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Use of mineral magnetic measurements to fingerprint suspended sediment sources: approaches and techniques for data analysis
Journal of Hydrology 202 (1997) 353–372
Use of mineral magnetic measurements to fingerprint suspended sediment sources: approaches and techniques for data analysis J. Walden a ,*, M.C. Slattery b, T.P. Burt c a
School of Geography and Geology, University of St Andrews, Purdie Building, North Haugh, St Andrews KY16 9ST, UK b Department of Geography, East Carolina University, Geenville, NC 27858-4353, USA c Department of Geography, University of Durham, Science Laboratories, South Road, Durham DH1 3LE, UK Received 23 September 1996; accepted 2 June 1997
Abstract Three analytical approaches, qualitative, statistical and quantitative, are evaluated when applied to mineral magnetic data to identify the relative sediment source contributions to suspended sediment loads within a small catchment system. The qualitative and statistical analyses provide useful information in their own right but, in addition, indicate the feasibility of quantitative sediment source ascription using a sediment unmixing model based upon a linear programming algorithm. The criteria for such modelling are considered and the model formulation outlined. Model testing and initial output suggest that, under certain conditions, unmixing models have considerable potential for the quantification of suspended sediment source contributions. Qualitative and statistical analyses provide a subjective means to judge the quality of the model output. A number of limitations within the approach are identified and some possible solutions to these limitations suggested. q 1997 Elsevier Science B.V. Keywords: Suspended sediments; Environmental magnetism; Sediment sources; Modelling
1. Introduction Information concerning suspended sediment sources is an essential prerequisite in attempts to elucidate linkages within the sediment delivery system between the field and the river. One approach (e.g. Oldfield et al., 1979; Walling et al., 1979; Caitcheon, 1993) has involved the use of mineral magnetic analyses to provide a compositional * Corresponding author. e-mail: [email protected] 0022-1694/97/$17.00 q 1997 Elsevier Science B.V. All rights reserved PII S00 22-1694(97)000 78-4
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fingerprint by which catchment sources can be compared with suspended sediments in order to investigate the likely sources for the latter. Slattery (1994) and Slattery et al. (in preparation) present results for such a study in a small catchment of the River Stour, north Oxfordshire (Fig. 1). Field observation indicated that erosion of cultivated fields provides an important source of suspended sediment to the River Stour. Slattery et al. (in preparation), after suitable data analysis, focus upon the interpretation of the magnetic data to examine the relative contributions from slope sources and channel erosion, and how these various sediment source areas change both within and between individual storm events. The approaches used in the data analysis are themselves of general interest and could be applied in other settings. Therefore, while some discussion of the environmental context will be made here, the data analysis techniques themselves and the computational steps involved form the focus of this paper. 1.1. Field setting The study catchment (Fig. 1) has a drainage area of 6.2 km 2, NW of Oxford and is a headwater of a tributary to the Warwickshire Avon. Two major soil series are present within the catchment, the Aberford and the Banbury Series (Jarvis et al., 1984) and the vast majority of the catchment consists of cultivated land. Field observation and mineral magnetic data summarised later suggested that three potential sediment source groups can be identified: Aberford series topsoils; Aberford series channel bank material; and, either topsoils or channel bank material from the Banbury soil series (which could not be distinguished magnetically). Representative field samples were collected from each of these potential sources. In addition, suspended sediment samples were collected using a Rock and Taylor automatic pump sampler over a period of some 12 months along with rainfall and discharge readings (Slattery, 1994). 1.2. Mineral magnetic analysis A series of standard mineral magnetic measurements (Thompson and Oldfield, 1986) including magnetic susceptibility (x), frequency dependent susceptibility (x fd), and isothermal remanence magnetisation (IRM) acquisition in magnetic fields between 20 and 1000 mT were made on the field samples. Particle size analysis of the suspended sediment samples showed that material coarser than 63 mm (4 f) was almost totally absent, suggesting that sand grade material from the catchment was not being transported as suspended load into the stream network. Magnetic analysis on the sediment sources was therefore performed only on material finer than 63 mm. Analysis of size-specific magnetic properties (separated using the method of Walden and Slattery, 1993) for the three sources showed that the differences in their respective particle size distributions had little influence on their magnetic properties, although this is accommodated in the modelling procedure. The mineral magnetic data were analysed in three ways. A qualitative analysis, using graphical techniques and the ‘standard’ interpretations given in the literature (e.g. Thompson and Oldfield, 1986; Maher, 1988; Oldfield, 1991) was followed by a statistical approach, using multivariate techniques (e.g. Oldfield and Clark, 1990; Walden et al., 1992) in order to provide a more quantitative and, hopefully, objective analysis. Finally, the data were
Fig. 1. Study catchment within the Stour River system, NW of Oxford, illustrating the distribution of the two major soil series and the locations of the source samples used in this work.
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subjected to an unmixing model (e.g. Thompson, 1986; Yu and Oldfield, 1989, 1993; Walden et al., 1993; Walling et al., 1993; Lees, 1994) which attempts to quantify the proportions of each catchment source to the suspended sediment samples based upon their respective magnetic properties. This three-stage data analysis procedure has been the subject of a detailed review by Lees (1994). She identified both the major advantages and limitations of the use of magnetic measurements for sediment source ascription in a range of sedimentary settings but these did not include a suspended sediment system such as that studied in this paper. Many of the conclusions drawn from her work are, however, applicable to such a system and will be considered here.
2. Criteria for successful quantification of sediment sources In the context of attempts to quantify sediment source contributions using magnetic data, Lees (1994) summarised the prerequisites for successful unmixing of sediment sources: 2.1. Definition of potential source material types It is critical to achieve optimal identification and definition of the source material properties as these represent the ‘end members’ of the model and strongly influence the eventual proportions of each source type ascribed to the sediment sample. This issue has a number of implications. 1. Field sampling needs to be organised appropriately to enable intra- and inter-source variation to be fully quantified (Lees, 1994). 2. Selection of the magnetic parameter values (e.g. mean) to represent each ‘end-member’ (source) is critical. Sensitivity of the model output to changes in the properties used to represent the sources should be considered to provide some idea of model reliability. 3. For successful modelling, the suspended sediment samples must have properties which lie wholly within the range of behaviour displayed by the values chosen to represent the sources. Errors in source definition, chemical alteration during transport or size selective transport of different sources may influence this. 2.2. Maximum number of source material types and data dimensionality Lees (1994) suggests that when using magnetic parameters for source modelling only a small number (three or four) of source types can realistically be used as magnetic parameters are generally only sensitive to one, two or possibly three ‘dimensions’ (e.g. iron mineral concentrations, types and grain size). This restricts modelling to systems where it is environmentally sensible to identify only three or four end-members for the modelling process. Where possible, parameters sensitive to magnetic grain size (x fd or anhysteretic remanent magnetization (x ARM)) or combining magnetic with other geochemical or mineralogical analyses could be considered to increase the dimensionality of the data
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Fig. 2. Relationships between source material properties and the suspended sediment samples to be unmixed. (a) The problem of sources which are numerical multiples of one another. The range of values displayed by three hypothetical source materials for two concentration-dependent parameters are plotted. Suspended sediment samples 1 and 3 can most simply be interpreted as being derived primarily from sources A and C, respectively. Sample 2 is more difficult however, as it could be derived solely from source B or represent some sort of mixture from either sources A and C or A, B and C. (b) ‘Ideal’ distribution of source material properties. Sediment source ascription of suspended sediment samples 1, 2 and 3 should be possible. In the case of sample 4 however, unmixing would not be possible and indicates either failure to identify a potential source, alteration of the magnetic properties of the suspended sediment during weathering and transport, or measurement error.
set. Lack of dimensionality can lead to groups of source samples that are ‘numerical multiples’ of one another (Fig. 2). 2.3. Assessing the feasibility of quantitative modelling The feasibility of source modelling can be assessed initially by considering a qualitative and statistical analysis of the data. Simple bivariate scatter plots (using parameters with different sensitivities) and multivariate statistical analysis using principal components, factor or cluster analysis (e.g. Oldfield and Clark, 1990; Walden et al., 1992; Lees, 1994; Walden and Smith, 1995) provide some indication of how successful any subsequent quantitative unmixing modelling is likely to be. 2.4. Parameter selection for modelling The parameters that are to be used in any numerical unmixing modelling need to meet a number of criteria. 1. Parameters should be linearly additive (Thompson, 1986; Lees, 1994). Thus, if two source materials have values for a particular magnetic parameter of x 1 and x 2, respectively, and are mixed in known proportions (p 1 and p 2), the resultant mixture, assuming perfect linear additivity, should have a value of this parameter (x r) which equals: xr = p1 x1 + p2 x2
(1)
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Table 1 Magnetic data for the various sample groups (x is expressed in units of 10 −7 m 3 kg −1; soft IRM, mid IRM, hard IRM and SIRM are expressed in units of 10 −5 Am 2 kg −1) N
x
Soft IRM (0–20 mT)
Mid IRM (20–300 mT)
Hard IRM (300–1000 mT)
SIRM
7 12 3
9.27 5.97 33.23
142.16 88.42 548.49
414.84 292.39 1228.83
41.74 29.02 50.42
598.74 409.83 1827.73
(b) Non-storm and storm suspended sediment samples Non-storm 9 6.53 110.34 Storm 24 9.35 138.10
338.65 396.12
34.35 41.31
483.33 575.53
(a) Source materials a Aberford TS Aberford CB Banbury TS + CB
a These values were derived from analysis of three discrete particle size fractions for each source sample and applying Eq. (1) to derive a value for a ‘standard’ particle size distribution (Slattery, 1994) to remove the minor effect of variation in the overall particle size distributions between each source.
This equation can be expanded to include additional sources and multiple variables using linear programming algorithms (e.g. Simplex algorithm, Thompson, 1986). Such techniques are commonly used in operational research (Taha, 1992). An iterative search is made to discover what combination of source material proportions minimises the difference between the modelled magnetic properties and the observed (measured) properties of a particular suspended sediment sample. 2. Difficulties can occur when linearly additive parameters used in the model vary by orders of magnitude. Parameters with large values may therefore dominate the model (which is attempting to minimise differences between the modelled properties and the actual properties of the sediment sample) although ‘weighting’ certain parameters can help overcome this problem.
3. Qualitative data analysis Table 1 summarises the magnetic properties for the three types of catchment source materials (Slattery, 1994). Unfortunately, in this study, reliable measurement of x fd was not possible given the low mass of many of the suspended sediment samples. Fig. 3 plots x (roughly proportional to the concentration of ferrimagnetic mineral species) vs. hard IRM (sensitive to the concentration of antiferromagnetic species). The samples from the three source material types plot as separate clusters and it appears that the assemblages of magnetic minerals within the sources show some measurable differences. Less encouragingly, Fig. 3 does suggest that the distribution of the three source types is closer to that shown in Fig. 2(a) than the ‘ideal’ shown in Fig. 2(b). This situation is likely to exist in many (the majority?) of natural field settings and while Fig. 3 does not suggest these sources are pure ‘numerical multiples’, this problem may need further consideration in any subsequent modelling. The vast majority of the suspended sediment samples (classified into ‘non-storm’ and
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Fig. 3. Plots of x (10 −7 m 3 kg −1) vs. hard IRM (10 −5 Am 2 kg −1) for the catchment source and suspended sediment samples.
‘storm’ types) exhibit magnetic properties which lie wholly within the distribution of the catchment source materials, suggesting that in numerical terms it should be possible to ‘unmix’ the suspended sediments on the basis of these three source material types alone. This does not exclude the possibility of alteration of the mineralogical composition of the suspended sediments during weathering and transportation but might indicate that any such effects have been relatively small. Fig. 3 also indicates that the non-storm and storm samples exhibit generally different magnetic properties. The non-storm samples show lower concentrations of magnetic minerals and plot in the same area of the figure as the Aberford channel bank materials. In contrast, the storm samples show higher concentrations of magnetic minerals and plot closer to the Aberford topsoil materials. This pattern makes ‘environmental’ sense as topsoil contributions might increase during periods of higher flow as a result of surface and overbank flow. Fig. 3 also suggests that the contribution to the suspended sediments from the Banbury series is much less than for the other two source types. Again, this would seem to be consistent within the field context (Fig. 1).
4. Statistical analysis Fig. 4 shows a plot of the variable and sample loadings from an R- and Q-mode factor analysis, following the methods of Davis (1986) and Walden and Smith (1995), based upon the linearly additive parameters x, ‘soft’, ‘mid’ and ‘hard’ IRMs and SIRM (IRM 1000mT) for the catchment samples and the suspended sediment samples. The eigenvalues for this analysis suggest that factors 1 and 2 explain over 95% of the variation in the raw data set. This is extremely high and would seem to confirm the conclusion of Lees (1994) discussed earlier concerning the dimensionality of some mineral magnetic data sets. From the positions of the original variables in the inset to Fig. 4, these results can be
Fig. 4. Plot of variable and sample factor loadings. Inset shows the distribution of all source and suspended sediment samples. Shaded area of the inset is shown in the main part of the figure, allowing distribution of the non-storm and storm suspended sediments to be seen in more detail.
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interpreted as follows: factor 1 is controlled by overall concentrations of magnetic minerals whereas factor 2 is more influenced by ‘hard’ IRM and therefore reflects antiferromagnetic mineral concentrations. The main part of Fig. 4 shows the centre of this factor space in an expanded form. As in Fig. 3, the Aberford channel bank and topsoil sources form two distinct clusters of samples, suggesting that they can be distinguished on the basis of the five magnetic parameters used in this analysis. The majority of the non-storm and storm suspended sediment samples plot within this same area on the factor diagram. Again, the non-storm samples show a closer affinity to the channel bank source materials and the storm samples to the topsoil source materials. Given the relatively large distance in factor space between the suspended sediment samples and the Banbury series source samples it can be inferred that this source makes less contribution to the sediment load of the stream system.
5. Conclusions from the qualitative and statistical analyses The qualitative and statistical examination of the magnetic data suggest that the source materials and the suspended sediment samples meet an acceptable number (if not all) of the criteria discussed by Lees (1994) and summarised earlier. Importantly: 1. The three source material types possess magnetic behaviours which can be distinguished using linearly additive parameters; 2. The majority of the suspended sediment samples display magnetic behaviour which lies within the range of behaviours exhibited by the three source types. Figs. 3 and 4 suggest at least two potential problems with these data for quantitative sediment source ascription, as follows. 1. Between-group variation in magnetic properties may lack some dimensionality (Fig. 3). This issue may influence the effectiveness with which certain suspended sediment samples can be unmixed. 2. Within-group variation in the magnetic properties of the three source types is clearly present. As a single value (for each magnetic parameter) has to be selected to represent the properties of each source in any unmixing model, some decision has to be made as to what that value should be. While mean values would seem the most obvious choice, the model’s sensitivity to the parameter values chosen needs to be tested. A number of ‘environmental’ conclusions can also be drawn from these initial qualitative and statistical analyses. 1. Given that the magnetic properties of the majority of the suspended sediment samples lie within the range of properties displayed by the three source material types, it might be possible to infer that all the major source types have been identified and that no major mineralogical alteration of the suspended sediments is occurring during the weathering and transportation processes. 2. Source contributions do vary under different flow conditions with Aberford channel bank material dominating in most low flow (non-storm) periods but with increasing
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contributions from Aberford topsoil during high flow (storm) events. This is consistent with field observation (Slattery, 1994). 3. The strongly magnetic Banbury Series source only makes a minor contribution to the suspended sediment load. This is consistent with the location of the source within the catchment (Fig. 1) and field observation.
6. Model formulation and use Before proceeding to build a specific model for the Stour catchment, the mathematical formulation of the unmixing model needs to be outlined. The basic form of the model used here follows Thompson (1986) and is commonly used in other environmental contexts (e.g. analysis of remotely sensed data: Richards, 1993). The model essentially carries out an iterative search to find the optimum combination of the source materials which, when linearly mixed, minimises the differences between the measured magnetic properties of the suspended sediment and the magnetic properties of the mathematical mixture of the sources. The optimisation process has to work within certain constraints namely: 1. the proportion of each source must be lie between 0 and 1; 2. the sum of all source proportions should total 1. The following notation is adopted below: p e a ij bj xi sj
number of magnetic parameters used in the modelling procedure number of end-members (sources) used in the modelling procedure measured value of magnetic parameter j in end-member (source) i measured value of magnetic parameter j in the natural sample being modelled hypothetical proportion of end-member i in the natural sample where x i $ 0 and x i # 1 simulated (modelled) value of magnetic parameter j in the simulated version of the natural sample e
sj = ∑ aij xi i=1
The minimum difference between the simulated and natural samples is found by minimising e 2 p p (2) ∑ ∑ aij xi − bj = ∑ (sj − bj )2 j=1
i=1
j=1
subject to the constraint that x i $ 0 and x i # 1 for each end-member i and e
∑ xi = 1
i=1
One problem with Eq. (2) is the presence of differences in the absolute scales by which the various magnetic parameters are measured. Small percentage differences in actual and modelled SIRM values expressed in thousands of units will exert greater control on the model than much larger percentage differences in actual and modelled x values expressed in tens of units. In Eq. (3) each variable is given a more even weighting in the model by
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expressing the differences between modelled and measured values as a percentage of the modelled value. p
∑ {[(sj − bj )=bj ] p 100}2
j=1
(3)
The model was run on a standard 486 DX2 PC using the Solver ‘add in’ component of Microsoft’s Excel 5 spreadsheet which allows optimisation routines to be constructed using a SIMPLEX algorithm. Fig. 5 shows an example of the spreadsheet used. The basic structure of the spreadsheet is given in Table 2. The user has to supply values to represent the properties of the source materials, the measured properties of the suspended sediment sample which has to be ‘unmixed’ and the initial starting proportions of each source from which the optimisation routine will move to find the ‘best’ solution. 6.1. Model testing To test that the model functioned satisfactorily, a number of hypothetical source mixtures were computed (based on Eq. (1)) using the mean values for each of the three source materials (Table 1) to represent x, soft, mid and hard IRMs and SIRM. The model successfully ‘unmixed’ these hypothetical mixtures in the correct proportions. In a very small number of cases the model showed some sensitivity to the initial starting proportions specified for the three sources. This problem was overcome by running the model from a number of different initial start conditions to ensure the optimum solution was being found. Similar testing was also done to examine the effect of how the ‘goodness of fit’ of the modelled magnetic properties is calculated relative to the measured values. Models based on both eqns (2) and (3) gave satisfactory results when trying to unmix hypothetical source mixtures. This suggests that for perfect mixtures of the three sources at least, the choice between Eq. (2) or Eq. (3) was not critical. Eq. (3) would seem however, on logical grounds, to be preferable and the initial discussion below is based on the model output using Eq. (3). 6.2. Unmixing the suspended sediment samples The testing procedure gave confidence in the model’s mathematical operation. As suggested by previous workers, however (e.g. Thompson, 1986; Yu and Oldfield, 1989, 1993; Walden et al., 1993; Lees, 1994; Shankar et al., 1994), such mathematical procedures are likely to be less robust when dealing with environmental samples where a number of factors (measurement error, chemical or mineralogical alteration, source variation, etc.) mean that few of the suspended sediment samples can be unmixed as perfect combinations of the mean values of the source materials. Mineral magnetic data for some 33 suspended sediment samples, representing both low flow and high flow conditions were available for unmixing and a number of these will be considered in detail here to illustrate the model’s potential and possible problems. A fuller interpretation of the results in terms of their environmental significance is provided in Slattery et al. (in preparation).
Fig. 5. Example of the unmixing model constructed using the Solver add-in in Microsoft’s Excel 5 spreadsheet. See text and Table 2 for explanation.
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Table 2 Basic structure of the spreadsheet shown in Fig. 5 Cells
Contents
G6–K8 G14–K14
The measured parameter values used to represent the properties of the three source materials The measured parameter values for the particular suspended sediment sample which is currently being unmixed The modelled parameter values for the simulated version of the suspended sediment sample currently being unmixed. These cells are linked to G6–K8 and C19–C21 by formula based on Eq. (1). For example, cell I21 contains the formula: ((C19*G6)) + (C20*G7) + (C21*G8) The modelled proportions of the three source materials. Solver is configured so that these cells are changed in order to minimise the value held in cell H26 Contains the differences and squared differences between the measured and modelled parameter values. As discussed elsewhere, these cells can be configured in a number of ways to force the model to treat variables of different orders of magnitude with equal weight Contains the sum of cells G22–K22. Solver is configured to minimise the value contained in this cell by changing the values held in cells C19–C21
G19–K19
C19–C21 G21–K22
F24
6.3. Reliable estimates of sediment source Both Figs. 3 and 4 offer some insight into the type of suspended samples for which the unmixing model might produce more or less reliable estimates of sediment source contributions. For example, while the suspended sediment samples 4, 10, 12, 17 and 20 all lie within the range of magnetic properties displayed by the source materials, they lie near to the extremes of those properties and therefore at some distance from the mean values of each source material type chosen to represent that source type within the unmixing model. In contrast, the mean values of both the non-storm and storm sample types lie nearer to the Aberford source means as do, for example, suspended sediment samples 2, 14 and 23. Table 3 shows the model output for selected suspended sediment samples. The results of the modelling process for the mean magnetic properties of the non-storm and storm samples are consistent with both Figs. 3 and 4 and seem sensible given their environmental context. Thus, the non-storm mean is dominated by material derived from the Aberford channel banks but with a significant proportion of Aberford topsoil. As discussed by Slattery (1994) and Slattery et al. (in preparation), material derived from the Aberford topsoil at higher flow conditions and subsequently stored on the channel bed is the most likely source of this contribution during lower flow levels. In contrast, the storm mean sample shows greater proportions of Aberford topsoil and a small contribution from the Banbury series source. Many of the higher flow events generated overbank flow (Slattery, 1994; Slattery et al., in preparation) providing an obvious mechanism for incorporation of greater amounts of Aberford topsoil into the suspended sediment system. The sum of squared differences is lower for the storm mean sample, suggesting that mathematically at least, the model is a better ‘fit’ for this sample than for the non-storm mean. Samples 2, 14 and 23 produce what would appear to be sensible proportions of the three source materials given their magnetic properties and their respective flow conditions. In each case, the sum of squared differences are also relatively low. Pairs of samples 3 and 6 (non-storm samples) and samples 15 and 18 (storm samples) show similar magnetic
31/8–4/9 4–7/9 7–14/9 16–23/11 25/9 21:00 h 20/10 10:00 h 27/11 20:06 h 30/11 10:10 h 18/12 11:10 h 18/12 11:40 h 18/12 12:40 h 18/12 14:10 h
Non-storm Storm
Date/time
TS, topsoil; CB, channel bank.
2 3 4 6 10 12 14 15 17 18 20 23
Sample
NS NS NS NS S S S S S S S S
7.2 6.5 4.9 6.7 12.7 7.8 10.1 10.7 13.2 11.0 11.0 9.2
127.5 114.1 91.8 123.4 183.6 112.2 161.1 187.8 208.8 157.8 179.6 133.7
110.3 138.1 363.0 371.2 327.8 353.4 601.0 463.2 424.0 425.6 494.7 409.7 444.8 364.7
338.6 396.1 38.0 26.6 13.6 29.2 102.8 68.5 45.2 42.0 31.7 37.6 20.6 52.1
34.3 41.3 528.5 511.8 433.1 506.0 887.3 643.9 630.3 655.3 735.2 605.2 644.9 550.5
483.3 575.5
SIRM
0.33 0.05 0.00 0.12 0.83 0.95 0.45 0.33 0.00 0.26 0.00 0.70
0.62 0.90 0.99 0.82 0.00 0.05 0.44 0.51 0.73 0.60 0.81 0.28
0.72 0.53
Ab CB
Modelled proportions
0.27 0.39
6.5 9.4
Hard IRM
n=9 n = 24
Mid IRM Ab TS
Soft IRM
Non-storm x (NS) or storm (S)
0.04 0.05 0.00 0.05 0.17 0.00 0.10 0.15 0.26 0.13 0.18 0.01
0.01 0.07
Ban CB + TS
278.53 235.82 1822.65 309.87 3923.43 1506.44 77.23 326.66 193.40 125.28 1074.40 36.65
188.70 11.78
Sum diffs 2
Table 3 Mineral magnetic properties of selected suspended sediment samples and the proportions of the three source materials ascribed by the unmixing model. The model output was produced by minimising the sum of the squared % differences between the measured and modelled versions of the five magnetic parameters (see text for explanation)
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properties (Figs. 3 and 4) and, encouragingly, the output from the unmixing model is both similar and environmentally sensible for each pair. 6.4. Less reliable estimates of sediment source Less confidence might be placed in the ability of the model to ascribe source proportions to samples 4, 10, 12, 17 and 20 and with the exception of sample 17, the sum of the errors appear relatively high, suggesting a poor fit between the modelled and measured magnetic properties. In each case, the qualitative interpretation of Figs. 3, and 5 provide a guide to the likely usefulness of the model output. For example, the model ascribes a channel bank contribution of almost 100% Aberford to sample 4. While the error term is relatively large, the position of sample 4 in Figs. 3 and 4 suggests the model output is environmentally sensible. The large error term is simply a function of the fact that this sample has magnetic properties which are more like the magnetically weaker of the Aberford channel bank source samples than the mean for this source group. In contrast, the source proportions ascribed to sample 10 with 0% Aberford channel banks, while mathematically the optimum solution, would seem to be unrealistic given the field setting. The measured magnetic properties of the sample are somewhat extreme relative to the source means. Although measurement error is a possible cause, two other possibilities, chemical alteration or selective transport, are more likely explanations. Further field observations would be required to determine the likelihood of either explanation. Alternatively, it may be that a more realistic source mixture for sample 10 would include a proportion of the Aberford channel banks, a smaller proportion of the Aberford topsoil and a slightly larger proportion of the Banbury series. This sample might be exhibiting the same problem as sample 2 in Fig. 2(a). The ‘numerical multiple’ problem means that the model cannot resolve between a number of possible mixtures which produce similar mathematical solutions, some of which make more environmental sense than others. For example, a mixture of 35%, 41% and 24% Aberford topsoil, channel banks and Banbury series, respectively, produces a slightly higher error term but would seem more realistic given the environmental setting. Samples 12, 17 and 20 might also exhibit this problem. Whichever of the above explanations is the actual cause of the unrealistic or poor numerical fit of the model, attempting to quantify the source contributions would seem unwise for those samples lying at the extremes of behaviour for the suspended sediments as a whole. In these cases, a qualitative interpretation of the particular sample data may be all that is justifiable. 6.5. Comparison with factor analysis When Eq. (2) is used to calculate the error term between the modelled and measured magnetic properties, in a number of cases the model ascribes significantly different source proportions. For example, sample 2 is modelled as 63% Aberford topsoil and 37% Aberford channel banks. While this might not seem to be unreasonable in terms of the environmental setting, the proportions given in Table 3, based upon Eq. (3), are much more consistent with the output from the factor analysis (Fig. 4). The position of sample 2
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lies almost directly between that of the positions of the mean samples for the two Aberford source types, but significantly closer to that of the Aberford channel bank mean, suggesting greater proportions of that source within the sample. If the relative distances in factor space of sample 2 are measured from the positions of the two Aberford source means, they suggest proportions almost identical to those given in Table 3 (allowing for the small Banbury series contribution). Similar calculations for other samples lying almost directly between these two source means on Fig. 4, including samples 3, 6 and 23, would seem to confirm that the model based upon Eq. (3) and the factor analysis provide similar indications of the sediment source proportions. This in turn, would seem to suggest that the use of Eq. (3) in the unmixing model is preferable to Eq. (2). 6.6. Sensitivity analysis All of the above analyses were based upon an unmixing model using the mean properties of the magnetic variables for the three source material types (Table 1). The sensitivity of the model output to these properties was tested by systematically changing their values and the output produced by the model varied in a predictable manner. For example, in one experiment, the parameter values for Aberford topsoil and Aberford channel banks were adjusted in steps of 5% (up to 20%) in opposite directions (effectively stretching or contracting the multivariate ‘distance’ between these two sources). Where the properties of individual suspended sediment samples remained between those of the two source types, the source proportions ascribed to them were very similar to those of the standard model using the mean source properties. Only as the change in the source material properties moved the source ‘closer’ in multivariate space to an individual suspended sediment sample did that sample produce significantly different unmixing results. In all cases, however, the model continued to produce similar source proportions for suspended sediment samples with comparable magnetic properties (e.g. samples 3 and 6). This suggests that even if the parameter values adopted for a given source are not accurate representations of that source, whilst the modelled source proportions will also be less accurate in absolute terms, the patterns in modelled source proportions for a particular set of suspended sediment samples should be similar. Identification of any such patterns might, in itself, be justification for the modelling. The testing of the model sensitivity suggested no logical reason why mean parameter values of each source type should not be adopted for modelling purposes.
7. Discussion These results emphasise a number of issues already raised, concerning both the modelling processingeneral and thespecific environmental settingfrom whichthese sampleswere drawn. 7.1. General issues Two important general issues are highlighted by these results. First, in examining the
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output from the model, it is clear that the qualitative and statistical analyses of the data have provided a useful guide concerning both the general feasibility of modelling and, more specifically, some indication of which individual samples might prove difficult to unmix for particular reasons. The model output can therefore be examined in a more critical fashion. While this in no way confirms how realistic or useful the model output might be in environmental terms, it does give some confidence in the numerical robustness of the modelling process itself. The environmental interpretation of the model output still requires some subjective judgement on the part of the researcher to assess the realism of the modelled sediment source proportions. Second, the accuracy of the quantitative estimates of source contributions is difficult to assess as the absolute values produced by the model will be different if the source materials are defined by different values of each parameter measured. The initial definition of the number and mean properties of the source materials is therefore both a critical component of the modelling process (Lees, 1994) and, even with the most rigorous field procedures, conditional upon an element of subjective judgement on behalf of the researcher. In this study, suspended sediment samples caught at the catchment outlet might have travelled only a few tens of metres. They may therefore have been derived from an individual section of channel bank (a bank slump, for example) and would possess the compositional properties of that particular portion of the channel bank source rather than the ‘mean’ properties of the channel banks in general. In a larger catchment system, such individual point source contributions are more likely to be diluted and will therefore be less significant. In contrast, the initial definition of the source types in a larger catchment system would clearly be a more difficult task. 7.2. Issues specific to this environmental setting Two main issues which are specific to this individual field setting are highlighted. First, these data do show an element of the ‘numerical multiple’ problem and therefore some caution is needed in interpretation of the quantitative output provided by the modelling process. In most cases however, comparison of the model output with the qualitative and statistical data analyses can allow spurious model results for particular suspended sediment samples to be identified. Despite the qualification above concerning the definition of the source material properties, the general nature of the model output would seem sensible given the environmental context. Thus, the relatively greater contribution of Aberford topsoil material during periods of higher discharges is consistent with field observations of overbank and surface flow during these periods. Identification of this pattern is in itself useful, even if it is difficult to assess the absolute accuracy of the proportions ascribed to each source. This problem may well present itself in other field settings and the use of additional compositional properties such as elemental geochemistry to provide greater dimensionality for the modelling algorithm to work with is recommended. Second, a number of explanations can be suggested to account for the fact that some of the suspended sediment samples display results which lie outside the mean values adopted for the source material types. Some effort should be made to identify the presence or absence of selective particle size transport or chemical alteration during transportation and the effect such processes might have on subsequent modelling. These issues are currently
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under investigation (Jenns, in preparation). An additional problem here may be small mass of the suspended sediment samples. Like most analytical equipment, magnetic instrumentation does display some sensitivity to sample mass (e.g. Dearing, 1994) and the bulk suspended sediment samples collected by some pump water samplers can be of very small mass. Material collected using continuous flow centrifuge equipment would therefore be an advantage in this type of work. While the influence of these factors can not be ruled out in the current field context, for many of the suspended sediment samples available, the modelling process seems to have produced realistic results even if those results are of unknown absolute accuracy.
8. Conclusions A number of conclusions can be drawn from this work which support the main findings of Lees (1994) in other types of sedimentary environments. 1. Identification of the major source material types within the sedimentary system and quantification of their compositional properties is a critical step in any attempt to quantify sediment source contributions using linear programming algorithms. Sources which do not have distinct compositional properties or are numerical multiples of one another will make attempts at source modelling much less reliable. 2. Qualitative and statistical analyses of compositional data which are being considered for sediment source unmixing perform two important tasks: assessment of how well the data fit the various criteria necessary for successful application of the modelling procedure and, once modelling is performed, provision of a useful means of verifying (at least in a numerical sense) how realistic the output produced by the model is likely to be for particular suspended sediment samples. 3. While the modelling procedure can reliably unmix ‘perfect’ mixtures of the source materials, field samples will not unmix without some errors. Such errors can have a number of causes including the natural levels of variability within each source type but factors such as compositional alteration or selective sediment transport must also be considered. 4. It would seem therefore, that unmixing models can be a useful development from initial qualitative and statistical analysis of suspended sediment source ascription, provided such quantitative results are interpreted with an full awareness of their possible limitations. It is also clear that there is considerable scope for further development of these types of modelling procedures provided the recommendations outlined by Lees (1994) and summarised here are carefully followed. 5. Within this particular field setting, it appears that the modelling procedure can offer some real insights into the proportions of the source material contributions to the suspended sediment system. While the absolute accuracy of the quantitative estimates of source material ascription is uncertain, it is encouraging that the values suggested for non-storm and storm flow conditions are consistent with both field observation and the qualitative appraisal of these same data. Further work, combining magnetic with other forms of compositional analyses is clearly warranted.
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Slattery et al. (in preparation) develop this final conclusion by examining the environmental interpretation of the model output in more detail within the context of this particular field setting and as a tool to assist other studies of sediment source ascription in suspended sediment systems.
Acknowledgements The authors wish to thank the School of Geography, University of Oxford for access to the facilities used in this work. J.W. would like to thank Dr Joan Lees (Coventry University), Prof. John Dearing (Liverpool University) and Dr Bill Macmillan (Oxford University) for useful discussions on the modelling procedures used in this paper.
References Caitcheon, G.G., 1993. Sediment source tracing using environmental magnetism: a new approach with examples from Australia, Hydrological Processes, 7, 349–358. Davis, J.C., 1986. Statistics and Data Analysis in Geology, 2nd edn. Wiley, New York. Dearing, J.A., 1994. Environmental Magnetic Susceptibility: Using the Bartington MS2 System. Chi Publishing, Kenilworth. Jarvis, M.G., Allen, R.H., Fordham, S.J., Hazeelden, J., Moffat, A.J., Sturdy, R.G., 1984. Soil Survey of England and Wales, Bulletin 15, Harpendon. Jenns, N.J., in preparation. Sediment source ascription and quantification using mineral magnetics: a palaeolimnological reconstruction of the sedimentation of Slapton Higher Ley. M.Sc. Thesis, University of Oxford, UK. Lees, J.A., 1994. Modelling the magnetic properties of natural and environmental materials. Unpublished Ph.D. Thesis, University of Coventry, UK. Maher, B.A., 1988. Magnetic properties of some synthetic sub-micron magnetites, Journal of Geophysical Research, 94, 83–96. Oldfield, F., 1991. Environmental magnetism; a personal perspective, Quaternary Science Reviews, 10, 73–85. Oldfield, F., Rummery, T.A., Thompson, R., Walling, D.E., 1979. Identification of suspended sediment sources by means of magnetic measurements, Water Resources Research, 15, 211–218. Oldfield, F., Clark, R.L., 1990. Lake sediment-based studies of soil erosion. In: J. Boardman, I.D.L. Foster, J.A. Dearing (Editors), Soil Erosion on Agricultural Land. Wiley, Chichester, pp. 201–230. Richards, J.A., 1993. Remote Sensing Digital Image Analysis, 2nd edn. Springer, Berlin. Shankar, R., Thompson, R., Galloway, R.B., 1994. Sediment source modelling: unmixing of artificial magnetisation and natural radioactivity measurements, Earth and Planetary Science Letters, 126, 411–420. Slattery, M.C., 1994. Contemporary sediment dynamics and sediment delivery in a small agricultural catchment, north Oxfordshire, U.K. Unpublished Ph.D. Thesis, University of Oxford, UK. Slattery, M.C., Burt, T.P., Walden, J., in preparation. Use of mineral magnetic measurements to fingerprint suspended sediment sources: a case study using a small agricultural catchment, Oxfordshire, UK. Taha, H.A., 1992. Operations Research: An Introduction, 5th edn. Macmillan, New York. Thompson, R., 1986. Modelling magnetization data using SIMPLEX, Physics of the Earth and Planetary Interiors, 42, 113–127. Thompson, R., Oldfield, F., 1986. Environmental Magnetism. Allen and Unwin, London. Walden, J., Smith, J.P., Dackombe, R.V., 1992. The use of simultaneous R- and Q-mode factor analysis as a tool for assisting interpretation of mineral magnetic data, Mathematical Geology, 24, 227–247. Walden, J., Slattery, M.C., 1993. Verification of a simple gravity technique for separation of particle size fractions suitable for mineral magnetic analysis, Earth Surface Processes and Landforms, 18, 829–833.
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Walden, J., White, K., Macmillan, W.D., Burt, T., Slattery, M., Parker, A., 1993. A comparison of qualitative, statistical and mathematical approaches for identification of natural magnetic mineral assemblages within sediment samples. European Geophysical Society XVIII General Assembly, Wiesbaden, Germany. Walden, J., Smith, J.P., 1995. Factor analysis: a practical application. In: D. Maddy, J.S. Brew (Editors), Statistical Modelling of Quaternary Science Data: A Practical Manual. Technical Guide Series, Quaternary Research Association, pp. 39–63. Walling, D.E., Peart, M.R., Oldfield, F., Thompson, R., 1979. Suspended sediment sources identified by magnetic measurements, Nature, 281, 110–113. Walling, D.E., Woodward, J.C., Nicholas, A.P., 1993. A multi-parameter approach to fingerprinting suspended sediment sources. In: N.E. Peters, E. Hoehn, Ch. Leibundgut, N. Tase, D.E. Walling (Editors), Tracers in Hydrology. IAHS Publication 215, pp. 328–338. Yu, L., Oldfield, F., 1989. A multivariate mixing model for identifying sediment source from magnetic measurements, Quaternary Research, 32, 168–181. Yu, L., Oldfield, F., 1993. Quantitative sediment source ascription using magnetic measurements in a reservoircatchment system near Nijar, S.E. Spain, Earth Surface Processes and Landforms, 18, 441–454
Use of mineral magnetic measurements to fingerprint suspended sediment sources: approaches and techniques for data analysis J. Walden a ,*, M.C. Slattery b, T.P. Burt c a
School of Geography and Geology, University of St Andrews, Purdie Building, North Haugh, St Andrews KY16 9ST, UK b Department of Geography, East Carolina University, Geenville, NC 27858-4353, USA c Department of Geography, University of Durham, Science Laboratories, South Road, Durham DH1 3LE, UK Received 23 September 1996; accepted 2 June 1997
Abstract Three analytical approaches, qualitative, statistical and quantitative, are evaluated when applied to mineral magnetic data to identify the relative sediment source contributions to suspended sediment loads within a small catchment system. The qualitative and statistical analyses provide useful information in their own right but, in addition, indicate the feasibility of quantitative sediment source ascription using a sediment unmixing model based upon a linear programming algorithm. The criteria for such modelling are considered and the model formulation outlined. Model testing and initial output suggest that, under certain conditions, unmixing models have considerable potential for the quantification of suspended sediment source contributions. Qualitative and statistical analyses provide a subjective means to judge the quality of the model output. A number of limitations within the approach are identified and some possible solutions to these limitations suggested. q 1997 Elsevier Science B.V. Keywords: Suspended sediments; Environmental magnetism; Sediment sources; Modelling
1. Introduction Information concerning suspended sediment sources is an essential prerequisite in attempts to elucidate linkages within the sediment delivery system between the field and the river. One approach (e.g. Oldfield et al., 1979; Walling et al., 1979; Caitcheon, 1993) has involved the use of mineral magnetic analyses to provide a compositional * Corresponding author. e-mail: [email protected] 0022-1694/97/$17.00 q 1997 Elsevier Science B.V. All rights reserved PII S00 22-1694(97)000 78-4
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fingerprint by which catchment sources can be compared with suspended sediments in order to investigate the likely sources for the latter. Slattery (1994) and Slattery et al. (in preparation) present results for such a study in a small catchment of the River Stour, north Oxfordshire (Fig. 1). Field observation indicated that erosion of cultivated fields provides an important source of suspended sediment to the River Stour. Slattery et al. (in preparation), after suitable data analysis, focus upon the interpretation of the magnetic data to examine the relative contributions from slope sources and channel erosion, and how these various sediment source areas change both within and between individual storm events. The approaches used in the data analysis are themselves of general interest and could be applied in other settings. Therefore, while some discussion of the environmental context will be made here, the data analysis techniques themselves and the computational steps involved form the focus of this paper. 1.1. Field setting The study catchment (Fig. 1) has a drainage area of 6.2 km 2, NW of Oxford and is a headwater of a tributary to the Warwickshire Avon. Two major soil series are present within the catchment, the Aberford and the Banbury Series (Jarvis et al., 1984) and the vast majority of the catchment consists of cultivated land. Field observation and mineral magnetic data summarised later suggested that three potential sediment source groups can be identified: Aberford series topsoils; Aberford series channel bank material; and, either topsoils or channel bank material from the Banbury soil series (which could not be distinguished magnetically). Representative field samples were collected from each of these potential sources. In addition, suspended sediment samples were collected using a Rock and Taylor automatic pump sampler over a period of some 12 months along with rainfall and discharge readings (Slattery, 1994). 1.2. Mineral magnetic analysis A series of standard mineral magnetic measurements (Thompson and Oldfield, 1986) including magnetic susceptibility (x), frequency dependent susceptibility (x fd), and isothermal remanence magnetisation (IRM) acquisition in magnetic fields between 20 and 1000 mT were made on the field samples. Particle size analysis of the suspended sediment samples showed that material coarser than 63 mm (4 f) was almost totally absent, suggesting that sand grade material from the catchment was not being transported as suspended load into the stream network. Magnetic analysis on the sediment sources was therefore performed only on material finer than 63 mm. Analysis of size-specific magnetic properties (separated using the method of Walden and Slattery, 1993) for the three sources showed that the differences in their respective particle size distributions had little influence on their magnetic properties, although this is accommodated in the modelling procedure. The mineral magnetic data were analysed in three ways. A qualitative analysis, using graphical techniques and the ‘standard’ interpretations given in the literature (e.g. Thompson and Oldfield, 1986; Maher, 1988; Oldfield, 1991) was followed by a statistical approach, using multivariate techniques (e.g. Oldfield and Clark, 1990; Walden et al., 1992) in order to provide a more quantitative and, hopefully, objective analysis. Finally, the data were
Fig. 1. Study catchment within the Stour River system, NW of Oxford, illustrating the distribution of the two major soil series and the locations of the source samples used in this work.
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subjected to an unmixing model (e.g. Thompson, 1986; Yu and Oldfield, 1989, 1993; Walden et al., 1993; Walling et al., 1993; Lees, 1994) which attempts to quantify the proportions of each catchment source to the suspended sediment samples based upon their respective magnetic properties. This three-stage data analysis procedure has been the subject of a detailed review by Lees (1994). She identified both the major advantages and limitations of the use of magnetic measurements for sediment source ascription in a range of sedimentary settings but these did not include a suspended sediment system such as that studied in this paper. Many of the conclusions drawn from her work are, however, applicable to such a system and will be considered here.
2. Criteria for successful quantification of sediment sources In the context of attempts to quantify sediment source contributions using magnetic data, Lees (1994) summarised the prerequisites for successful unmixing of sediment sources: 2.1. Definition of potential source material types It is critical to achieve optimal identification and definition of the source material properties as these represent the ‘end members’ of the model and strongly influence the eventual proportions of each source type ascribed to the sediment sample. This issue has a number of implications. 1. Field sampling needs to be organised appropriately to enable intra- and inter-source variation to be fully quantified (Lees, 1994). 2. Selection of the magnetic parameter values (e.g. mean) to represent each ‘end-member’ (source) is critical. Sensitivity of the model output to changes in the properties used to represent the sources should be considered to provide some idea of model reliability. 3. For successful modelling, the suspended sediment samples must have properties which lie wholly within the range of behaviour displayed by the values chosen to represent the sources. Errors in source definition, chemical alteration during transport or size selective transport of different sources may influence this. 2.2. Maximum number of source material types and data dimensionality Lees (1994) suggests that when using magnetic parameters for source modelling only a small number (three or four) of source types can realistically be used as magnetic parameters are generally only sensitive to one, two or possibly three ‘dimensions’ (e.g. iron mineral concentrations, types and grain size). This restricts modelling to systems where it is environmentally sensible to identify only three or four end-members for the modelling process. Where possible, parameters sensitive to magnetic grain size (x fd or anhysteretic remanent magnetization (x ARM)) or combining magnetic with other geochemical or mineralogical analyses could be considered to increase the dimensionality of the data
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Fig. 2. Relationships between source material properties and the suspended sediment samples to be unmixed. (a) The problem of sources which are numerical multiples of one another. The range of values displayed by three hypothetical source materials for two concentration-dependent parameters are plotted. Suspended sediment samples 1 and 3 can most simply be interpreted as being derived primarily from sources A and C, respectively. Sample 2 is more difficult however, as it could be derived solely from source B or represent some sort of mixture from either sources A and C or A, B and C. (b) ‘Ideal’ distribution of source material properties. Sediment source ascription of suspended sediment samples 1, 2 and 3 should be possible. In the case of sample 4 however, unmixing would not be possible and indicates either failure to identify a potential source, alteration of the magnetic properties of the suspended sediment during weathering and transport, or measurement error.
set. Lack of dimensionality can lead to groups of source samples that are ‘numerical multiples’ of one another (Fig. 2). 2.3. Assessing the feasibility of quantitative modelling The feasibility of source modelling can be assessed initially by considering a qualitative and statistical analysis of the data. Simple bivariate scatter plots (using parameters with different sensitivities) and multivariate statistical analysis using principal components, factor or cluster analysis (e.g. Oldfield and Clark, 1990; Walden et al., 1992; Lees, 1994; Walden and Smith, 1995) provide some indication of how successful any subsequent quantitative unmixing modelling is likely to be. 2.4. Parameter selection for modelling The parameters that are to be used in any numerical unmixing modelling need to meet a number of criteria. 1. Parameters should be linearly additive (Thompson, 1986; Lees, 1994). Thus, if two source materials have values for a particular magnetic parameter of x 1 and x 2, respectively, and are mixed in known proportions (p 1 and p 2), the resultant mixture, assuming perfect linear additivity, should have a value of this parameter (x r) which equals: xr = p1 x1 + p2 x2
(1)
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Table 1 Magnetic data for the various sample groups (x is expressed in units of 10 −7 m 3 kg −1; soft IRM, mid IRM, hard IRM and SIRM are expressed in units of 10 −5 Am 2 kg −1) N
x
Soft IRM (0–20 mT)
Mid IRM (20–300 mT)
Hard IRM (300–1000 mT)
SIRM
7 12 3
9.27 5.97 33.23
142.16 88.42 548.49
414.84 292.39 1228.83
41.74 29.02 50.42
598.74 409.83 1827.73
(b) Non-storm and storm suspended sediment samples Non-storm 9 6.53 110.34 Storm 24 9.35 138.10
338.65 396.12
34.35 41.31
483.33 575.53
(a) Source materials a Aberford TS Aberford CB Banbury TS + CB
a These values were derived from analysis of three discrete particle size fractions for each source sample and applying Eq. (1) to derive a value for a ‘standard’ particle size distribution (Slattery, 1994) to remove the minor effect of variation in the overall particle size distributions between each source.
This equation can be expanded to include additional sources and multiple variables using linear programming algorithms (e.g. Simplex algorithm, Thompson, 1986). Such techniques are commonly used in operational research (Taha, 1992). An iterative search is made to discover what combination of source material proportions minimises the difference between the modelled magnetic properties and the observed (measured) properties of a particular suspended sediment sample. 2. Difficulties can occur when linearly additive parameters used in the model vary by orders of magnitude. Parameters with large values may therefore dominate the model (which is attempting to minimise differences between the modelled properties and the actual properties of the sediment sample) although ‘weighting’ certain parameters can help overcome this problem.
3. Qualitative data analysis Table 1 summarises the magnetic properties for the three types of catchment source materials (Slattery, 1994). Unfortunately, in this study, reliable measurement of x fd was not possible given the low mass of many of the suspended sediment samples. Fig. 3 plots x (roughly proportional to the concentration of ferrimagnetic mineral species) vs. hard IRM (sensitive to the concentration of antiferromagnetic species). The samples from the three source material types plot as separate clusters and it appears that the assemblages of magnetic minerals within the sources show some measurable differences. Less encouragingly, Fig. 3 does suggest that the distribution of the three source types is closer to that shown in Fig. 2(a) than the ‘ideal’ shown in Fig. 2(b). This situation is likely to exist in many (the majority?) of natural field settings and while Fig. 3 does not suggest these sources are pure ‘numerical multiples’, this problem may need further consideration in any subsequent modelling. The vast majority of the suspended sediment samples (classified into ‘non-storm’ and
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Fig. 3. Plots of x (10 −7 m 3 kg −1) vs. hard IRM (10 −5 Am 2 kg −1) for the catchment source and suspended sediment samples.
‘storm’ types) exhibit magnetic properties which lie wholly within the distribution of the catchment source materials, suggesting that in numerical terms it should be possible to ‘unmix’ the suspended sediments on the basis of these three source material types alone. This does not exclude the possibility of alteration of the mineralogical composition of the suspended sediments during weathering and transportation but might indicate that any such effects have been relatively small. Fig. 3 also indicates that the non-storm and storm samples exhibit generally different magnetic properties. The non-storm samples show lower concentrations of magnetic minerals and plot in the same area of the figure as the Aberford channel bank materials. In contrast, the storm samples show higher concentrations of magnetic minerals and plot closer to the Aberford topsoil materials. This pattern makes ‘environmental’ sense as topsoil contributions might increase during periods of higher flow as a result of surface and overbank flow. Fig. 3 also suggests that the contribution to the suspended sediments from the Banbury series is much less than for the other two source types. Again, this would seem to be consistent within the field context (Fig. 1).
4. Statistical analysis Fig. 4 shows a plot of the variable and sample loadings from an R- and Q-mode factor analysis, following the methods of Davis (1986) and Walden and Smith (1995), based upon the linearly additive parameters x, ‘soft’, ‘mid’ and ‘hard’ IRMs and SIRM (IRM 1000mT) for the catchment samples and the suspended sediment samples. The eigenvalues for this analysis suggest that factors 1 and 2 explain over 95% of the variation in the raw data set. This is extremely high and would seem to confirm the conclusion of Lees (1994) discussed earlier concerning the dimensionality of some mineral magnetic data sets. From the positions of the original variables in the inset to Fig. 4, these results can be
Fig. 4. Plot of variable and sample factor loadings. Inset shows the distribution of all source and suspended sediment samples. Shaded area of the inset is shown in the main part of the figure, allowing distribution of the non-storm and storm suspended sediments to be seen in more detail.
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interpreted as follows: factor 1 is controlled by overall concentrations of magnetic minerals whereas factor 2 is more influenced by ‘hard’ IRM and therefore reflects antiferromagnetic mineral concentrations. The main part of Fig. 4 shows the centre of this factor space in an expanded form. As in Fig. 3, the Aberford channel bank and topsoil sources form two distinct clusters of samples, suggesting that they can be distinguished on the basis of the five magnetic parameters used in this analysis. The majority of the non-storm and storm suspended sediment samples plot within this same area on the factor diagram. Again, the non-storm samples show a closer affinity to the channel bank source materials and the storm samples to the topsoil source materials. Given the relatively large distance in factor space between the suspended sediment samples and the Banbury series source samples it can be inferred that this source makes less contribution to the sediment load of the stream system.
5. Conclusions from the qualitative and statistical analyses The qualitative and statistical examination of the magnetic data suggest that the source materials and the suspended sediment samples meet an acceptable number (if not all) of the criteria discussed by Lees (1994) and summarised earlier. Importantly: 1. The three source material types possess magnetic behaviours which can be distinguished using linearly additive parameters; 2. The majority of the suspended sediment samples display magnetic behaviour which lies within the range of behaviours exhibited by the three source types. Figs. 3 and 4 suggest at least two potential problems with these data for quantitative sediment source ascription, as follows. 1. Between-group variation in magnetic properties may lack some dimensionality (Fig. 3). This issue may influence the effectiveness with which certain suspended sediment samples can be unmixed. 2. Within-group variation in the magnetic properties of the three source types is clearly present. As a single value (for each magnetic parameter) has to be selected to represent the properties of each source in any unmixing model, some decision has to be made as to what that value should be. While mean values would seem the most obvious choice, the model’s sensitivity to the parameter values chosen needs to be tested. A number of ‘environmental’ conclusions can also be drawn from these initial qualitative and statistical analyses. 1. Given that the magnetic properties of the majority of the suspended sediment samples lie within the range of properties displayed by the three source material types, it might be possible to infer that all the major source types have been identified and that no major mineralogical alteration of the suspended sediments is occurring during the weathering and transportation processes. 2. Source contributions do vary under different flow conditions with Aberford channel bank material dominating in most low flow (non-storm) periods but with increasing
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contributions from Aberford topsoil during high flow (storm) events. This is consistent with field observation (Slattery, 1994). 3. The strongly magnetic Banbury Series source only makes a minor contribution to the suspended sediment load. This is consistent with the location of the source within the catchment (Fig. 1) and field observation.
6. Model formulation and use Before proceeding to build a specific model for the Stour catchment, the mathematical formulation of the unmixing model needs to be outlined. The basic form of the model used here follows Thompson (1986) and is commonly used in other environmental contexts (e.g. analysis of remotely sensed data: Richards, 1993). The model essentially carries out an iterative search to find the optimum combination of the source materials which, when linearly mixed, minimises the differences between the measured magnetic properties of the suspended sediment and the magnetic properties of the mathematical mixture of the sources. The optimisation process has to work within certain constraints namely: 1. the proportion of each source must be lie between 0 and 1; 2. the sum of all source proportions should total 1. The following notation is adopted below: p e a ij bj xi sj
number of magnetic parameters used in the modelling procedure number of end-members (sources) used in the modelling procedure measured value of magnetic parameter j in end-member (source) i measured value of magnetic parameter j in the natural sample being modelled hypothetical proportion of end-member i in the natural sample where x i $ 0 and x i # 1 simulated (modelled) value of magnetic parameter j in the simulated version of the natural sample e
sj = ∑ aij xi i=1
The minimum difference between the simulated and natural samples is found by minimising e 2 p p (2) ∑ ∑ aij xi − bj = ∑ (sj − bj )2 j=1
i=1
j=1
subject to the constraint that x i $ 0 and x i # 1 for each end-member i and e
∑ xi = 1
i=1
One problem with Eq. (2) is the presence of differences in the absolute scales by which the various magnetic parameters are measured. Small percentage differences in actual and modelled SIRM values expressed in thousands of units will exert greater control on the model than much larger percentage differences in actual and modelled x values expressed in tens of units. In Eq. (3) each variable is given a more even weighting in the model by
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expressing the differences between modelled and measured values as a percentage of the modelled value. p
∑ {[(sj − bj )=bj ] p 100}2
j=1
(3)
The model was run on a standard 486 DX2 PC using the Solver ‘add in’ component of Microsoft’s Excel 5 spreadsheet which allows optimisation routines to be constructed using a SIMPLEX algorithm. Fig. 5 shows an example of the spreadsheet used. The basic structure of the spreadsheet is given in Table 2. The user has to supply values to represent the properties of the source materials, the measured properties of the suspended sediment sample which has to be ‘unmixed’ and the initial starting proportions of each source from which the optimisation routine will move to find the ‘best’ solution. 6.1. Model testing To test that the model functioned satisfactorily, a number of hypothetical source mixtures were computed (based on Eq. (1)) using the mean values for each of the three source materials (Table 1) to represent x, soft, mid and hard IRMs and SIRM. The model successfully ‘unmixed’ these hypothetical mixtures in the correct proportions. In a very small number of cases the model showed some sensitivity to the initial starting proportions specified for the three sources. This problem was overcome by running the model from a number of different initial start conditions to ensure the optimum solution was being found. Similar testing was also done to examine the effect of how the ‘goodness of fit’ of the modelled magnetic properties is calculated relative to the measured values. Models based on both eqns (2) and (3) gave satisfactory results when trying to unmix hypothetical source mixtures. This suggests that for perfect mixtures of the three sources at least, the choice between Eq. (2) or Eq. (3) was not critical. Eq. (3) would seem however, on logical grounds, to be preferable and the initial discussion below is based on the model output using Eq. (3). 6.2. Unmixing the suspended sediment samples The testing procedure gave confidence in the model’s mathematical operation. As suggested by previous workers, however (e.g. Thompson, 1986; Yu and Oldfield, 1989, 1993; Walden et al., 1993; Lees, 1994; Shankar et al., 1994), such mathematical procedures are likely to be less robust when dealing with environmental samples where a number of factors (measurement error, chemical or mineralogical alteration, source variation, etc.) mean that few of the suspended sediment samples can be unmixed as perfect combinations of the mean values of the source materials. Mineral magnetic data for some 33 suspended sediment samples, representing both low flow and high flow conditions were available for unmixing and a number of these will be considered in detail here to illustrate the model’s potential and possible problems. A fuller interpretation of the results in terms of their environmental significance is provided in Slattery et al. (in preparation).
Fig. 5. Example of the unmixing model constructed using the Solver add-in in Microsoft’s Excel 5 spreadsheet. See text and Table 2 for explanation.
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Table 2 Basic structure of the spreadsheet shown in Fig. 5 Cells
Contents
G6–K8 G14–K14
The measured parameter values used to represent the properties of the three source materials The measured parameter values for the particular suspended sediment sample which is currently being unmixed The modelled parameter values for the simulated version of the suspended sediment sample currently being unmixed. These cells are linked to G6–K8 and C19–C21 by formula based on Eq. (1). For example, cell I21 contains the formula: ((C19*G6)) + (C20*G7) + (C21*G8) The modelled proportions of the three source materials. Solver is configured so that these cells are changed in order to minimise the value held in cell H26 Contains the differences and squared differences between the measured and modelled parameter values. As discussed elsewhere, these cells can be configured in a number of ways to force the model to treat variables of different orders of magnitude with equal weight Contains the sum of cells G22–K22. Solver is configured to minimise the value contained in this cell by changing the values held in cells C19–C21
G19–K19
C19–C21 G21–K22
F24
6.3. Reliable estimates of sediment source Both Figs. 3 and 4 offer some insight into the type of suspended samples for which the unmixing model might produce more or less reliable estimates of sediment source contributions. For example, while the suspended sediment samples 4, 10, 12, 17 and 20 all lie within the range of magnetic properties displayed by the source materials, they lie near to the extremes of those properties and therefore at some distance from the mean values of each source material type chosen to represent that source type within the unmixing model. In contrast, the mean values of both the non-storm and storm sample types lie nearer to the Aberford source means as do, for example, suspended sediment samples 2, 14 and 23. Table 3 shows the model output for selected suspended sediment samples. The results of the modelling process for the mean magnetic properties of the non-storm and storm samples are consistent with both Figs. 3 and 4 and seem sensible given their environmental context. Thus, the non-storm mean is dominated by material derived from the Aberford channel banks but with a significant proportion of Aberford topsoil. As discussed by Slattery (1994) and Slattery et al. (in preparation), material derived from the Aberford topsoil at higher flow conditions and subsequently stored on the channel bed is the most likely source of this contribution during lower flow levels. In contrast, the storm mean sample shows greater proportions of Aberford topsoil and a small contribution from the Banbury series source. Many of the higher flow events generated overbank flow (Slattery, 1994; Slattery et al., in preparation) providing an obvious mechanism for incorporation of greater amounts of Aberford topsoil into the suspended sediment system. The sum of squared differences is lower for the storm mean sample, suggesting that mathematically at least, the model is a better ‘fit’ for this sample than for the non-storm mean. Samples 2, 14 and 23 produce what would appear to be sensible proportions of the three source materials given their magnetic properties and their respective flow conditions. In each case, the sum of squared differences are also relatively low. Pairs of samples 3 and 6 (non-storm samples) and samples 15 and 18 (storm samples) show similar magnetic
31/8–4/9 4–7/9 7–14/9 16–23/11 25/9 21:00 h 20/10 10:00 h 27/11 20:06 h 30/11 10:10 h 18/12 11:10 h 18/12 11:40 h 18/12 12:40 h 18/12 14:10 h
Non-storm Storm
Date/time
TS, topsoil; CB, channel bank.
2 3 4 6 10 12 14 15 17 18 20 23
Sample
NS NS NS NS S S S S S S S S
7.2 6.5 4.9 6.7 12.7 7.8 10.1 10.7 13.2 11.0 11.0 9.2
127.5 114.1 91.8 123.4 183.6 112.2 161.1 187.8 208.8 157.8 179.6 133.7
110.3 138.1 363.0 371.2 327.8 353.4 601.0 463.2 424.0 425.6 494.7 409.7 444.8 364.7
338.6 396.1 38.0 26.6 13.6 29.2 102.8 68.5 45.2 42.0 31.7 37.6 20.6 52.1
34.3 41.3 528.5 511.8 433.1 506.0 887.3 643.9 630.3 655.3 735.2 605.2 644.9 550.5
483.3 575.5
SIRM
0.33 0.05 0.00 0.12 0.83 0.95 0.45 0.33 0.00 0.26 0.00 0.70
0.62 0.90 0.99 0.82 0.00 0.05 0.44 0.51 0.73 0.60 0.81 0.28
0.72 0.53
Ab CB
Modelled proportions
0.27 0.39
6.5 9.4
Hard IRM
n=9 n = 24
Mid IRM Ab TS
Soft IRM
Non-storm x (NS) or storm (S)
0.04 0.05 0.00 0.05 0.17 0.00 0.10 0.15 0.26 0.13 0.18 0.01
0.01 0.07
Ban CB + TS
278.53 235.82 1822.65 309.87 3923.43 1506.44 77.23 326.66 193.40 125.28 1074.40 36.65
188.70 11.78
Sum diffs 2
Table 3 Mineral magnetic properties of selected suspended sediment samples and the proportions of the three source materials ascribed by the unmixing model. The model output was produced by minimising the sum of the squared % differences between the measured and modelled versions of the five magnetic parameters (see text for explanation)
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properties (Figs. 3 and 4) and, encouragingly, the output from the unmixing model is both similar and environmentally sensible for each pair. 6.4. Less reliable estimates of sediment source Less confidence might be placed in the ability of the model to ascribe source proportions to samples 4, 10, 12, 17 and 20 and with the exception of sample 17, the sum of the errors appear relatively high, suggesting a poor fit between the modelled and measured magnetic properties. In each case, the qualitative interpretation of Figs. 3, and 5 provide a guide to the likely usefulness of the model output. For example, the model ascribes a channel bank contribution of almost 100% Aberford to sample 4. While the error term is relatively large, the position of sample 4 in Figs. 3 and 4 suggests the model output is environmentally sensible. The large error term is simply a function of the fact that this sample has magnetic properties which are more like the magnetically weaker of the Aberford channel bank source samples than the mean for this source group. In contrast, the source proportions ascribed to sample 10 with 0% Aberford channel banks, while mathematically the optimum solution, would seem to be unrealistic given the field setting. The measured magnetic properties of the sample are somewhat extreme relative to the source means. Although measurement error is a possible cause, two other possibilities, chemical alteration or selective transport, are more likely explanations. Further field observations would be required to determine the likelihood of either explanation. Alternatively, it may be that a more realistic source mixture for sample 10 would include a proportion of the Aberford channel banks, a smaller proportion of the Aberford topsoil and a slightly larger proportion of the Banbury series. This sample might be exhibiting the same problem as sample 2 in Fig. 2(a). The ‘numerical multiple’ problem means that the model cannot resolve between a number of possible mixtures which produce similar mathematical solutions, some of which make more environmental sense than others. For example, a mixture of 35%, 41% and 24% Aberford topsoil, channel banks and Banbury series, respectively, produces a slightly higher error term but would seem more realistic given the environmental setting. Samples 12, 17 and 20 might also exhibit this problem. Whichever of the above explanations is the actual cause of the unrealistic or poor numerical fit of the model, attempting to quantify the source contributions would seem unwise for those samples lying at the extremes of behaviour for the suspended sediments as a whole. In these cases, a qualitative interpretation of the particular sample data may be all that is justifiable. 6.5. Comparison with factor analysis When Eq. (2) is used to calculate the error term between the modelled and measured magnetic properties, in a number of cases the model ascribes significantly different source proportions. For example, sample 2 is modelled as 63% Aberford topsoil and 37% Aberford channel banks. While this might not seem to be unreasonable in terms of the environmental setting, the proportions given in Table 3, based upon Eq. (3), are much more consistent with the output from the factor analysis (Fig. 4). The position of sample 2
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lies almost directly between that of the positions of the mean samples for the two Aberford source types, but significantly closer to that of the Aberford channel bank mean, suggesting greater proportions of that source within the sample. If the relative distances in factor space of sample 2 are measured from the positions of the two Aberford source means, they suggest proportions almost identical to those given in Table 3 (allowing for the small Banbury series contribution). Similar calculations for other samples lying almost directly between these two source means on Fig. 4, including samples 3, 6 and 23, would seem to confirm that the model based upon Eq. (3) and the factor analysis provide similar indications of the sediment source proportions. This in turn, would seem to suggest that the use of Eq. (3) in the unmixing model is preferable to Eq. (2). 6.6. Sensitivity analysis All of the above analyses were based upon an unmixing model using the mean properties of the magnetic variables for the three source material types (Table 1). The sensitivity of the model output to these properties was tested by systematically changing their values and the output produced by the model varied in a predictable manner. For example, in one experiment, the parameter values for Aberford topsoil and Aberford channel banks were adjusted in steps of 5% (up to 20%) in opposite directions (effectively stretching or contracting the multivariate ‘distance’ between these two sources). Where the properties of individual suspended sediment samples remained between those of the two source types, the source proportions ascribed to them were very similar to those of the standard model using the mean source properties. Only as the change in the source material properties moved the source ‘closer’ in multivariate space to an individual suspended sediment sample did that sample produce significantly different unmixing results. In all cases, however, the model continued to produce similar source proportions for suspended sediment samples with comparable magnetic properties (e.g. samples 3 and 6). This suggests that even if the parameter values adopted for a given source are not accurate representations of that source, whilst the modelled source proportions will also be less accurate in absolute terms, the patterns in modelled source proportions for a particular set of suspended sediment samples should be similar. Identification of any such patterns might, in itself, be justification for the modelling. The testing of the model sensitivity suggested no logical reason why mean parameter values of each source type should not be adopted for modelling purposes.
7. Discussion These results emphasise a number of issues already raised, concerning both the modelling processingeneral and thespecific environmental settingfrom whichthese sampleswere drawn. 7.1. General issues Two important general issues are highlighted by these results. First, in examining the
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output from the model, it is clear that the qualitative and statistical analyses of the data have provided a useful guide concerning both the general feasibility of modelling and, more specifically, some indication of which individual samples might prove difficult to unmix for particular reasons. The model output can therefore be examined in a more critical fashion. While this in no way confirms how realistic or useful the model output might be in environmental terms, it does give some confidence in the numerical robustness of the modelling process itself. The environmental interpretation of the model output still requires some subjective judgement on the part of the researcher to assess the realism of the modelled sediment source proportions. Second, the accuracy of the quantitative estimates of source contributions is difficult to assess as the absolute values produced by the model will be different if the source materials are defined by different values of each parameter measured. The initial definition of the number and mean properties of the source materials is therefore both a critical component of the modelling process (Lees, 1994) and, even with the most rigorous field procedures, conditional upon an element of subjective judgement on behalf of the researcher. In this study, suspended sediment samples caught at the catchment outlet might have travelled only a few tens of metres. They may therefore have been derived from an individual section of channel bank (a bank slump, for example) and would possess the compositional properties of that particular portion of the channel bank source rather than the ‘mean’ properties of the channel banks in general. In a larger catchment system, such individual point source contributions are more likely to be diluted and will therefore be less significant. In contrast, the initial definition of the source types in a larger catchment system would clearly be a more difficult task. 7.2. Issues specific to this environmental setting Two main issues which are specific to this individual field setting are highlighted. First, these data do show an element of the ‘numerical multiple’ problem and therefore some caution is needed in interpretation of the quantitative output provided by the modelling process. In most cases however, comparison of the model output with the qualitative and statistical data analyses can allow spurious model results for particular suspended sediment samples to be identified. Despite the qualification above concerning the definition of the source material properties, the general nature of the model output would seem sensible given the environmental context. Thus, the relatively greater contribution of Aberford topsoil material during periods of higher discharges is consistent with field observations of overbank and surface flow during these periods. Identification of this pattern is in itself useful, even if it is difficult to assess the absolute accuracy of the proportions ascribed to each source. This problem may well present itself in other field settings and the use of additional compositional properties such as elemental geochemistry to provide greater dimensionality for the modelling algorithm to work with is recommended. Second, a number of explanations can be suggested to account for the fact that some of the suspended sediment samples display results which lie outside the mean values adopted for the source material types. Some effort should be made to identify the presence or absence of selective particle size transport or chemical alteration during transportation and the effect such processes might have on subsequent modelling. These issues are currently
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under investigation (Jenns, in preparation). An additional problem here may be small mass of the suspended sediment samples. Like most analytical equipment, magnetic instrumentation does display some sensitivity to sample mass (e.g. Dearing, 1994) and the bulk suspended sediment samples collected by some pump water samplers can be of very small mass. Material collected using continuous flow centrifuge equipment would therefore be an advantage in this type of work. While the influence of these factors can not be ruled out in the current field context, for many of the suspended sediment samples available, the modelling process seems to have produced realistic results even if those results are of unknown absolute accuracy.
8. Conclusions A number of conclusions can be drawn from this work which support the main findings of Lees (1994) in other types of sedimentary environments. 1. Identification of the major source material types within the sedimentary system and quantification of their compositional properties is a critical step in any attempt to quantify sediment source contributions using linear programming algorithms. Sources which do not have distinct compositional properties or are numerical multiples of one another will make attempts at source modelling much less reliable. 2. Qualitative and statistical analyses of compositional data which are being considered for sediment source unmixing perform two important tasks: assessment of how well the data fit the various criteria necessary for successful application of the modelling procedure and, once modelling is performed, provision of a useful means of verifying (at least in a numerical sense) how realistic the output produced by the model is likely to be for particular suspended sediment samples. 3. While the modelling procedure can reliably unmix ‘perfect’ mixtures of the source materials, field samples will not unmix without some errors. Such errors can have a number of causes including the natural levels of variability within each source type but factors such as compositional alteration or selective sediment transport must also be considered. 4. It would seem therefore, that unmixing models can be a useful development from initial qualitative and statistical analysis of suspended sediment source ascription, provided such quantitative results are interpreted with an full awareness of their possible limitations. It is also clear that there is considerable scope for further development of these types of modelling procedures provided the recommendations outlined by Lees (1994) and summarised here are carefully followed. 5. Within this particular field setting, it appears that the modelling procedure can offer some real insights into the proportions of the source material contributions to the suspended sediment system. While the absolute accuracy of the quantitative estimates of source material ascription is uncertain, it is encouraging that the values suggested for non-storm and storm flow conditions are consistent with both field observation and the qualitative appraisal of these same data. Further work, combining magnetic with other forms of compositional analyses is clearly warranted.
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Slattery et al. (in preparation) develop this final conclusion by examining the environmental interpretation of the model output in more detail within the context of this particular field setting and as a tool to assist other studies of sediment source ascription in suspended sediment systems.
Acknowledgements The authors wish to thank the School of Geography, University of Oxford for access to the facilities used in this work. J.W. would like to thank Dr Joan Lees (Coventry University), Prof. John Dearing (Liverpool University) and Dr Bill Macmillan (Oxford University) for useful discussions on the modelling procedures used in this paper.
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