Using particle size distributions to fingerprint suspended sediment sources—Evaluation at laboratory and catchment scales

Applications of sediment source fingerprinting studies are growing globally despite the high costs and workloads associated with the analyses of conventional fingerprint properties on target sediment samples collected using traditional methods. To this end, there is a need to test new fingerprint properties that can overcome these challenges. Sediment particle size could potentially contribute here since it is relatively easy to measure but, until now, has rarely been deployed as a fingerprint itself. Instead, particle size has been used to ensure that source and target sediment samples are more directly comparable on the basis of the fingerprints used. Accordingly, this work examined whether particle size distributions (PSDs) could be used as a reliable fingerprint for apportioning sediment sources, in combination with a grain size un‐mixing model. Application of PSDs as a fingerprint was tested at two scales: (i) in a laboratory setting where soil samples with known PSDs were used to generate artificial mixtures to evaluate un‐mixing model results, and (ii) a catchment setting comparing PSDs in a confluence‐based approach to test if downstream target sediment PSDs could be un‐mixed into the contributions of sediment coming from an upstream and a tributary sampling site. Laboratory results showed that the known proportions of the two, three and four soil samples in the artificial mixtures were predicted accurately using the AnalySize grain size un‐mixing model, giving average absolute errors of 9%, 8% and 6%, respectively. Catchment results showed variable performances when comparing un‐mixing results with sediment budget estimations, with the best results obtained at higher discharge values during storm runoff events. Overall, our results suggest the potential of using PSDs for estimating contributions of sediment sources delivering SS with distinct PSDs when sources are located at short distance to the downstream sampling site.

easy to measure but, until now, has rarely been deployed as a fingerprint itself.
Instead, particle size has been used to ensure that source and target sediment samples are more directly comparable on the basis of the fingerprints used. Accordingly, this work examined whether particle size distributions (PSDs) could be used as a reliable fingerprint for apportioning sediment sources, in combination with a grain size un-mixing model. Application of PSDs as a fingerprint was tested at two scales: (i) in a laboratory setting where soil samples with known PSDs were used to generate artificial mixtures to evaluate un-mixing model results, and (ii) a catchment setting comparing PSDs in a confluence-based approach to test if downstream target sediment PSDs could be un-mixed into the contributions of sediment coming from an upstream and a tributary sampling site. Laboratory results showed that the known proportions of the two, three and four soil samples in the artificial mixtures were predicted accurately using the AnalySize grain size un-mixing model, giving average absolute errors of 9%, 8% and 6%, respectively. Catchment results showed variable performances when comparing un-mixing results with sediment budget estimations, with the best results obtained at higher discharge values during storm runoff events. Overall, our results suggest the potential of using PSDs for estimating contributions of sediment sources delivering SS with distinct PSDs when sources are located at short distance to the downstream sampling site.

K E Y W O R D S
AnalySize, end-member mixing model, grain size distribution, sediment fingerprinting, sediment origin 1 | INTRODUCTION Information on sediment origin can help target remedial actions to mitigate erosion in river catchments (Belmont et al., 2011). The sediment fingerprinting approach is a widely-adopted method to assemble this information, allowing the quantification of the relative contributions of different sources to target suspended sediment (SS) collected downstream (see reviews by e.g., Collins et al., 2020Collins et al., , 2017Haddadchi et al., 2013;Owens et al., 2016). To apply the method, both source and SS samples need to be collected. Potential sources are normally sampled manually, while SS is often collected using time-integrated sediment traps (e.g., García-Comendador et al., 2021;Pulley & Collins, 2021), or automatic water samplers (e.g., Legout et al., 2021;Vale et al., 2020). Selected properties or 'fingerprints' are then measured on the SS and compared with the corresponding fingerprint values measured on the potential source samples. This comparison allows for estimations of the relative contribution of each source to the target SS using un-mixing models.
Various approaches have been adopted to account for particle size in sediment fingerprinting studies to facilitate direct comparison between the properties of target SS and possible sources. The most commonly-applied approach is to fractionate SS and source samples by sieving (Laceby et al., 2017). Here, source materials and target SS samples are commonly sieved to <63 μm (Walling et al., 1993), since this fraction is considered to account for most of the SS load transported by rivers (e.g., Legout et al., 2013;Walling et al., 2000). In other studies, samples are sieved to different fractions and separate fingerprint analyses performed for isolated fractions (e.g., Gaspar et al., 2022Gaspar et al., , 2019Motha et al., 2002). Another approach is to sieve and then apply correction factors (e.g., Collins et al., 1997b;He & Walling, 1996). However, the underlying assumptions used for these correction factors were challenged by Smith and Blake (2014) due to the fact that positive linear relationships between particle size and fingerprint concentrations do not apply to all fingerprint properties (Horowitz, 1991;Russell et al., 2001). Given these uncertainties, recent reviews have stressed the need to consider both the most representative particle size fraction for the target sediment in question and to examine dependency of fingerprint properties on particle size, especially where a broad size fraction is used .
Alternatively, the confluence-based sediment fingerprinting approach has been proposed to facilitate direct comparison between the properties of downstream target SS samples and possible sources (i.e., different tributaries used to represent upstream catchment sources) (Collins et al., 1996;Collins et al., 1997c;Nosrati et al., 2018;Nosrati et al., 2019;Patault et al., 2019;Vale et al., 2016). Here, uncertainties regarding which particle size fractions are delivered from hillslope sources to streams are minimized, reducing potential uncertainties associated with particle size enrichment or depletion and the concomitant effects on fingerprint properties (Laceby et al., 2017).
However, in-stream hydrodynamic processes result in mobilization of different SS size fractions and affect SS flocculation, that might still cause uncertainty as to which particle sizes are present at different sections of the stream (e.g., Droppo, 2004;Grangeon et al., 2014), challenging fingerprint conservation. While the consideration of particle size in sediment fingerprinting is mainly limited to investigating its controls on fingerprint values, there is evidence that particle size can be used directly as a fingerprint property or tracer (Kranck & Milligan, 1985;Laceby et al., 2017). For example, Vale et al. (2016) applied a confluencebased approach to the Manawatu River catchment (New Zealand), collecting fine sediments from the riverbed using a trowel. The authors showed that varying rock types, situated in different subcatchments and drained by different tributaries, were linked to differences in SS D 50 values. In the same catchment, Vale et al. (2020) linked patterns in SS dynamics during storm events to differences in particle sizes. They argued that the finer particle size of mudstone (D 50 of 16 μm) likely allowed prolonged entrainment in the water during storm events, whereas the transport of coarser mountain range and unconsolidated sediment (D 50 of 44 μm) ceased as the storm events progressed. The results of such studies therefore suggest that temporal changes in sediment source contributions can be fingerprinted using observed changes in particle sizes or particle size distributions. Existing work that included particle size for the sole purpose of tracing (Li et al., 2020), reported the use of particle size statistics (e.g., D 60 , D 70 and well as clay and silt percentages) for fingerprints to identify sediment sources of core sediment. Another study (Tang et al., 2018) looked at the spatial and temporal variability of SS source particle size input and the effects of sediment size sorting in reservoir dam deposits. Droppo et al. (2005) suggested rather than using particle size, particle shape and fractal dimension could be used to trace SS sources. Furthermore, the idea of using particle size distributions (PSDs) for sediment source fingerprinting purposes was raised in an abstract by Liu et al. (2014), where the possibility to measure PSDs from potential soil sources and compare those with the target SS collected by sediment traps was proposed.
A corresponding publication on this proposal has not been found at the time of publication of the present study.
Many recent sediment fingerprinting studies underscore increasing opportunities to measure sediment PSDs. This can be achieved using laboratory equipment such as the Beckman Coulter LS 13320 (Beckman Coulter, Inc., Fullerton, CA) and Mastersizer 3000 (Malvern Instruments Ltd, Worcestershire, UK) laser diffraction particle size analysers (as used by e.g., Patault et al., 2019 andGarcía-Comendador et al., 2021), and in-field equipment such as the LISST sensor (Sequoia Scientific, Bellevue, WA, USA), also based on laser diffraction (as used by e.g., Czuba et al., 2015;Upadhayay et al., 2021). Differences in sediment PSDs are regularly used in sedimentology to infer past sediment provenance and to reconstruct past changes in, for example, climatic conditions or tectonic processes (Beuscher et al., 2017;Dietze et al., 2012). To this end, Weltje (1997) first used PSD data together with an end-member mixing model (EMMA) to estimate the proportions of different sediment sources. Subsequent research led to the development of other end-member grain size un-mixing models such as DRS-unmixer (Heslop et al., 2007), EMMAgeo (Dietze et al., 2012), AnalySize (Paterson & Heslop, 2015), BEMMA (Yu et al., 2016) and BasEMMA . These grain-size un-mixing models use the whole PSD data as input, whereas within the sediment fingerprinting community linear multivariate un-mixing models are used most widely (e.g., MixSIAR: Stock et al., 2018;Stock & Semmens, 2016, FingerPro: Lizaga et al., 2020. We propose the use of tracing contemporary SS sources with PSDs as a fingerprint in combination with an end-member grain size un-mixing model (AnalySize). To this end, we: (i) evaluate unmixing model performances using artificial laboratory mixtures, with known proportions of soil samples sieved to different size fractions, and; (ii) un-mix target SS samples from a catchment scale confluence-based approach based on differences in upstream source SS PSDs, while relating the un-mixing model performances to differences in upstream source D 50 values and observed water discharges.

| Laboratory experiments
Laboratory experiments were performed to evaluate the grain-size un-mixing model AnalySize under controlled conditions. Both soil samples and artificial mixtures, composed of these different soil samples, were suspended inside a tank set-up and PSD was measured using a LISST sensor. The PSDs of both the soil samples and mixtures were then used to evaluate the grain-size un-mixing model, according to the known soil sample contributions present in the mixtures. The tank set-up, as well as the soil samples and mixtures, were used previously in Lake et al. (2022) to investigate the feasibility of using absorbance measurements obtained with a submerged spectrophotometer for un-mixing source soil sample contributions.

| Soil samples and artificial mixtures
Soil sampling was carried out at six different sites in Luxembourg (see Table A.1 for details on sampling site coordinates). Sites were selected based on differences in geochemistry and mineralogy . Soil samples were collected using a trowel, after removal of the top layer of soil (0-5 cm). Care was taken to collect only material that appeared homogeneous in colour. The samples were then dried at room temperature, disaggregated with a pestle and mortar, and sieved into three different size fractions: <32, 32-63 and 63-125 μm. This resulted in 17 soil samples (the 63-125 μm fractions for soil 6 was omitted due to the low quantities present). Soil samples are hereafter indicated by #soil. fraction, with 'soil' representing the soils (n = 6), and 'fraction' the sieved particle size fraction (0.1 for <32 μm;  (Table 1). Mixtures 1-9 were composed of soil samples sieved to different size fractions. Mixtures 10-25 were composed of soil samples sieved to the same particle size fraction. These two approaches were tested to see if both distinct differences in source PSDs (soil sources sieved to different fractions) and small differences in source PSDs (soil sources sieved to same size fraction) could be used for un-mixing. results (100-1000 mg L À1 , at 100 mg L À1 increments). A background signal (using demineralised water), measured before the start of every experiment, was saved onto the instrument and automatically compensated for during the experiments (to eliminate influence on the measurements of e.g., small scratches on the measurement window). For each theoretical concentration, the LISST sensor measured over a 10-min period at 1.5 second interval, using a random shape algorithm (Sequoia Scientific, 2018). After each theoretical concentration was measured, three samples were collected using a pipette. Samples were transferred into pre-weighed aluminium buckets and dried to quantify the concentrations inside the tank (i.e., 'measured concentrations').

| Laboratory set-up
A Vibromixer (DrM, Dr. Mueller AG, Switzerland) mixing device was used to keep the soil samples and mixtures in suspension (see Lake et al., 2022 for details on the settings and initial tests on mixing performances). From the results in Lake et al., 2022, it appeared that measured concentrations were lower than the theoretical concentrations, with differences increasing with an increase in particle size. Soil samples sieved to the same size fractions presented similar differences between measured and theoretical concentrations. Since mixtures 1-9 used soil samples sieved to different size fractions, the actual in-tank contributions differed from the theoretical input contributions. Therefore, input contributions for these mixtures were compensated according to the measured soil sample concentrations.

| Field experiments
The field experiment was carried out at the confluence of a tributary draining a sub-catchment with different underlying geology, which was hypothesized to yield SS with distinct PSDs (as discussed in Walling et al., 2000) compared to the rest of the catchment. Field T A B L E 1 Soil sample input contributions (%) for the mixtures 1-9, based on theoretical input contributions, and adapted input contributions (bold), based on measured concentrations in the tank set-up F I G U R E 1 Photograph (a), and schematic representation (b) of the laboratory tank set-up. The data obtained from the spectrophotometer are discussed in Lake et al. (2022).
samples were collected using automatic water samplers (i.e., discrete samples) at pre-set times at the two upstream and downstream sites.
PSDs, measured on the samples were introduced into the grain-size un-mixing model to identify the origin of the downstream target SS. A sediment budget, through a simple mass-balance, was used to evaluate the model results.

| Study area
The study area is located in the Attert River basin (247 km  A). Sampling at the three sites was undertaken at the same time.
Until analyses, samples were stored in a cold room (4-5 C). At each of the three sites, turbidity was measured at 5-min intervals using a S::can spectro::lyser™ probe (Scan Messtechnik GmbH, Vienna, Austria).
The AnalySize algorithm is inspired by hyperspectral image analysis (Paterson & Heslop, 2015). Its un-mixing principle is similar to that of mass balance un-mixing models widely used by the sediment fingerprinting community (e.g., Collins et al., 1997b;Lizaga et al., 2020;Stock et al., 2018), where data that are to be un-mixed can be described as a linear mixture of the contributing end-members. End-member abundance must be >0 and sum to 1 (100%). In the AnalySize algorithm, the PSD data are expressed as relative abundances of each size class and must sum to one. The unmixing principle (Equation 1) can be expressed in matrix notation (Paterson & Heslop, 2015): where X is the observed data (PSD of a target SS sample; one specimen per row), A the abundance matrix of the constituent endmembers (i.e., relative contribution of each tributary) whose signatures are given by S (PSD of the tributaries; one end-member per row), and sampling and measurement errors are represented by E. As described by Paterson and Heslop (2015), due to the imposed constraints, there is no closed form solution to equation (1), which thereby has to be solved numerically.
Within AnalySize, the target SS PSD data were loaded using the 'Load Data' button. End-member PSDs were entered using the 'Defined' end-member option, as source PSD was measured and could be directly used to determine its abundance. Based on the PSDs of the tributary sources and target SS, AnalySize displays several performance indicators, including EM-r 2 (indicating the maximum squared linear correlation between the end member [EM] PSDs, being a measure of linear independence between the potential sources).

| Un-mixing of artificial laboratory mixtures
The PSDs of the soil samples measured in the tank set-up were used as source data to un-mix the PSDs measured on the artificial mixtures.
Source data were created by averaging all recorded PSDs over all concentrations. Mixture PSD data were introduced for each single measurement separately, with AnalySize predicting, for each measurement, the relative abundance of the soil samples mixed in the tank set-up. In the present study, size classes ranging from 1 to 500 μm were included for analysis. Modelled results were compared with the known relative soil sample contributions (section 2.1.2).

| Un-mixing of suspended sediment field samples
For consistency with the laboratory results, the upper size limit for the Mastersizer measurements on the field samples was set to 500 μm. This approach allowed the inclusion of the main PSD peak, while eliminating (smaller) peaks at larger particle size ranges (>500 μm) that were associated with small leaves or coarser particles for soil sample #1.2 (83% input contribution) started between 80% and 100%, decreasing in a stepwise manner to ranges of 30%-50%,

| Field experiments: Model evaluation using sediment budget estimates
An overview of discharge and precipitation data is shown in Figure 4, with selected periods in which field sampling was performed highlighted. Discharge and precipitation, as well as maximum measured SS concentrations (SSC) during the periods are shown in During the storm runoff events, D 50 values measured on the discrete samples showed an initial increase during the rising limb of the hydrograph and then a decrease before the discharge peak. 3.3 | Field experiments: Relationships between model performance, discharge, source particle size and organic matter content Model performance improved with increasing discharge (Figure 6a).
For discharges <4 m 3 s À1 , a wide range of model performances was  Figure A.4). Consequently, results for the higher concentrations would in that scenario be more constant and more accurate. Similar observations (i.e., higher inaccuracy at lower concentrations) were reported in Lake et al. (2022).
In contrast to other studies using shear cells to investigate flocculation effects (e.g., Biggs & Lant, 2000, who used  4.2 | Un-mixing field SS samples: Influence of discharge, source particle size, and organic matter content on model performance The catchment scale field experiments suggested that discharge exerts a strong control on the model performance. Walling et al. (2000) argued that, during the initial phase of storm hydrographs (i.e., rising limb), sediment is transported from a range of different sources, and subsequent changes in particle size could be linked to changes in contributions from those different sources. After these initial sources (e.g., sediment stored on the riverbed) are depleted, however, alternative sources within the catchment can become dominant.
This can result in more constant source contributions and thus a more constant texture for sediment in the stream. The latter scenario provides better conditions for making reliable source contribution estimations using PSDs as a fingerprint property. The improved accuracy of sediment fingerprinting estimates during high discharges (>4 m 3 s À1 ) could also be linked to the limited settling, and thereby, improved mixing of sediment being routed through the channel system (Agrawal & Pottsmith, 2000). Discharges exceeding this threshold were observed for 12% of the time (Downstream site) during the study period ( Figure 4; 10/03/2021-21/07/2021), with a mean measured discharge during that period of 2.5 m 3 s À1 . During this 12% of the time, 82% of the total SS load (Downstream site) was transported.
Besides the potential changes in SS source PSDs, different flocculation processes could affect the observed in-stream PSDs (e.g., Droppo, 2004;Grangeon et al., 2014). Suspended sediment floc sizes, in combination with their shape and density, determine the potential of particles to be transported due to their relationship with settling velocity (Williams et al., 2008). This corroborates with our observations that under high-flow conditions, measured PSDs appeared to be more reliable for the use of un-mixing when compared with low-flow conditions. Droppo (2004) argued that the aggregated sizes of SS particles are mostly being controlled by particle concentration and flow shear stress. However, the effect of these dominant inchannel flocculation processes on the measured PSDs (e.g., Grangeon F I G U R E 6 Model performance deviation (i.e., absolute difference between the modelling results and the calculated sediment budget) as (a) a function of discharge, and (b) ΔD 50 (i.e., median particle size differences between both sources). A model performance deviation of 0% indicates no difference between the two sets of data. The discharge threshold values as discussed in the text are shown by a vertical dotted line (discharge: 4 m 3 s À1 , (a)). Results for the largest events (periods a, C, F and G) are shown individually; smaller events and low flow (periods B, D and E) are shown together. et al., 2012) was assumed to be rather limited, as settling was assumed to be mostly absent (especially under high-flow conditions).
This suggests that most SS material observed at the source sites was transported to the downstream target SS site regardless of any flocculation occurring in between. To account for any of these in-stream flocculation processes between the sites, we hypothesized during this proof-of-concept study that these effects were minimized by measuring and comparing only the sources and downstream absolute PSDs (i.e., primary particles). Thereby, due to the absence of clear erosion or deposition between the source sites and the target SS sampling site (confirmed by visual observations), it was assumed here that the SS transported downstream was a simple sum of the SS from the upstream sources.
An increase in the D 50 values was observed at the start of the monitored storm events, which could suggest the remobilisation of sediment stored on the riverbed (e.g., Lawler et al., 2006;Walling et al., 2000). 4.3 | Critical considerations for using particle size data for sediment source fingerprinting Application of the approach presented herein uses differences in PSDs to discriminate between the sources. A first indication of potential differences in PSDs can be gained by looking at potential contrasts based on geology and soils (Walling et al., 2000), as was undertaken for the field experiment part of this study. This preliminary screening can help to avoid situations in which D 50 values for different tributaries or soil sources are not sufficiently differentiated (as observed in a recent confluence-based fingerprinting study by Patault et al., 2019). Results presented herein, nonetheless, indicated that to achieve accurate un-mixing results, differences in D 50 values can be relatively small (Figure 6b). This is also true for period G, with a deviation between the un-mixing results and sediment budget of 16%; that is, the sampling period with the best performing performance. Here differences in source D 50 values were, on average, only 6 μm.
Similarly, attention should be directed to collecting representative samples. Samples collected at different depths (Bainbridge et al., 2012) or at different distances from the channel bank (Walling et al., 2000) can manifest distinctive SS particle sizes. This latter point relates to our suggestion that for period G, a higher level of turbulence could have resulted in better mixing of the SS in the water column, leading to more representative sampling and more representative PSD data. This situation appeared to improve the unmixing results, even with the relatively small differences between source D 50 values. Sampling is also affected by the field equipment used. Field samples were collected using automatic water samplers, for which installation was subject to sampling site limitations. The pumping might, as reported by Grangeon et al. (2012), create a vortex at the inlet opening of the tube that could affect the amount of SS collected and its corresponding particles sizes. This issue highlights the potential uncertainties associated with the automatic samplers deployed.
To analyse particle size, different instruments are available (herein we presented the use of two instruments: the LISST and Mastersizer).
As results may differ depending on the type of equipment used (Bieganowski et al., 2018), we recommend that due care and attention are exercised when PSDs or D 50 values are compared both within and between studies. Furthermore, many different measurement protocols were found in existing literature that can affect measurements, including different machine settings (e.g, rotating stirrer speed), sample preparations (treatment with dispersive agent, duration of ultrasound) and sampling collections (number of measurements) (e.g., Dietze et al., 2012;García-Comendador et al., 2021;Grangeon et al., 2012;Patault et al., 2019;Pulley et al., , 2017. Therefore, in the absence of a standard protocol to measure PSDs, it is a good practise to use the same equipment and apply similar measurement protocols when aiming to compare PSD data directly (Bieganowski et al., 2018).
Sediment source fingerprinting results using PSD data could also be compared with un-mixing results using conventional fingerprinting properties and one of the current un-mixing models used by the international scientific community. This would allow some degree of independent validation of PSDs as a fingerprint. The independent validation of sediment source fingerprinting estimates has been rarely undertaken (e.g., Batista et al., 2022;Gaspar et al., 2019). To validate estimated source proportions using PSDs as a fingerprint herein, we used sediment budget estimates generated using conventional water sampling; this has, to date, been used in few sediment fingerprinting studies (e.g., Collins et al., 1998;Dabrin et al., 2021;Tiecher et al., 2022), mainly due to the extra costs associated with the installation of equipment and sampling (Collins et al., 2020Collins & Walling, 2004).

| CONCLUSIONS
In this research, the use of PSDs to fingerprint suspended sediment sources was tested at laboratory and catchment scales. To this end, we used an end-member grain size un-mixing modelling algorithm (AnalySize). The laboratory tests, using mixtures with soil samples sieved to different size fractions, resulted in accurate un-mixing results for the two, three and four soil samples mixtures tested.
Observed absolute errors (7 ± 4%) were found to be in the same range or even smaller compared with other research using artificial mixtures to evaluate un-mixing model accuracy. Field data were collected using a confluence-based approach, with relatively short distances (ca. 3 km) between the source sampling sites and the target SS sampling site. The corresponding un-mixing results were more accurate at higher discharges (with an average deviation of 19% from the estimated sediment budget, for discharges >4 m 3 s À1 ). The approach described herein, using PSDs in combination with a grain-size unmixing model, could support the growing sediment fingerprinting community with an additional fingerprint that is relatively easy to obtain. This is especially of merit since PSD measurements are already routinely made in many sediment source fingerprinting studies.

ACKNOWLEDGEMENTS
Discharge data for the Attert at Reichlange (Upstream site) was generated by the Luxembourg water agency (Administration de la Gestion de l'Eau