from reality to model: operationalism and the value chain of particle-size analysis of natural...

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2 (2007) 383–401www.elsevier.com/locate/sedgeo

Sedimentary Geology 20

From reality to model: Operationalism and the value chain ofparticle-size analysis of natural sediments

Daniel Hartmann ⁎

Ben Gurion University of the Negev, Beer Sheva, Israel

Abstract

This paper deals with key issues concerning operationalism and the value chain in particle-size analysis (PSA), and addressesconceptual problems of PSA measurement. In order to obtain the highest quality of information contained in a set of sedimentsamples, one has to follow an approach called operationalism, i.e. a set of recipe-like sequential operations by which a scientificproposition can be verified or rejected. Review of the literature indicates that particle sizing as a methodology suffers fromexcessive verbosity and professional jargon, and has never really matured. Is the PSA crisis a result of a fundamental failure ofconcepts and paradigms, or is it just a technical problem related to work methods? Although PSA is fundamental to theunderstanding of sedimentary processes, as well as being a basic tool in earth sciences and engineering, there is still no generallyaccepted and standardized mode of operationalism after more than a century of intensive scientific work. The sedimentologicalcommunity is called upon to come up with a unified and standardized approach.© 2007 Elsevier B.V. All rights reserved.

Keywords: Sediments; Grain size; Paradigms; Measurements; Scales; Standards

1. Introduction

1.1. General

The study of sedimentary systems and processes isessential to the understanding of present and past earth-surface processes. Three main factors interact indynamic sedimentary systems: a) The size, shape andspecific gravity of the sedimentary particles, b) the two-and three-dimensional morphology of the system, and c)the forces acting upon the system (Fig. 1). These factorsconstitute a process–response system which evolves intime and space, and fall under the heading ‘depositional

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sedimentary environments’ (Friedman et al., 1992;Boggs, 2001; among many others).

Ancient sedimentary systems are subjects of studywhere the acting forces cannot be directly measured orquantified. Indeed, often even the morphologicalevidence has faded or vanished. Geological researchon sedimentary deposits is therefore by definition a postmortem approach. Subsequently, earth scientists havedeveloped the study of proxies to replace the missinginformation. Particle size, for example, is used as aproxy for climate change and sea-level fluctuations(Prins et al., 2000; Stuut et al., 2002a,b).

Unlike the rock record, most modern depositionalenvironments enable to observe the three control factorsof the dynamic system. However, such studies are usuallylimited to low- and medium-energy situations, notrepresentative of high-energy forces and morphologies.

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Fig. 1. The sedimentary–morphodynamic process response system.

Fig. 2. The four branches of particle-size analysis.

384 D. Hartmann / Sedimentary Geology 202 (2007) 383–401

Moreover, field studies are limited in extent and time span,mapping andmeasurements on both large and small scalesbeing often reduced to a few spot locations. Therefore, theinformation content of the obtained evidence is an impor-tant, often the only option, for reconstructing the entiredynamic system.

The idea that there is process-related information in thetextural properties of sediments is relatively old (Udden,1894, 1898), and much sedimentological research duringthe first six decades of the 20th century was devoted toparticle-related studies (see Pettijohn, 1957). During thesetimes, the oil and gas industries were the driving force inthe search for a predictive capacity, i.e. the recognition anddiscrimination of ancient sedimentary environments. Suchgeological reconstructions are usually based on a smallnumber of localized samples, mostly from boreholes. Inreconstructing these environments, sedimentologistsadopted the geological paradigm ‘the present is the keyto the past’, andmore and more geological work was doneon modern sedimentary environments for basic under-standing, ground-truthing and calibration purposes (Folkand Ward, 1957; Friedman, 1967; Folk, 1971; Flemming,1988; Hartmann, 1988a, 1991). Induction from theseempirical studies showed the way to the interpretation offossil data.

The study of sediment dynamics proceeds along fourmajor branches (Fig. 2):

1) The study of the morphodynamics of sedimentarysystems, where the three factors (sediments, forces andmorphology) can be sampled and measured directly.The sub-environments of a coastal-dune system(Mason and Folk, 1958; Hartmann, 1991), the sub-environments of dunes (Folk, 1971; Vincent, 1986;McArthur, 1987), or the sub-environments of a fluvialsystem (Folk and Ward, 1957) are some examples.Sampling is usually along profiles in the direction ofthe assumed major sediment transport direction. Such

an approach only captures a limited temporal andspatial snapshot of the dynamic system, and shouldtherefore aim at a high spatial and temporal resolution.Work is often restricted by limited resources, anddifficulties in sampling high-energy events. Tounderstand the system and its sub-environments apopulation approach, here called “Process OrientedPopulation Statistics” or POPS (Hartmann, 1988a;Hartmann and Christiansen, 1992), is suggested. Thisapproach has been employed for quite some time, andcan be found in many classical sedimentary studies(Fox et al., 1966; Friedman, 1967, 1979; and manyothers). The approach requires that the sedimentarysub-environments and samples have to be mutuallyconnected by the process and therefore should not bespaced too far apart.

2) The study of surface sediments over relatively largeareas without distinct sub-environments is herecalled “Sediment Dispersal and Trend Analysis” orSEDITRANS. This approach was first used by Swiftet al. (1971), Swift et al. (1972), and Swift andLudwick (1976), and subsequently developed furtherby McLaren (1981), McLaren and Bowles (1985),Gao and Collins (1992, 1994), and Le Roux (1994).SEDITRANS is limited to surface sediment sampleswhich are mutually connected by the sedimentarydispersal process and should therefore be taken fromthe active layer only. Sampling is usually conductedunder relatively calm conditions following majordynamic events. The resulting SEDITRANS mapscan be supported by measurements of the actingforces before and during the sediment sampling andby morphological surveying of the investigated area.

3) Samples taken from sediment traps (Shih and Komar,1990a,b; Greeley et al., 1996). Depending on the natureof the investigated sedimentary system and the flux of

385D. Hartmann / Sedimentary Geology 202 (2007) 383–401

sediments entering the traps, the samples can representvery short dynamic events of a few seconds or minutes,especially for coarser sediments (gravel and sand), orvery long periods of time for fine sediments depositedduring very low flux conditions (e.g., deepsea mud orfar traveled aeolian dust). Trap samples are stronglyinfluenced by trap properties and their efficiency(Rasmussen andMikkelsen, 1998), and it is not alwaysevident whether their particle-size distributions repre-sent prevailing dynamic conditions or are a result oftrap parameters.

4) Most sedimentary research is based on samples fromoutcrops, trenches or drill cores that are not mutuallyconnected. Therefore, sedimentary successions are notnecessarily related directly by sedimentary processesand the samples are not mutually connected. It is bygeological paradigms and reasoning that we assumeconnections between superjacent samples and thatlarge-scale geological, meteorological and oceano-graphic processes bond them (Stuut et al., 2002a,b).Samples, especially those from deepsea cores, may beseparated by large distances and this casts uncertaintyon the causal relations between their particle-sizedistributions.

During the last three decades a new concept, the so-called “morphodynamic approach”, has emerged fromthe related hydraulic sciences (Short, 1999; Masselinkand Hughes, 2003; Cowell et al., 2003a,b; Dodd et al.,2003; inter alia). The morphodynamic approach focuseson two factors of the dynamic sedimentary system,namely the morphology and the forces, largely dis-regarding particle properties or simplifying them tosome basic characterizations such as median size(Grunnet et al., 2004). The step from the morphody-namic approach to sediment transport studies is veryshort. However, ‘sediment transport’ as presented innumerous publications (Van Rijn, 1993; Davis et al.,2002) tends to treat sediment properties in a reductionistmanner, commonly representing them by some arbitrarysingle ‘particle-size’. This precludes any sorting orsorting differentiation of particle sizes, i.e. size sorting isnot taken into account.

Technical progress over the last decades has improvedthe measurement techniques and instrumentation for thequantification of forces and of various elements ofmorphology and increasing the amount of field sampling,providing a better basis for inductivemodelling. Inmodernmorphodynamic research, one expects that the mostmodern methodologies and instrumentation are used(Morang et al., 1997). In analogy to sedimentologists,engineers and geomorphologists are scientists who use the

information contained in themorphodynamic elements fortheir understanding of the physical world. While theempirical morphodynamic field approach works its wayfrom samples to theory and uses an inductive approach,those who are modeling the processes use the deductiveapproach and work their way backwards, from physicaltheories to samples. However, it seems that deductivemodels, which are built on physical theory, gain no benefitfrom this advance. Pilkey and Dixon (1996) discuss thediscrepancies between theoretical and empirical morpho-dynamic approaches to coastal sedimentary behavior andshow how inept theoretical modeling is in predicting aswell as in long-term hindcasting.

1.2. Methodology

Particle-size analysis as a scientific method wasestablished by the pioneering work of Udden (1894,1898) and Wentworth (1922, 1929) between the 1890sand 1920s. They introduced the routine use of measure-ment by sieving, and the logarithmic scale with derivedhistograms and curves to present the measured data.

Particle-size analysis can be used in two entirelydifferent ways: the first and simplest one (a) is descriptive:to perform a “standard” particle-size analysis on a fewsediment samples, and then use the results for documen-tation and crude comparison. The second way (b) is aparadigmatic one, implying that the statistical informationcontained in particle-size data is related to sedimentaryprocesses. Such a paradigm about the informationcontained in particle-size data was very appealing, andthroughout the 1930s to the early 1970s geologists madewidespread use of particle-size studies for this purpose (seePettijohn, 1957; 1975; Krumbein and Graybill, 1965;Griffiths, 1967; Friedman and Sanders, 1978; Friedmanet al., 1992; Lewis and McConchie, 1994; Boggs, 2001).However, instead of dealing directly with the dynamicalprocesses, the focus was on ‘depositional sedimentaryenvironments’, reflecting the idea that all dynamicsedimentary processes follow a similar sequence of events,namely particle entrainment, transport and deposition. Allthree processes include sediment sorting. Therefore,according to this concept, different depositional environ-ments such as fluvial, aeolian, lacustrine, supra- andsublittoral or shallowmarine systemswill each be revealedin a set of bivariate diagrams by showing different patternsin their textural relationships (Friedman, 1979).

If one assumes that there is process-related informa-tion concealed in the distributions of particle-size data, itshould reveal much about the factors (forces andmorphology) that cannot be measured directly. In simpleform such factors are revealed in a sedimentary body by


trends of downdrift fining or coarsening (Nordstrom,1989). The concepts of ‘sorting’ (Friedman, 1962) and‘relative sorting’ (Walger, 1961) deal with morecomplex information, attaining even greater complexityin concepts such as ‘environmental discrimination’(Friedman, 1967, 1979) relating changes of particle-size distributions in different depositional environmentsand ‘sediment trend analysis’ (McLaren and Bowles,1985; Gao and Collins, 1992), which relate to changesoccurring in the direction of transport.

A different approach, which uses samples notdirectly related per se, purports that deep-sea sedimen-tary sequences far away from a sediment source, canreveal climatic and dynamic changes in that basin (Stuutet al., 2002a; Weltje and Prins, 2003). These analyses ofeven higher complexity include, besides particle-sizedata, also mineralogical and geochemical information(Stuut et al., 2002b).

1.3. The fate of particle-size analysis

Despite the vast amount of studies undertaken from the1950s to the 1970s, the feeling prevailed that findingsbased on particle sizing remained rather inadequate andunsatisfactory (Ehrlich, 1983), and disagreement ran rifeover standards of success and failure. Boggs (2001, page73), summarizing a ‘particle-size’ century, wrote: “Thus,it appears that after several decades of intensive researchinto the techniques and significance of grain-size analysis,during which the techniques for interpreting grain-sizedata have come to demand increasingly more-sophisti-cated statistical applications, there is little consensus as totheir reliability. Such is science!” Further on he concludesthat “…grain size reflects processes, not environments…”.This conclusion is his personal burial of a geologicalconcept that dominated one hundred years of research.

The decline of particle-size analysis triggeredmultiple efforts in the search for a solution andaccording to Law (1980) there began a process ofscientific fragmentation, as different particle-size practi-tioners developed their own variants in the course ofinterpreting their data and statistics. According to Law(1980) this process led to disagreement over standardsof success and failure in the area of particle-sizeanalysis. Were we perhaps expecting too much fromPSA and should it be restricted to the purpose oftabulation and documentation, as in procedure (a)mentioned above? What do we know, even after morethan a century of detailed investigations, about thequality of our PSA-related knowledge and its value? Areour modes of sedimentary knowledge acquisition andour modes of creating certainties universal?

The 1970s show a general decline in particle-relatedstudies in the geological community. From the mid-seventies there were many voices questioning the waysscientists approach particle-related studies and theirinformational value (Selley, 1970; Vandenberghe, 1975;Reed et al., 1975; Tucker and Vacher, 1980; Sedimen-tation Seminar, 1981; Ehrlich, 1983; Ehrlich and Full,1987; Size, 1987; Forrest and Clark, 1989; Boggs,2001). Law (1980) reflects in his paper on the declineand fragmentation of particle-size analysis and othersedimentological techniques such as ‘grain-shape anal-ysis’ and ‘heavy mineral analysis’. He notes that in the1920s–1930s the tools of clastic sedimentary studieswere limited to a small repertoire of techniques. Bet-ween about 1930 and 1950, particle-size analysis seemsto have been the single most important method and inthose years it underwent intense development. In the1950s and 1960s, methods for studying properties ofindividual particles flourished, together with parallelapproaches, mostly dealing with sedimentary structuresand sedimentary architectures, which are morphologicalfeatures and not grain properties. Despite the success ofthe latter, and the subsequent interest in hydro- andaerodynamic and other modes of sediment transport, aminority of sedimentologists retained a staunch commit-ment to particle-size analysis (Bagnold and Barndorff-Nielsen, 1980; McLaren and Bowles, 1985; Hartmann,1991; Flemming and Ziegler, 1995, inter alia).

Discrete depositional units are composed of particleswhich can be described by their textural attributes aswell asby the nature of their grains, such as mineral and chemicalcomposition, size, shape, density, volume, weight, andsettling velocity. Nevertheless, no consensus has beenreached for almost a century on standard procedures ofsampling, on standard procedures of PSA, and on thepresentation of its results. Despite the very long tradition,the level of methodological and instrumental sophisticationapplied in ‘particle-size’ analysis is low compared to thehigh level of methodologies and instrumentation used forthe relative newcomer “morphodynamics” and relatedscientific and engineering applications.

The best way to objectively judge the ‘particle-sizeanalysis’ (PSA) situation and come up with recommen-dations for the most adequate scientific work, is toperform a system analysis and a value chain analysis forour endproduct from the PSA — namely, scientificsedimentary knowledge extraction. Such an analysisrequires a differentiation between the technical methodsused and the basic concepts and paradigms applied.

Some topics in this paper have previously beenaddressed by Pettijohn (1957), Griffiths (1967), andothers. They critically discussed the way samples are


taken, size analysis is performed, statistics are calculated,and the meaning of spot sampling. Unfortunately, thosebasic technical questions have remained unanswered formany decades and little effort was expended by thesedimentological community to rectify these matters, e.g.,by Workshop I (1986) and Workshop II (1987). Somesuggestions for a unified approach were presented in thevolume edited by Syvitski (1991). Unfortunately, thosemeetings and publications had little impact, as demon-strated by the published literature since then (Boggs,2001). In this paper, I describe the particle-size value chain,its operationalism, and some concepts andmethods neededto unravel the information content of particle-size analysis.

2. Operationalism and value chain

2.1. General

In order to obtain the highest quality of informationpotentially contained in a set of sediment samples, one hasto follow an approach called operationalism, i.e. a set ofrecipe-like sequential operations by which, at the end ofthe chain of activities, a scientific proposition can beverified or rejected (Fig. 3). Operationalism is a theory inthe philosophy of sciencewhich insists on experimentationas a prerequisite to objectivity. Focusing on concepts, itrequires precisely defined experimental operations toprevent them from being meaningless. A similar approachis known from a business management perspective whereit is called a value chain. The value chain is a systematicapproach to examining the development of competitiveadvantage (Porter, 1998). The chain consists of a series ofsequential optimal operations that create and build a valueat the end of the process. They culminate in the sum-totalof value delivered by an organization. The success of abusiness depends on following the exact steps prescribed,

Fig. 3. The value chain of particle-size analysis and i

and verifying the quality of each part of the chain. This iscalled the Quality Assurance (QA) procedure or “do itright the first time”. Once a successful chain has beenconceptualized and tested, it can be reproduced again andagain as long as one sticks to the exact prescriptions and tothe QA procedures to keep bad results out of the finalproduct. It is clear that in order to attain the end of the valuechain, or to actually produce a good sedimentary scientificdiscovery, decision or prediction, the necessary steps mustbe taken in the right order, and these must always becoupled with QA procedures.

In science, the set of operations is the process calledthe scientific method. Science as a way of gainingobjective knowledge has been successful because thereis an almost universal agreement on a basic frameworkof operations. Thus in sedimentary research, particle-size studies should always follow the same format,irrespective of the journal in which it is published. Theformat consists of specific steps, starting with samplingand going on to sample preparation and splitting,measurement of a chosen property, data storage, samplestatistics, and the presentation of results in the form oftables, bivariate or ternary plots, surface grids, sequen-tial graphs, statistics and SEDITRANS maps. Thesemay be topped by a verbal presentation and interpreta-tion (Fig. 3). By using such standardized sequentialgeneric procedures, scientists do not have to spend timeestablishing the parameters of a discussion and can getto the “essence” without tripping over vocabulary orbiased views.

Besides much agreement, there is also much debateabout operationalism in science. Ideally, scientificpropositions should be tested through formal experi-mentation. However, some areas of engineering sedi-mentology, such as modern sediment transport studies,are seldom amenable to true field experimentation and

ntegrated Quality Assurance (QA) procedures.


most of the research is done either by down-scaledlaboratory experiments or by conceptualization andcomputer modeling (Pilkey and Dixon, 1996). More-over, many important scientific breakthroughs wereinitially independent of experiment, but were laterproven correct in practice, e.g. the concept of platetectonics, or the existence of huge oil reserves beneaththe North Sea. The various concepts related to sedimenttransport and sorting, and to sediment trend analysis(Swift et al., 1971, 1972; Swift and Ludwick, 1976;McLaren, 1981; McLaren and Bowles, 1985; Hartmannand Christiansen, 1988) have as yet no sound physicalbasis, and explanations are largely based on theoreticalassumptions.

Another concern is the inherent “reductionism art” ofmost scientific inquiry — the desire to know muchabout very little. Sedimentary experiments are largely“reductionist” as they explore small pieces of nature inan attempt to explain larger, more complex unities. As aresult, scientists often observe the ‘trees’ without seeingthe ‘forest’. Only by sufficient field work and goodmapping of the elements of a problem and goodvisualization of its variables can one start comprehend-ing it. Therefore, astronomers invest huge resources intotelescopes and space probes to visualize and map thestars and other cosmic objects. Biologists and micro-biologists are doing the same with binoculars andelectron-microscopes, and earth scientists take sedimentsamples to obtain basic information for mapping andunderstanding sedimentary processes. Unfortunately,since the introduction of computers at the end of the20th Century, too often the modern ‘sophisticatedscientific’ approach is to “let the modelers and theircomputers do the job”.

2.2. The sedimentary value chain

Physical operationalism traditionally requires that aresult must be reproducible. If one submits a set ofsamples to all the steps leading to measurements,anyone else who works on this set and is properlytrained should obtain comparable results. Curiously, theconcepts and results presented by Folk andWard (1957),Friedman (1979), McLaren and Bowles (1985) andothers could not always be reproduced by othersedimentologists (Tiniakos, 1978; Kachholz, 1982;and many unpublished MSc and PhD theses). Thereason for the failure is not at all clear. As it is notcommon to publish negative evidences or controversialexperiments in peer-reviewed journals (Peters, 1991),such results are missing from our knowledge base.However, the sedimentological literature of the last half

century contains much non-constructive controversyand confusion (e.g., Sedimentation Seminar, 1981),mostly due to the fact that the peer-reviewed literaturetends to reject meaningless or negative evidences,thereby preventing its use to improve the value chain.

There are many ways to take a sediment sample, andthere is no consensus which is the best (Walger, 1961;Griffiths, 1967; Emery, 1978; Grace et al., 1978). Thesame applies to the spatial or temporal density ofsampling positions, to the way in which samples shouldbe treated, especially those of poly-mineralic, poly-component or poly-bioclastic composition, or whichconsist of particle aggregates. There are various tech-niques of particle-size analysis, such as sieving, settling,image processing (Sime and Ferguson, 2003), orelectro-optical techniques for measuring particle prop-erties (Agrawal et al., 1991). In addition, particle-sizeanalyses employ different levels of resolution, forexample 1 phi, 0.5 phi, 0.25 up to 0.01 phi. The statis-tical treatment is also not standardized and employsseveral types of probability functions (Christiansen andHartmann, 1988a; Hartmann, 1988b; Brown andWohletz, 1995; Hartmann and Flemming, 2002; Weltjeand Prins, 2003). In addition, a variety of statisticalprocedures are used to describe grain-size distributionsand generate texture parameters (graphical methods,percentiles, moments, least square, maximum likeli-hood, maximum entropy etc.). Rarely is attention givento the variance associated with the estimated parameters(Christiansen and Hartmann, 1988b; Jensen, 1988).

In order to obtain reproducible measurements, onehas to apply precise and acceptable operational defini-tions of the elements building the value chain, forexample “particles”, “sediments”, “textural attributes”,“sampling”, “sedimentation unit”, “particle-size analy-sis”, “particle-size statistics”, and “SEDITRANS”. Theuse of measurement-oriented concepts increases thetestability of theories. Thus, when performing ‘SedimentDispersal and Trend Analysis’ in which changes ofparticle-size distributions occurring in the direction ofsediment transport are related to each other, the basicelements of the value chain have to be identified withoutconfusing their sequence (Hill and McLaren, 2001,2003; Hartmann and Flemming, 2002).

3. Concepts and models

Already at the beginning of the 20th century it wasrealized that grain size and the frequency distributions ofparticle sizes – on a logarithmic scale – bear importantinformation about depositional processes and sedimentaryenvironments (Wentworth, 1922, 1929; Krumbein, 1934,


1937, 1938; Krumbein and Pettijohn, 1938). As a conse-quence, sediments deposited in different environments arelikely to reveal different particle-size distributions. Otherconceptual models consider the relationship betweenvarious sedimentation processes in different depositionalenvironments, their direction and magnitude, and theireffect on the entire size distribution. Size sorting in theprocess of sediment transport is another importantconceptual model. It implies that different fluids such asair, water, ice, and different flow stages have differentcapacities to transport different particle sizes (Inman, 1949;Passega, 1957, 1964; Friedman, 1961; Griffiths, 1967).

The recognition that particle size is an importantsource of information was the initial reason for theestablishment of particle-size analysis as an importantsource of information, in the first place. This led to theinvestigation of sampling methods (Walger, 1961;Emery, 1978; Grace et al., 1978), the definition of theso-called sedimentation units (Otto, 1938), the study ofrelationships between the four statistical moments(Friedman, 1979; Sly et al., 1983; Hartmann, 1988a),and the debate about ‘relative sorting’ (Walger, 1961,Flemming, 1977). Unfortunately, these ideas anddiscussions never matured sufficiently into a unifiedoperational concept. Instead, they paradoxically seem tohave triggered a process of fragmentation (Law, 1980).

3.1. Descriptive statistics

Sedimentologists have traditionally been usingfour groups of statistical parameters to describeunimodal size distributions: a combination of a loca-tion parameter (mean, mode, median, etc.) with a scaleparameter (spread, standard deviation, sorting, andvariance), and two additional shape parameters: skew-ness (a measure of asymmetry/symmetry) and kurtosis(a measure of peakedness). At the beginning of the 20thCentury the statistical conceptual model was alreadyfairly sophisticated, demonstrating that sedimentsexhibit a large variability in distributional shapes, theresult of different processes with varying directions andmagnitude.

This statistical method was conceptually linked to themathematical–statistical model presented by Pearsonearly in 20th Century (Pearson, 1895, 1901, 1916; inLeRoy, 1981). This model was opposed to the“Gaussian weltanschauung” adopted by many othersciences and statistical textbooks published since then.However, due to its quantification complexity, Pear-son's statistical approach was never really followed orappreciated. Disciplines such as geochemistry (Ahrens,1954), biology (Koch, 1966, 1969), and even applied

physics (Kolmogorov, 1941; Hamilton et al., 2003) weresatisfied with the mathematically very limited Gauss(normal or log-normal) model and never tried the muchmore complex Pearson method. The bell-shapedGaussian function, also known as the ‘normal’ distri-bution or its logarithmic transformation, the log-normalmodel (Krumbein, 1938), was considered by a verylarge volume of scientific and statistical literature to bethe best standard model. This ‘normal’ distribution isactually a conceptual model declaring that there arealways ‘normal’ processes generating ‘normal’ orGaussian distributions. Ignorance and misunderstandingover the years reinforced this misconception, althoughempirical data based on a large number of observationsrarely (if ever) showed a symmetrical, bell-shapeddistribution. The misunderstanding is not only scientif-ically but also linguistically and epistemologicallymistaken, because geologists were using the first fourmoments to describe grain-size distributions withoutbeing aware that the normal and log-normal functionshave only two parameters (mean and variance).Variations in the values of the third and fourth momentsare indicators of non-normality. “Normality” or theGaussian function is described by a symmetrical bell-shaped curve with infinite, i.e. non-truncated tails,which are the product of an infinitely balanced process.Most sediments, however, are characterized by discrete,non-symmetrical size distributions with truncated tails,which express the natural size limits of the availableparticles. Furthermore, sedimentary processes are al-ways force- and time-limited, non-symmetrical andunbalanced (Hartmann, 1988b; Christiansen and Hart-mann, 1988a, 1991).

Sedimentologists, noting that PSAs often showunimodal, negatively or positively skewed and variouslypeaked size distributions, traditionally use the statisticalmoments skewness and kurtosis to show how far thedistributions are away from being ‘normal’. In spite ofthis awareness, the term ‘log-normal’ distribution iscommon in the literature. One could say that some of theconflicts emanating from PSA are directly related to thewording of the common statistical paradigms in use.Another problem is the mistaken usage of statistics-related epistemology in modern sedimentology. Pear-son's model (e.g., in LeRoy, 1981) about the availabilityof a wide range of mathematically linked statisticaldistribution forms, and its modern version in the form ofthe hyperbolic distributions, (Barndorff-Nielsen andChristiansen, 1988; Barndorff-Nielsen et al., 1991;Hartmann and Christiansen, 1992) was in fact nevercorrectly approached and hence not adopted by modernscientists.

Fig. 4. Obtaining knowledge from a particle-size value chain:a) without Quality Assurance (QA) (present situation); b) with QualityAssurance (QA) procedures.


As calculation of the four statistical moments of theparticle-size histogram was a very laborious task ina world without computers, some simplified andprovisional methods using percentile statistics weredeveloped in the first half of the 20th Century, leading tothe use of the so-called graphic parameters (e.g., Folkand Ward, 1957). This approach was highly creative andmost appropriate a few decades ago. Curiously, eventoday these transient PSA tools are still in use, as isreflected in modern publications, textbooks and class-room lectures. Today, almost every school kid possessesa personal computer or has access to one with the abilityto perform all sorts of complicated statistical calcula-tions for accurate mathematical parameter estimations.However, as long as the ruling epistemology of statisticsand particle-size analysis remains in place, misconcep-tions and resulting confusion will obscure data analysisand interpretation.

A large body of unimodal empirical data showsparticle-size distributions that do not appear as a straightline on a log-normal probability scale. Following ideasmainly presented by Visher (1969), some sedimentol-ogists have abandoned the idea of possible assortment indistributional shapes. Their statistical descriptive per-ceptions diverted back into the path of the conceptualmodel relating everything to ‘normal’ distributions.Therefore, treating non-normal grain size distributionstends to regard them as being composed of a few (log)-normal subpopulations. Visher (1969) applied theconcept of mixed log-normal populations. Manyadherents of this opinion were supporters of the “log-normal concept” and hence advocated the idea thatskewed unimodal distributions were composed of threelog-normal components. Therefore, one of their firststeps during particle-size analysis was to “unmix” thosedistributions. Tanner (1964) had already demonstratedthat a mixture of two unimodal populations can producethree straight line segments. The persistence of this“mixture” misunderstanding and complexity isaddressed in Christiansen et al. (1984) who showedthat a precise unimodal log-hyperbolic distributioncould easily be mistaken for a mixture of three log-normal subpopulations.

3.2. Resolution and sampling

Natural phenomena can be considered at differentlevels of resolution (Krumbein and Graybill, 1965;Mandelbrot, 1977; Dott, 1988; Hartmann, 1988a;Hanson et al., 2003; Cowell et al., 2003a,b; Doddet al., 2003) as shown schematically in Fig. 4. PSA canprovide knowledge only if we perform our value chain

at one and the same level of resolution during the entirescientific operation. One of the most important aims insediment dynamics research is recognizing the directionof sediment transport. Sediment transport is intimatelyassociated with grain-sorting (e.g., Curray, 1960;Griffiths, 1967; Swift and Ludwick, 1976; McLaren,1981; McLaren and Bowles, 1985; Hartmann, 1991;Gao and Collins, 1992; Le Roux, 1994).

When studying spatial or temporal grain-sortingprocesses, one has to take into account different levels ofresolution and, in consideration of the value chain, onehas to employ the same temporal and spatial scalesthroughout the study. This is indeed common practice inmodern morphodynamic studies, both by modeling orempirical approaches (Cowell et al., 2003a,b; Hansonet al., 2003; Dodd et al., 2003). Use is made ofaggregated-scale behavior models for coastal studiesand management purposes, which distinguish betweenlow-order (geological) time scales of 108 to 103 years,medium-order (engineering) time scales of 102 to100 years, and high-order or very short (event andsynoptic) time scales of 10−1 to 10−8 years, i.e. days toseconds.

Qualitative and quantitative spatial and temporalaspects in grain-sorting processes within a sedimentary


basin or part thereof (Folk, 1971; Flemming, 1977;Kachholz, 1982; Lancaster, 1986; Hartmann, 1988a,1991; Hartmann andChristiansen, 1992) differ dependingon whether grain-sorting processes are tracked in smalltidal inlets (Hartmann and Bowman, 1993), along shortsegments of a particular river (Folk and Ward, 1957), onsingle aeolian dunes (Barndorff-Nielsen et al., 1982;Hartmann and Christiansen, 1988), along cross-sectionsof an aeolian dune (Vincent, 1996), or within singlelaminae (Walger, 1961; Ehrlich, 1964; Emery, 1978;Grace et al., 1978; Cheel and Middleton, 1986a,b). Themain difference in such studies has to do with sampling,namely the decision which part of the deposit orsedimentation unit should be sampled.

Some authors proposed that a single lamina re-presents the true ‘basic’ sedimentation unit in eventstudies. Dyer (1986), summarizing the findings of manystudies about turbulent bursting and resulting sedimentmovement, rejected this assumption. His findings aremore in accordance with the model of a sedimentationunit as originally defined by Otto (1938). According toDyer a single lamina represents a single bursting event.However, non-graded or inversely-graded laminae maybe produced by the combination of a burst of varyingduration and intensity, and settling lag. Thus, in sed-imentology we have to distinguish between event

Fig. 5. Levels of resolution in sedimentary

characterization (analogous to weather) and facies char-acterization (analogous to climate). According-ly, “event” sampling needs to be distinguished from“facies” sampling.

Those observations raise the question to what extentconventional sedimentary studies are able to stay at oneand the same level of resolution. At a very high level ofresolution, single-burst sedimentation units may yieldimportant information about the bursting phenomenon.At a lower level of resolution, the varying bursts are justa noisy component in the dynamic pattern, and theresearcher would try to bypass them by sampling thesedimentation unit which represents the entire activelayer and not the laminae of which it is composed. Astudy dealing with the seasonal variations of a beachwill consider a stormy day as a noise element or a“burst” in the seasonal pattern, and so on. In each case,the different level of resolution demands a differentsampling strategy.

To distinguish between various time–space scalesone can adopt the nomenclature of Cowell et al. (2003b)in their coastal-tract systems and system scales, forexample meta-scale sorting (zero and first order), macro-scale sorting (second order), meso-scale sorting (thirdand fourth order), and micro-scale sorting (fifth and sixthorder) (Fig. 5). Different spatial scales are connected to

studies: temporal and spatial scales.


different temporal scales: meta-scale sorting may berelated to long-term processes (geological time scale)(Dott, 1988; Flemming, 1988; Stuut et al., 2002a; Weltjeand Prins, 2003), macro-scale sorting with seasonalactivity (Hartmann, 1991), meso-scale sorting withsingle (meteorological or one storm) events (Barndorff-Nielsen et al., 1982), micro-scale sorting with single“incidents” or a few minutes of wind activity (Hartmannet al., 1994; Namikas, 2003) or one breaking wave(Hartmann, 1988a), and super micro-scale sorting with“individual occurrences” (a wind gust moving a fewgrains) (McEwan and Willetts, 1991; Rice et al., 1996).

The different sorting processes acting at differenttemporal–spatial scales (as for example a barrier–islandsystem with its related sub-systems, a delta–wedge, tidalsand banks, a double crescentic bar system in a particularcoastal segment, a single seif dune, a single ripple, alamina (comprising a few grains) together define aprocess–response system (Krumbein and Graybill,1965). When dealing with such a feedback model, it isimperative that the researcher remains at the same scalefor all three elements (forces, sediments andmorphology).A feedback model can achieve sedimentary equilibrium(Dott, 1988) and the grains will then reflect the “true”dynamic situation. Equilibrium implies that process,forces, material and geometry form a self-correctingbalance and that the forces are saturated. However, such asedimentary system can also be at any intermittent stagewhich is not necessarily in equilibrium, and then thegrains will not reflect the equilibrium dynamics of theenvironment but the sorting stage they happen to havereached. The forces are thus unsaturated. Similar topicsare dealt with by Hanson et al. (2003) and Dodd et al.(2003). In such a case it would be erroneous to draw directconclusions about the dynamic processes on the basis ofthe grain distributions (Hartmann, 2002). Since differentenvironments and dynamic sedimentary systems needdifferent time spans to achieve equilibrium, one of the firstissues to be resolved before sampling is to establish therelationship between the three elements of the sedimen-tary system and the stage they are in.

Different levels of resolution demand different sam-pling methods and different sampling densities reflectingthe scale of sorting which is investigated (Davis andConley, 1977; Mandelbrot, 1977; McPherson and Lewis,1978; Flemming and Ziegler, 1995). Plant et al. (2002)discuss the scale of errors in nearshore bathymetric dataand its relation to sampling density. According to them, theresulting aliasing in bathymetric maps caused by samplinglimitations is an artifact of a non-appropriate sampling rate.They add that measurement errors can significantlycontaminate the variability at resolved scales, and may

lead to large errors in the representation of the scales ofinterest. Hardly any sedimentological paper deals withthese topics (Hartmann, 1988a).

3.2.1. Effect of geological phenomena and of time scaleAs mentioned above, geological phenomena and

events can be viewed at different levels of resolution.Once a resolution level has been chosen, it would beinappropriate to change to another level in the course ofthe same investigation. Typical questions to be asked,for example, are: Is the research interest focused on anaeolian sedimentary basin (Folk, 1971; Lancaster,1986), a single dune (Tsoar, 1978; Barndorff-Nielsenet al., 1982; McArthur, 1987; Hartmann and Christian-sen, 1988), alongshore variations of sediments (Masse-link, 1992), the dynamic layer of a specific nearshoremorphology (depth of activity/disturbance or mixing-zone) (Greenwood and Mittler, 1984; Greenwood andSherman, 1984; Kraus, 1985; Hartmann, 1991; Hart-mann and Christiansen, 1992), the uppermost lamina ofripples on a single dune of a specific morphology (Tsoar,1975), or beach lamination (Walger, 1961; Bridge,1978; Emery, 1978; Cheel and Middleton, 1986a,b)?

3.2.2. Effect of forcing agentsThe same questions about the level of resolution

must be considered with regard to the forcing agents(Morang et al., 1997). One level would be appropriate tolong-term forcing, such as the annual distribution ofwave parameters and wave climate (e.g. Goldsmith andSofer, 1983) that induce a long-term along-shoreunidirectional sediment transport (e.g. Carmel et al.,1984; Hartmann, 1988a; Perlin and Kit, 1999), or thedistribution of wind parameters (climate) that influencethe large-scale morphology of dunes (e.g. Sneh andWeissbrod, 1983). Seasonal activity which governsmorphological features should be measured by shortertime scales, such as the development of nearshore barsystems (Goldsmith et al., 1982; Bowman and Gold-smith, 1983), or the movement of a longitudinal dune(e.g., Tsoar and Yaalon, 1983).

Whereas the macro-measurement approach is appropri-ate for the study of the wave or wind regimes (climate) in arelatively large area, micro-measurements are only suitedfor investigations at a high level of resolution in a veryrestricted area and within a relatively short time frame.

In studying marine and beach environments, dynamicparameters (waves and currents) are typically measuredover time periods of about 15 min (Morang et al., 1997).This short time can be very eventful, influenced by eddiesand bursts and, in some sub-environments such as rip-heads, it can be very variable (Bowman et al., 1988).


Sedimentologists rarely carry out comparative studies atsuch high resolution levels (Hartmann, 1988a).

3.2.3. Sediment samplingSampling techniques and grids should be chosen

according to the phenomenon or event to be studied(Size, 1987). A priori, the variability of a sedimentaryphenomenon or an event is often not known. A fewsediment samples will give quick results (e.g., Masselink,1992; Vincent, 1996), but how reliable are these resultsand what knowledge will be gained at the end of theparticle-size value chain? The sedimentological literatureis full of papers based on a rather small number ofsamples (Barndorff-Nielsen et al., 1982; Komar, 1985;Lancaster, 1986; Lancaster et al., 1987), whereas othersare based on many hundreds or even thousands ofsamples (Bryant, 1977; Flemming, 1977; Tiniakos, 1978;Kachholz, 1982; Hartmann, 1988a; Flemming andZiegler, 1995). The number of samples is influenced byboth scientific and economical considerations. In eithercase, the sampling is the most important step in thesedimentological investigation. If we collect samples notrepresentative of the phenomenon or event and thensubmit them to meticulous measurements and processing,the results may nevertheless be of limited use for theendproduct in our value chain. This problem has rarelybeen discussed. Kothyari (1995) mentions a general ab-sence of sampling standards for fluvial sediments. Riceand Church (1996) discuss the influence of surfacesampling of fluvial gravel on the precision of percentileestimates, and refer to some other work dealing withsampling problems in the fluvial literature.

The overall sampling density (number of samples persurface unit) in an investigated area (cf., Flemming,1977) should be one of the most important items incomparing research by different authors. However, onehas to make allowance for the dynamic nature of thesampled sedimentary unit and the time frame that itrepresents.

Walger (1961) suggested that we introduce asampling error when mixing material from differentlaminae. Emery (1978) and Cheel and Middleton(1986a) tried to resolve this problem. However, theconcept and definition of a layer should be related to thelevel of resolution we work in (Fig. 5), and not just takenas something arbitrarily very thin and very small.

3.3. The population concept and population dynamics

According to Krumbein and Graybill (1965, p. 61),“A geological population comprises a class of objects,events, or numbers that are of direct interest in a

geological study”. This means that a scientist hascomplete control of the conceptual population withwhich his study is concerned, but this conceptualgeological population has to be defined, mentioning atleast three characters:

1) Specification of the elements of the population (e.g.dimensions, mineralogy, chemical composition, fos-sil content etc.);

2) Specification of the various attributes of theelements, and the kind of measurements to bemade (for particle size it could, for example, be thesize as registered by a standard sieving procedure, asseen under a microscope, as registered by settlingtube, or as seen by one of the modern electro-opticalinstruments);

3) Specification of the limits of the population. Theselimits may apply to the samples, or to somelimitations of the measuring device.

Sedimentologists, dealing with the sediment blanketof a specific sedimentary basin or one of its environ-ments/sub-environments/elements, have to make thisconceptual decision and make these working defini-tions. Their concept should encompass the entiredistribution of the population, its nature being deter-mined by the objective of the study (Miller, 1954; Millerand Olson, 1955; Griffiths, 1960; Krumbein, 1960;Greenwood, 1969). After making the decision, oneshould consider how to sample this population and whatthe relationships between the individual samples mightbe. Are they mutually connected by the sedimentaryprocesses under investigation or are they taken random-ly from a larger population under scrutiny? Usually, thespatial distribution of sediments is aligned and orientedin response to the dynamic processes being studied. Thisshould draw our attention to the possibility that samplesmay not be random as required by statistical procedures.On the contrary, sediments are usually taken in asystematic manner, designed to obtain more or less evensample coverage of a larger population. This raises thequestion regarding the number of samples that wouldadequately represent the true sediment population. Thus,a certain relationship must be pre-assumed between thesamples from the defined population and the processesacting upon them, all this within the framework of anappropriate level of resolution (Otto, 1938; Miller, 1954;Middleton, 1962; Jopling, 1964; Flemming, 1977;McPherson and Lewis, 1978). Only within such aframework, through sedimentological considerationsand statistical analysis one can gain knowledge aboutthe sedimentary morphodynamic processes.


A unimodal grain-size distribution describing asingle sediment sample is sometimes portrayed as apopulation. On the other hand, if the cumulative curveof a particle-size distribution is a segmented line on(log)-normal probability paper, it is commonly regardedas composed of two or three populations or subpopula-tions (Visher, 1969; Ashley, 1978; Viard and Breyer,1979; Bryant, 1986; inter alia). This means that theindividual grains are the samples and all the grains ofone sample are actually the investigated population. “Itis important to note that the population is, in fact, the‘sample’ itself, not the beach. …, no valid inference canbe drawn from the size distribution of the spot samplesabout the size distribution of the beach as a whole”(Middleton, 1962, p. 755).

Similar to the definition of the term “population”, it ispossible to define a spot sample as a population. Thepurpose of the study plays a role in choosing adefinition. Shea (1974, p. 993) remarked that “Popula-tions were generally not defined, and the conclusionsreached were not restricted to the population sampled”.Therefore a study dealing with a sedimentary environ-ment or event should enlarge the concept of a populationto the entire mass of grains interacting with theenvironment and with the sedimentary process (activelayer) which are the target population, and to call thesingle sediment sample by its name: a sample. Ac-cording to McLaren (1981, p. 623) “A grain size dis-tribution cannot, by itself, identify the environment ofdeposition with any certainty”, because it is only onesample drawn from an unknown and undefinedpopulation. Unfortunately, much of the literature dealingwith textural analysis ignores this very crucial point.

An environment would be quite understandablethrough a definition of its population (Miller, 1954;Miller and Olson, 1955; Krumbein, 1960; Krumbeinand Graybill, 1965) at a proper level of resolution. Forexample, the grains of an active layer of an investigatedarea would represent the sedimentary target population.This ‘true’ population is not entirely available for directstudy because of resource limitations, and therefore afinite number of samples should be taken on asystematic sampling grid. Hartmann (1988a, 1991)reports how samples were taken in a few samplingcampaigns in different littoral sub-environments. Theelements of the working (sampled) populations are thesesamples and if the number of samples is large enough,they may serve to represent the true population. Fieldsamples commonly consist of many millions of sandgrains which must be reduced in number (or mass) bysplitting into sub-samples, which consist of perhapssome tens of thousands of grains (for settling tube or

electro-optical measurements). By measuring settlingvelocities in a settling tube, Hartmann (1988a, 1991)and Goldbery and Tehori (1987) obtained a distributionof values (up to 750 fractions for sand). Combined, allthese sample distributions represent the samplingpopulation, which can consequently stand for the truegrain population in the larger study area. This approachwas pioneered by Folk and Ward (1957), who measuredthe sand and gravel frequency modes of hundreds ofsamples to learn the sedimentology of a fluvialenvironment. Kachholz (1982) used the same conceptfor littoral sediments, studying the grain-size modes ofseveral thousands of sand samples. Balsillie and Tanner(1999) refer to the same procedure and call the statisticsrelated to samples “suite statistics” as distinguishedfrom “composite statistics” for the physically combinedsamples, to produce a suitable composite sample.

Hartmann (1988a, 1991) combined all empiricalparticle-size distributions and not only the modes. Thisapproach was previously used by Russel (1968) andShea (1974) in an attempt to overcome the problem ofthe deficiencies of clastic particles of certain sizes. Theirapproach was on a regional, very low level of resolution,whereas in the case of Hartmann, the sampled popula-tions were from a 60 km beach segment, the ‘targetpopulation’, and the investigation was at a higher levelof resolution.

The guiding concept was that if the true sedimentpopulation is a probabilistic entity, then the combinationof all the single distributions, which are the distributionsof the measurements, should result in a stable empiricaldistribution, whether unimodal, bimodal, or evenpolymodal. In Hartmann's (1988a) study, only thecombined distributions were called populations, thesebeing geological populations which he called super-samples. Super-samples can be generated by eitherphysical or computational mixing, as already pointedout by Balsillie and Tanner (1999).

3.4. Quality Assurance, errors and noise

In order to keep the value chain at the highest possiblelevel, Quality Assurance (QA) procedures are required.QA and quality control are today standard practice inenvironmental monitoring (Theocharopoulosa et al.,2001; Asmund et al., 2004), especially in soil pollutionand soil quality evaluations. The representativity andreliability of the results are dependent on soil sampling,soil pre-analysis treatment, and soil analysis. This shouldserve as a model for particle-size studies, too.

QA procedures would require us to consider everyelement of the value chain (Fig. 3) and, in addition, to


look for errors in logic when trying to understand anatural system (Winkelmolen, 1982). Sieving has fordecades been used to obtain grain-size data because it is arelatively simple, though crude procedure and theconcept of sieving is seemingly easy to understand andto apply. From a logical point of view it would have beenmore appropriate to look for hydraulic attributes (such assettling velocity) which are more closely related to thetransport behavior of particles, i.e. the physical forcingagents and the hydraulic properties of the grains. Mostsedimentological laboratories which perform grain-sizeanalysis by settling tube, convert the measured settlingvelocities into calculated ‘equivalent grain size’ relative toa defined standard, e.g. quartz spheres (Gibbs, 1972,1974; Goldbery and Tehori, 1987; Guillen and Palanques,1997). Thus, the problem of information content inparticle sizing is partly confounded by the way we look atsamples and measure sedimentary processes. Sorting andsorting differentiation of sediments can be observedalmost everywhere. However, these phenomena cannotbe easily reproduced even today, and only a constant andrepeated check of our conceptual and working models(Bagnold, 1979; Ehrlich, 1983; McLaren and Bowles,1985; Christiansen and Hartmann, 1988a, 1991; Hart-mann and Flemming, 2002) may produce a more exactpicture of the physical world.

In addition to errors in logic made along the links ofthe value chain, every step in the value chain of a scien-tific investigation inherently incorporates a combinationof information (or signal) and noise. A scientific valuechain should keep the information/noise ratio as high aspossible by means of sustainable QA procedures.

Barndorff-Nielsen and Christiansen (1988); Barn-dorff-Nielsen et al. (1991); Hartmann (1988a, 1991);Hartmann and Christiansen (1992), among others, haveshown that sedimentary processes such as erosion,winnowing, transport, sorting, and deposition areprobabilistic. Dyer (1986, p. 311, referring to others)explains the onshore–offshore transport of grains byusing the skewness of the probability distribution ofsome wave attributes, obtaining a set of values for eachattribute. This and similar sets contain information andsuperimposed noise, (Fig. 4, but also see Otto, 1938;Jopling, 1964; McLaren and Bowles, 1985) dependingon the sedimentary environment. Sediment noise mayconsist of the local contribution of bioclasts, more thanone source for the sediments, mixing of different layersby bioturbation, gustiness or short-duration dynamicevents, etc. In the littoral environment, a local river may‘contaminate’ the sediments brought by a major river. Ata lower resolution level, the absence of a bar can exposeone beach segment to higher energy than a neighboring

segment sheltered by a bar. A local patch of shellmaterial can coarsen a beach deposit in comparison withneighboring beach segments subject to the samehydrologic conditions.

Figs. 3 and 5 show a general system for analyzinggeological phenomena and events. However, every stepalso contains some natural and man-made noise. Thenatural noise is inherent in the information and shouldbe recognized and considered; the man-made noiseshould be recognized, reduced or, if possible, eliminat-ed. What do we know a priori about the sediment noisein a given locality? Natural noise may often beconsidered as random noise. Analyzing many samplesfrom a particular population can expose the distributionof the population for a given property (Hartmann andChristiansen, 1992), but we still see things through oureyes (or our instruments and tools). Our aim should thusbe to use the most objective and flexible “eyes”, as forexample settling velocity measurements instead of sieveanalysis. The inherent sediment noise (Bryant, 1977;McLaren and Bowles, 1985) can be quite distractive.The problem is that we usually do not know beforehandwhat is information and what is noise. Only very largedatabanks can provide clues about the more intricate,informational properties of the investigated phenome-non (Flemming, 1977; Hartmann, 1988a, 1991; Hart-mann and Christiansen, 1992).

In dynamic investigations we have to integrate oursampling over short time intervals (about 15 min in thenearshore environment). Where a sample comprises afew seconds, it cannot bear proper information becauseit is not possible to decide whether it is information ornoise. In most sedimentological sampling known fromthe literature, the investigator relies on his educatedintuition (Winkelmolen, 1982). Lowright (1973) andMcLaren (1981), among others, point out that a singlesediment sample has nomeaning for the identification of adepositional environment. This is especially true forstudies performed in beach or fluvial environments whichare very variable in space and time. How many samples,then, are required to produce a reliable information signalin a given investigation? This question needs carefulconsideration in every new study.

3.5. Size measurements

Any measurement technique involves the recording ofinformation together with noise, and a characteristicfeature of numerical measurements is their inconsistencyin repeated measurements (Krumbein and Graybill,1965). Four kinds ofmeasurement error are distinguished,associated respectively with the observer, the instrument,


the operational definition and the measurement processitself. Gross errors are usually large in magnitude andirregular in occurrence. Systematic errors are more subtleas they may be produced by an ill-functioning instrumentor by inadequate computing tools. Errors of method occurwhen there is a discrepancy between the conceptualdefinition of the quality to be measured and theoperational definition used to make the measurements.In the case of particle-size analysis, typical questions arewhether or not to use sieve-size, optical-size, electro-optical and laser or settling-size, and which technique andinstrumental configuration would be “best” (Gibbs, 1972;Agrawal et al., 1991; McCave and Syvitski, 1991;Syvitski et al., 1991; Molinaroly et al., 2000). Apartfrom these errors there still remain unpredictable randomerrors. The danger in the first three error types is that theywill be ignored or even misinterpreted as representingproper environmental signals (Visher, 1969; Christiansenet al., 1984). A strongly critical view is presented inWinkelmolen (1982, p. 264): “... procedures such assieving and settling tube measurements are stochasticprocesses, so that the results obtained should at least bepartially attributed to the measuring techniques”.

Where several different techniques and analyticalinstruments are used (as for particle-size and particle-shape analysis) inter-instrumental and inter-laboratorycalibrations have to be made for meaningful compar-isons. However, one of the main problems is that sievingis a traditional measurement technique and many mea-surements have been obtained by this method over thepast century. For this reason most scientists feel boundto this technology. Even today, with a wide spectrum ofavailable instrumental techniques, many authors ofparticle-size studies feel obliged to relate results to thesieving “standard”.

Rubin (2004) points out that particle-size analysis isusually performed in the laboratory on samples thathave been taken out of their natural context. To over-come this, Rubin introduces a new method for the in situdetermination of grain size from digital images ofriverbed sediments. Particle size is thus determinedwithout destroying the spatial framework, while thesedimentary process is running. The method canvirtually provide real-time particle-size analyses, andis moreover much faster than the conventional methods.Nevertheless, it is not quite clear what “particle-size” isactually measured by this new technique.

4. Summary and conclusions

This paper advocates the use of operationalism andthe value chain in particle-size analysis. It seeks to

generate debate by summarizing and reviewing keyissues about PSA concepts, paradigms and models, aswell as measurements and parameterization of PSA.We may ask again whether the crisis in PSA is theresult of a fundamental failure of concepts and para-digms related to sedimentary particles and their texturalattributes, or whether it is merely a technical issuerelated to how PSA is performed. If the last assumptionis correct, then the question is whether the problemcan be solved by simply improving our methods andtechniques.

The most common error in debating particle-sizeanalysis and its contribution to understand sedimentaryprocesses is the confusion between method and theory.From the perspective of operationalism (the yardstick ofempirical science), any science should initially bedefined by its techniques and then by its theories. Thesystematic analysis of this issue has clearly shown that‘particle sizing’ as a methodology and tool to map,visualize, develop and support theories dealing withsedimentary processes, has never really matured. Over-flowing verbalism and professional jargon in the PSAliterature over the last century have hopelessly cloudedthe issue and there is no agreement on how to do itcorrectly.

Rossi et al. (2003) definemeasurement as an empiricalprocess allowing assignment of numbers to attributes ofobjects or events in such away as to represent the relationsamong them. Particle-size measurements are meaningfulas they reproduce, in a numerical space, relations that canbe related to situationswhich actually take place in the realworld. When we measure a sedimentary property such asparticle-size distribution, we assume that this can provideus with some kind of real-world information and that theaim of the PSA is to reveal this information. Thisassumption should be in our mind at all times, and byjoining forces we may eventually arrive at some unifiedmethodology and its applications. Although PSA isfundamental to the study of sedimentary processes, anda basic practical tool in the earth sciences and engineeringfor over a century, it still lacks a standardized mode ofoperationalism. It is time that the sedimentologicalcommunity rises to this challenge.

Acknowledgments

This study benefited from financial support while Iwas on sabbatical at Bremen University and the DFGResearch Center ‘Ocean Margins,’ Bremen, Germany,and the Hanse Institute for Advanced Study, Delmen-horst, Germany. I also thank Monique Delafontaine,Jacobus LeRoux, Dan Bowman and Burg Flemming for


their valuable and critical suggestions and discussions atthe early stages of the manuscript. Incisive and highlyconstructive editorial comments by two anonymousreviewers who helped in the final revision of this paperwere received with sincere gratitude.

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