Sediment Transport

Available online at www.sciencedirect.com

2 (2007) 473–488www.elsevier.com/locate/sedgeo

Sedimentary Geology 20

Sediment transport patterns determined from grain size parameters:Overview and state of the art

J.P. Le Roux ⁎, E.M. Rojas

Departamento de Geología, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 13518, Correo 21, Santiago, Chile

Abstract

Grain size trends have been applied in many diverse sedimentary environments to determine sediment transport paths, generallycoinciding with information from tracer studies, current measurements and the orientation of sedimentary structures. The differentmethods proposed to date are critically analysed and compared with reference to recent field studies. It is concluded that the two-dimensional methods produce comparable results and may in fact complement each other.

In spite of the advances, several problems still exist, which include the sampling method and density, the choice of trend types,the relative weight of grain size parameters and the interpretation of results. These are discussed together with possible solutions.© 2007 Elsevier B.V. All rights reserved.

Keywords: Sediment trend analysis; STA; Grain size trends; Sediment transport

1. Introduction

Grain size trends seem to be a natural result ofsediment transport processes (Krumbein, 1938; Russell,1939; Swift et al., 1972; Stapor and Tanner, 1975;McCave, 1978; Harris et al., 1990), which is primarilyrelated to the effects of abrasion and selective sorting.Early studies suggested that the grain size decreases inthe direction of transport (Pettijohn and Ridge, 1932;Plumley, 1948; Yeakel, 1962; Mothersill, 1969; Petti-john et al., 1972; Self, 1977) but other investigationssometimes indicated the opposite (McCave, 1978;Nordstrom, 1981, 1989). Because of this uncertainty,later investigators preferred a combination of grain sizeparameters, such as the mean size Dμ, sorting σ, andskewness Sk (McLaren, 1981). McLaren and Bowles(1985), based on a rigorous examination of the

⁎ Corresponding author. Tel.: +56 2 6784123; fax: +56 2 6963050.E-mail address: [email protected] (J.P. Le Roux).

0037-0738/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.sedgeo.2007.03.014

processes involved, concluded that sediments alwaysbecome better sorted downstream whereas Dμ can eitherincrease together with a decrease in Sk or decreasetogether with an increase in Sk. Gao and Collins (1991)argued from theoretical considerations that deposits canalso become coarser and more negatively skewed in thedownstream direction whereas Self (1977) reporteddeposits becoming finer and more positively skewedalong the transport path. Of the eight possiblecombinations, four types of granulometric trends seemto dominate in nature. Expressed in terms of ϕ units(Folk and Ward, 1957), these are:

Type 1 : r1Nr2;Dl1bDl2; Sk1NSk2Type 2 : r1Nr2;Dl1NDl2; Sk1bSk2Type 3 : r1Nr2;Dl1NDl2; Sk1NSk2Type 4 : r1Nr2;Dl1bDl2; Sk1bSk2

ð1Þ

with the subscripts 1 and 2 indicating sampling sites 1and 2 along the direction of transport.

mailto:[email protected]

http://dx.doi.org/10.1016/j.sedgeo.2007.03.014

Fig. 1. The McLaren and Bowles (1985) method compares all possible sample pairs located along the sampling lines. The trends are statisticallyanalysed to determine the dominant direction along each survey line.

474 J.P. Le Roux, E.M. Rojas / Sedimentary Geology 202 (2007) 473–488

Using these trends, several methods have beendeveloped to define sediment transport paths. Thesetechniques have been applied to engineering anddredging schemes (e.g. McLaren and Powys, 1989),environmental studies (McLaren et al., 1981; McLaren,1983, 1984; McLaren and Little, 1987; McLaren et al.,1993a,b; Uriarte et al., 1998; Pascoe et al., 2002), and ingeneral sedimentological investigations (McCave,1978; Nordstrom, 1981, 1989; McLaren and Collins,1989; Zhang and Zhu, 1989; Gao and Collins, 1992,1994; Gao et al., 1994; Vanwesenbeeck and Lanckneus,2000; Mallet et al., 2000; Carriquiry et al., 2001; Ríoset al., 2002; Poizot et al., 2006).

2. Methodology

2.1. Analysis of grain size distributions

Grain size parameters such as the mean, sorting andskewness are usually obtained from analyses of the grainsize distributions by sieve or settling techniques.Sediment sieve size (Dv) is construed as the diameter ofthe largest sphere that would pass through the retainingsieve whereas the fall or settling size (Ds) is considered tobe the diameter of a quartz-density sphere with the samesettling velocity as the sediment particle. Both methodshave advantages and drawbacks and may producesignificantly different results, although the settlingdiameter Ds is probably a better measure of size interms of sediment dynamics (Le Roux, 2005).

The grain size parameters are commonly determinedfrom the grain size distribution expressed in ϕ units(ϕ=− log2 D). A cumulative frequency curve is plottedusing an arithmetic scale on the abscissa for the sizeclasses and either an arithmetic or probability scale onthe ordinate for the cumulative weight frequency, whichsums to 100%. Graphical or moment methods are thenused to calculate the grain size parameters.

Very little work has been done on the influence ofdifferent methods for determining the grain size para-meters on spatial sediment trends. However, becausetrends are defined by the relative values among datastations, rather than their absolute values, the specificmethod employed is probably of minor importance. Hilland McLaren (2001) determined two sets of descriptivestatistics, one derived from log-hyperbolic curves fitted tograin size data and the other computed using a model-independent method, to generate transport vectors in fourareas where the transport direction was known unequiv-ocally. Both sets correctly predicted the direction oftransport with essentially the same statistic significance.They concluded that the use of log-hyperbolic distributionsprovides no particular advantage in the analysis of grainsize trends.

2.2. Analysis of sediment transport trends

Earlier attempts to define sediment transport patternsbased on grain size parameters followed an essentiallyone-dimensional approach (e.g.McCave, 1978;McLaren,1981; McLaren and Bowles, 1985). Some statisticalmodifications to this approach were subsequently pro-posed by Lucio et al. (2004). Gao and Collins (1992)introduced a two-dimensional treatment of grain size databased on a modification of the McLaren (1981) method,comparing two data stations at a time. Le Roux (1994b,c)proposed an approach based on the comparison of groupsof five stations at a time, using a modified vector analysisprocedure to determine the transport vectors. Asselman(1999) modified the Gao and Collins (1992) method andimplemented it in a Geographical Information Systemtogether with geostatistical analysis. Rojas et al. (2000)fitted planes to a central station and two neighbouringstations at a time, employing the dip direction of all thegenerated planes around the central station to definevectors and subsequently averaging the vectors around the

Fig. 2. The McLaren and Bowles (1985) method produces differenttransport directions depending on the direction selected for the surveylines. E–W and NE–SW survey lines would produce trends towardsthe east and southwest respectively, although the real trend is towardsthe southeast.

475J.P. Le Roux, E.M. Rojas / Sedimentary Geology 202 (2007) 473–488

central station. Rojas (2003) used the gradient between thecentral station and surrounding stations to define vectormagnitudes and developed a computer program to obtainthe optimum relative weights of the different grain sizeparameters. These methods are briefly discussed below.

2.2.1. The McLaren–Bowles methodMcLaren and Bowles (1985) compared the grain size

parameters of all possible sample pairs located along thesampling lines (Fig. 1). A z-score significance test wasused to determine transport directions with a certainlevel of confidence, accepting only those vectors wherez is larger than the threshold value:

z ¼ x� Np=MðNpqÞN1:645ð95% confidenceÞ orN2:33ð99% confidenceÞ ð2Þ

where x is the number of pairs representing the possibletrends in one of the two opposing directions, n thenumber of samples in a sequence, p the probability ofrandom occurrence (=0.125 if all eight possible trendsare considered) and q=1−p. N, the total number ofpossible pairs, is given by:

N ¼ ðn2 � nÞ=2: ð3Þ

The trend is finally accepted or rejected byqualitatively evaluating a multiple correlation coeffi-cient (R2) between the mean, sorting and skewness ofeach sample in the sequence.

The advantage of this method is that it is easy toapply. The main disadvantage is that it is one-dimensional, in that vectors can go only in one of twodirections parallel to the survey lines. The method is

therefore subjective in the sense that the survey linedirections are chosen by the researcher and that differentline orientations will produce different transport direc-tions (Asselman, 1999). Fig. 2 shows general sedimenttransport towards the south-southeast (grey arrowperpendicular to thin, straight lines, which representthe grain parameter contours). If the N–S survey linesare selected, then the obtained transport direction will betowards the south. However, if the E–W lines arechosen, then it will be towards the east, almost at rightangles to the real direction of transport. Choosing thediagonal survey lines would yield south-easterly andsouth-westerly directions respectively. If no supportinginformation on the real transport direction is available,therefore, the possibility that the south-easterly directionbe chosen would be only 1 in 4, and even then theobtained direction would be parallel to the real trendonly if the sample lines happen to be perpendicular tothe grain parameter contours. If the real direction oftransport should change downstream, the establishedtrends would also continue along the chosen surveylines and would therefore fail to reflect such localchanges. Although Lucio et al. (2004) proposed someimproved statistical tests for the McLaren–Bowlesmethod, these cannot eliminate the basic problem. Thefact that all possible pairs at any distance along thesampling line are compared may also lead to distortions,because neighbouring stations may be completelyunrelated at a certain critical distance (Asselman, 1999).

2.2.2. The Gao–Collins methodGao and Collins (1992) used a grid of sampling

stations and defined trends by comparing the grain sizeparameters of each sample with its nearest neighbours inany direction lying within a characteristic distance. Thelatter is defined as the space-scale of the particular studyarea, normally taken as the maximum sampling interval.Trend vectors are drawn by simply connecting thestations showing type 1 or 2 trends (Fig. 3) and have unitlengths. Summing the vectors at each data stationproduces a single vector for this site R(x,y):

Rðx; yÞ ¼X

rðx; yÞi ð4Þwhere r(x,y)i is a trend vector at the data station i.

Finally, a filtering procedure is performed to removebackground noise, by averaging the resultant vectors ofeach station and its surrounding neighbours. This isequivalent to the following mathematical transformationfor the station at which R(x,y) is defined:

Ravðx; yÞ ¼ 1=ðk þ 1Þ½Rðx; yÞ þX

Rj� ð5Þ

Fig. 3. The Gao and Collins (1992) method compares each sample with its nearest neighbours in any direction lying within a “characteristic distance”(radius of half-circle in a). The vector means are calculated for the different stations (b) and filtered by averaging the value of each station and itsnearest neighbours (c).


where Rj is the summed trend vector obtained on the basisof Eq. (4) at a neighbouring station j, and k is the totalnumber of such stations. The residual vectors form ageneral pattern representing the net sediment transporttrends.

TheGao–Collinsmethod is also simple to apply, eithermanually or using a computer program (Gao, 1996). It ismore objective than the McLaren–Bowles method(Asselman, 1999) and is two-dimensional in the sensethat vectors are drawn between each station and theneighbouring stations around it. If interpolation is appliedbetween sampling stations to obtain a regular grid, themethod is also less sensitive to irregularities in thesampling configuration. However, Le Roux (1994a)demonstrated that the assumption that transport takesplace from point to point (i.e. from the station to itsneighbour) could lead to distortions in the resultantvectors. For example, the sum of the four obtained vectors(black arrows) in Fig. 2 would produce a mean directionsomewhat to the west of the real trend, and depends verymuch on the relative distribution of sampling stations inrelation to the grain parameter contours. This isexacerbated by the fact that the vectors are of unit length,which obscures the significance of the vector magnitudeand affects the final station vector.

The accuracy of the smoothing operation employedin this method to reduce background noise also dependson the relative distribution of sampling sites, decreasingwhere this is irregular. Le Roux et al. (2002) appliedsmoothing to a set of regularly distributed, completelyrandom data and found that statistically valid trends maybe produced in this way, so that this procedure shouldnot be applied until the statistical validity of theunsmoothed data has been established. Asselman

(1999) also suggested that smoothing should not beperformed, as it reduces the spatial resolution and leadsto a loss of valuable information.

A further disadvantage of the method is that itsimultaneously compares different types of trendsbetween any station and its neighbours. The trend typedepends on the transport process and it is thereforeunlikely that more than one trend type can exist at anyparticular station. The choice of a specific trend typewhere more than one is indicated by the method alsointroduces a certain element of bias (Le Roux, 1994a).

Finally, the length of the characteristic distance, i.e.the maximum sampling interval, can also have animportant effect on the overall trends. If this distance islarge, then too many neighbouring stations may becompared at a time, which will produce very smoothtransport patterns that may be unrelated to the real trend.This aspect is discussed further in Section 4.2.

2.2.3. The Asselman methodAsselman (1999) modified the Gao–Collins method

and implemented it in a Geographic Information Systemusing the programs GSTAT (Pebesma, 1995) andPCRaster (Van Deursen and Wesseling, 1992). As afirst step, separate raster maps are made of the mean,sorting and skewness using block kriging for interpo-lation (Burgess and Webster, 1980a,b). Each raster cellis then compared with its neighbouring cells and avector is defined when a type 1 or 2 trend is present. Thetrend vectors in the three raster maps are then comparedcell by cell, accepting only those trends that areidentified on all three maps, which are averaged toproduce a single vector (Fig. 4). Not only the nearestneighbouring stations are used but all stations within the

Fig. 4. The Asselman (1999) method prepares raster maps of the different grain size parameters using block kriging for interpolation (a, b). Each rastercell is compared with its neighbouring cells to define vectors (c), which are then compared with the vectors for the same cells in the other raster maps.These are averaged to produce a single vector (d).

Fig. 5. The Le Roux (1994b) method performs a modified vectoranalysis based on combined, dimensionless grain size parameters. Thevalue of the central station is subtracted from those of the satellitestations. Negative values are added to stations on opposite radials,which are expressed as proportions of the total value and substitutedfor the proportional frequency of recorded directions in normal vectoranalysis (a). Four satellite stations located on the principal radials at anequal distance from a central station are required for the vectoranalysis, so that irregularly distributed stations are mathematicallymoved to these positions (b).


optimum range. The trend vectors are statistically testedby Monte Carlo simulation (Hammersley and Hands-comb, 1979). The model is run initially with interpo-lated raster maps obtained from block kriging. This alsoprovides the estimation error, which is subsequentlyused to generate 100 possible realizations of input mapsfor each grain size parameter employing conditionalGaussian simulation. The model is run 100 times and theaverage and standard deviation of the model outcomesare computed. The average directions obtained with theMonte Carlo analysis provide an indication of sedimenttransport directions whereas the standard deviationsprovide information on the precision of the identifieddirections.

This method is less sensitive to irregular stationdistributions than the Gao–Collins method and alsoreduces the errors associated with station intervals,because semi-variograms are used to determine themaximum range. As it considers either type 1 or 2 trendsseparately for each analysis, there is a smaller possibilityof introducing bias than in the Gao–Collins method.However, as in the Gao–Collins method, transport isconsidered to take place from point to point and the initialvectors are considered to be of unit length, which maydistort the real transport directions. “Trends” between twopoints are far more likely to exist than among groups ofstations and, even when these are eventually averaged,the resultant vector may deviate from the real trend (see

discussion by Le Roux, 1994a). Asselman (1999)considered only type 1 or 2 trends but other trend types(e.g. 3 or 4) can also be added to the method.

Fig. 6. The Rojas et al. (2000) and Rojas (2003) methods interpolatethe sample values taking into account their positions relative to eachpixel, which forms part of a regular grid of coordinates (rows andcolumns).


The interpolation of data using block krigingprobably has an effect upon the inherent directionalinformation but this is difficult to evaluate quantitative-ly. The use of an optimum range, if too large, may alsobe subject to the same potential error as the character-istic distance of Gao and Collins (1992).

2.2.4. The Le Roux methodLe Roux (1994b,c) combined the grain size para-

meters into dimensionless numbers, with each parameterconsidered to be of equal importance. He used a centralstation and four satellite stations located on the principalradials at an equal distance from the central station. Amodified vector analysis was carried out, substitutingthe dimensionless grain size parameters for the propor-tional frequencies of recorded directions normally usedin vector analysis (Fig. 5a). An iterative trigonometrictechnique was employed in the case of irregularlydistributed stations to restore the values to the principalaxes at equal distances from the central station (Fig. 5b).The Watson (1966) non-parametric test was used (LeRoux et al., 2002) to statistically analyse the resultingvectors. This is given by:

u2 ¼ ½u⁎2 þ ð0:1=n2Þ � ð0:1=nÞ�½1þ ð0:8=nÞ� ð6Þwhere

u⁎2 ¼ Rðhi=360Þ2 � ð2=nÞRðihi=360Þþ ð1=nÞRðhi=360Þþnf1=nRðhi=360Þ � ½ð1=nÞRðhi=360Þ�2 þ 1=12g:

ð7Þ

If u⁎2bu2, with u2N0.187 for a confidence level of95% and u2N0.267 for 99%, the null hypothesis can berejected and the alternative hypothesis (i.e. that thedistribution is non-random) can be accepted.

The Le Roux method has the advantage that groupsof five stations are considered at a time, so that theproblems associated with a point-by-point comparisonare eliminated. A modified vector analysis of the grainsize parameters for the group of stations only producesresults if a trend really exists, for which a magnitude iscomputed instead of using a unit vector length as in theother methods. The maximum distance betweenstations can be chosen (e.g. by constructing semi-variograms as proposed by Asselman, 1999) and therelative weight of the different grain size parameters,which are normalised at the outset, can be changed. Asthe method is applicable to either regular or irregulardistributions of sampling stations, interpolation is notrequired and no information is therefore lost or altered.The method also has the advantage that trend types 1,

2, 3 and 4 can be analysed separately or in com-bination, applying the Watson test to determine thestatistical validity of the results. A disadvantage of themethod is that it cannot be performed manually, so thata computer program must be used (Le Roux, 1994b;Le Roux et al., 2002).

2.2.5. The Rojas methodsRojas et al. (2000), Rojas (2003) and Rojas and Le

Roux (2003) combined the grain size parameters(including the kurtosis K) into a linear granulometricfacies function (FF) given by:

FF ¼ f ðDl; r; Sk;KÞ ¼ C1Dl þ C2rþ C3Skþ C4K

ð8Þ

where C1 … C4 are coefficients depending on thedepositional environment and transport processes.

Using the distribution of FF values over the studyarea, a three-dimensional digital facies map (DFM) isconstructed. The DFM can be considered as a matrix ofpixels on a regular grid of coordinates (rows andcolumns) so that the original values have to beinterpolated taking account of their positions relative toeach pixel (Fig. 6). Each pixel value is determined usingthe nearest neighbouring stations falling within each ofthe four quadrants around the pixel. The FF values ofthese neighbours are weighted according to theirdistance from the central pixel, assigning a minimumweight to the farthest of the four neighbours. The pixelvalue is plotted as a vertical distance on the DFM.

Vectors are assigned to the generated set of pixelvalues using one of two methods. Rojas et al. (2000)determined all the possible planes that can be fittedbetween the central pixel and two neighbouring pixels


within the specific radius (Fig. 7a). Points located tooclose to a line are defined by a critical minimum interiorangle formed by the three points and discarded. Thevectors are defined by the dip direction of the planes andsummed to give a resultant vector. In themethod of Rojas(2003), the gradients between the central pixel andneighbouring pixels are measured, which are assigned tothe magnitudes of horizontal vectors with the samedirections (Fig. 7b). The gradients are used instead offrequencies in normal vector analysis, so that the methodis somewhat similar to that of Le Roux (1994c).

The vectors generated by these granulometricmethods on the data stations of the DFM are comparedwith the vectors from measured sedimentary structuresinterpolated onto the same points. The angular error inradians (AE) between the generated (granulometric) andobserved (sedimentary structures) vectors is calculatedon each of the points where both vectors can bedetermined. “False negatives” (FN), defined as pointswhere vectors are observed but none are generated, aswell as “true positives” (TP), i.e. points where vectorsare both observed and generated, are counted andincorporated into a formula representing the meanglobal error (MGE) as follows:

MGE ¼ ½ðRAEi=pÞ þ FN�=ðFNþ TPÞ ð9Þ

It should be noted that the FN are required because avector magnitude threshold is defined below whichgenerated vectors are discarded. These points areconsidered to be a serious problem by assigning themthe same importance as a maximum angular error (π).The MGE varies between 0 and 1, reaching a maximumwhere no vectors are generated at locations wherecomparison vectors do exist (TP=0), or when the

Fig. 7. The Rojas et al. (2000) method determines vectors using the dipdirection of all possible planes that can be fitted between the centralpixel and two neighbouring pixels within a specific radius (a). TheRojas (2003) method measures the gradient between the central pixeland neighbouring pixels, assigning these to the magnitudes ofhorizontal vectors with the same directions (b).

generated vectors point in the direction opposite to thoseof the comparison vectors. It is a minimum where thecomparison and generated vectors coincide.

This methodology allows the optimum coefficients tobe determined for each specific depositional environ-ment. Employing a computer algorithm, the coefficientsC1 to C4 of the FF are modified incrementally anditeratively, using a limited and discrete range of values,to obtain a set of optimum coefficients with a minimumMGE for the data and method being used. In caseswhere no comparison vectors exist, the Watson (1966)non-parametric statistical test (Eqs. (6) and (7)) is usedto find the optimum coefficients by maximising u2,using a similar computer algorithm. The role of thesampling density can also be studied by eliminatingstations along the grid and recording its effect on theMGE.

The basic method of Rojas (2003) can be applied toall the other methods, with the difference that thesampling points have to be interpolated onto a regulargrid with a resultant loss of directional information.However, as observed vectors (obtained from sedimen-tary structures or other data) can be interpolated onto thesame grid, the generated and observed vectors can becompared directly and the system can be trained toproduce the lowest global mean error or highest Watsonstatistic by adjusting the coefficients.

The main advantage of the Rojas methods is that theoptimum weights of the grain size parameters areobtained, so that the error between observed andgenerated vectors is minimised. Different methods cantherefore be compared and those producing the lowestMGE are considered to be the most accurate. Althoughthe method takes all possible trend types into account, itis not possible to deduce the specific trend type from theresultant coefficients. The Rojas (2003) method is also apoint-to-point comparison and furthermore does notapply the correction to the final magnitude suggested byLe Roux (1994c), with the result that the vectors close tothe principal axes receive magnitudes proportionatelyhigher than those farther away.

3. Application and testing of the methods

3.1. General results

Many studies employing grain size trend analysishave been carried out over the last decade, includingdepositional environments as diverse as continentalshelves (Lanckneus et al., 1993; Gao et al., 1994; Zhuand Chang, 2000; Shi et al., 2002; Ravaioli et al., 2003;Cheng et al., 2004; Poizot et al., 2006), submarine

Table 1Results of minimising the mean global error (MGE) by varying thegrain size parameter coefficients (a) while comparing the generatedvectors with observed vectors on the Pescado Delta and (b) whilemaximising the Watson statistic

Gao and Collins(1992)

Rojas et al.(2000)

Rojas(2003)

Le Roux(1994c)

a) Pescado Delta

Entire delta 0.24 0.21 0.24 0.21River inlet 0.37 0.43 0.48 0.36Delta front 0.67 0.63 0.75 0.47Delta slope 0.13 0.21 0.33 0.19Prodelta 0.24 0.22 0.28 0.19

b) Watson statistic

Entire delta 0.29 0.22 0.30 0.21River inlet 0.63 0.51 0.57 0.57Delta front 0.78 0.75 0.90 0.60Delta slope 0.15 0.22 0.37 0.20Prodelta 0.44 0.26 0.32 0.22

Bold print emphasizes lowest values among the four methods.


canyons (Liu et al., 2002), bays (Calhoun et al., 2002; LeRoux et al., 2002; Ríos et al., 2002; Duman et al., 2004),estuaries (McLaren et al., 1993a; Gao, 1996; Wu andShen, 1999; Mallet et al., 2000; Pascoe et al., 2002; VanLancker et al., 2004), fjords (McLaren et al., 1993b),deltas (Carriquiry et al., 2001; Rojas, 2003), shorefaces(Uriarte et al., 1998), beaches (Pedreros et al., 1996; VanLancker et al., 2004), barrier reefs and inlets (Stewartet al., 2000), tidal inlets (Gao and Collins, 1992; Jia et al.,2003), tidal sandbanks (Vanwesenbeeck and Lanckneus,2000), intertidal sandflats (Grant et al., 1997), and evenriver floodplains (Asselman, 1999). With the exceptionof Vanwesenbeeck and Lanckneus (2000), all of thesestudies concluded that the vectors produced by spatialgrain size distributions coincide largely with trendsderived from sedimentary structures, tracer minerals or

Fig. 8. Vectors generated by the Rojas (2003) method, compared to vectorLlanquíhue, southern Chile.

direct observation of currents. Moreover, the grain sizetrends assisted in discriminating between local, recentsources and regional, older sources of bottom sedimentmaterial (Ravaioli et al., 2003), areas undergoing erosionor deposition of sediments (McLaren et al., 1993a; Wuand Shen, 1999; Ríos et al., 2002; Shi et al., 2002), fairand stormy weather processes (Pedreros et al., 1996),seasonal transport patterns (Liu et al., 2002; Ríos et al.,2002) and different transport and depositional mechan-isms (Wu and Shen, 1999; Carriquiry et al., 2001).

3.2. Comparison of the different methods

Few comparative studies have been carried out on therelative accuracy of the various methods. Liu et al.(2002) compared the results of three different methodsas applied to an inner shelf area in the head region of asubmarine canyon. These included a combination offiltering and the empirical orthogonal (eigen) function(or EOF) technique (normally applied to meteorologicaland oceanographic studies), the McLaren method andthe Gao–Collins model. They found that the results ofthe three methods not only agree but also complementone another.

In a study of Lirquén Harbour, south-central Chile,Ríos et al. (2002) compared the methods of McLarenand Bowles (1985), Gao and Collins (1992) and LeRoux (1994c). Two sets of samples were taken at thesame stations during June (winter) and December(summer) 1997. The results were compared with currentmeasurements and the effect of waves on the bottomsediments as hindcast from measured wind speedsduring the two sampling periods. The McLaren–Bowlesmethod detected macro-scale transport patterns andindicated the same general trend for both seasonswhereas both the Gao–Collins and Le Roux methods

s obtained from sedimentary structures on the Pescado Delta in Lake

Fig. 9. Large-scale wave ripples in Lake Llanquíhue, showingdifference in grain size between the troughs and crests.


were able to detect local transport components as well asa seasonal variation in transport patterns.

One of the most complete and informative studies onthe use of grain size parameters to determine sedimenttransport patterns was done on a small Gilbert-typedelta in Lake Llanquíhue, southern Chile (Rojas, 2003).The delta was sampled by scuba diving along a150×200 m grid laid out underwater. Daily recordswere taken of the wind and wave direction, the waveperiod, and the direction and strength of underwatercurrents. It was concluded that little sediment transporttakes place on the delta during fair weather conditionsbut that storms affect the whole delta up to depths of25 m (Rojas and Le Roux, 2005).

The orientation of sedimentary structures such ascurrent ripples, wave ripples, combined wave and currentripples and crescent marks, as well as the orientation ofsticks and leaves were measured where present. Care wastaken to sample both the troughs and crests of ripples, assignificant differences in the grain size were observed. Atotal of 261 samples were subjected to sieve analysis toobtain the grain size distribution. As different transportprocesses operate in different parts of the delta, separatestudies were conducted over the river mouth area, deltafront, slope and prodelta. The values of C1–C4 wereallowed to vary between −5 and 5, and all possiblecombinations within this range were tested to find theMGE for the entire delta and its sub-environments.

Table 1 (part a) shows the results of minimising theMGE, comparing the generated vectors with theobserved vectors. The optimum coefficients definingthe FF were found to vary not only according to the sub-environment but also according to the specific methodemployed. For the delta as a whole, the Le Roux (1994b)and Rojas et al. (2000) methods give the lowest MGE of0.21, compared to 0.24 for the Gao and Collins (1992)and Rojas (2003) methods. Fig. 8 compares the vectorsgenerated by the Rojas (2003) method with the observedvectors. For the different sub-environments, the bestresults were obtained in all cases by the Le Rouxmethod,except for the delta slope where the Gao–Collins methodgave a lower MGE.

Table 1 (part b) also shows the results when thecoefficients are allowed to vary so that the Watsonstatistic is maximised. Again, the Le Roux (1994b)method gives the lowest GME for the delta as a whole, aswell as for the delta front and prodelta. The Gao andCollins (1992) and Rojas et al. (2000) methods producethe lowest GME on the delta slope and in the river moutharea respectively. However, all four methods generatecomparable results, which also agree very well with theobserved transport vectors.

4. Problems and pitfalls

Sediment trend analysis has generally produced goodresults in many different studies but there are a number ofpitfalls that should be taken into account by investigators.

4.1. Sediment sampling method

Seafloor samples are normally taken by grabsamplers such as the Petit–Ponar or Van Veen types,which usually penetrate at least 5–10 cm into the sub-surface. Depending on the sedimentation rate, differentdepositional events are therefore likely to be repre-sented. Residual transport patterns derived from samplestaken in this way may thus reflect the combinedprocesses operative over a relatively long time interval.If the rate of sedimentation is known where, forexample, a certain amount of material has to be removedby dredging at regular time intervals, then this effect canbe taken into account and seasonal transport patternsmay be determined successfully (Ríos et al., 2002). Forshort-term events such as storms, however, samplesshould probably incorporate only the top centimetre orso, in which case conventional grab samplers would beinappropriate.

Asselman (1999) used 50×50 cm artificial grassmats as sediment traps in an alluvial floodplainenvironment, deployed a few days before inundation.In the marine environment, this would be impracticalbut a possible solution to the problem may be to usesticky grease on a flat metal plate that is allowed to cometo rest on the seafloor. The grease can be dissolved torelease the sediment, using settling tube analysis todetermine the grain size distribution as only a few gramsare required.

Fig. 10. Error associated with using too large a “characteristicdistance” within which to compare neighbouring stations, according tothe method of Gao and Collins (1992). The “characteristic distance” isthe greatest distance between two neighbouring stations in the studyarea, in this case separated by a peninsula. At stations 1 and 2, virtuallythe same neighbouring stations are used to define their mean vectors,so that these would have almost similar values. This would producevery smooth overall patterns but could be completely meaninglessbecause point-to-point comparisons almost always produce “trends”.


The presence or absence of sedimentary structurescan have a very important effect on the local grain sizedistribution. Because of hydrodynamic processes,small-scale current ripples are usually much finerthan larger-scale dunes whereas flat beds can be eitherfine (if deposited) or coarse (if left as a lag). Comparinggrain size parameters over an area where differentcurrent velocities or water depths produce variousstructures along the transport path can cause trends thatare related more to the structures than to the actualdirection of transport. Even over the same bedforms,large differences in grain sizes may be present. Waveripples, for example, often display troughs that aremuch coarser than their crests (Fig. 9), and grain sizetrends can be strongly affected depending on whethereither troughs or crests are sampled at any particularlocation. Rojas (2003) sampled ripple crests andtroughs separately by scuba diving, finding that thebest residual transport patterns on a local scale areproduced when only ripple crests or troughs areanalysed at a time but that vectors are poorly definedif troughs and crests are used alternately. On a moreregional scale, this effect is less noticeable. As scubadiving is not always possible, this means that samplersshould incorporate a surface area large enough toinclude both the crests and troughs of structures. If asufficiently large (say, 50×50 cm), grease-coveredmetal plate is used, however, it would effectivelysample only the ripple or dune crests. In this way,sampling can be standardised.

A recent development is the use of automated,image-based granulometry to determine grain sizeparameters. Ruben (2004) describes a digital cameradesigned to obtain high-quality images of the sedimentgrains on the surface, which is used to determine thegrain size distribution using an autocorrelation algo-rithm. Although the technique is less sensitive thanlaboratory analysis to tails in the grain size distribution,it is 100 times as fast and is also ideal for sampling onlythe surficial sediment. Franciskovic-Bilinski et al.(2003) showed that results comparable to thosedetermined by conventional sieve and Coulter-counteranalysis can be obtained using image analysis, with theadvantage that the process is much less time-consuming.

4.2. Distribution and density of sampling stations

For optimum results, most of the methods employedto date (e.g. Asselman, 1999; Rojas et al., 2000; Rojas,2003) require a regular distribution of data stations, withthe exception of the Le Roux (1994c) method. Althoughthe methods of McLaren and Bowles (1985) and Gao

and Collins (1992) can be applied to an irregular grid, aloss of accuracy can be expected (Le Roux, 1994a).Interpolation may be used to transpose the data onto aregular grid but this alters the original data distributionand diminishes the reliability of the methods, in thesame way that filtering or smoothing can distort theresults (Le Roux et al., 2002). Asselman (1999)concluded that interpolation techniques should in anycase not be used when there is no spatial correlationbetween samples — for example, where the samplingstations are too far apart. In her GIS-based method, thesesituations resulted in semi-variograms showing whitenoise or pure nugget effects (Burgess and Webster,1980a).

The optimum space-scale of sampling has alwaysbeen one of the unknown factors in sediment trendanalysis. Gao and Collins (1992) compared all neigh-bouring stations falling within the “characteristicdistance” from the central station, which they took asthe maximum sampling interval for the particular studyarea. In Yangpu Harbour (southern China), for example,a characteristic distance of 2.15 km was used (Gao andCollins, 1992) but, in Christchurch Harbour (a similar,estuarine type of environment), the characteristicdistance was only 220 m (Gao, 1996). This is arbitraryand therefore unsatisfactory, as it depends entirely onthe decision of the particular investigator.

A more serious error involving the characteristicdistance is illustrated by the recent paper of Poizot et al.(2006). These authors used a semi-variogram to de-termine the characteristic distance, which in this case


turned out to be very large. Fig. 10 illustrates that, in sucha situation, virtually the same neighbouring stations arecompared when moving from one central station to thenext. The difference in the resultant mean vectorsproduced at any two adjacent stations would thus bevery small, which is why a smooth overall pattern isobtained. However, even random data would producesuch smooth “trends”, which would be completelymeaningless. If real trends do exist, this method shouldmore or less reflect the overall transport pattern but itcould be greatly distorted.

The best distance to use between individualsampling stations obviously depends on the sedimen-tary environment. On continental shelves, samplingstations may be several hundred metres or evenkilometres apart whereas bays, harbours and estuariesmay require more densely spaced samples, on a scaleof tens to hundreds of metres. Asselman (1999) used50-m spacing between stations on river floodplaindeposits and constructed semi-variograms to deter-mine the maximum range within which stationsshould be taken into account around every centralstation. The sills for mean size, sorting and skewnessvaried between about 250 and 400 m, which meansthat beyond this distance the difference betweensampling pairs remained constant. Samples in thisparticular type of environment should therefore not bemore than about 250 m apart, as they have no spatialrelationship beyond this distance.

Rojas (2003) used 10-m spacing between samplingstations on a small lacustrine Gilbert-type delta.Applying different methods to determine the meanglobal error while progressively eliminating samplingstations at random, he found that the MGE showedvirtually no change and remained at a minimum up to asampling density of about 40% of the initial samplingdensity. Comparing the Gao–Collins, Le Roux, Rojas,and Rojas et al. methods, the Gao–Collins and Le Rouxmethods were found to be the least sensitive to thesampling density, remaining at a minimum up to adensity of about 35%. Below this sampling density, theMGE increased sharply.

As a general rule, spacing between samples shouldprobably be a minimum of 15 m and a maximum ofabout 400 m, taking into account the specific deposi-tional environment. A spacing of 50–250 m is probablya good rule of thumb. On continental shelves, samplingdistances of up to a kilometre may be considered butthere are no studies to confirm this assumption. The bestpractice will always be to space the samples as closely aspossible and then to determine the maximum rangebetween stations from semi-variograms.

4.3. Grain size analysis

The specific method used to calculate the grain sizeparameters does not seem to play a large role in theresultant grain size trends (Hill and McLaren, 2001),although Hartmann and Flemming (2002) questioned thisassumption. The results of moment methods areanalogous to those of graphic techniques, but their deri-vation employs the entire grain population so that theyare more representative. However, where graphictechniques are especially appropriate for the analysis ofopen-ended distributions, moment methods should not beapplied unless all the grain sizes present lie within thedefined grain size limits (McManus, 1988). If, forexample, more than 1% of the population is present aspan residue, the use of moment methods may lead tomisleading, if not meaningless, results (McManus, 1988).

Hartmann (1988) argued from a mathematical andstatistical point of view that natural, unimodal grain sizedistributions are log-hyperbolic, rather than log-normal.The use of such a distribution model may thus haveadvantages over the traditional methods to determinegrain size parameters, which needs to be investigated.

Many grain size distributions are bi- or polymodaldue the mixing of sediment populations from differentsource areas or because of different transport processes.As such non-unimodal distributions can affect thesediment transport pathways obtained from trendanalysis, future studies should take this effect intoaccount by first unmixing the grain size distributions.Weltje (1997) proposed a method to decompose suchmixed populations using numerical–statistical methods.

4.4. Trend type

Different trend types can produce opposite transportvectors, so that the decision on which type to use is oftencrucial. Where there is additional information onprobable sediment transport pathways, the trend typethat produces the best correspondence with the observedor inferred directions can be employed. However, in theabsence of such information, trend types should bechosen on purely statistical grounds.

McLaren and Bowles (1985) considered two possibletrend types and analysed them separately, comparing allpossible pairs of stations along the sampling lines. Influvial environments, they found that only type 2 trends(coarser, better sorted, more positively skewed) pro-duced statistically significant results. In lacustrineenvironments, type 3 trends are dominant whereaslongshore transport produces type 2 trends. Asselman(1999) considered only types 1 and 2 trends, finding that


type 1 is more suitable for defining transport pathwayson river floodplains.

Gao and Collins (1992) took either type 1 or type 2trends into account between two neighbouring stations,summing different vectors at any specific station toproduce a single vector. However, no indication wasgiven on how vectors were chosen in cases where bothtrend types are present, which may introduce an ele-ment of bias (Le Roux, 1994a). It would be betterpractice to analyse different trend types separately andthen to compare the results with additional information,or to choose the trend type with the highest vectormagnitude or Watson (1966) statistic (Le Roux et al.,2002; Rojas, 2003).

In a study of sediment transport patterns in LirquénHarbour, southern Chile (Le Roux et al., 2002), differenttrend types produced different results, all statistically validaccording to the Watson (1966) test. The results showed avector mean of 220° for type 1 trends (vector magnitudeVM=33%), 096° for type 2 trends (VM=40.3%), 095°for type 3 trends (VM=32.9%) and 152° for type 4 trends(VM=48.8%). Based on the vector magnitude, type 4trends may be considered to best represent the actualtransport patterns, which seems to be supported by the factthat strong northerly to north-westerly winds duringwinter can push the whole water column towards theinterior of the N-facing harbour during storms (Ahumadaet al., 1983). However, weaker bottom currents measuredduring winter also indicate an SW flow, possibly pickedup by trend type 1. Trend types 2 and 3, on the other hand,seem to coincide with currents observed during summer,so that even these directions cannot be discarded. All fourtrend types showed weak and variable trends (as definedby the vector magnitude) in the eastern part of the harbour,where the most severe siltation problems also occur.Considering these results, it seems clear that the choice oftrend type must be based on either a thorough under-standing of the depositional and transport processes or onadditional information on likely sediment transport paths.

The method of Rojas (2003) does not consider anyspecific trend type and simply optimises the coefficientsfor the different grain size parameters. By maximisingthe Watson (1966) statistic, the produced trends andcoefficients in fact closely agree with results obtainedfrom minimising the MGE between observed andgenerated vectors, which implies that this method canbe used even where no additional information exists onsediment transport pathways. In a sense, this is similar tothe method of Le Roux et al. (2002) in which the trendtype with the highest vector magnitude (which deter-mines the Watson statistic) can be chosen. The onlydifference (and advantage) is that the specific trend type

is known in the Le Roux (1994c) method, facilitating theunderstanding and interpretation of transport anddepositional processes.

4.5. Relative weight of grain size parameters

TheMcLaren–Bowles and Gao–Collins methods takeonly the relative differences between the grain sizeparameters into account whereas Asselman (1999)considered all three parameters to be of equal value. LeRoux (1994b) normalised the grain size parameters so thateach has the same weight but the computer program (LeRoux et al., 2002) allows for different weights to beallocated to each parameter. However, it is uncertain howthe weight factor should be taken into account, especiallyin different depositional environments. Rojas (2003)determined the optimum coefficients for the differentgrain size parameters, which varied not only according tothe depositional sub-environment but also with thespecific method being employed. The significance ofthe different coefficients is therefore difficult to determineand it cannot be assumed that the same coefficients can beused in other or even in similar environments. Further-more, as the initial parameters are not normalised, it isdifficult to compare their actual weights. The grain size,for example, may have a range 15 times larger than therange of the kurtosis when multiplied with its optimumcoefficient, so that the influence of the kurtosis may beminimal. In general, however, larger coefficients meanthat the specific parameter has a greater influence onminimising the GME or maximising the Watson statistic.

4.6. Filtering

Because the filtering procedure proposed by Gao andCollins (1991) reduces the spatial resolution, its use wasnot recommended by Asselman (1999). Moreover,applying the TRANSVEC program to data generatedrandomly on a computer, Le Roux et al. (2002) foundthat none of the four trend types produced valid trendsaccording to the Watson (1966) statistic. However, aftersmoothing the data using a technique similar to thatemployed in the Gao–Collins method, some trend typesdid produce statistically “valid” trends. It was concludedthat smoothing should only be carried out if theunsmoothed vectors already produce statistically validpatterns.

4.7. Interpretation of results

Trend vectors obtained from grain size parame-ters are not necessarily indicative of the direction of


transport but depend on the environment of deposi-tion. For example, if applied to meandering riverdeposits, the vectors are likely to be at right angles tothe direction of transport, as the grain size variation onpoint bars is much greater into the thalweg than alongthe latter. This is because the current velocity in-creases down the point bar into the channel, which isalso responsible for the fining-upward cycles typicalof meandering river deposits. Similar effects mayoccur in estuaries with sandbars. On tidal flats,opposite current directions during ebb and flow tidesmay cancel out any grain size trends, especially ifsamples penetrate too deep into the subsurface.However, as this environment is normally exposedand sampled during the ebb tide, tidal flat records maybe biased towards a seaward transport direction if onlythe uppermost sediment layer is sampled. This wouldnot necessarily reflect the dominant transport directionin such an environment.

Gilbert-type deltas are an example of the complex-ity of transport processes that may occur in any singledepositional environment. Rojas and Le Roux (2005)studied the sedimentation processes on a small(200×150 m) Gilbert-type delta in Lake Llanquíhue,southern Chile. They concluded that lakeward-direct-ed bottom currents during storms are the mostimportant agents responsible for sediment transport.These currents would theoretically produce type 4trends on the delta front. However, sampling could becarried out only during fair weather periods, whenwaves had already partially reworked the shallowerparts of the delta. As the water velocity beneath wavesincreases in shallower water, the grain size wouldincrease shoreward whereas sediment maintained insuspension by the turbulence would also give rise to adecrease in skewness in this direction. If assumed thatthe sorting increases (deteriorates) onshore, a type 4trend will result but the actual, shoreward direction oftransport will be opposite to that normally assumed fora type 4 trend. Two completely different transportprocesses and directions can thus produce the sametrend. On the steep (30°) delta slope, sedimenttransport takes place mostly by gravity processes,which are assisted by bivalves burrowing the surfaceand continuously causing small avalanches. The grainsize therefore increases down the delta slope, whereassorting and skewness decrease so that a type 3 trend isrepresented.

Clearly, every sedimentary environment is unique,so that interpretations of sediment transport paths asrevealed by grain size trends must be based on athorough understanding of the processes involved.

5. Conclusions

Grain size parameters have been used successfully inmany different sedimentary environments to derivesediment transport paths. Most methods are based ontwo dominant trend types (1 and 2) but it is clear thatother trend types cannot be discarded. The type of trendproduced depends on the specific transport process,which should be taken into account in each particularenvironment.

The spacing between sampling stations depends onthe sedimentary environment but, as a rule of thumb,50–250 m should produce good results. It is recom-mended that the sampling density be as close as possiblebut that semi-variograms be constructed to determinethe maximum range between sampling stations for anyparticular environment. Semi-variograms should not beused to determine the characteristic distance, as this canlead to serious errors. Most methods work better with aregular grid of sampling stations but, in practice, thisoften requires interpolation between data stations, whichmay lead to a loss of resolution and accuracy. The LeRoux (1994b) method, however, can also be applied toirregular grids.

Samples should be taken as shallow as possible,preferably from the top 1 cm of the deposit and takinginto account the possible influence of bedforms. The useof a 50×50 cm metal plate smeared with sticky, solublegrease is recommended, which would diminish thepossibility of taking samples of dune troughs in somecases and crests in others. Otherwise, an underwatercamera located at a fixed distance from the bottomshould be employed to take photographs of the sampleposition in relation to possible bedforms.

The particular method used to determine the grainsize distribution and parameters does not seem to be tooimportant, as the relative values between samplingpoints are more important than the absolute values.However, moment measures should not be used foropen-ended grain size distributions.

The few comparative studies of the various methodsindicate that the two-dimensional techniques producemore representative trends than one-dimensional meth-ods, with the Le Roux method producing the bestoverall results in one specific, well-constrained study.However, it is probably better to use different methods,as they may complement each other. The Rojas methodof training the system to produce the maximum Watsonstatistic is particularly useful where different transportprocesses may operate, as it takes all possible trendtypes into account. The coefficients obtained may beused to change the weights of the different parameters in


the Le Roux et al. (2002) computer program, whichwould allow the specific trend type to be identified.

It is recommended that filtering or smoothing of theoriginal vectors should only be carried out once theirstatistical validity has been established, as this proce-dure can produce trends that do not actually exist innature.

Acknowledgements

Dr. Burg Flemming and two anonymous reviewersmade valuable comments that helped to improve thispaper. The research was completed while the first authorheld a fellowship at the Hanse Institute for AdvancedStudy in Delmenhorst, Germany.

References

Ahumada, R., Rudolph, A., Martinez, V., 1983. Circulation andfertility of waters in Concepción Bay. Estuarine, Coastal and ShelfScience 16, 95–105.

Asselman, N.E.M., 1999. Grain size trends used to assess the effectivedischarge for floodplain sedimentation, River Waal, the Nether-lands. Journal of Sedimentary Research 69, 51–61.

Burgess, T., Webster, R., 1980a. Optimum interpolation and isarithmicmapping I. The semi-variogram and punctual kriging. Journal ofSoil Science 31, 315–331.

Burgess, T., Webster, R., 1980b. Optimum interpolation and isarithmicmapping II. Block kriging. Journal of Soil Science 31, 505–524.

Calhoun, R.S., Fletcher, C.H., Harney, J.N., 2002. A budget of marineand terrigenous sediments, Hanalei Bay, Hawaiian Islands. Sedi-mentary Geology 150, 61–87.

Carriquiry, J.D., Sanchez, A., Camacho-Ibar, V.F., 2001. Sedimentationin the northern Gulf of California after cessation of the ColoradoRiver discharge. Sedimentary Geology 144, 37–62.

Cheng, P., Gao, S., Bokuniewicz, H., 2004. Net sediment transportpatterns over the Bohai Strait based on grain size trend analysis.Estuarine, Coastal and Shelf Science 60, 203–212.

Duman, M., Avci, M., Duman, S., Demirkurt, E., Duzbastilar, M.K.,2004. Surficial sediment distribution and net sediment transportpattern in Izmir Bay, western Turkey. Continental Shelf Research24, 965–981.

Folk, R.L., Ward, W.C., 1957. Brazos River bar: a study in thesignificance of grain size parameters. Journal of SedimentaryPetrology 27, 3–26.

Franciskovic-Bilinski, S., Bilinski, H., Vdovic, N., Balagurunathan,Y., Dougherty, E.R., 2003. Application of image-based granulo-metry to siliceous and calcareous estuarine and marine sediments.Estuarine, Coastal and Shelf Science 58, 227–239.

Gao, S., 1996. A FORTRAN program for grain size trend analysis todefine net sediment transport pathways. Computers & Geosciences22, 449–452.

Gao, S., Collins, M., 1991. A critique of the “McLaren method” fordefining sediment transport paths — discussion. Journal ofSedimentary Petrology 61, 143–146.

Gao, S., Collins, M., 1992. Net sediment transport patterns inferredfrom grain size trends, based on definition of “transport vectors”.Sedimentary Geology 81, 47–60.

Gao, S., Collins, M., 1994. Analysis of grain size trends, for definingsediment transport pathways in marine environments. Journal ofCoastal Research 10, 70–78.

Gao, S., Collins, M.B., Lanckneus, J., De Moor, G., Van Lancker, V.,1994. Grain size trends associated with net sediment transportpatterns: an example from the Belgian continental shelf. MarineGeology 121, 171–185.

Grant, J., Turner, S.J., Legendre, P., Hume, T.M., Bell, R.G., 1997.Patterns of sediment reworking and transport over small spatialscales on an intertidal sandflat, Manukau Harbour, New Zealand.Journal of Experimental Marine Biology and Ecology 216, 33–50.

Hammersley, J.M., Handscomb, D.C., 1979. Monte Carlo Methods.Chapman and Hall, London.

Harris, P.T., Patiaratchi, C.B., Keene, J.B., Cole, A., 1990. Modellingthe evolution of a linear sandbank field, Moreton Bay, Queensland.Report of Results Obtained During the Cruise of A.M. Brolga inJuly, 1989, vol. 41. Ocean Sciences Institute, University of Sydney.

Hartmann, D., 1988. The goodness-of-fit to ideal Gauss and Rosindistribution: a new grain size parameter — discussion. Journal ofSedimentary Petrology 58, 913–917.

Hartmann, D., Flemming, B., 2002. Discussion of: Steven H. Hill andPatrick McLaren, 2001. A comparison between log-hyperbolic andmodel-independent GSD in sediment trend analysis (STA®).Journal of Coastal Research 18, 592–595.

Hill, S.H., McLaren, P., 2001. A comparison between log-hyperbolicand model-independent grain size distribution in sediment trendanalysis. Journal of Coastal Research 17, 931–935.

Jia, J.J., Gao, S., Xue, Y.C., 2003. Sediment dynamic processes of theYuehu inlet system, Shandong Peninsula, China. Estuarine,Coastal and Shelf Science 57, 783–801.

Krumbein, W.C., 1938. Size–frequency distribution of sediments andthe normal phi curve. Journal of Sedimentary Petrology 8, 84–90.

Lanckneus, J., De Moor, G., Van Lancker, V., De Schaepmeester, G.,1993. The use of the McLaren model for the determination ofresidual transport directions on the Gootebank, southern NorthSea. Progress in Belgian Oceanographic Research, vol. 1. Instituteof Marine Research and Air Sea Interaction (IRMA), pp. 75–94.

Le Roux, J.P., 1994a. Net sediment transport patterns inferred fromgrain size trends, based upon definition of “transport vectors” —comment. Sedimentary Geology 90, 153–156.

Le Roux, J.P., 1994b. A spreadsheet template for determining sedimenttransport vectors from grain size parameters. Computers &Geosciences 20, 433–440.

Le Roux, J.P., 1994c. An alternative approach to the identification ofnet sediment transport paths based on grain size trends.Sedimentary Geology 94, 97–107.

Le Roux, J.P., 2005. Grains in motion: a review. Sedimentary Geology178, 285–313.

Le Roux, J.P., O'Brien, R.D., Ríos, F., Cisternas, M., 2002. Analysis ofsediment transport paths using grain size parameters. Computers &Geosciences 28, 717–721.

Liu, J.T., Liu, K.J., Huang, J.C., 2002. The effect of a submarinechannel on the river sediment dispersal and inner shelf sedimentmovements in southern Taiwan. Marine Geology 181, 357–386.

Lucio, P.S., Dupont,H.S., Bodevan, E.C., 2004. Sediment transport pathsin the Westerschelde: one-dimensional alternative to determinesediment trend. Journal of Coastal Research 20, 771–775.

Mallet, C., Howa, H.L., Garlan, T., Sottolichio, A., Le Hir, P., 2000.Residual transport model in correlation with the sedimentarydynamics over an elongate tidal sandbar in the Gironde Estuary(Southwestern France). Journal of Sedimentary Research 70,1005–1016.


McCave, I.N., 1978. Grain size trends and transport along beaches: anexample from eastern England. Marine Geology 28, M43–M51.

McLaren, P., 1981. An interpretation of trends in grain sizemeasurements. Journal of Sedimentary Petrology 51, 611–624.

McLaren, P., 1983. Coastal sediments of the Strait of Juan de Fuca:implications for oil spills. Current Research, Pt A. GeologicalSurvey of Canada Paper 83-1A, pp. 241–244.

McLaren, P., 1984. The Whytecliff oil spill, British Columbia:sediment trends and oil movement on a beach. Current Research,Pt B. Geological Survey of Canada Paper 84-1A, pp. 81–85.

McLaren, P., Bowles,D., 1985. The effects of sediment transport on grainsize distributions. Journal of Sedimentary Petrology 55, 457–470.

McLaren, P., Collins, M.B. 1989. Sediment transport pathways in theSevern Estuary and Bristol Channel: Severn Barrage Dev. Proj.Working Document Ref. STPG/GEOSEA/3.1(iii)f STPG/GEO-SEA/3.1(iii)f.

McLaren, P., Little, D.I., 1987. The effects of sediment transport oncontaminant disposal: an example from Milford Haven. MarinePollution Bulletin 18, 586–594.

McLaren, P., Powys, R.I.L., 1989. The use of sediment trends to assessthe fate of dredged material. Proceedings of WODCON XII WorldDredging Congress, pp. 223–233.

McLaren, P., Barrie, W.B., Sempels, J.M., 1981. The coastalmorphology and sedimentology of Cape Hatt: implications forthe Baffin Island Oil Spill Project (BIOS). Current Research, Pt B.Geological Survey of Canada Paper 81-1B, pp. 153–162.

McLaren, P., Collins, M.B., Gao, S., Powys, R.I.L., 1993a. Sedimentdynamics of the Severn Estuary and inner Bristol Channel. Journalof the Geological Society 150, 589–603.

McLaren, P., Cretney, W.J., Powys, R.I., 1993b. Sediment pathways in aBritish-Columbia fjord and their relationship with particle-associat-ed contaminants. Journal of Coastal Research 9, 1026–1043.

McManus, J., 1988. Grain size determination and interpretation. In:Tucker, M. (Ed.), Techniques in Sedimentology. Blackwell, Oxford,pp. 63–85.

Mothersill, J., 1969. A grain size analysis of longshore bars andtroughs, Lake Superior, Ontario. Journal of Sedimentary Petrology39, 1317–1324.

Nordstrom, K.F., 1981. Differences in grain size distribution withshoreline position in a spit environment. Northeastern Geology 3,252–258.

Nordstrom, K.F., 1989. Downdrift coarsening of beach foreshoresediments at tidal inlets: an example from the coast of New Jersey.Earth Surface Processes and Landforms 14, 691–701.

Pascoe, G.A., McLaren, P., Soldate, M., 2002. Impact of offsitesediment transport and toxicity on remediation of a contaminatedestuarine bay. Marine Pollution Bulletin 44, 1184–1193.

Pebesma, E.J., 1995. GSTAT: geostatistical modelling, prediction andsimulation. Computer ProgramManual. ftp://pop.frw.ruu.nl/pcraster.

Pedreros, R., Howa, H.L., Michel, D., 1996. Application of grain sizetrend analysis for the determination of sediment transport pathwaysin intertidal areas. Marine Geology 135, 35–49.

Pettijohn, F.G., Ridge, J.D., 1932. A textural variation series of beachsands from Cedar Point, Ohio. Journal of Sedimentary Petrology 2,76–88.

Pettijohn, F.G., Potter, P.D., Siever, R., 1972. Sand and Sandstone.Springer, New York, NY.

Plumley, W.J., 1948. Black Hills terrace gravels: a study in sedimenttransport. Journal of Geology 56, 526–577.

Poizot, E., Mear, Y., Thomas, M., Garnaud, S., 2006. The applicationof geostatistics in defining the characteristic distance for grain sizetrend analysis. Computers & Geosciences 32, 360–370.

Ravaioli, M., Alvisi, F., Vitturi, L.M., 2003. Dolomite as a tracer forsediment transport and deposition on the northwestern Adriaticcontinental shelf (Adriatic Sea, Italy). Continental Shelf Research23, 1359–1377.

Ríos, F., Cisternas, M., Le Roux, J.P., Correa, I., 2002. Seasonalsediment transport pathways in Lirquén Harbor, Chile, as inferredfrom grain size trends. Investigaciones Marinas, vol. 30.Universidad Católica de Valparaíso, pp. 3–23.

Rojas, E.M. 2003. Determinación de vectores de transporte utilizandoinformación exclusivamente granulométrica: aplicación al deltatipo Gilbert, del río Pescado, Llago Llanquíhue, X Región, Chile.Masters Thesis, Universidad de Chile.

Rojas, E.M., Le Roux, J.P., 2003. Determinación de vectores detransporte, utilizando información granulométrica: aplicación aldelta tipo Gilbert del río Pescado, Lago Llanquíhue, X Región,Chile. Proceedings X Congreso Geológico Chileno, SociedadGeológica de Chile, Santiago (CD Rom).

Rojas, E.M., Le Roux, J.P., 2005. Sedimentary processes on a Gilbert-type delta in Lake Llanquíhue, southern Chile. Revista Geológicade Chile 32, 19–31.

Rojas, E.M., Le Roux, J.P., Cisternas, M., 2000. Metodología yalgoritmos que permiten determinar las direcciones de transportede sedimentos utilizando parámetros granulométricos: caso teóricoy aplicación a una cuenca activa. Abstract Volume IX CongresoGeológico Chileno, vol. 1. Sociedad Geológica de Chile, Santiago,pp. 539–543.

Ruben, D.M., 2004. A simple autocorrelation algorithm for determin-ing grain size from digital images of sediment. Journal ofSedimentary Research 74, 160–165.

Russell, R.D., 1939. Effects of transportation of sedimentary particles.In: Trask, P.D. (Ed.), Recent Marine Sediments. Society ofEconomic Paleontologists and Mineralogists, Tulsa, OK, pp. 32–47.

Self, R.P., 1977. Longshore variation in beach sands, Nautla area,Veracruz,Mexico. Journal of Sedimentary Petrology 47, 1437–1443.

Shi, X.F., Chen, C.F., Liu, Y.G., Ren, H., Wang, H.Y., 2002. Trendanalysis of sediment grain size and sedimentary processes in thecentral South Yellow Sea. Chinese Science Bulletin 47, 1202–1207.

Stapor, F.W., Tanner, W.F., 1975. Hydrodynamic implications ofbeach, beach ridge and dune grain size studies. Journal ofSedimentary Petrology 45, 926–931.

Stewart, L.K., Heap, A.D., Woolfe, K.J., 2000. Evaluating theinfluence of tidal currents on the distribution of silt in Nara Inlet,central Great Barrier Reef, Australia. Sedimentary Geology 136,59–69.

Swift, D.J.P., Ludwick, J.C., Boehmer, W.R., 1972. Shelf sedimenttransport: a probability model. In: Swift, D.J.P., Duane, D.B., Pilkey,O.H. (Eds.), Shelf Sediment Transport — Process and Pattern.Dowden, Hutchinson and Ross, Stroudsburg, PA, pp. 195–223.

Uriarte, A., Franco, J., Borja, A., Valencia, V., Castro, R., 1998.Sediment and heavy mineral distribution and transport in a coastalarea affected by a submarine outfall in the Basque Country(northern Spain). Water Science and Technology 37, 55–61.

Van Deursen, W.P.A., Wesseling, C.G., 1992. The PC-RASTERpackage. Department of Physical Geography Technical Report.University of Utrecht.

Van Lancker, V., Lanckneus, J., Hearn, S., Hoekstra, P., Levoy, F.,Miles, J., Moerkerke, G., Monfort, O., Whitehouse, R., 2004.Coastal and nearshore morphology, bedforms and sedimenttransport pathways at Teigemouth (UK). Continental ShelfResearch 24, 1171–1202.

Vanwesenbeeck, V., Lanckneus, J., 2000. Residual transport paths on atidal sand bank: a comparison between the modified McLaren

ftp://pop.frw.ruu.nl/pcraster


model and bedform analysis. Journal of Sedimentary Research 70,470–477.

Watson, G.S., 1966. The statistics of orientation data. Journal ofGeology 74, 786–797.

Weltje, G.J., 1997. End-member modeling of compositional data:numerical–statistical algorithms for solving the explicit mixingproblem. Journal of Mathematical Geology 29, 503–549.

Wu, J.X., Shen, H.T., 1999. Estuarine bottom sediment transport basedon the ‘McLaren model’: a case study of Huangmaohai Estuary,South China. Estuarine, Coastal and Shelf Science 49, 265–279.

Yeakel, L.S., 1962. Tuscarora, Juanita and Bald Eagle paleocurrentsand paleogeography in the central Appalachians. GeologicalSociety of America Bulletin 73, 1515–1540.

Zhang, H., Zhu, D., 1989. The stability of Yangpu Harbour, a tidal inleton the west coast of Hainan Island, China (in Chinese). HaianGongcheng 8, 31–38.

Zhu, Y., Chang, R., 2000. Preliminary study of the dynamic origin ofthe distribution pattern of bottom sediments on the continentalshelves of the Bohai Sea, Yellow Sea and East China Sea.Estuarine, Coastal and Shelf Science 51, 663–680.

Documents

Sediment Transport