A Novel Laboratory Technique for Measuring Grain‐Size‐Specific Transport Characteristics of Bed Load Pulses

Although several laboratory studies on the propagation of bed load pulses were carried out in the last decades, most studies neglect grain‐size‐specific aspects or use invasive measurement techniques. To remedy the situation, we present a novel, time‐efficient and non‐destructive laboratory technique to investigate grain‐size‐specific transport characteristics of bed load pulses. The method consists of a through‐water, high‐resolution image acquisition followed by the application of a supervised color classification algorithm (Gaussian Maximum Likelihood Classification). The analyzed bed load pulse consisted of five different grain size classes of dyed quartz sand and gravel, each having a unique color. The initial experimental bed was uni‐colored and contained the same size fractions as the augmented pulse. Quality assessment based on a confusion matrix approach and basic random sampling showed a high classification performance. By statistically analyzing the temporal and spatial color distribution of the experimental reach, characteristic parameters to describe the propagation behavior were determined. The bed load pulse presented in the application example initially showed strong deviations in the grain‐size‐specific advection and dispersion, and advection proved to be predominant in the transport process.


Introduction
Sediment dynamics in riverine systems are subject to spatial and temporal fluctuations, such as bed load pulses.Bed load pulses are observed in a wide variety of stream types and under a wide variety of hydrological and sedimentological boundary conditions.In the last 30 years many field, laboratory and numerical studies have been dealing with this topic (e.g., Aigner et al., 2017;Dhont & Ancey, 2018;Humphries et al., 2012;Liébault et al., 2022;Lisle et al., 1997;Morgan & Nelson, 2019;Sklar et al., 2009).The origins of bed load pulses are also highly diverse and complex.For instance, pulses can originate seasonally due to different hydrological boundary conditions and a variability in sediment availability (Liébault et al., 2022).However, they also occur under constant flow rates and sediment supply as found in laboratory flumes (Dhont & Ancey, 2018).Research showed that transport heterogeneity and grain sorting play an important role when it comes to pulse occurrence and propagation (Dhont & Ancey, 2018;Recking et al., 2023;Sklar et al., 2009).Nonetheless, many studies still neglect heterogeneity in the transport and pulse formation process.
In this study, we focus on bed load pulses that result from spatial and temporal sediment surplus, particularly from gravel augmentation.Riverine ecosystems are increasingly affected by human activities and climate change.
Dams and other transverse structures are likely to trap incoming sediments, leading to disturbed sediment continuities and significantly impair river connectivity (Grill et al., 2019).A common approach to counteract problems caused by such disturbances are gravel augmentations, where the artificial supply of sediments can either be installed as deposits at the riverbank or directly dumped into the river by hopper barges.Augmentations tackle hydraulic engineering purposes to stabilize the bed, secure fairways, protect infrastructure (Goelz, 2002) or target ecological habitat improvement in geomorphologically and biologically dysfunctional streams (Bunte et al., 2004).
In order to achieve best possible outcome and design of these measures, information on the temporal and spatial extent of the added sediment is required.Hence, the planning and implementation remains challenging and is often accompanied with many uncertainties.Owing to the necessity of understanding the transport behavior of augmented sediment pulses, several experimental studies on pulse propagations and their technical and morphological effects were carried out in the last decades (e.g., Cui et al., 2003;Humphries et al., 2012;Nelson et al., 2015;Sklar et al., 2009;Venditti et al., 2010aVenditti et al., , 2010b)).Despite the fact, that the importance of grain size for augmentations is well known, only few of these studies elaborate this issue (Cui et al., 2003;Sklar et al., 2009;Venditti et al., 2010a).Furthermore, in previous studies invasive measurement techniques have emerged, which are time-consuming and potentially destructive, distorting the ongoing processes and possibly influencing the experimental outcome.One approach is the removal of a defined extent of the surface layer by hand, which is then dried and sieved (e.g., Nelson et al., 2015;Sklar et al., 2009;Venditti et al., 2010a).To keep the surface layer unaltered, previous studies determined surface grain size distributions by manually measuring grain sizes from images and defined grid intersections.This method is less destructive but still highly time-consuming (e.g., Hassan et al., 2021;Saletti & Hassan, 2020).
To tackle this issue, we developed a non-destructive and highly time-efficient measurement technique, constituting of an underwater image acquisition of a colored sediment pulse followed by a post-processing based on a Gaussian Maximum Likelihood Classification (GMLC).The classification accuracy was evaluated using a basic random sampling and confusion matrix approach.Furthermore, a comparison with an unsupervised k-means color clustering is provided.A grain-size-specific Péclet number is introduced to compare the advective and dispersive transport rates of the different size fractions.We tested the applicability and the accuracy of the novel method based on a laboratory flume experiment, proving high model performance and suitability to investigate pulse propagation.The method presented in the paper has several new features.For example, a separate consideration of the pulse material at grain size class level is provided, which, in addition to determining surface grain size distributions, also enables the determination of grain-size-specific transport and distribution parameters.This represents a novelty in the field of sediment and bed load pulse research and, therefore, is an improvement on prior techniques.

Experimental and Measurement Setup
The experiment was conducted in a hydraulic glass-sided flume consisting of (a) an inlet basin, (b) the experimental section of 10-m length and 0.3-m width and (c) an outlet section with an adjustable flap gate to control water levels and flow conditions.The whole system rests on a sub construction which enables a tilting of the flume.A frequency-controlled pump at the outlet section recirculates the water back to the inlet section.A detailed sketch of the experimental setup is illustrated in Figure 1.
The experimental section is filled with a heterogeneous uni-color sediment mixture ranging from 0.7 to 6 mm.A sediment feeder (SF) at the beginning of the section adds the required amount of sediment during the experiment and the transported sediments are collected in a sediment trap (ST) which is located at the end of the flume.To investigate the grain-size-specific transport characteristics of augmented sediment pulses under controlled laboratory conditions, a unique measurement setup was provided as also depicted in Figure 1.The centerpiece of the measurement setup is a camera system for through-water imaging (UWIP) and subsequent image processing.Special emphasis was put on the selection of the camera lens, ensuring low geometrical distortions.Within the present study a Nikon D7100 camera with a Nikon AF-S Nikkor 28 mm f/1.8 G lens was used.Hence, the maximum barrel distortion (≈1.30%) at a focal length of 28 mm justifies the omission of a possible geometric distortion correction (Orrú et al., 2014).The recorded images build basis to analyze the surface grain size distribution and consequently to calculate the distribution parameters of the transported gravel plume.Details

10.1029/2023WR036712
regarding the image acquisition and the further processing are provided in the following subsections.In addition, an adjustable point gauge (PG) was used for check measurements of the water levels and bed surface elevations.The flow rate was measured with an inductive flow measurement system (IDM).

Experimental Procedure
First, suitable initial conditions for the experiment had to be accomplished.Therefore, the experimental section within the tilted flume was filled with a heterogeneous uni-color mixture and scraped evenly parallel to the flume's bottom (I = 0.005).Next, the equilibrium transport rate was determined iteratively.Thus, the fed sediment input (SI ti ) was equated with the measured output (SO ti 1 ) using an iteration time step of 10 min.This process was pursued until the mean bed slope (S) matched I and (SI ti ) converged toward (SO ti ).Subsequently, the actual experiment starts with the augmentation of a high amount of colored sediments (HCSI) using the programmable sediment feeder, as depicted in Figure 2a.The augmentation phase lasted 60 s with a feeding rate of 0.187 kgs 1 .The additionally added sediment amounted 0.006 m 3 which, when evenly spread along the experimental section, corresponds to a 2.5 mm elevation change.During the remaining experiment a constant rate of 0.0167 kgs 1 , adding uni-colored heterogeneous sediment with same mass fractions as the experimental was used.Table 1 provides an overview of the different grain size classes, their coloring, and the mass fractions used in the application experiment.The flow rate was kept constant at 0.0078 m 3 s 1 , leading to a mean water depth (h) of 7.5 cm.
Since each grain size class of the added pulse has a unique color, a detailed analysis of the fractional transport characteristics is obtained from images of the bed surface and the GLMC algorithm.Section 2.3 and 2.5 provide an explanation on how this GMLC method and the further data evaluation works.Every 5 min the test run was carefully interrupted by raising the flap gate at the outlet section and simultaneously decreasing the flow rate to a  minimum.When reaching a constant water level, data acquisition was performed including a detailed image recording of the bed surface.The advantage of this method is that a settlement or other distortions of the experimental bed due to draining and filling are minimized.To proceed with the experiment the flap gate was carefully lowered whereas the frequency of the pump was gradually increased until the required value was reached.The next 5 min interval started after free-flowing conditions in the experimental section were present.The whole experiment divides into four sequences of 5 min, summing up to a total time of 20 min.

Gaussian Maximum Likelihood Classification (GMLC)
As each color in the acquired images represents a different grain size class, the spatial distribution of color also indicates the spatial grain size distribution.And, since each pixel represents a unique point in the RGB color space, an assignment of the pixels within the raster images to a unique color class is required for further analysis.Therefore, a classification method well known in remote sensing and geoinformatics was applied.The GMLC is a statistical method commonly used for land cover classification based on aerial and satellite imagery that considers previously categorized sample data (supervised method with predetermined training samples) (e.g., Ahmad & Quegan, 2012b;Erbek et al., 2004;Shivakumar & Rajashekararadhya, 2018).Due to the assumption of a normal data distribution of each class the method is designated "Gaussian", constituting one of the two main principles of this method.Therefore, the probability of an object belonging to each of the predetermined classes is calculated to assign it to the class with the highest probability value.The Bayes' theorem is the second fundamental principle of the GMLC.For two events (A) and (B) with P(B) > 0, the probability of occurrence of the event (A), given that the event (B) has also occurred (P(A|B)), can be derived by the probability of occurrence of event (B) given that the event (A) has also occurred (P(B|A)) (Mather & Tso, 2016): For the present classification problem Equation 1 can be re-written, where the probability of a pixel x i belonging to the class w j is given by (Mather & Tso, 2016): The conditional probability P(x i |w j ) is also referred to as "likelihood function" and P(w j ) and P(x i ) state the a priori probabilities.Further, the probability of occurrence of pixel (x i ) in one of the (k) classes is given as follows (Ahmad & Quegan, 2012a): Assuming that the pixels within the classes are Gaussian distributed and that the a priori probabilities of occurrence are equal leads to:  Water Resources Research 10.1029/2023WR036712 An equal a priori probability was assumed as prior to the experiment no reliable information on the expected surface sorting during pulse propagation was available.In addition, the choice to use equal mass fractions also reinforces this assumption.Thus, the pixel is assigned to the class with the highest value of the likelihood function (Mather & Tso, 2016).Since a Gaussian distribution of the data of each class is assumed, one can also expect the conditional probability being normally distributed (Mather & Tso, 2016;Strahler, 1980): where C j is the covariance matrix of class w j with dimensions n and μ j represents the vector of the class' mean.By taking the natural logarithm of Equation 5for simplification we get: In our case, all classes have the same number of dimensions (n = 3).To be able to distinguish between the different color classes, each pixel must be assigned to one distinct cluster.This procedure is termed hard clustering.Consequently, the first term of Equation 6 can be taken as a constant, not affecting the final ranking for the considered classes, and Equation 6 can be reduced to: The second term of Equation 7 basically represents the Mahalanobis distance, which accounts for the spatial correlation between the given characteristics (Mahalanobis, 1936).
Figures 3a-3c illustrate the distribution of pixels in the given RGB color space for an example classification.The shape of the distribution of the objects (pixels) of a given class in three dimensions can be described by an ellipsoid.Hence, when only looking at a two-dimensional feature space, the maximum likelihood function delineates equi-probabilistic contours of elliptical shape, constituting decision boundaries (Mather & Tso, 2016).In Figures 3d and 3e slices of the probability ellipsoids (90%, 75%, and 50% confidence interval) are plotted based on the mean of each class and the three-dimensional covariance matrix (Vermeesch, 2018).An example classification is illustrated in Figure 4, where the location of the six color classes in the RGB space is shown together with an original image from the experimental set and the classification result.
The achievable accuracy of this classification method mainly depends on three key aspects: (a) Recording quality of the images used for further processing.In the present set up a digital single lens reflex camera (Nikon D7100) with a resolution of 24MP together with an LED light for optimal illumination guaranteed high data quality.(b) Picking class-features as divergent as possible for the class preparation in advance of the experiments.Since in the present study we are working with image data represented in the RGB color space, special emphasis was put on the color selection of the different classes.It is therefore proposed to carry out preliminary studies in which mixtures of different color combinations are analyzed under the given laboratory conditions.(c) Quality of the manual training data selection.As in general the training data is acquired manually which represents a subjective process a careful selection has to be guaranteed.However, based on the high-resolution images, the human eye's ability to distinguish between the six distinct colors can be assumed as very high.In the present study the training data collection was done manually using the high-resolution images from the experiment.The data selection can also be performed with pixel values from independently taken pictures.In this case it is important to guarantee similar recording conditions as during the test run (e.g., illumination, ISO light sensitivity value, exposure time, focal aperture, etc.).

Quality Assessment
The quality of the method presented was quantitatively evaluated by use of a confusion matrix.This approach states a well-proven tool for accuracy assessment of image classification techniques and is widely used in the field of remote sensing (e.g., Ahmad & Quegan, 2012b;Erbek et al., 2004;Shivakumar & Rajashekararadhya, 2018).
Within the matrix pixels assigned to a specific class (Equation 7) are compared with a supervised reference  classification, which is done manually.Due to the capability of the human's eye to distinctly distinguish between the six different classes and the high quality of the recorded images this method is assumed as the most accurate.The validation data compilation was done by simple random sampling, which is a common procedure when dealing with large data sets (Foody, 2002).The confusion matrix provides information regarding the accuracy of assignment of each individual class as well as the overall accuracy (OA) of the color clustering, which is calculated as follows: OA = number of correctly classif ied samples total number of samples × 100 (8) Note that the correctly classified data points, that is, where the classification outcome matches the actual validation assignment, are given by the diagonal of the matrix.Analogously to the OA assessment, the accuracy for each class is calculated using the number of correctly classified pixels per cluster and dividing it with the total number of pixels classified within the same cluster.This quantity is also termed producer's accuracy (PA).It includes the error of omission, which refers to the ratio of manually observed pixels of class w j that is not classified in the image (Story & Congalton, 1986): Another measure that can be derived from the confusion matrix is the so-called user's accuracy (UA), dividing the number of correctly classified pixels in each cluster by the actual pixel count according to the reference analysis.Consequently, UA indicates the probability of a pixel being assigned to the correct class, including the error of commission (Story & Congalton, 1986): In summary, the confusion matrix provides valuable information of classification errors (over-and underprediction) and brings overlaps and delimitation weaknesses between two or more classes to light.
In addition to the confusion matrix validation of the GMLC results, we provide a comparison with an unsupervised method.Here, the k-means algorithm was chosen, as its probably the most popular unsupervised clustering algorithm for image segmentation (Mather & Tso, 2016).Initial condition of the k-means algorithm is either a predefined set of feature vectors or a randomly generated set of feature vectors, which defines the initial mean location of n clusters within the feature space.Next, each data point is assigned to its nearest cluster center c k , which is commonly based on the Euclidean Distance D E (Mather & Tso, 2016): where x i is the observed vector of the ith data point and μ j gives the mean vector of the jth class.The algorithm proceeds by recalculating each cluster center c k based on the assigned data points (Mather & Tso, 2016): Next, each data point gets reassigned to its nearest cluster center.This procedure continues until the variation between two iteration steps remains under a defined threshold and thus the termination criterion is reached (Mather & Tso, 2016).

Calculation of Advection and Dispersion Parameters
Two main parameters used for the characterization of solute and contaminant transport processes are the advection and dispersion parameter.The transport of a medium by another medium not only leads to a displacement of the material further downstream but also to a (longitudinal) spreading along its transported path.Reiterer et al. (2022) showed that the transport behavior of local short-term sediment inputs can be sufficiently predicted using the analytical solution of the one-dimensional advection-dispersion equation (1D-ADE).Thus,

Water Resources Research
10.1029/2023WR036712 within this study the derivation of these two parameters is of main interest.By statistically analyzing the spatial distribution of the transported substance at a given time t one can compute the advection term, which is directly linked to the first raw moment μ of the distribution: As the advection term describes the shift of the plume's center over time it represents the mean transport velocity.
For the grain-size-specific analysis, the classified images built basis for the further statistical evaluation.Therefore, the camera positions were arranged in such a way, that the entire surface was represented by the images.Next, the images were clipped to avoid overlapping at the edges of the photos.Figure 2b depicts a schematic sketch of the image acquisition setup.Hence, each clipped image represents a b E × l E = 0.3 × 0.22 m extent of the experimental section at station x i .Based on x i and the corresponding proportion of classified pixels p i in consideration of the total number of pixels of the same class, the first raw moment μ is calculated as follows: where x 1 , …, x k are the longitudinal stations of the k considered images and p 1 , …, p k are the corresponding percentages of classified pixels in the k images.For example, when considering the blue colored grain size class, p i is given by the number of blue classified pixels in the extent at station x i divided by the total number of blue pixels in the entire experimental reach.The dispersion coefficient denotes the longitudinal spreading during the transport process and is therefore related to the second central moment σ 2 : With μ calculated by Equation 14, the second central moment σ 2 is given as: By applying Equations 13 and 15, v x and D x are calculated.
These two quantities can be further used to determine the Péclet number, which is a fundamental and often applied dimensionless quantity in the field of multiphase flows.In the past, Pe already proved its usability for the characterization of bed load pulses.For example, Lisle et al. (1997) used Pe to investigate the sediment wave propagation in physical model tests and numerical simulations.Similarly, Morgan and Nelson (2019) numerically studied the effect of different sediment pulse characteristics based on the evolution of Pe.In general, Pe relates the magnitude of the advection to the level of dispersion in a transport process: Thus, in the present case of one-dimensional mass transport Pe defines as follows: where L is a characteristic length (Lisle et al., 1997).To consider the different grain size classes, L is set to the mean diameter d mi of each class.Consequently, the higher this grain-size-specific Péclet number is, the more distinct the advection process.In contrast, a lower Pe indicates a more dominant dispersive process.

Quality Assessment
To quantify the accuracy of the proposed method a random sampling of 200 data points (pixels) was performed.At randomly generated pixel coordinates a validation classification was done manually, which then was compared with the GMLC and k-means results by generating the corresponding confusion matrices.Table 2 shows the confusion matrix of the GMLC, whereas the k-means confusion matrix is given in Table 3.
The overall accuracy of the GMLC method is 98%, which is significantly higher than the accuracy of the k-means clustering (68%).Both the user's accuracy (94%-100%) and the producer's accuracy (87%-100%) of the GMLC indicate a high level of accuracy for all color classes.From 200 randomly selected data points only four were misclassified.All errors occurred in shaded regions at the edges of grains and were mistakenly assigned to the gray color class.Hence, further optimization of the illumination conditions could potentially increase the classification accuracy.Additionally, the implementation of a priori class probabilities could improve the achievable accuracy (Shivakumar & Rajashekararadhya, 2018).
In contrast to GMLC, k-means clustering poorly performs for certain color classes.For example, the user's accuracy reveals a overprediction of the green and black color class.The producer's accuracy, however, shows that the algorithm significantly underpredicts the gray colored grains.Whereas many gray data points get assigned to the green color cluster, the algorithm fails to predict actual green pixels.This can also be clearly seen in Figure 5, which shows a comparison of the model performances based on a 2000 × 2000 pixels extent.The original image (Figure 5b) is plotted between the classification results from GMLC (Figure 5a) and k-means clustering (Figure 5c).While the GMLC classifies the test extent on a high level of accuracy, k-means significantly overestimates the green faction, mainly at the expense of the gray class.While GMLC takes into account the three dimensional distribution (orientation and shape) of the color classes, kmeans clustering neglects such information.Here, the minimization of the within-cluster variances based on the squared Euclidean distances leads to creation of compact clusters (see Figure 5f).As a result, misclassification occurs especially for elongated classes such as the gray color class.To solve this problem, other distance measures (e.g., Mahanalobis Distance) could be implemented.

Grain-Size-Specific Transport Behavior
The grain-size-specific characteristics of the sediment pulse propagation have been investigated by means of determining the advection and dispersion coefficients for each fraction.First, the mean shift (μ) and variance (σ 2 ) of each grain fraction were calculated based on Equations 14 and 16.Next, by applying Equations 15 and 17 the corresponding advection (v x ) and dispersion coefficients (D x ) were determined, as depicted in Figures 6a and 6b.
As the experiment advances in time the advection term shows a distinct decrease for all fractions.The grain-sizespecific transport velocities during the first five minutes exhibit an increasing trend towards the coarsest fraction, featuring strong deviations between the classes.Interestingly, this trend mitigates and the velocities level out as the experiment proceeds.After five minutes the coefficient of variance (cv = σ vx /μ vx ) is around 23% and reduces to less than half of its initial value toward the end of observation.These initial deviations are also present for the derived dispersion coefficients.Starting with a value of almost 30%, cv drops to only 2% at 15 min.Subsequently, the cv again slightly rises to about 10% after 20 min.Whereas the advection coefficient shows a distinct decrease over time, no significant trend was found for the dispersion coefficient.While fractions d i > d m showed comparably high values of v x and D x , for fractions with d i < d m relatively small v x and D x were present.The classified images of the 5 min acquisition even exhibit several individual grains of the coarsest fractions (black, blue) located in the last third of the experimental section, which consequently feature remarkably high transport distances.An explanation for the smaller translation and spreading of the small fractions is given by Church and Hassan (1992).They observed, that particle clasts with sizes smaller than 50% of the sub surface diameter (d i < 0.5d sub ) have a high probability of being trapped.In contrast, large particles are less prone to trapping and thus their travel distance mainly depends on exposure and inertia (Church & Hassan, 1992).This phenomenon was already observed by Einstein (1950), proposing that small particles either hide between larger ones or in the laminar sub-layer.A comparison of the fractional mean displacements (μ) with their standard deviations (σ) is provided in Figure 6c.Linear regression analysis shows a strong correlation between the mean displacement of the sediment plume and its spreading (R 2 = 0.90).Moreover, the point-dotted linear regression line in Figure 6c shows a significantly lower slope than 45°, indicating a dominance of advection over dispersion.With the determined advection and dispersion terms, the grain-size-specific Péclet number is calculated using Equation 18.
The temporal evolution of Pe is plotted in Figure 6d, showing a decreasing trend for all grain size fractions.In detail, the present augmentation pulse evolved through a combination of advection and dispersion, featuring a predominant advective component, which weakens throughout the experiment.Similar to our observations, Sklar et al. (2009) divide the transport process into two main phases (a) an initial phase with more rapid movement of the added sediment wave, and (b) an ensuing phase of slower movement.The present observations are also consistent with the numerical results of Morgan and Nelson (2019), which report on a distinct decay of Pe over time.Furthermore, their investigations complement our findings regarding the predominant advective component.Despite one single test case, all their numerically investigated wave propagations featured a larger shift of the plume's center (μ) in comparison to the pulse's standard deviation (σ).Sklar et al. (2009) also reports on a predominant advective component in his laboratory experiments.

Advantages, Limitations and Research Perspective
In the context of laboratory research on bed load pulses our proposed method has several advantages that are worth mentioning.
First, the through-water data acquisition allows for an efficient non-destructive analysis of the developed bed surface, solely recommending a leveling of the water surface to improve quality of the images.Depending on the required accuracy and the water level and flow situation, an uninterrupted and thus completely non-invasive image acquisition could be performed, which further enhances the proposed method.For supercritical flow conditions and high bed mobility, special attention should be paid to the camera settings (e.g., focal aperture, exposure time, etc.) and the illumination to guarantee the required quality of the images.Second, the method is highly time-efficient in terms of data collection and subsequent processing.While the overall time requirement of our method is in the range of 10-30 min, draining the model, collecting data, and carefully refilling can take several hours, not to mention the tedious further evaluation.Up to now, comparable research dealing with pulse propagation and grain-size-specific aspects was either limited to destructive or time-consuming methods.For instance, Sklar et al. (2009) and Venditti et al. (2010a) used two different methods for surface sampling.After draining their model, 0.25 m × 0.25 m extents of the surface at five different locations along the flume were spraypainted, manually removed, dried, sieved and weighted, which is highly time-consuming and partly destructive.
Their second method used obtained images of the drained surface at a 2 m increment and grid based, grain diameter point counts, comparable to a Wolman count (Sklar et al., 2009).This method is less destructive but still very time-consuming.It is important to point out that Sklar et al. (2009) and Venditti et al. (2010a) focus on the surface grain size distributions, whereas the present study analyzes transport and spreading features.However, although the investigations in the present application example slightly differ from the intended investigations of Sklar et al. (2009) and Venditti et al. (2010a), our method also allows a determination of areal grain size distributions without any modification.Another benefit of our method is the coverage of the whole experimental bed.Instead of just getting point samples at different locations our method allows for an analysis of the entire bed surface.
Besides the variety of benefits that comes with the new method, there are some limitations that should also be considered.As the classification method relies on optical access to determine grain size classes, only a nondestructive sampling of the surface distribution can be performed.If additional sampling of the subsurface is required, either core sampling, vertical slots or a layer wise scraping of the grains has to be conducted, which leads to a destruction of the surface.Another point worth mentioning is that the calculated advection and dispersion parameters are based on the measured surface distributions of the augmented pulse.This, however, might not necessarily reflect the morphodynamic response.If, for example, vertical sorting processes are dominant in the propagation process, the surface grain size distribution might significantly vary from the subsurface.Consequently, advection and dispersion terms from subsurface and surface differ as well.
The presented application example refers to gravel augmentations in small to medium sized rivers.Hence, the sediment pulse depicted a significant surplus compared to the equilibrium transport rate at the same flow rate.With the same principle transport characteristics of local bed load sources of various kind can be examined.For instance, St. Pierre Ostrander et al. (2023) conducted laboratory research on the transport characteristics of bed load supplied by a tributary river channel during channelized flash flood events.Using bathymetric laser scans, they determined that high supply of sediment causes a downstream propagating, dispersing cone of strongly right skewed shape.Another application case is the investigation of bed load transport during reservoir flushing operations.Gold et al. (2023) experimentally investigated the effect of different gate opening patterns on the flushing efficiency of run-of-river hydropower plants (RoR HPP) during moderate flood flows.Therefore, the GLMC could be used to further investigate sorting effects.Bed load transport in streams is permanently governed by advection and dispersion due to its stochastic nature and the exchange of particles between the bed and the transport layer (Lajeunesse et al., 2018).Already in 1936, Einstein et al. (1936) investigated the probability of particle displacement by analyzing the propagation of tracer particle plumes in a laboratory channel.By applying our color classification method and further evaluation procedure, identical transport properties can be determined.

Water Resources Research
10.1029/2023WR036712 These are only a few of many possible applications and since grain size analyses are used in most model tests with heterogeneous sediments, our novel method offers a non-destructive and above all fast alternative to conventional methods.

Conclusions
In this paper we introduce a novel non-destructive laboratory approach to investigate the grain-size-specific transport behavior of bed load pulses.The method combines a through-water image acquisition followed by application of a Gaussian Maximum Likelihood Classification (GMLC).It has been tested on a hydraulic flume experiment, aiming to simulate a large bed load pulse generated by gravel augmentation.Therefore, a multicolored sediment input was supplied on a uni-color experimental bed.The accuracy was evaluated by means of a confusion matrix approach based on a random sampling of 200 data points.High classification performance was found for the GMLC for all six investigated color classes.Furthermore, the comparison with unsupervised clustering (k-means) showed the superiority of the GMLC in processing multivariate color data, especially for complex data distributions within classes.The pulse in the application example initially showed significant differences in fractional advection and dispersion.Coarser classes featured higher values of v x and D x .Advection proved to be predominant in the transport process, although the augmented plume clearly evolved by a combination of advection and dispersion.The presented method enables a highly time-efficient and accurate grain size detection of the entire experimental section.Finally, a variety of other possible application examples besides augmented bed load pulses is discussed, demonstrating the wide applicability of this method in the field of sediment research.

Figure 2 .
Figure 2. Experimental procedure, data acquisition and processing.(a) Conceptual sketch of the colored sediment input and the subsequent image recording for the Gaussian Maximum Likelihood Classification (GMLC).(b) Sketch of further processing, where each image represents an extent along the flume at station x i , having a width of b E = 0.3 m and a length of l E = 0.22 m.The proportion of classified pixels in the extent under consideration of the total number of pixels of the observed class is denoted by p i .
Grain size classes 1 to 5 represent the augmented sediment pulse with d m = 2.7 mm (HCSI).Class 0 indicates the prepulse experimental bed with equal grain size distribution.a Mean diameter = d m .

Figure 3 .
Figure 3. Example plot of predetermined training data for the six observed classes.(a) Histogram plot showing frequency of pixels of each class for red raster band (b) Green raster band (c) Blue raster band.(d) Slice of probability ellipsoids in the R-G plane (90%, 75%, and 50% confidence interval) (e) G-B plane (f) B-R plane.

Figure 4 .
Figure 4. Application of the GMLC.(a) Mean for each of the six classes in the RGB color space.(b) Zoomed extent of the bed surface.(c) Gaussian Maximum Likelihood Classification result.

Figure 5 .
Figure 5.Comparison of the model performances based on a 2000 × 2000 pixel extent.(a) GMLC result.(b) Original image.(c) k-means clustering result.(d) GMLC -Clustered data points in the RGB color space, where each data point is colored according to the corresponding cluster mean.(e) Comparison of the overall accuracy and producer's accuracy of both classification methods.(f) k-means -Clustered data points in the RGB color space, where each data point is colored according to the actual cluster mean.

Figure 6 .
Figure 6.Temporal evolution of the grainsize specific transport characteristics.(a) Advection coefficient v x showing a significant decrease during the experiment.(b) Evolution of dispersion coefficient D x over time.(c) Mean μ versus standard deviation σ of augmented colored sediment pulse.(b) Evolution of grain-size-specific Péclet numbers Pe over time.

Table 1
Grain Size Classes, Color, Grain Size Range, and Mean Diameter (d m ) and Mass Fraction (%)

Table 2
Confusion Matrix Comparing GMLC With Validation Data Set