Estimating floating macroplastic flux in the Santa Ana River, California

Study region: The Santa Ana River middle reach, a small coastal urban catchment in Southern California, USA experiences a Mediterranean climate and lowflows dominated by wastewater effluent. Study focus: River macroplastic flux can inform watershed management of plastic pollution. However, continuous macroplastic monitoring is not possible, so concentrations must be predicted during unobserved periods. We monitored macroplastic concentration and aimed to improve macroplastic flux estimation using strategies commonly employed in estimating mineral sediment flux. New hydrological insights for the region: Floating macroplastic size distributions were statistically equivalent between lowflow and stormflow samples – evidence that channel processes controlled macroplastic size distribution or macroplastic size distributions outside the channel were the same as inside. Concentrations fell during the falling limb of one hydrograph and rose during the rising limb of another hydrograph. A generalized additive model (GAM) revealed that macro-plastic concentration increased in response to small discharge increases but decreased for the largest discharges. Macroplasitc depletion (relative to discharge) occurs at high flow magnitudes or during the falling limb. The annual mass flux of floating macroplastic was 27.4 (2.8 – 84.8) tonnes 1 yr (cid:0) 1 or 18.2 (2.9 – 222.2) tonnes 1 yr (cid:0) 1 as predicted using mean concentration or the GAM, respectively. With little data, the mean concentration approach may be appropriate but likely underestimates uncertainty – which will require extensive monitoring to reduce.

to downriver ecosystems, the pollution at the study location, and changes in the magnitude of upriver plastic sources (Schmidt et al., 2017;Watkins et al., 2019). Macroplastic (> 5 mm) is known to make up most of the mass of plastic in the environment and break down to form many more abundant microplastics (particles < 5 mm) Moore et al., 2011). Rigorous estimates of river macroplastic flux are critical for addressing the global crisis of plastic pollution (Bai et al., 2021) but has been much less studied than microplastic flux (van Emmerik, 2021).
River macroplastic flux is typically quantified by multiplying river discharge (m 3 s − 1 ) by macroplastic concentrations (count or mass 1 m − 3 ). Continuous river stage (m) measurements are available in many locations within the United States and are periodically calibrated to discharge (m 3 s − 1 ), velocity (m 1 s − 1 ), depth (m), and other river flow characteristics by the United States Geological Survey (USGS). However, no methods to continuously monitor river macroplastic concentration are currently in use. One needs to make predictions about unobserved macroplastic concentrations to quantify macroplastic flux.
Mineral sediment transport has a long history of research and can inform strategies for studying plastic transport (Waldschläger et al., 2022). Unobserved concentrations of fluvial particulate matter are often predicted using discharge regime, hydrograph rising and falling limb behavior, and rating curves fit to river discharge (Gray, 2018;Rose et al., 2018;Walling, 1977). Changes in discharge reflect combined changes in the supply and transport of water to the monitoring stations and affect changes in the river's transport properties (e.g., turbulence, velocity, depth). The ratio between the flux of water and the flux of particulates at any moment is reflected in the average concentration of the particulate in the flow. Multiple orders of magnitude of variability around the concentration-discharge rating curves are typical, particularly in the small mountainous rivers characteristic of coastal California (Gray, 2018). This variability is due in part to stochastic processes like storm sequence (East et al., 2018), spatio-temporal characteristics (Aguilera and Melack, 2018), and antecedent watershed conditions (Fisher et al., 2021;Gray et al., 2015;Warrick and Rubin, 2007), which can cause changes in the processes controlling water and sediment delivery and routing (Gray et al., 2014). Temporal structure to this variability can manifest in concentration-discharge relationships from hydrograph rising and falling limb behavior (Williams, 1989)(i.e., different rising vs falling limb concentration-discharge relationships) to interdecadal scale trends (Gray, 2018;Warrick et al., 2013). A "first flush" event is common for sediment, whereby high concentrations are flushed during the first large storm event of the year (Sansalone John J. and Cristina Chad M., 2004). The particle size distribution of the suspended load may shift with hydrologic mode (stormflow, lowflow) and can be diagnostic of sources and transport pathways of mineral sediment (Li Yingxia et al., 2005;Slattery and Burt, 1997). Investigating temporal patterns in concentration-discharge relationships can provide insight into transport and supply processes and be used to refine flux estimation (Farnsworth and Milliman, 2003;Gray et al., 2014;Warrick and Rubin, 2007). We build from these foundations of fluvial sediment concentration-discharge relationships to advance the fundamentals of macroplastic concentration-discharge relationships.
Early research on plastic pollution suggested that macroplastic concentration-discharge relationships should be considered in estimating plastic discharge from rivers. River macroplastic count to mass ratios were assumed constant in literature ( Van Emmerik et al., 2019) despite changes in hydrological mode, suggesting stable particle size distributions but changes in macroplastic size distributions have not been tested. Our first aim was to test the hypothesis that macroplastic size distributions were stable regardless of hydrologic mode. Stormflow events have been observed to increase macroplastic concentration compared to lowflow  but macroplastic concentration discharge rising and falling limb behavior has not been tested in the literature. Our second  ", 2018). W on the map is the airport weather station where the meteorological data used in this study was taken. The basemap is the ESRI Dark Basemap, where urban areas and roads are lighter gray, and darker areas are natural lands. (B) The survey reach and study location in the channel. Satellite imagery of the study reach is from Google Earth, and the survey location is downstream of the Van Buren Bridge in Riverside, CA. objective was to test whether rising and falling limb behavior or storm timing play a role in these event to seasonal scale concentration-discharge relationships. Rating curves have been observed between plastic concentration and discharge as decreasing (van Emmerik et al., 2018;Watkins et al., 2019), increasing (Moore et al., 2011), stable (Wagner et al., 2019), and nonmonotonic (Haberstroh et al., 2021), reflecting a similar diversity of rating curves that can be watershed or even event specific as seen in other particulate transport studies. This underscores the need for more regional studies on plastic concentration discharge rating curves and resultant flux estimation. Our third goal was to assess the macroplastic concentration-discharge rating relationship in the Santa Ana River, and evaluate its use to estimate the annual flux of macroplastic at our study location during the study year. In total, these objectives serve to inform science about transport processes of macroplastic in rivers and inform society about how to best manage macroplastic pollution.

Study location
The Santa Ana River drains a small mountainous watershed (total area: 6900 km 2 , area at survey location: 2341 km 2 ) and experiences a hot dry summer Mediterranean climate regime, with > 90% of its 61 cm of average annual precipitation occurring between October-April (Fig. 1). The study location on the Santa Ana River was monitored where the river crosses the Van Buren Bridge in Riverside, CA, which was 1.8 km downriver from USGS gage 11066460. The bridge above the stream was used during stormflow sampling and sampling was conducted in the stream during lowflow. The main stem of the Santa Ana River in the vicinity of sample collection displays two major hydrologic regimes: low magnitude (mean daily discharge (USGS codes: par 60, stat 00003) = 1.8 m 3 s − 1 ) flows supported entirely by wastewater discharge, and flashy storm flows (mean daily discharge: 14.0 m 3 s − 1 ; and 2 year recurrence interval daily flow of 64.3 m 3 s − 1 ) (Fig. S1). Most of the time, the Santa Ana middle reach is a losing river with discharge decreasing downriver unless fed by a stormflow event or at wastewater input points. Naturally, the study location would have no or little flow without wastewater input for most of the year. Wastewater systems are separated from stormwater in the watershed, so the wastewater treatment plant does not treat stormwater. The sampled reach is low gradient (slope = 0.004), sandy fine gravel bedded, and includes a vegetated riparian corridor that persists between flood control levees. These characteristics are typical of interior trunk streams in Southern California, and thus the study location is a suitable representative of streams draining highly urbanized watersheds in this region.
Pathways and fate of macroplastic at the study reach depend on water and trash management within the watershed and channel. A large amount of accumulated trash exists as standing stock within the channel riparian area (Moore et al., 2016), but there have not been previous studies on trash flux through the Santa Ana River. Potential sources of macroplastic to the channel are suspected to be runoff from upstream urban areas, direct dumping within the river, and unmanaged waste from populations of unhoused people that live within the riparian area (Cowger et al., 2019;Moore et al., 2016). Urban trash runoff is mitigated through street sweeping and trash capture devices in storm drains Riverside City, 2021;Riverside County, 2010). However, to our knowledge, there are no systematic mitigation measures for removing the trash within the channel. The watershed upriver of the sample location includes 31% developed land use. Immediately adjacent and upriver of the sample location is the central Inland Empire metropolitan area, including Riverside and San Bernardino cities. Wastewater facilities that input to the Santa Ana have secondary or tertiary treatment before the wastewater is transferred to the channel. They are suspected to be a negligible source of macroplastic due to the filtration used during the treatment processes. Near the watershed's headwaters are mountains with primarily rural populations, but these sections are generally disconnected from the sampling reach due to dams at the foothills of many mountain tributaries and the losing nature of the river channel most of the year. Downriver of the study location is the Prado Dam, which likely prevents most trash flux from the study reach from reaching the ocean due to cleanup activities at the dam.

Methods
Methodological descriptions were written to ensure the reproducibility and interpretability of the study methodology following best practices for microplastics research, recognizing that there were no recommendations for macroplastic .

Macroplastic measurements
River macroplastic samples were collected in the Santa Ana River from the downriver side of the Van Buren bridge in Riverside, California (Fig. 2, 3, & 4). A steel box trawl (designed by Dr. Marcus Eriksen of 5 Gyres) with a square 0.16 m 2 intake and 5 mm polyester rope net was lowered from a bridge to the thalweg of the river using a portable crane (USGS Type A Crane with 3 Wheel Truck) attached to the trawl with rope and a boat shackle. As the thalweg moved locations, we followed it with the sampler. On average, half of the net was submerged if the net was not resting on the river bed. To sample lowflows, we waded into the river and set the net in the thalweg of the channel on the river bed. The total number of samples collected was limited to 20 throughout 5 sampling events (Fig. 4) due to Southern California's highly episodic and fast-moving river flow. Our goal was to sample multiple time points during all 2018 water year (October 1st 2018 -September 30th 2019) stormflow events and during three lowflow events. However, stormflow in Southern California is highly episodic, making it challenging to collect stormwater samples since three field technicians were required to be available during a 24 h window of potential operations with only 1-2 day notice. Additionally, Southern California stormflow can be fast-moving (> 3 m/s), forcing sampling to stop when conditions become too dangerous due to large objects (e.g., trees, dumpsters, tires, beds) flowing down the river or the sampling equipment violently jumping out of the water. Because of these issues, we could only sample during 2 of 5 stormflows in water year 2018.

Hydrologic measurements
All river hydrologic data were obtained from the USGS river gage 11066460 located 1.8 km upriver from the macroplastic sampling location (USGS, 2016b). The river gage was inspected. Flow conditions and morphological characteristics were similar to the survey location. Continuous stage data (15 min) (gage height) (USGS parameter 65) were acquired along with measurements of channel discharge (USGS parameter 61), river velocity (USGS parameter 55), channel cross-sectional area (USGS parameter 82632), and channel width (USGS parameter 4) from 2018 to 01-10 to 2020-04-21. Measurements were taken by USGS staff using their standard protocols for each measurement. The channel cross-section shape was generally rectangular at both the survey and gage locations. The river cross-sectional area was divided by width to estimate the average river depth. USGS measurements were used to create rating curves using linear regression on log 10 transformed stage and measured variables. Log 10 transformation bias (log 10 correction) was corrected using the approach of Ferguson (Ferguson, 1986). The adjusted r squared (adjRSQ) value was derived for each regression in R to describe the amount of variability around the regression. The discharge rating curve was (log 10 (discharge) = 5.1 * log 10 (gage height) -1.49, adjRSQ = 0.76, log 10 correction = 1.09, p value = 10 − 16 ). The velocity rating curve was (log 10 (velocity) = 1.24 * log 10 (gage height) -0.58, adjRSQ = 0.44, log 10 correction = 1.02, p value = 10 − 9 ). The depth rating curve was (log 10 (depth) = 2.67 * log 10 (gage height) -2.03, adjRSQ = 0.73, log 10 correction = 1.03, p value = 10 − 16 ). Uncertainty in USGS rating curves was propagated using bootstrap simulation (resampling with replacement, n = 10,000) of the USGS measurements. River slope was estimated using the 1/9th arc-second digital elevation model from the National Elevation Dataset (USGS, 2017) and Google Earth. River shear velocity (u * ) was estimated as: where (h) is the average river depth, (g) is the acceleration due to gravity, and (s) is the river slope (de Leeuw et al., 2020). Daily precipitation ( Fig. 4) was downloaded from Midwestern Regional Climate Center's cli-MATE application (Midwestern Regional Climate Center, 2021) for the KRAL airport weather station near the sample location ( Fig. 1).

Fig. 3.
(A) net deployment from inside a channel, (B) net deployment from a bridge, (C) an example of a sample that will be visually sorted for macroplastic.

Plastic particle characterization
Macroplastics were visually sorted from the samples and photographed with a scale in the image (Fig. 5A). We used Image J (Schindelin et al., 2012) to quantify particle projected area (Fig. 5B) for each particle using Image J's color thresholding, manual tracing, and particle size analysis routines ( Fig. 5A & B). Particle projected area is the area of the image which contains the particle. The particle projected area contains no information about the particles' third dimension (the height). We did not account for the third dimension of the particles in this analysis. Instead, we standardized the smallest dimension to be out of view by laying the largest dimensions facing upward to the camera view, and in our opinion, the advantages of the high throughput reproducible approach outweighed the loss of measuring the third dimension. Small artifact "particles" visible at the fringes of particles ( Fig. 5B) were removed by restricting the minimum particle size to 1 mm 2 . Nominal particle size was estimated as the square root of the particle projected area. Particles are well separated by this technique and outlined precisely. Our suspected error in particle size measurement using this technique is less than 1 mm.
All suspected plastic particles were subjected to a sink-swim test by placing them in fresh water from the lab de-ionized water faucet, agitating the particle until no surface bubbles were visible, and assessing if the particle floated or sank. All particles were labeled as settling or buoyant.
A subset of 88 out of 944 particle identities were validated using Fourier-transformed infrared (FTIR) spectroscopy and 30 particles with pyrolysis gas chromatography mass spectrometry (PY-GCMS). The smallest particles of the samples were chosen for validation because they were the most likely to be misidentified (Kroon et al., 2018). For FTIR, a Thermo Nicolet 6700 attenuated total reflectance (ATR) FTIR was used at 4/cm spectral resolution with daily background recording for the spectral range from 400 to 4000 wavenumbers (1/cm). Spectral analysis was done in Open Specy (Cowger et al., 2021a) with smoothing conducted with a Savitzky-Golay filter with a window size of 12 points and a 3rd order polynomial, baseline correction conducted with the imodpolyfit routine using an 8th order polynomial, and a min-max normalization before identification. Identification was conducted using Pearson correlation and a 0.5 uncertainty threshold using the entire spectral range. In Pyrolysis GCMS, the plastic sample was pyrolyzed in a quartz tube at a temperature of 750 C by using the CDS-2000 Pyroprobe. The Agilent 6890 N GC used a CDS-1500 Valved GC Interface held at 320 C and the hydrogen gas flow rate was 1.2 ml min − 1 in constant flow mode. The column characteristics were DB-5 (0.25 mm OD x 60 m L; 0.25 µ film thickness) fused-silica capillary column. The CDS-1500 GC Interface valve was closed after one min. The column oven temperature was initially held at 45 • C for 2 min and then ramped to 320 • C at 20 • C min − 1 rate. The column oven was held at 320 • C Fig. 4. The hydrograph (mean daily average cubic meters per second) from October 1st 2018 to October 30th 2019. Y axis (discharge and daily precipitation) is in log 10 scale while x axis is in days with quarterly tickmarks. Red stars mark the days when samples were acquired. Hyetograph in blue (daily precipitation in mm) is overlayed but uses the same values as discharge. for 19 min resulting in a total run time of 34.75 min. The MS electron Multiplier (EM) auto-tune voltage was adjusted by 200 V above the auto-tune voltage. Data acquisition was performed in full-scan mode from 29 to 600 amu by using the Agilent ChemStation Software. The Injector and the Mass Spectrometer Transfer Line Heater were maintained at 320 • C. The mass spectrometer Quadruple and Source temperatures were held at 150 • C and 230 • C.
Results from spectral analysis demonstrated highly accurate visual differentiation of plastic from the samples. Pyrolysis GCMS identified 28 of the 30 particles as plastic, 1 particle as non-plastic, and 1 particle as unknown. FTIR identified 67 as plastic and 3 particles as non-plastics, with 18 that could not be identified. Pyrolysis GCMS utilized a two-tier approach comprising of peak fingerprinting and mass spectra of marker peaks. The two-tier confirmation approach provided increased confidence in the quality of the polymer identification data. Pyrolysis GCMS was used to further validate our FTIR analysis by comparing 8 particles with both techniques resulting in 6 particles having the same identity with both techniques, 1 particle being identified as a different polymer (polyethylene instead of polypropylene), and 1 particle not being able to be identified by either Pyrolysis or FTIR (SI).
Thirteen macroplastics from these samples with rising velocities (positively buoyant) were randomly chosen to measure rising velocities and reported in another publication (Waldschläger et al., 2020). They were composed of expanded polystyrene, polyethylene, and polypropylene, and had powers roundness ranges from 2.2 to 5.9, Corey shape factor from 0.07 to 0.88, dimensionless diameter of 2. 5-30.81, and rising velocities ranging from 0.221 to 1.69 m/s.

Estimating macroplastic concentrations and uncertainties
Three types of macroplastic concentrations (count 1 , projected area 1 , or mass 1 meter − 3 ) were estimated along with their uncertainties. All three calculations required an estimate of sample water volume. Submerged net depth was set to 0.2 m (half of the net height) or the average river depth, whichever was smaller. We multiplied the depth of the submerged net by the width of the net (0.4 m) to get the submerged cross-section of the net. Uncertainty of submerged depth was incorporated by simulation for each sample using a uniform probability density function from 0.1 to 0.3 m. The average river velocity (see Section 3.1.2 Hydrologic Measurements) from the USGS rating curve (linear model on log 10 transformed data with log 10 bias correction) was multiplied by the submerged cross-sectional area and the sample duration to quantify the sample's water volume. River velocity rating curve uncertainties were incorporated into sample size uncertainty using bootstrap simulation of the model fit (resampling with replacement, n = 10,000).
We removed a subset of macroplastics from our observations that would have biased our results: settling particles and particles < 5 mm. Microplastic particles can be transported in surface load, wash load, bed load, and rising or settling suspended load (Cowger et al., 2021b). Surface sampling (conducted in this study) best measures surface load because bed load and settling suspended load particles will preferentially pass beneath the sampler uncollected. Therefore, we limited this study to particles with a high likelihood of being in surface load transport (positively buoyant particles). We compared the freshwater settling plastics with the positively buoyant particles by size and count for all samples (Fig. 6). We found that positively buoyant plastics were the most common plastic-type in the samples (98%). The spectral analysis also corroborated that the vast majority of plastic materials were polyethylene, polypropylene, and polystyrene (expanded foam), which are more likely to float in water (Muthuvairavasamy, 2022). We removed the 17 settling particles from further analysis. We also noticed that the particle size distribution decreased in abundance around 5 mm in size, which corresponded to the net's mesh size. All particles smaller than 5 mm were removed from further analysis. We permuted all estimated shear velocities and all observed rising velocities of the particles to derive Rouse numbers.
The Rouse number (P) is derived by dividing the particle settling velocity w s by the multiple of β a parameter that adjusts the assumption of parabolic eddy diffusivity (set to 1), k the von Karmen constant (set to 0.4), and u * the shear velocity. The largest mean Rouse number was − 2.5, suggesting that most particles observed were in surface load transport (Cowger et al., 2021b). Therefore, we Fig. 6. (A) Nominal particle size distributions (the square root of the projected surface area) for settling and rising particles in this study. Violin plots are centered with notched box plots within (95% confidence interval). Violin plots are a smoothed and symetric representation of the probability density function of the particle size distributions. Dots show points beyond 1.5 times the interquartile range. Particle abundances dropped off for particles smaller than 5 mm in nominal particle size (the size of the mesh on the net). (B) Pie chart showing the number of particles found with settling velocities (yellow) and rising velocities (purple). There were many more particles with rising velocities (931) than with settling velocities (17). assumed that all particles in this study were transported at the surface of the water column. We used the depth-integrated average concentration estimate introduced by (Lebreton et al., 2017) and (Cowger et al., 2021b) to have a small bias for surface sampling of particles in surface transport.
Count, area, and mass concentrations were calculated by dividing the abundance by sample volume. Count concentration was calculated by counting the number of particles in the sample (after removing bias-causing particles described in 3.2) and dividing it by the total sample water volume. Count uncertainty (due to fragmentation from handling, missing particles, and inadequate sampling of particle counts) estimated as up to ± 10% of the sample count and was propagated using a uniform probability density function from 0% to 10%. Area concentration (mm 2 m − 3 ) was calculated by summing the projected surface area from all particles in the samples and dividing it by the sample volume. Area uncertainty was estimated in the same way as count uncertainty. We measured the mass of 124 of the suspected macroplastics imaged for particle size measurement. We derived a linear regression on log 10 transformed data between the particle projected area and the mass of the particle (log 10 (particle mass (g)) = 1.13 * log 10 (particle area (mm 2 ) -4, adjRSQ = 0.63, log 10 correction = 1.36, p value < 10 − 16 ) (Fig. 7) and corrected for log 10 transformation bias (Ferguson, 1986). Then we used the regression to estimate the mass of all particles from our samples. Mass concentrations (g 1 m − 3 ) were computed by dividing the total mass of macroplastic by the sample volume. Mass uncertainty was computed in the same way as area and count uncertainties. Uncertainties were propagated using 10,000 simulations of the observed values for macroplastic and river variables. The 95% quantiles from the simulations was used as the confidence interval for each value.

Lowflow and stormflow particle size distribution
Stormflow samples were visually separated from lowflow samples using the hydrograph's slope change inflection points. All particles from stormflow and lowflow samples were pooled to make two particle size distributions (empirical cumulative density function). We used the two-sample Kolmogorov-Smirnov test to assess the null hypothesis that the particle size distributions of stormflow and lowflow were from the same distribution.

Hydrograph rising and falling limb behavior and storm timing
We tested for hydrograph rising and falling limb behavior and storm timing effects on the macroplastic concentration-discharge relationship. To assess rising and falling limb behavior, we connected the sample concentration-discharge values for each sampling day with a line, and drew an arrow indicating the relationship's direction through time. Stormflow periods were determined using the description in 3.5. The rising limb was separated from the falling limb by assessing whether the discharge increased (rising limb) or decreased (falling limb) at the sample time. Storm timing was assessed by plotting the 2018 water year discharge time series (October 1st 2018 -September 30th 2019) plus the month of October 2019 to include the final sample in the study. We described the likely Fig. 7. Each black dot is a particle with a particle mass (g) (y axis) and projected area (mm 2 ) (x axis). Axes are log10 transformed. The blue line represents the linear fit on log 10 transformed data. The gray area is the 95% confidence interval around the central tendency of the fit. The regression equation, adjusted r squared, log 10 correction value, and p value are printed in the top lefthand corner of the plot. relationships between the timing and magnitude of the stormflows and the concentration-discharge relationships observed. Since only two stormflow events were sampled, we did not compute statistics on these trends and used them as a heuristic tool to identify future areas of study.

Macroplastic concentration-discharge rating curve
We assessed the concentration-discharge rating curve for count and mass concentrations using generalized additive modeling with a smoothing spline. This model allows the variety of concentration-discharge rating curves (non-monotonic and monotonic) to be fit (Gray, 2018). We tested the assumption of normality for log 10 transformed concentrations using the Shapiro-Wilk test, and decided that we would use the assumption of normality for the model (count concentration, W = 0.92, p value = 0.08 | mass concentration, W = 0.97, p value = 0.82). We fit the generalized additive model to log 10 transformed macroplastic concentrations and discharge using a smoothing spline (k = 7), a gaussian distribution, and restricted maximum likelihood estimation for reduced bias in parameter estimates with the mgcv package (Wood, 2011). We assessed our confidence in the model fit (probability of null hypotheses that the smoothing spline parameter = 0) using the p-value (alpha = 0.05), and percent deviance explained (similar to R squared) for goodness of fit.

Estimating annual mass flux
To estimate the macroplastic mass flux in the 2018 water year and assess the importance of uncertainties and concentrationdischarge rating curves, we tested two commonly employed techniques, mean concentration extrapolation and a concentrationdischarge rating curve (Gray, 2018). Continuous discharge (15 min interval discharge) of the 2018 water year was estimated from the continuous stage using a rating curve (Section 3.1.2). Using mean concentration extrapolation, we estimated mass flux by assuming steady mean concentration using the mean mass concentration observed from our dataset. Total discharge (from summing continuous discharge) for the water year 2018 was multiplied by the mean mass concentration to predict the annual flux. Using the generalized additive model rating curve (see 3.6), we predicted macroplastic concentration for every continuous discharge time point. Total mass flux was computed by multiplying macroplastic concentration by discharge and summed for the entire year. For both methods, confidence intervals were derived using 10,000 simulations. During simulations, we resampled our observed data for macroplastics and river variables, added in other uncertainty metrics, and reran each model described throughout all methods sections with confidence intervals representing the 95% quantiles of the simulations.

Lowflow and stormflow particle size distribution
We tested for differences in the macroplastic size distributions during lowflow and stormflow. Smaller size classes were exponentially more abundant than larger sizes for both hydrologic regimes (Fig. 8). A similar particle size distribution has been observed for microplastic particles (Kooi and Koelmans, 2019). The maximum distance between the two cumulative distribution functions was 0.080 (p-value = 0.66). The particle size distributions of macroplastics in stormflow and lowflow samples were statistically indistinguishable based on the Kolmogorov-Smirnov test. There was also high goodness of fit (adjRSQ = 0.63) between particle mass and particle projected area observed in our study (Fig. 7). van Emmerik et al. (2018) assumed a constant count-mass ratio for macroplastic floating in rivers, which would be suspected if the particle size distribution were also stable there. Assuming this stability continues in the future and is widespread, mean count-mass-area conversion ratios (common conversions in the field) should be constant regardless of discharge at a given site. Future work should compare our particle size distribution to distributions elsewhere to look for spatial variability.
What can the uniform particle size distributions of macroplastics in riverflow tell us about watershed macroplastic pollution pathways and transport processes? The particle size distribution of macroplastics in riverflow expresses the macroplastic source's particle size distribution and the channel's hydrologic transport characteristics. Large, positively buoyant particles only need a minimum water depth of ~ 25-50% of their particle size to become mobilized (Braudrick and Grant, 2000). From a transportability perspective, it is unsurprising that we did not see a particle size preference because the river has an average depth of 0.16 m during lowflow conditions, which could mobilize the largest particle (0.4 m) that can fit in the opening of the sampling net. From a source fingerprint perspective, the water at the site is nearly 100% wastewater effluent during lowflow conditions. Macroplastic during these lowflow conditions can only be sourced from the channel. A predominant control of macroplastic size distributions during stormflow may have occurred in the river channel, or the particle size distribution of macroplastic outside the channel was the same as inside the channel. Future inquiry into particle size distributions of surface transportable macroplastics in the channel bed, riparian area, and watershed would help us better understand differences in the particle size distributions between regions. Other quantifiable macroplastic fingerprints like probability density functions of shapes, colors, and polymer type may also assist pathway description in future studies.

Hydrograph rising and falling limb behavior and storm timing
We assessed the impact of rising and falling limb behavior and storm timing on macroplastic concentration. Count concentrations ranged from 0.034 to 24 num 1 m − 3 and had a median concentration of 0.25 num 1 m − 3 and a mean of 1.89 num 1 m − 3 . Mass concentrations ranged from 0.00047 to 2.99 g 1 m − 3 and had a mean concentration of 0.22 g 1 m − 3 and a median of 0.016 g 1 m − 3 . Macroplastic concentrations rose during the rising limb of one hydrograph (2019-2-2) and fell during the falling limb of another hydrograph (2019-1-17) (Fig. 9). The same phenomenon was observed for mass concentrations (Fig. 10). Although we did not have adequate data to assess hysteresis in this study, these results point toward likely hysteretic patterns. Assuming that macroplastic has stable hysteretic patterns, clockwise hysteresis would explain this trend. Clockwise hysteresis is also commonly found for natural mineral sediment . Another macroplastic hydrograph sampling event in Northern California also observed clockwise hysteresis with macroplastic with the largest macroplastic concentration transporting during the very beginning of the stormflow (5 Gyres and EOA inc, 2016). Stenstrom and Kayhanian (2005) also found that greater than 50% of litter flushes from roadsides in Southern California during the first 2 hr of stormflow. Although rising and falling limb behavior can be stable at stream reaches (which would allow us to combine rising and falling limbs of different hydrographs), it has proven to be unstable for sediment in the Santa Ana river (Warrick and Rubin, 2007). We have learned from this study that count and mass macroplastic concentrations were depleted relative to discharge for the falling limb of one hydrograph compared to the rising limb of another hydrograph. To fully characterize a hysteretic pattern, a follow-up study is needed to collect data throughout a complete hydrograph on both sides of the peak discharge.
A "first flush" event is common for many pollutants in Southern California, whereby high sediment concentrations are flushed during the first large storm event of the year. We found that an earlier storm event (1/17/2019) did not have higher concentrations than the later storm (2/2/2019). It is possible that we missed the first flush event since two stormflow events occurred before 1/17/ 2019 (Fig. 4). It is also possible that the first flush event coincided with the 2/2/2019 event that we sampled. First flush events require a minimum storm magnitude threshold before they initiate (Kim et al., 2004). Future inquiry into first flush events for macroplastic should survey the first few hours of each stormflow of the year to better assess the role of storm timing (5 Gyres and EOA inc, 2016).

Macroplastic concentration-discharge rating curve
Our results show a statistically significant (p value < 0.05) rating curve between discharge and concentration (log 10 (count concentration) = s(log 10 (discharge)) -0.47, log 10 correction = 1.18, DE = 70.5%, n = 20, p value = 0.00027) (Fig. 11). The p value is the probability that the smoothing spline for the generalized additive model is zero. The same relationship was observed for mass concentrations (Fig. 12). The rating curve was nonmonotonic, with the highest macroplastic concentration in the center of the observed discharges and the lowest concentrations at the highest and lowest discharges. One explanation for this observed phenomenon is that as discharge increased, it could tap into additional sources of macroplastic at a rate of supply higher than that of water. However, water increased more rapidly than plastic at the highest discharges, resulting in lower concentrations. In the Santa Ana River, the flow covers a larger region of the channel corridor between levees during higher flows and can access all available macroplastics on the channel bed surface. Increases in discharge after that increase the flow depth in the channel, but do not access additional channel bed surface storage, which would result in a decrease in concentration if channel surface storage is a primary storage location of buoyant plastic pollution in the sampled flows. The only other study of macroplastic concentration discharge relationships in Southern California (Moore et al., 2011) found generally higher concentrations by mass and count during wet weather flows but did not relate that to discharge magnitudes.
Interestingly, the concentration ranges observed for surface floating macroplastic in the Los Angeles river in 2004 by (Moore et al., 2011) (0-81 g 1 m − 3 , 0 -18 num 1 m − 3 ) overlaps with the concentration ranges observed in this study (0.00047 -2.99 g 1 m − 3 , 0.034 -24 num 1 m − 3 ). A recent study also observed a nonmonotonic trend with the highest plastic concentrations at small increases in discharge (Haberstroh et al., 2021). However, concentration-discharge rating curves with a positive slope (5 Gyres and EOA inc, 2016), negative slope (van Emmerik et al., 2018), and no trend (Wagner et al., 2019) have been observed in other regions. We still do not know what the primary driving force of variability is in concentration-discharge rating curves between watersheds.

Estimating annual macroplastic flux
We used two flux estimation strategies to assess the impact of accounting for the concentration-discharge rating curves described in 3.3. The annual flux estimate based solely on mean concentration was 27 (2.82-84.8) metric tonnes and the concentration-discharge rating curve estimate (Fig. 12) was 18.2 (2.9-222.2) metric tonnes (Fig. 13). There is considerable overlap in the confidence intervals between the estimates. There was more uncertainty resulting from the concentration-discharge model fit because we introduced the uncertainty of the generalized additive model into the estimate. This underscores the importance of robust uncertainty assessment in flux estimation strategies, which can change the interpretation of the suitability differences between models. At this time, we would  Generalized additive model using discharge to predict mass concentration. Deviance explained, sample size, and p-value for the smooth term are given. Uncertainties were bootstrapped around each observation and uncertainty range in discharge and concentration is given for each observation.
recommend using the mean concentration to estimate flux since it is a simpler model, but it likely underestimates uncertainty because systematic dependence on discharge and time is not included. More data is required to assess the differences between these estimates.
Future work should pursue the processes behind our preliminary findings of hydrograph rising and falling limb behavior and nonmonotonic concentration-discharge relationships to decrease the uncertainty in those relationships for the Santa Ana River. The particle mass conversion from particle projected area could be improved by including morphological characteristics in the model or estimating particle density and the third dimension. Fig. S2 shows particle size-to-mass relationships split up by particle morphologies. Some of the variability in the trend appears to be due to these morphological characteristics which likely correlate to both the third dimension and particle density. Studies investigating fluxes elsewhere should assess whether similar relationships exist and account for them in their flux estimates accordingly.

Conclusions
This study was based on limited data (20 data points at one site) and should be considered as initial evidence toward a processbased understanding of macroplastic fate and transport processes in urban Southern California watersheds. Lowflow and stormflow samples had the same particle size distribution, suggesting that the channel is a critical location where particle size distributions are propagated or that the particle size distribution outside of the channel is the same as in the channel. All relationships observed held in terms of macroplastic mass concentration and count concentration likely due in part to the stable particle size distributions. Higher macroplastic concentrations were observed during the rising limb of a storm and lower concentrations observed during a near-peak falling limb, suggesting macroplastic source depletion early in storms or rapid mobility of macroplastic. However, future studies should measure macroplastic concentrations over the full range of a single hydrograph to fully investigate hysteretic patterns. Macroplastic concentrations were nonmonotonically related to discharge. Water year macroplastic flux estimates made using mean concentration and the concentration-discharge rating curve were not statistically distinguishable. Mean concentration may be appropriate to estimate flux when data availability is very low, but future studies should follow up on the findings revealed here to decrease uncertainty and further investigate the dependence of macroplastic concentration discharge relationships on time at the event to seasonal scale. A deeper analysis of sources and transport processes outside of the channel in the watershed would greatly advance our current understanding of how macroplastic is transported in this system. These phenomena may be particularly important in small, mountainous semi-arid systems such as the Santa Ana River where in-channel storage of macroplastics may be particularly high, and the readily mobilized by flashy stormflow regimes.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.