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Keywords:

  • Erodibility;
  • Erosion rates;
  • Sediment transport;
  • Sediment stability;
  • Uncertainty

Abstract

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

Quantitative prediction of the erodibility of muds and mud-sand mixtures is, at present, seldom possible without resorting to direct measurements, preferably in situ. A variety of devices and protocols have been developed for erosion testing, but a considerable degree of uncertainty remains with regard to the accuracy and comparability of the resulting data. This paper argues that differences in experimental protocols and data analysis procedures are a major contributing factor to uncertainty in estimates of sediment erodibility. In particular, the likelihood of a time-dependent erosion rate response under typical erosion testing conditions means that the time history of applied forcing and the chosen protocols for analyzing and interpreting data directly affect derived erosion parameters. Several straightforward ways to address this problem are suggested, including standardization of experimental design and data analysis protocols, explicit recognition and adoption of appropriate erosion model(s), and allowing for potential time/depth changes in erodibility. Experimentalists should also archive and share erosion-test time series, not just derived parameters, so that data sets may be reanalyzed within a different framework if necessary. An example is presented from an intercomparison experiment between the Virginia Institute of Marine Sciences Sea Carousel and the University of Maryland Center for Environmental Science Microcosm System, carried out in the upper Chesapeake Bay (Maryland, USA) in May 2002. Derived parameters appear to be incompatible when the data are analyzed using different procedures, but real similarities and differences are readily apparent when the data are analyzed using the same procedures.


EDITOR'S NOTE:

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

This paper is among 9 peer-reviewed papers published as part of a special series, Finding Achievable Risk Reduction Solutions for Contaminated Sediments. Portions of this paper were presented by the author at the Third International Conference on Remediation of Contaminated Sediments held in New Orleans, Louisiana, USA in January 2005.

INTRODUCTION

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

It has long been recognized that the factors affecting the erodibility (the inverse of stability) of muds and sand-mud mixtures are many and complex. For purely fine, cohesive sediment beds, erodibility is a function of sediment grain size, water content, mineralogical composition, organics, cation exchange capacity, and biological activity, as well as the ionic composition, pH, and temperature of the water (Mehta 1986; Tsai and Lick 1987; Roberts et al. 1998; Paterson et al. 2000). Water content is perhaps the most important of these factors. Laboratory remolded sediments tend to show little change in water content with depth into the bed (Roberts et al. 1998), but deposited fine sediments often show profound changes with depth, especially near the sediment surface (Figure 1). When sediments are mixtures of sands and muds, armoring of the bed surface by winnowing of the fines also becomes an important factor limiting erodibility (Wiberg et al. 1994; Reed et al. 1999).

One consequence of this complexity has been the recognition that fine sediment erodibility is very difficult to predict a priori, so that in practice it must be measured at each site. A number of techniques to measure fine sediment erodibility have been developed, ranging from laboratory flume tests of sediment samples from the field (Parchure and Mehta 1985; Tsai and Lick 1987) to in situ tests using either submersible flumes placed on the bottom (Gust and Morris 1989; Amos et al. 1996; Maa et al. 1998; Ravens and Gschwend 1999; Tolhurst et al. 2000)or carefully collected cores (McNeil et al. 1996; L.P. Sanford et al., unpublished data). Bottom-landing in situ erodibility tests become much more difficult as the depth of the water body increases, such that most in situ erodibility data are from relatively shallow water or intertidal mud flats. Another technique that has been used with reasonable success is simultaneous measurement of naturally occurring near-bottom current/stress and suspended sediment concentration, inferring erosion behavior from the relationship between the two (deVries 1992; Sanford and Halka 1993). A potential problem with this technique is that the inferred parameters are highly dependent on assumptions about horizontal homogeneity, vertical turbulent diffusion, and settling/deposition. In spite of a general acceptance of the present need for site-specific studies, the eventual goal of understanding and predicting fine sediment erodibility on the basis of more readily measured sediment properties remains a very important one.

A 2nd consequence of the complexity of fine sediment erosion processes has been the adoption of multiple formulations for interpreting data and modeling erosion. Perhaps the most commonly used formulation is simple linear erosion with a constant critical stress, in 1 of 2 forms:

  • equation image((1a))
  • equation image((1b))
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Figure Figure 1.. Dependence of erosion rate on sediment bulk density at different levels of applied shear stress for a medium silt (left), from Roberts et al. (1998). Variation of sediment dry density near the surface of a deposited fine sediment bed (right, top), from Parchure and Mehta (1985). Variation of shear strength (same as τc) within the upper 1 cm of the sediment column shown in top panel (right, bottom), from Parchure and Mehta (1985). All figures reproduced by permission of the American Society of Civil Engineers.

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(Ariathurai and Krone 1976; Lang et al. 1989; Sanford and Halka 1993; Sanford and Maa 2001), where E is erosion rate, M (or M′) is a constant of proportionality, τb is the applied bottom shear stress, and τc is the critical stress for erosion. Also common are power law expressions, with or without a critical stress:

  • equation image((2))

(Lick 1982; Lavelle et al. 1984; Maa et al. 1998; Roberts et al. 1998), where n is an empirically derived exponent. Exponential expressions with a depth-varying critical stress have also been used (Parchure and Mehta 1985; Chapalain et al. 1994), as have adaptations of expressions from noncohesive sediment transport modeling (Wiberg et al. 1994; Harris and Wiberg 2002). Almost all sediment transport models, regardless of the erosion expression used, are quite sensitive to variations in erosion parameters.

Environmental research is often technology dependent, with new advances in measurement techniques often leading to major advances in thinking. However, the goal of decreasing uncertainty in estimates of fine sediment erodibility has lagged behind improvements in technology such as in situ erosion-testing devices and sophisticated numerical sediment-transport models. Huge, mostly unexplained, scatter in reported erosion rates (Figure 2) remain the norm. This state of affairs is due to 3 factors:

  • 1.
    Real differences in erodibility, as described above, which need to be better understood to develop a predictive capability.
  • 2.
    Differences in instrument calibration or performance, which must be understood and corrected in order to accurately compare data collected with different devices.
  • 3.
    Differences in experimental design and data analysis protocols, which must be understood and corrected before we can proceed with either of the other 2 goals.

A testament to the importance of the 2nd and 3rd factors is that data collected using the same instrument and procedure often show more consistent trends in behavior (Roberts et al. 1998) than do intercomparisons across many instruments and protocols (Figure 2).

This paper argues that differences in experimental design and data analysis protocols are a major contributing factor to uncertainties in sediment erodibility/stability estimates. The magnitude of the resulting uncertainty relative to other sources of variability is not known at present, but it must be addressed. Straightforward recommendations are offered for remedying this problem, primarily through standardization of protocols and controlled intercomparison experiments.

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Figure Figure 2.. Comparison of erosion rate estimates from different instruments and in different locations, from Gust and Morris (1989) by permission of the Journal of Coastal Research.

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DEVELOPMENT

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

An often-unrecognized problem with many erosion testing protocols is the implicit assumption that erosion rate is constant over the duration of a test time step. This assumption allows erosion rate to be calculated as the total change in depth or eroded mass divided by the duration of the time step, one of the most common methods (but not the only method) of estimation. However, any process that acts to limit the available supply of erodible sediment over an erosion test time step must result in a decreasing erosion rate over that time step. The limitation may be due to increasing bulk density (Figure 1), which leads to decreasing erodibility, or to decreasing sediment availability as fines are winnowed out of sand-mud mixtures. Situations do exist in which erosion rate is essentially constant in time, such as for a homogeneous remolded fine sediment with no appreciable coarse fraction, or for deeply buried, consolidated sediments. However, rapid time variation in erosion rate is common enough that it should not simply be assumed away.

Sanford and Maa (2001) showed that assuming an erosion law of the form shown in Equation 1b and assuming that critical stress increases linearly with depth of erosion leads to a time-varying erosion rate of the form

  • equation image((3))

for a typical erosion test time step with constant applied shear stress τb, where τc0 is the critical stress at the beginning of the time step and λ is the rate of sediment depletion. This exponential decay in erosion rate over time scales of minutes has been observed in many erosion experiments on deposited sediments, either as a decreasing erosion rate or as an exponential rise towards some equilibrium eroded mass (Parchure and Mehta 1985; Chapalain et al. 1994; Maa et al. 1998; Piedra-Cueva and Mory 2001; Aberle et al. 2004). Values of the sediment depletion time scale λ−1 from Sanford and Maa (2001) are in the range of 2 to 7 min.

The specific form of the erosion law in Equation 1b is not the only one that predicts a rapidly time-varying erosion rate in the presence of changing sediment erodibility. As another example, consider the power law erosion expression presented by (Roberts et al. 1998):

  • equation image((4))

Where A, n and k are empirical constants and ρb is sediment bulk density. Setting n = 2 (its approximate value for fine sediments in Roberts et al. 1998), differentiating Equation 4 with respect to time t, rearranging, and setting b/dt = 0 as during a typical erosion test time step, yields

  • equation image((5))

The solution to Equation 5 for initial erosion rate E0 is

  • equation image((6))

B is the rate of sediment depletion in this case. Using reasonable values of E0 = 0.01 cm/s and k = 2.9 cm3/g from Figure 1 (Roberts et al. 1998), and an estimate of dρ/dz = 0.062 g/cm4 corresponding to the dry density gradient shown in Figure 1 (Parchure and Mehta 1985) yields B−1 = 9 min. The erosion rate should decrease to half of its initial value in this time according to Equation 6.

There are several possible consequences of a time-varying erosion rate for erosion test design and interpretation. The most obvious is that a time-varying erosion rate implies a 1st order dependence on the time history of stress application. Thus, given identical sediment erodibility gradients, a sequence of short time steps (Beaulieu et al. 2005) will yield different erosion behavior than does a sequence of long time steps (Parchure and Mehta 1985) or a continuously increasing stress (Gust and Morris 1989) or a sequence of short bursts of stress (Tolhurst et al. 2000). Another consequence is that different investigators have adopted different interpretations of the effective erosion rate during an erosion test time step (Figure 3). This is particularly problematic when a single representative value is desired. Thus, many investigators interpret erosion rate for each applied stress as the average over the time interval, whereas others interpret erosion rate as the average after the initial spike in response (Ravens and Gschwend 1999), and others report erosion rate as the value of the initial spike (Maa et al. 1998). Explicitly time-variable formulations allow for an expected time-varying response (Sanford and Maa 2001; Aberle et al. 2004), but interpretation of observed time-varying behavior depends on the erosion model assumed (compare Eqns. 3 and 6, for example). These differences in experimental protocols and data interpretation are a major factor in the orders of magnitude differences in erosion rates observed, even in controlled intercomparison experiments (Tolhurst et al. 2000).

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Figure Figure 3.. Erosion rate definitions of (1) Maa et al. (1998), (2) Sanford and Maa (2001), (3) Average, (4) Ravens and Gschwend (1999). Erosion time series from Aberle et. al (2004) with permission from Elsevier.

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Erosion test intercomparisons indicate differences in critical stress estimates, as well, but these are often less drastic than differences in erosion rate estimates (Tolhurst et al. 2000). Several general approaches to deriving a critical stress estimate are used. In many cases, critical stress is defined as the stress for which a “significant” increase in concentration is 1st observed. Others define critical stress as the zero intercept of an erosion rate versus stress regression (e.g., Sanford et al. 1991). Others consider the concept of critical stress to be unimportant (Lavelle and Mofjeld 1987), or define it but do not use it in reporting erosion rate results (Roberts et al. 1998). The most common and important conceptual difference is that critical stress is often defined as the single value at which erosion of the surface sediments begins, in sharp contrast to the concept of a critical stress that increases with depth into a deposited sediment bed.

Another important aspect of the many and varied approaches to experimentally estimating sediment erodibility is that the erosion formulation assumed, the test conditions, the experimental protocols, and the data interpretation all affect appropriate use of the derived erosion parameters. Because complete details are seldom reported and standardized approaches do not exist, the potential for errors in the translation between reported erosion test results and their implementation in models is large. Estimates of τc and E derived assuming 1 underlying erosion formulation should not be used to parameterize a different formulation, for example. The danger is that users of reported experimental erosion parameters will tend to accept the interpretations of experimentalists as being universally applicable although they are actually quite specific to the experimental conditions and the assumptions of the data analysis.

Two additional consequences of the current multiplicity of approaches are apparent, over and above associated uncertainties in sediment erodibility. First, a lack of agreement on standard approaches and interpretations may impede progress towards understanding the factors that control fine sediment erodibility. Methods-related differences may mask real similarities or differences between different sites and sediments, and the current emphasis on spatial/geographical variability deflects research on temporal variability in erodibility caused by disturbance, consolidation, bioturbation, and other factors. Second, an abundance of incompatible experimental approaches may lead to modeling headaches, rather than to solutions. For example, if the erosion formulation used in a model must match the assumptions behind the reported empirical erosion parameters, then what formulation should be used when the experimental conditions and assumptions are not known, or when more than one source of data are available?

RECOMMENDATIONS

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

The problems outlined here may be addressed in several straightforward ways, and resulting uncertainties in sediment erodibility estimation reduced. In many cases, these are ideas that have been put forward previously, at least in part.

First, erosion testing protocols and data analysis procedures should be standardized. This does not mean that all researchers should use the same devices or cover the same ranges of forcing; this would be counterproductive, because different tools are needed to answer different questions. However, standardizing to a limited set of protocols and adoption of a limited set of data analysis procedures will allow more informed use of the resulting data and more informative comparison of different methods. A good starting point would be agreement on a standard time step for stress application, one that would allow in situ experiments to be completed in a timely manner but also allow identification of any time scale for erodible sediment depletion. An important part of protocol standardization is explicit recognition of the erosion model underlying each approach, and demonstration that the chosen model is an appropriate one. Thus, if the time course of an erosion experiment indicates rapid changes in erosion rate at a constant level of applied stress, the data should be analyzed in a time-varying sense and not forced into a time-invariant context. In general, time-varying erosion should be expected when large gradients in bed density are present, such as near the sediment-water interface of deposited sediment beds. A simple check is to require that the chosen erosion model, parameterized using the results of an erosion test, be able to reproduce the time history of that same test.

Second, more direct intercomparisons of in situ erosion testing devices and protocols (Tolhurst et al. 2000) and adoption of laboratory standards for fine sediment erosion testing are needed. For example, a standard cohesive bed consisting of a specified mixture of abiotic clays, equilibrated with water of a specified chemical composition for a fixed duration might be adopted for laboratory calibration. Rather than simply pointing out that large differences exist between different devices and protocols, intercomparison experiments should seek to reconcile the differences, and the participating investigators should modify their protocols accordingly. When the test sediments and testing protocols are identical, remaining differences due to system design or operation can be addressed more efficiently. Archiving and sharing of original experimental time series of applied stress and erosion response for analysis by others, rather than reporting only derived erosion parameters, is an important part of this effort.

Third, experimentalists should collect and report supporting data for their erosion measurements on a routine basis. Previous lists of important parameters controlling fine sediment erodibility have been quite complete (Mehta 1986) and perhaps overwhelming; it may be that a subset of the most important parameters will be sufficient (Aberle et al. 2004). Such a parameter list might include salinity, temperature, sediment water content, mineralogy, grain size distribution, organic carbon fraction, exopolymeric polysaccharide concentration, and a basic description of the benthos. Where possible, vertical profiles of these parameters should be measured as well. Without these data, attempts to understand the causes of natural variability in sediment erodibility, and to predict erodibility on the basis of more easily measurable sediment characteristics, can only be partially successful.

Fourth, the users of erosion test data (modelers and other experimentalists) should be aware of the circumstances under which reported erosion parameters were collected and analyzed, and should attempt to use the same model formulation as the original study. If use of the same formulation is not possible, reanalysis of the original erosion test time series in the context of the user's model formulation may be indicated.

Finally, the entire community of experimentalists, modelers, and environmental managers concerned with fine sediment stability should recognize the potential for dynamic variability in sediment erodibility. In this context, in situ erosion test data are best viewed as snapshots of a dynamically varying process for comparison to model predictions, rather than as fixed boundary conditions for erosion behavior. More research on the dynamic variability of erodibility in response to disturbance, deposition history, consolidation, and bed armoring is needed, including controlled laboratory experiments.

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Figure Figure 4.. Site of erosion test intercomparison experiment (left), the VIMS Sea Carousel (center) and the UMCES Microcosm system (right).

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AN EXAMPLE

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

As an example of the apparent differences that can result from different analysis procedures, and their potential reconciliation when the same analysis procedures are used, results from a recent in situ erosion test intercomparison in the Chesapeake Bay are presented here. The data presented here are from a comparison between erodibility measurements made with the Virginia Institute of Marine Sciences Sea Carousel (Maa et al. 1993) and the University of Maryland Center for Environmental Sciences (UMES) Microcosm (L.P. Sanford et al., unpublished data) at a site in the muddy upper Chesapeake Bay (Figure 4) in May 2002. The results derived using the standard analysis protocols of the 2 research groups are shown in Figure 5. It is hard to see any relationship between the 2 sets of results in this figure. However, when both data sets are analyzed using protocols based on Sanford and Maa (2001), real similarities and differences are more apparent (Figure 6). In particular, the critical stress profiles are quite similar, indicating an approximately 3-fold increase in the top 1 mm of sediments. The erosion rate constant profiles overlap partially, but in general the Sea Carousel-derived values are higher than the Microcosm values; the cause for this has not yet been determined. This example is not presented to claim superiority of 1 device or protocol over the other, but rather to demonstrate the degree to which treatment of the data alone can result in uncertainty.

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Figure Figure 5.. Results from the intercomparison tests carried out on 7 May 2002. Data analyzed using standard protocols of each research group. Sea Carousel results (left); Microcosm results (right).

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Figure Figure 6.. Reanalysis of Sea Carousel data using Microcosm protocols. Time series of stress and instrument response, along with model fits (left). Derived eroded mass/depth profiles of critical stress and erosion rate constant (right); 0.1 kg m−2 is approximately 1 mm of erosion.

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Acknowledgements

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References

Research support was provided by the Maryland Sea Grant College project R/P 52 and the US Army Corps of Engineers award DACW42–03-C-0035. Jerome P.-Y. Maa graciously provided his data for the intercomparison analysis. Giselher Gust invented, calibrated, and developed the original Microcosm design. Patrick Dickhudt and Steven Suttles were instrumental in the development of the UMCES Microcosm Erosion System and the analysis protocols. Two anonymous reviewers' suggestions are also appreciated. UMCES Contribution no. 3876.

References

  1. Top of page
  2. Abstract
  3. EDITOR'S NOTE:
  4. INTRODUCTION
  5. DEVELOPMENT
  6. RECOMMENDATIONS
  7. AN EXAMPLE
  8. Acknowledgements
  9. References
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