence relative to that of turbulence generated from the channel bed. The bedform generated a turbulent wake that was composed of eddies with significant anisotropic properties. The eddies and, to a lesser degree, turbulence arising from velocity shear at the bed substantially reduced settling velocities relative to the settling velocities predicted in the absence of turbulence. The eddies tended to advect sediment particles in their primary direction, diffuse particles throughout the flow column, and reduced settling likely due to production of a positively skewed vertical-velocity fluctuation distribution. Study results suggest that the bedform wake has a significant impact on particle-settling behaviour (up to a 50% reduction in settling velocity) at a scale capable of modulating local suspended transport rates and bedform dynamics. © 2020 John Wiley & Sons, Ltd.     

Velocity and turbulence variations at the edge of saltmarshes

Saltmarsh vegetation significantly influences tidal currents and sediment deposition by decelerating the water velocity in the canopy. In order to complement previous field results, detailed profiles of velocity and turbulence were measured in a laboratory flume. Natural Spartina anglica plants were installed in a 3 m length test section in a straight, recirculating flume. Different vegetation densities, water depths and surface velocities were investigated. The logarithmic velocity profile, which existed in front of the vegetation, was altered gradually to a skimming-flow profile, typical for submerged saltmarsh vegetation. The flow reduction in the denser part of the canopy also induced an upward flow (the current was partially deflected by the canopy). The skimming flow was accompanied by a zone of high turbulence co-located with the strongest velocity gradient. This gradient moved upward and the turbulence increased with distance from the edge of the vegetation. Below the skimming flow, the velocity and the turbulence were low. The structure of the flow in the canopy was relatively stable 2 m into the vegetation. The roughness length (z₀) of the vegetation depends only on the vegetation characteristics, and is not sensitive to the current velocity or the water depth. Both the reduced turbulence in the dense canopy and the high turbulence at the top of the canopy should increase sediment deposition. On the other hand, the high turbulence zone just beyond the vegetation edge and the oblique upward flow may produce reduced sedimentation; a phenomenon that was observed near the vegetation edge in the field.     

Development of bedforms due to waves blocked by a counter current

Experiments are conducted in a laboratory flume on the propagation of a surface wave against unidirectional flow with a sediment bed. This article presents the spatial variation of bedforms induced by the wave-blocking phenomenon by a suitably tuned uniform fluid flow and a counter-propagating wave. The occurrence of wave-blocking is confirmed by finding a critical wave frequency in a particular flow discharge in which the waves are effectively blocked and is established using the linear dispersion relation. The purpose of this work is to identify wave-blocking and its influence on the development of bedforms over the sediment bed. Interestingly bedform signatures are observed at a transition of bedforms in three zones, with asymmetric ripples having a steeper slope downstream face induced by the incoming current, followed by flat sand bars beneath the wave-blocking zone and more symmetric ripples below the wave-dominated region at the downstream. This phenomenon suggests that the sediment bed is segmented into three different regions of bed geometry along the flow. The deviations of mean flows, Reynolds stresses, turbulent kinetic energy, and power spectral density due to the wave-blocking phenomenon are presented along the non-uniform flow over sediment bed. The bottom shear stress, bed roughness and stochastic nature of the bedform features are also discussed. The results are of relevance to engineers and geoscientists concerned with contemporary process as well as those interested in the interpretation of palaeoenvironmental conditions from fossil bedforms. © 2019 John Wiley & Sons, Ltd.     

Aeolian processes across transverse dunes. I: Modelling the air flow

This paper discusses a two-dimensional second-order closure model simulating air flow and turbulence across transverse dunes. Input parameters are upwind wind speed, topography of the dune ridge and surface roughness distribution over the ridge. The most important output is the distribution of the friction velocity over the surface. This model is dynamically linked to a model that calculates sand transport rates and the resulting changes in elevation. The sand transport model is discussed in a separate paper. The simulated wind speeds resemble patterns observed during field experiments. Despite the increased wind speed over the crest, the friction velocity at the crest of a bare dune is reduced compared to the upstream value, because of the effect of stream line curvature on turbulence. These curvature effects explain why desert dunes can grow in height. In order to obtain realistic predictions of friction velocity it was essential to include equations for the turbulent variables in the model. In these equations streamline curvature is an important parameter. The main flaw of the model is that it cannot deal with flow separation and the resulting recirculation vortex. As a result, the increase of the wind speed and friction velocity after a steep dune or a slipface will be too close to the dune foot. In the sand transport model this was overcome by defining a separation zone. Copyright © 1999 John Wiley & Sons, Ltd.     

Velocity characteristics along a small step–pool channel

This paper summarizes measurements of velocity along three reaches of a small mountain channel with step–pool bedforms. A one‐dimensional electromagnetic current meter was used to record velocity fluctuations at 37 fixed measurement points during five measurement intervals spanning the peak of the annual snowmelt hydrograph. Measurement cross‐sections were located upstream from a bed‐step, at the step lip, downstream from the step, and in a uniform‐gradient run. Data analyses focused on characteristics of velocity profiles, and on correlations between velocity characteristics and the potential control variables bedform type, reach gradient and flow depth. To test the hypothesis that velocity characteristics are related to channel bedform types, ANOVA and ANCOVA tests were performed for the average velocity and coefficient of variation of point velocity data. Results indicate that high frequency velocity variations correlate to some degree with both channel characteristics and discharge. Velocity became more variable as stage increased, particularly at low‐gradient reaches with less variable bed roughness. Velocity profiles suggest that locations immediately downstream from bed‐steps are dominated by wake turbulence from mid‐profile shear layers. Locations immediately upstream from steps, at step lips, and in runs are dominated by bed‐generated turbulence. Adverse pressure gradients upstream and downstream from steps may be enhancing turbulence generation, whereas favourable pressure gradients at steps are suppressing turbulence. The bed‐generated turbulence and skin friction of runs appear to be less effective energy dissipators than the wake‐generated turbulence and form drag of step–pool bedforms. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of wave–bedform feedbacks on the formation of,and grain sorting over shoreface-connected sand ridges

The influence of wave–bedform feedbacks on both the initial formation of shoreface-connected sand ridges (sfcr) and on grain size sorting over these ridges on micro-tidal inner shelves is studied. Also, the effect of sediment sorting on the growth and the migration of sfcr is investigated. This is done by applying a linear stability analysis to an idealized process-based morphodynamic model, which simulates the initial growth of sfcr due to the positive coupling between waves, currents, and an erodible bed. The sediment consists of sand grains with two different sizes. New elements with respect to earlier studies on grain sorting over sfcr are that wave-topography interactions are explicitly accounted for, entrainment of sediment depends on bottom roughness, and transport of suspended sediment involves settling lag effects. The results of the model indicate that sediment sorting causes a reduction of the growth rate and migration speed of sfcr, whereas the wavelength is only slightly affected. In the case where the entrainment of suspended sediment depends on bottom roughness, the coarsest sediment is found in the troughs; otherwise, the finest sediment occurs in the troughs. Compared to previous work, modeled maximum variations in the mean grain size over the topography are in better agreement with field observations. Settling lag effects are important for the damping of high-wavenumber mode instabilities such that a preferred wavelength of the bedforms is obtained.     

Modulation of the flow structure by progressive bedforms in the Kinoshita meandering channel

An in‐house fully three‐dimensional general‐purpose finite element model is applied to solve the hydrodynamic structure in a periodic Kinoshita‐generated meandering channel. The numerical model solves the incompressible Reynolds‐averaged Navier–Stokes equations for mass and momentum, while solving the k ? ε equations for turbulence. The free surface is described by the rigid‐lid approximation (using measured water surface data) for flat (smooth‐bed) and self‐formed (rough‐bed) conditions. The model results are compared against experimental measurements in the ‘Kinoshita channel’, where three‐dimensional flow velocities and turbulence parameters were measured. This validation was carried out for the upstream‐valley meander bend orientation under smooth (flat bed) conditions. After validation, several simulations were carried out to predict the hydrodynamics in conditions where either it was not possible to perform measurements (e.g. applicability of the laboratory acoustic instruments) and to extrapolate the model to other planform configurations. For the flat smooth‐bed case, a symmetric (no skewness) planform configuration was modeled and compared to the upstream‐skewed case. For the self‐formed rough‐bed case, prediction of the hydrodynamics during the progression of bedforms was performed. It appears that the presence of bedforms on a bend has the following effects: (i) the natural secondary flow of the bend is disrupted by the presence of the bedforms, thus depending on the location of the dune, secondary flows might differ completely from the traditional orientation; (ii) an increment on both the bed and bank shear stresses is induced, having as much as 50% more fluvial erosion, and thus a potential increment on the migration rate of the bend. Implications on sediment transport and bend morphodynamics are also discussed in the paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental study on transient and steady‐state dynamics of bedforms in supply limited configuration

The purpose of the present study is to investigate experimentally the development of bedforms in a configuration where the sediment supply is limited. The experimental setup is a rectangular closed duct combining an innovative system to control the rate of sediment supply Q_in , and a digitizing system to measure in real time the 3D bedform topography. We carried out different sets of experiments with two sediment sizes (100 µm and 500 µm) varying both the sediment supply and the water flow rate to obtain a total of 46 different configurations. After a transient phase, steady sub‐centimeter bedforms of various shapes have been observed: barchans dunes, straight transverse dune, linguoid transverse dunes and bedload sheets. Height, spacing, migration speed, and mean bed elevation of the equilibrium bedforms were measured. For a given flow rate, two regimes were identified with fine sediment: (i) a monotonic increasing regime where the equilibrium bedform height and velocity increase with the sediment supply rate Q_in and (ii) an invariant regime for which both parameters are almost independent of Q_in. For coarse sediment, only the first regime is observed. We interpret the saturation of height and velocity for fine sediment bedforms as the transition from a supply‐limited regime to a transport‐limited regime in which the bedload flux has reached its maximum value under the prevailing flow conditions. We also demonstrate that all experiments can be rescaled if the migration speed and height of the bedforms are, respectively, divided and multiplied by the cube of the shear velocity. This normalization is independent of grain size and of bedform morphology. These experimental results provide a new quantification of the factors controlling equilibrium height and migration speed of bedforms in supply‐limited conditions against which theoretical and numerical models can be tested.     

What is suspended sediment?

Suspended sediment is conventionally regarded as that sediment transported by a fluid that it is fine enough for turbulent eddies to outweigh settling of the particles through the fluid. Early work in the fluvial field attributed suspension to turbulence, and led to the notion of a critical threshold for maintaining sediment in suspension. However, research on both turbulence structures and the interactions between suspended sediment and bedforms in rivers has shown a more complex story and, although there appear to have been no studies of the impact of bedforms on aeolian suspended sediment concentrations, turbulent flow structures and transport rates of saltating particles have been shown to be affected. This research indicates that suspended sediment neither travels with the same velocity as the flow in which it is suspended, nor is it likely to remain in suspension in perpetuity, even under conditions of steady flow or in unsteady flow the where dimensionless critical threshold is permanently exceeded. Rather, like bedload, it travels in a series of hops, and is repeatedly deposited on the bed where it remains until it is re‐entrained. Is there, therefore, a qualitative difference between suspended and saltating sediment, or is it just a quantitative difference in the size of the jump length and the frequency of re‐entrainment? It is our contention that the distinction of suspension as a separate class of sediment transport is both arbitrary and an unhelpful anthropocentric artefact. If we recognize that sediment transport is a continuum and applies to any fluid medium rather than split into different “processes” based on arbitrary thresholds and fluids, then recognizing the continuity will enable development of an holistic approach sediment transport, and thus sediment‐transport models that are likely to be viable across a wider range of conditions than hitherto. Copyright © 2015 John Wiley & Sons, Ltd.     

Detailed bed topography and sediment load measurements for two stepdown flows in a laboratory flume

Streams and rivers, particularly smaller ones, often do not maintain steady flow rates for long enough to reach equilibrium conditions for sediment transport and bed topography. In particular, streams in small watersheds may be subject to rapidly changing hydrographs, and relict bedforms from previous high flows can cause further disequilibrium that complicates the prediction of sediment transport rates. In order to advance the understanding of how bedforms respond to rapid changes in flow rate,...     

Sand particle velocities over a subaqueous dune slope using high-frequency image capturing

This work presents measurements and analysis of sand particle velocities over a subaqueous dune with median sand diameter of 0.85 mm. Time-lapse images of the mobile bed and an automated particle image velocimetry (PIV)-based cross-correlation method are used to obtain mean velocity of sand particles. This technique is shown to be consistent with measurements obtained with manual tracing. The measurements indicate an increase in mean particle velocity over a dune slope. Three regions are distinguished over the dune slope: (1) region of fluctuating particle velocity, (2) region of increasing particle velocity, and (3) region of maximum particle velocity. The observations are aligned with experimental and numerical modelling studies, indicating fluctuations in flow velocity over a dune stoss slope. We furthermore show that the standard deviation of the mean particle velocity is affected by the slope location and decreases from the lower slope towards the upper slope. The particle velocity variability is discussed in the context of general onset and cessation of sediment transport, the effect of the reattachment zone, sweep-transport events, and the existence of superimposed bedforms. With this work we bridge the gap between measurements of bedload transport at the particle-scale and at the bedform-scale. © 2019 John Wiley & Sons, Ltd.     

An experimental study on the ripple–dune transition

Flume experiments were conducted on different bed stages across the ripple–dune transition. As flow velocity increases, an initially flat bed surface (made of fairly uniform sandy material) is gradually transformed into a two‐dimensional rippled bed. With further increase in velocity, two‐dimensional ripples are replaced by irregular, linguoid ripples. As the average velocity necessary for the ripple–dune transition to occur is imposed on the bed surface, these non‐equilibrium linguoid ripples are further transformed into larger, two‐dimensional dunes. For each of these stages across the transition, a concrete mould of the bed was created and the flow structure above each fixed bed surface investigated. An acoustic Doppler velocimeter was used to study the flow characteristics above each bed surface. Detailed profiles were used along a transect located in the middle of the channel. Results are presented in the form of spatially averaged profiles of various flow characteristics and of contour maps of flow fields (section view). They clearly illustrate some important distinctions in the flow structure above the different bedform types associated with different stages during the transition. Turbulence intensity and Reynolds stresses gradually increase throughout the transition. Two‐dimensional ripples present a fairly uniform spatial distribution of turbulent flow characteristics above the bed. Linguoid ripples induce three‐dimensional turbulence structure at greater heights above the bed surface and turbulence intensity tends to increase steadily with height above bed surface in the wake region. A very significant increase in turbulence intensity and momentum exchange occurs during the transition from linguoid ripples to dunes. The turbulent flow field properties above dunes are highly dependent on the position along and above the bed surface and these fields present a very high degree of spatial variability (when compared with the rippled beds). Further investigations under natural conditions emphasizing sediment transport mechanisms and rates during the transition should represent the next step of analysis, together with an emphasis on quadrant analysis. Copyright © 2001 John Wiley & Sons, Ltd.