Adrien Castinel¹

Jean Mainguy²

Sylvie Combes³

Christine Gaspin²

Denis Milan¹ ³

Cécile Donnadieu¹

Carole Iampietro¹

Géraldine Pascal³

Olivier Bouchez¹
email: olivier.bouchez@inrae.frclaire.hoede@inrae.fr

Claire Hoede²

Benefits of PacBio HiFi long reads for metagenomic whole genome analysis

Whole metagenomics analysis aim to provide an overview of the biodiversity and the functions of bacterial communities. Currently, those analysis are performed on Illumina short read sequencers that provide the advantage of generating less than 1% sequencing error. The arrival of the HiFi technology (PacBio Sequel II) allow us to sequence long read fragments of several Kb with a low error rate.

One of the aim of the SeqOccIn project (Sequencing Occitanie Innovation, https://get.genotoul.fr/seqoccin/) is to acquire expertise in metagenomics to better characterize microbial communities inside complex matrices. In the framework of this project, we developed the metagenomics shotgun protocol on the PacBio Sequel II sequencer and carry out a comparative study of the assemblies obtained with PacBio long reads and Illumina short reads data.

Introduction Conclusion

The DNA miniprep kit has been selected to extract DNA for long read sequencing. With enough sequencing depth, HiFi reads produce high quality assemblies but also imply a higher cost. That's why direct read annotation seems promising as it could required less sequencing depth. Howewer our first analysis on the mock shows that this approach is less accurate than assembly annotation results. We are currently working on the method to improve the results. How to analyse metagenomic HiFi reads?

Assembly annotation Direct read annotation

Assembly

HiFi reads Assembly step : using metaFlye [START_REF] Kolmogorov | metaFlye: scalable long-read metagenome assembly using repeat graphs[END_REF], HiCanu [START_REF] Nurk | HiCanu: accurate assembly of segmental duplications, satellites, and allelic variants from high-fidelity long reads[END_REF] or Hifiasm meta [START_REF] Cheng | Haplotype-resolved de novo assembly using phased assembly graphs with hifiasm[END_REF] Analysis of the assembly (using metagWGS adapted to HiFI reads)

Fig. 2 :Fig. 3 :

 23 Fig. 2: Bacterial genomes of mock Zymobiomics are assembled in one contig by HiFi reads. The genome fraction is the fraction of the reference genomes covers by the assembly. Each block in a bar represents a contig. Bacterial genomes are well covered by all assemblies but Illumina assembly is much more fragmented

Fig. 4 :

 4 Fig. 4: The assemblies are far less fragmented with HiFi reads than with Illumina reads. Nx is a measure of the assembly contiguity.

Fig. 5 :

 5 Fig. 5: Direct read annotation produces less accurate taxonomic profile than assembly annotation on mock Zymobiomics.

Fig. 1 :

 1 Fig.1:The DNA Miniprep kit showed less biases compared to the two other kits. The 16S rRNA gene sequenced on Illumina MiSeq allowed us to evaluate the percentage of each species found in the microbial mock community and to compare it with the expected theoretical percentage. Among the three kits tested, the DNA Miniprep kit showed less biases compared to the two others.


Treilles Robin
email: robin.treilles@enpc.fr

Johnny Gasperi

Tramoy Romain

Dris Rachid

Gallard Anaïs

Partibane Chandirane

Tassin Bruno

Microplastic and microfiber fluxes in the Seine River: Flood events versus Dry periods

Keywords: microplastic, microfiber, microlitter, plastic pollution, flood, hydrological conditions Graphical

Studies on the influence of hydrodynamic conditions on anthropogenic microfiber (MF) and microplastic (MP) distributions in freshwater environments are sparse. In this study, we studied the influence of urbanisation gradient on the spatial variability of MFs and MPs.

Temporal variability was also assessed by comparing the concentrations and fluxes of MFs and MPs under low flow conditions with those during the January-February 2018 flood event.

For each period, Seine river water was collected upstream and downstream of Greater Paris and filtered through an 80 µm net at three different sampling sites. MFs were counted using a stereomicroscope, while MPs were analysed using micro-Fourier transform infrared spectroscopy coupled with siMPle analysis software. The highest concentrations of MFs and MPs were reported at the furthest downstream sites during both periods. However, high water flowrates and urbanisation gradient did not significantly impact MF and MP concentrations, sizes, or polymer distributions. The median MF and MP concentrations were 2.6 and 15.5 items/L and their interquartile ranges were 1.6 and 4.9 items/L (n=10), respectively, illustrating relatively stable concentrations in spite of the urbanisation gradient and variations in the flowrate. In contrast to the concentration, size, and polymer distribution characteristics, MP mass fluxes were strongly affected by river flow. MF and MP fluxes show increases in the number and mass of particles from upstream to downstream. The downstream site presents high MP mass fluxes, which range between 924 and 1675 tonnes/year. These results may indicate significant MP inputs from the Paris Megacity through wastewater treatment plant effluents and untreated stormwater. The January-February 2018 flood event, which represented 14.5% of the year (in terms of time), contributed 40% of the yearly MP mass fluxes. Thus, flood events contribute strongly to MP fluxes.

Introduction

Microlitter, such as microfibers (MFs) and microplastics (MPs), represent a threat to marine [START_REF] Cole | Microplastics as contaminants in the marine environment: A review[END_REF][START_REF] Gall | The impact of debris on marine life[END_REF][START_REF] Jamieson | Microplastics and synthetic particles ingested by deep-sea amphipods in six of the deepest marine ecosystems on Earth[END_REF] and freshwater environments [START_REF] Blettler | Plastic pollution in freshwater ecosystems: macro-, meso-, and microplastic debris in a floodplain lake[END_REF]). An increasing number of studies have investigated the transport of microlitter in freshwater environments. The development of microlitter analysis in environmental matrices such as surface waters [START_REF] Horton | Microplastics in freshwater and terrestrial environments: Evaluating the current understanding to identify the knowledge gaps and future research priorities[END_REF] and sediments [START_REF] Klein | Occurrence and Spatial Distribution of Microplastics in River Shore Sediments of the Rhine-Main Area in Germany[END_REF] has led to significant advances in assessing the concentration of these particles. However, very few studies have been conducted on the influence of hydrological conditions and urbanisation gradients on microlitter concentrations in rivers.

Several studies have observed higher concentrations of microlitter during low-flow periods than in high-flow conditions [START_REF] De Carvalho | Urbanization and hydrological conditions drive the spatial and temporal variability of microplastic pollution in the Garonne River[END_REF][START_REF] Rodrigues | Spatial and temporal distribution of microplastics in water and sediments of a freshwater system (Antuã River, Portugal)[END_REF][START_REF] Watkins | A case study investigating temporal factors that influence microplastic concentration in streams under different treatment regimes[END_REF][START_REF] Wu | Spatial-temporal distribution of microplastics in surface water and sediments of Maozhou River within Guangdong-Hong Kong-Macao Greater Bay Area[END_REF]. This difference in concentrations was attributed to a dilution effect.

Other studies did not observe significant differences in microlitter concentrations between low and high-flow conditions [START_REF] Schmidt | Multi-temporal surveys for microplastic particles enabled by a novel and fast application of SWIR imaging spectroscopy -Study of an urban watercourse traversing the city of Berlin, Germany[END_REF][START_REF] Wagner | Relationship between Discharge and River Plastic Concentrations in a Rural and an Urban Catchment[END_REF]. According to these studies, other parameters may influence the microlitter concentrations. Several studies did not evaluate variation linked to flowrate seasonality, but focused on the impact of rain events during low-flow conditions. [START_REF] Hitchcock | Storm events as key moments of microplastic contamination in aquatic ecosystems[END_REF] showed that under low-flow conditions, the MP concentration of a small urban estuary river increased during two days of heavy rain, from 400 particles/m 3 to 17 000 particles/m 3 . [START_REF] Wong | Microplastic pollution of the Tamsui River and its tributaries in northern Taiwan: Spatial heterogeneity and correlation with precipitation[END_REF] observed a correlation between MP concentrations and precipitation in freshwater environments and noted a strong impact of runoff on MP distribution. Rain events may increase the MP input in rivers owing to the leaching of soil and sealed surfaces. Rain events can lead to combined sewer overflows and untreated stormwater discharge to rivers [START_REF] Blettler | Plastic pollution in freshwater ecosystems: macro-, meso-, and microplastic debris in a floodplain lake[END_REF]. Thus, rain events may induce a flushing effect, that is, an increase in the MP input to freshwater resulting from mismanaged urban water [START_REF] Schmidt | Multi-temporal surveys for microplastic particles enabled by a novel and fast application of SWIR imaging spectroscopy -Study of an urban watercourse traversing the city of Berlin, Germany[END_REF]. Other studies have suggested that there is no simple correlation between river flow and MP concentration [START_REF] Kataoka | Assessment of the sources and inflow processes of microplastics in the river environments of Japan[END_REF][START_REF] Wagner | Relationship between Discharge and River Plastic Concentrations in a Rural and an Urban Catchment[END_REF]. [START_REF] Kataoka | Assessment of the sources and inflow processes of microplastics in the river environments of Japan[END_REF] observed a correlation between MP concentrations and water quality, but no relationship between MP concentrations and flowrates. Other studies have shown that flood events may play a key role in plastic debris loads in rivers [START_REF] Roebroek | Plastic in global rivers: are floods making it worse?[END_REF][START_REF] Tramoy | Transfer dynamic of macroplastics in estuaries -New insights from the Seine estuary: Part 1. Long term dynamic based on date-prints on stranded debris[END_REF]. [START_REF] Veerasingam | Influence of 2015 flood on the distribution and occurrence of microplastic pellets along the Chennai coast, India[END_REF] observed a significant increase in MP pellet concentrations in beach sediments after a flood event. These pellets may have been remobilised and more easily migrated from land to sea. [START_REF] Hurley | Microplastic contamination of river beds significantly reduced by catchment-wide flooding[END_REF] showed that a significant amount of the MP load stored in channel-bed sediments was exported after a flood. According to these studies, MPs may be efficiently flushed from the river to the sea during a flood. Anthropogenic MFs are rarely considered in these studies, even though they are ubiquitous contaminants [START_REF] Zhao | Microscopic anthropogenic litter in terrestrial birds from Shanghai, China: Not only plastics but also natural fibers[END_REF]. Thus, the relationship between microlitter concentration, flow rates, and precipitation is still debated.

Several studies concerning the influence of the urbanisation gradient have observed higher MP concentrations in urbanised, densely populated, and downstream areas [START_REF] Kataoka | Assessment of the sources and inflow processes of microplastics in the river environments of Japan[END_REF][START_REF] Schmidt | Multi-temporal surveys for microplastic particles enabled by a novel and fast application of SWIR imaging spectroscopy -Study of an urban watercourse traversing the city of Berlin, Germany[END_REF][START_REF] Wagner | Relationship between Discharge and River Plastic Concentrations in a Rural and an Urban Catchment[END_REF][START_REF] Wu | Spatial-temporal distribution of microplastics in surface water and sediments of Maozhou River within Guangdong-Hong Kong-Macao Greater Bay Area[END_REF]. In several of these studies, MP concentrations were correlated with population density [START_REF] Kataoka | Assessment of the sources and inflow processes of microplastics in the river environments of Japan[END_REF][START_REF] Wu | Spatial-temporal distribution of microplastics in surface water and sediments of Maozhou River within Guangdong-Hong Kong-Macao Greater Bay Area[END_REF]. According to [START_REF] Wagner | Relationship between Discharge and River Plastic Concentrations in a Rural and an Urban Catchment[END_REF], plastic concentrations may be constant in rural areas but increase linearly in urban areas owing to inputs associated with urban discharge during rainy weather. [START_REF] Rodrigues | Spatial and temporal distribution of microplastics in water and sediments of a freshwater system (Antuã River, Portugal)[END_REF] observed higher concentrations upstream of the catchment studied. This observation may be a particular to the sampling site, as the upstream part of the catchment studied has a higher population density [START_REF] Rodrigues | Spatial and temporal distribution of microplastics in water and sediments of a freshwater system (Antuã River, Portugal)[END_REF]. However, [START_REF] Wong | Microplastic pollution of the Tamsui River and its tributaries in northern Taiwan: Spatial heterogeneity and correlation with precipitation[END_REF] observed no correlation between MP concentrations and population density. Thus, various conclusions may be drawn, depending on the sampling site.

In this study, MF and MP concentrations were estimated at three different sampling sites upstream and downstream from Greater Paris during low flow conditions, as well as during a flood event that occurred in January-February 2018. The main objectives of this work were to evaluate the influence of the urbanisation gradient and different hydrological conditions on the MF and MP concentrations and fluxes.

Materials and methods

Sampling sites

Three sampling sites were selected: (i) the first site, noted "Upstream", is located 100 km upstream of Paris (Greater Paris, 8.9 million capita, 2 546 km 2 , 3 700 cap/km 2 ) and downstream of the moderately dense city of Troyes (Troyes Champagne Metropolis, 170 167 capita, 889 km 2 , 191 cap/km 2 , with a waste water treatment plant capacity of 260 000 population equivalent) ; (ii) the two other sites are located 20 and 45 km downstream of Paris and noted as "Downstream 1" and "Downstream 2", respectively. Upstream is less impacted by industrial activities, whereas Downstream 1 and 2 correspond to a dense urbanised area. Downstream 1 is located downstream from three significant waste water treatment plants (noted as WWTP, "Seine Centre", "Seine Amont" and "Marne Aval", which have treatment capacities of 240 000, 600 000 and 75 000 m 3 per day, respectively), Downstream 2 is located downstream of the most significant WWTP of Paris Megacity (Seine Aval, which has a treatment capacity of 1 700 000 m 3 per day, according to the Parisian Public Sanitation Authority) and is also located downstream of the confluence between the Seine River and Oise River, which is one of its main tributaries (Figure 1). The

Sampling method

Three sampling campaigns were performed during contrasting hydrological conditions: two campaigns were conducted during the flood event that occurred in January-February 2018, represented by the numbers 1 and 2 in Figure 2 (01/26/18 and 02/21/18, Qmax Paris = 1710 m 3 /s, with a 10 year return period of Q10 = 1650 m 3 /s and a 100 year return period of Q100 = 2400 m 3 /s) and one campaign was conducted during the dry season during a low water level period, represented by the number 3 in Figure 2 (07/17/18, Q Paris = 155 m 3 /s). The Seine River was monitored by a surveillance network that followed the flow variations (Figure 2).

Samples were collected at each site during the same day in the following order: Upstream, Downstream 1, and Downstream 2. One extra sample was collected on 02/21/18 from the Upstream sampling site (2 bis, green arrow in Figure 2). The first campaign (01/26/18) corresponded to a period of increasing flow just before the flow peak. The following campaign in February 2018 corresponded to a decrease in the water flowrate. The daily flowrates and water levels of each sampling campaign are presented in the supplementary data (Table S1). Between 20 and 30 L of water were manually collected from the bridges using a metal bucket and filtered through an 80 µm net. Plastic materials were banned to avoid any on-site contamination. The net was systematically rinsed before and after sampling. The samples were then stored in glass containers in a cold room (4°C).

Analytical procedure

Samples were sieved using a 5 mm and a 1 mm sieve and separated into the 1-5 mm fraction and <1 mm fraction. Sieving did not prevent the entrance of long fibers (> 5 mm) in the <1 mm fraction, owing to their small diametres. Particles in the 1-5 mm fractions were inspected under a stereomicroscope. Based on their colour, shape, and texture, suspected plastic particles were set aside and characterised using infrared spectroscopy with attenuated total reflectance (ATR-FTIR, Thermo ScientificTM iD7 accessory). This method is based on [START_REF] Dris | A first overview of textile fibers, including microplastics, in indoor and outdoor environments[END_REF] For the <1 mm fraction, organic matter was oxidised using 30 wt% H2O2 digestion at 40°C for 48 h with 50 mL of solution and magnetic stirring (300 rpm).

Digestion was conducted at temperatures ≤ 40°C to avoid thermal degradation of the MFs [START_REF] Treilles | Impacts of organic matter digestion protocols on synthetic, artificial and natural raw fibers[END_REF]. The solution was filtered through a metallic filter (Ø = 90 mm, porosity = 14 µm). MP particles were then separated from mineral matter by densimetric separation in a NaI solution (ρ ≥ 1.6 g.cm -3 ) in a separating funnel. The supernatant was filtered using the same metallic filters and the microlitter was characterised.

Because of their shapes, the automatization of MF detection with µFTIR and processing software cannot be implemented confidently. Indeed, confusions between MFs and MP fragments were frequently observed with automated µFTIR detection. For this reason, all MFs were manually counted under a stereomicroscope (Leica MZ12, with a size detection limit of 50 µm) coupled with an image analysis software (Histolab) according to the method developed by [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF], while MPs were counted and chemically characterized by µFTIR imaging, with no shape distinction. MFs are all anthropogenic fibers, including synthetic and non-synthetic fibers. This results in possible crossed data between MFs and MPs. However, we decided to keep the data in this form, as the size distribution between MPs and MFs is significantly different (Figure 5). Indeed, most of MPs are below 250 µm whereas MFs are above 1000 µm (Figure 5). This overlap of data may thus be negligible.

Once the MFs were counted, metallic filters were plunged in a crystallizer with 20 mL of filtered water and the particles were removed using an ultrasonic bath for 30 s. The filtered water was then poured into a 100 mL glass bottle. This resuspension step was repeated three times. Then, the metallic filter was rinsed one last time with 40 mL of filtered water.

The glass bottle was vigorously stirred for 1 min to homogenise the content. Then, 10 to 20 mL of this volume, i.e., 10 to 20 %, was filtered onto a Whatman® anodisc inorganic filter membrane (porosity: 0.2 µm, Ø 25 mm, with a filtration surface of Ø 14 mm).

The anodisc filters were analysed with Fourier transform infrared spectroscopy coupled with a microscope, using the Thermo Scientific Nicolet™ iN10 µFTIR in transmission mode. A Thermo Scientific® MCT/A Cooled Imaging detector with a spectral range of 4000 to 1200 cm -1 was used to avoid interference with the anodisc filter. An autobaseline correction was applied to all spectra. After the spectral background was defined, the mapping analysis mode was used on one scan. All particles on three 6 × 6 mm infrared maps were analysed, corresponding to 70% of the filtration surface of the filter. An atmospheric suppression correction was applied to all spectra. Maps were analysed using the siMPle analysis software developed by Aalborg University, Denmark and the Alfred Wegener Institute, Germany (Liu et al., 2019). This method has a size detection limit of 25 µm. Each spectrum identified as a plastic polymer by the siMPle software was checked by an operator for false positives. Particular attention was paid to PE spectra, as false positives of these particles have been observed in other studies [START_REF] Witzig | When Good Intentions Go Bad-False Positive Microplastic Detection Caused by Disposable Gloves[END_REF]. siMPle assesses the number of particles and estimates an order of magnitude for the mass and volume of MPs, as detailed in Kirstein et al., 2021. MP concentrations were extrapolated to the initial sampling volumes. Because the number of samples remained small, non-parametric statistics were used in the analysis.

Several precautions were applied to mitigate contamination. Glass vessels and filters were all heated to 500°C for 2 h before use. All solutions used were filtered on GF/D Whatman glass fibre filters (Sigma Aldrich, porosity: 2.7 µm). The vessels were rinsed with filtered water and filtered using 50% ethanol. Laboratory coats of 100% cotton were worn and plastic materials were avoided. The samples were stored in glass bottles. Glass bottles and all beakers were covered with aluminium foil. The samples were sieved using a laminar flow cabinet. Contamination during the different extraction steps was evaluated using procedural blanks (n=10), which underwent the same steps as the samples.

Results and discussion

Microfiber and microplastic concentrations

During the flood event, MF concentrations ranged between 1.3 and 3.7 items/L, whereas MP concentrations ranged from 10.4 to 34.4 items/L (Figure 3). In low flow conditions, MF concentrations ranged from 1.9 to 5.5 items/L, whereas MP concentrations ranged from 9.3 to 26.5 items/L (min-max values). Median MF contamination was 0.3 items/L with an interquartile range of 0.2 (n=10) whereas median MP contamination was 0.2 items/L with an interquartile range of 0.2 (Figure 3).

Variations in the minimum and maximum concentrations of all samples were calculated for each sampling site, under low flow conditions and during the flood (variation in concentration = (Max-Min)/Min) * 100) (Table 1). Upstream and Downstream 1 presented relatively low variations between the minimum and maximum concentrations for both MFs (< 25%) and MPs (<71%) (Table 1). Downstream 2 presented the highest MF (229.8%) and MP concentrations (318.0%) (Figure 3) and the highest variability between minimum and maximum values (Table 1). [START_REF] De Carvalho | Urbanization and hydrological conditions drive the spatial and temporal variability of microplastic pollution in the Garonne River[END_REF][START_REF] Kataoka | Assessment of the sources and inflow processes of microplastics in the river environments of Japan[END_REF][START_REF] Wong | Microplastic pollution of the Tamsui River and its tributaries in northern Taiwan: Spatial heterogeneity and correlation with precipitation[END_REF]. The concentrations we found are comparable to those found in Cooks River, Australia (between 0.4 and 17.4 items/L, [START_REF] Hitchcock | Storm events as key moments of microplastic contamination in aquatic ecosystems[END_REF] and in the Maozhou River, China (between 3.5 and 25.5 items/L, [START_REF] Wu | Spatial-temporal distribution of microplastics in surface water and sediments of Maozhou River within Guangdong-Hong Kong-Macao Greater Bay Area[END_REF]. We found that MPs were more abundant than MFs. Several studies have also reported fewer fibers than other shapes in freshwater samples [START_REF] Mani | Seasonal microplastics variation in nival and pluvial stretches of the Rhine River -From the Swiss catchment towards the North Sea[END_REF][START_REF] Mao | Distribution and characteristics of microplastics in the Yulin River, China: Role of environmental and spatial factors[END_REF][START_REF] Wu | Spatial-temporal distribution of microplastics in surface water and sediments of Maozhou River within Guangdong-Hong Kong-Macao Greater Bay Area[END_REF]. Stereomicroscope counting did not enable the detection of MFs below 50 µm. Therefore, we may have underestimated the MF concentration. Despite a strong urban gradient and high water flow variability between sampling sites, MF and MP concentrations during low flow conditions have the same order of magnitude as the concentrations estimated during the flood event of January-February 2018 (Figure 3 and Table 1). Downstream 2 presented the highest variability (Table 1) and the highest concentrations (Figure 3) of MPs and MFs, both during low-flow conditions and the flood event. This may indicate a significant release of MPs related to WWTPs. However, Downstream 2 is located downstream the confluence with the Oise River (Figure 1), which was also flooded. This tributary is less urbanised and may dilute the microlitter inputs at this sampling site. However, the flood event did not significantly change the concentrations observed at the different sampling sites. As previously noted, contradictory results were found regarding the influence of water levels and flows on MP concentrations. The dilution of MPs during flood events has been reported in several studies [START_REF] Rodrigues | Spatial and temporal distribution of microplastics in water and sediments of a freshwater system (Antuã River, Portugal)[END_REF][START_REF] Watkins | A case study investigating temporal factors that influence microplastic concentration in streams under different treatment regimes[END_REF][START_REF] Wu | Spatial-temporal distribution of microplastics in surface water and sediments of Maozhou River within Guangdong-Hong Kong-Macao Greater Bay Area[END_REF], but does not seem to occur in the Seine River. Recent studies have shown that stormwater runoff could be a significant source of macroplastics (Treilles et al., 2021b) and microplastics during rain events (C. Liu et al., 2019;Treilles et al., 2021a). Precipitation may increase microlitter inputs through stormwater runoff. The increase in the flowrate during a flood implies remobilisation of the sediments owing to an increase in the shear strength, as well as remobilisation of MF and MP stored in sediments [START_REF] Hurley | Microplastic contamination of river beds significantly reduced by catchment-wide flooding[END_REF]. However, in the Seine River, waterway traffic may greatly influence this distribution. In 2019, 23.7 millions of tons of goods were transported by waterway traffic in the Seine River basin (Voies Navigables de France, 2020). This intense activity influences the sediment dynamics, which are not in a steady state [START_REF] Vilmin | Modélisation du fonctionnement biogéochimique de la Seine de l'agglomération parisienne à l'estuaire à différentes échelles temporelles (phdthesis)[END_REF]. Waterway traffic intensively remobilises sediments even under low-flow conditions. This could partially explain the similar values observed between the flood and low-flow conditions. To ensure better comparability between studies, waterway traffic and sediment dynamics in a study area should be precisely recorded. The concentrations found in the Seine River are very high compared to those presented in a previous study on this river (~3x10 -4 MPs/L ; [START_REF] Dris | Microplastic contamination in an urban area: a case study in Greater Paris[END_REF]. The Seine River concentrations are also high compared to those found in the Rhine (~ 1 × 10-3MPs/L ; [START_REF] Mani | Microplastics profile along the Rhine River[END_REF]. Contrary to [START_REF] Wong | Microplastic pollution of the Tamsui River and its tributaries in northern Taiwan: Spatial heterogeneity and correlation with precipitation[END_REF], we found no statistically significant correlations between precipitation and concentration (Spearman's rs test, p = 0.89). Regarding the spatial variations, concentrations between the upstream and downstream areas were of the same order of magnitude. This is consistent with previous data collected by [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF], who did not notice a significant impact of the urban gradient or variations in the flow rate on the MF or MP concentrations in the Seine River. These observations were confirmed by the present study at a larger scale. Based on the size and shape of the particles, the siMPle analysis software enables MP mass concentration estimates. However, it was not possible to estimate the mass of the MFs that we counted using a stereomicroscope. The order of magnitude for MP mass concentrations was comparable between the low flow period and the flood event, as shown in Table 2. We did not observe a significant concentration gradient between the upstream and downstream sites of Greater Paris in terms of mass concentrations, which is consistent with the results of [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF]. In addition, Downstream 2 presented the highest mass concentrations in number of particles (Table 2). MP mass concentrations in freshwater environments have been only rarely estimated. Using the total weight/number of microplastics and non-metric multidimensional scaling (nMDS), Rodrigues et al., 2018 reported 4). The MF size distribution showed the presence of large MFs >5 mm (Figure 5).

In low-flow conditions, the median MF sizes of Upstream, Downstream 1, and Downstream 2 samples ranged from 2500 to 3480 µm, whereas the median MP size ranged from 96 to 248 µm (Figure 4). As for the flood event, the MF size distribution showed the presence of large MFs >5 mm (Figure 5). In contrast, the median MP size was below 250 µm. The MF and MP size distributions during the flood and low-flow conditions are detailed in the supplementary data (Table S2 and Table S3). The mean values were always higher than the median values owing to the presence of large particles (> 5 mm for MFs and > 1 mm for MPs) (Figure 4). during the flood; p = 0.33). The same trend was observed for MPs (MW test, n=147 in lowflow conditions and n=354 during the flood; p = 0.09). MFs and MPs found in the analytical blanks were significantly smaller than the particles analysed in the samples (MW test, p <0.05). The median number of MF and MP found in each analytical blank was 9 and 4, respectively, with a median size of 1800 µm and 104 µm, respectively (n=10).

More than 20% of MFs belonged to the > 5 mm size class (Figure 5). The minimum and maximum MF sizes of all the samples were 313 and 32328 µm, respectively. Even though more than 60% of MFs are smaller than 4 mm, the <1 mm size class is not the most abundant, in contrast with the size distribution of MFs found in atmospheric fallout [START_REF] Allen | Atmospheric transport and deposition of microplastics in a remote mountain catchment[END_REF]. This size distribution differs from that found in a previous study on the Seine River, for which >1 mm was the most significant fraction [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF].

More than 60% of MPs were smaller than 250 µm (Figure 5). This shows the importance of using a small mesh size for MP sampling. A 300 µm net may be inefficient in collecting the most significant MP size classes. The minimum and maximum MP sizes of all samples combined were 32 µm and 2 528 µm, respectively. When all samples were combined (for low flow periods and during the flood), 20% of all MPs were smaller than 80 µm. This may indicate that: (i) the 80 µm net clogged and stored small MPs or (ii) MP aggregates with various MP sizes could have accumulated in the net and could have been separated during organic matter digestion.

Polymer distribution

Polypropylene (PP) is the most common polymer (56-90%), followed by polyethylene (PE, 3-19%) and polyester (PES, 0-26%) in all samples (Figure 6). The category "other" from Figure 6 contains seven polymers, as detailed in the supplementary data (Table S4). For all samples, PP was always the most abundant polymer. PP and PE are commonly used in packaging, while PES is used in plastic bottles and textiles. The results do not show significant differences in polymer distributions between low flow conditions and the flood event (Figure 4-6, Table S4). The most significant polymers found in our samples (PP, PE, PES) are the same as the most representative polymers of macroplastic debris found in rivers [START_REF] Van Emmerik | A methodology to characterize riverine macroplastic emission into the ocean[END_REF]. These macroplastics may have formed MPs through fragmentation, which could explain the similarity in the polymer nature between these studies. The flood event had no significant impact on the type of polymer transported. S6), we calculated the MF and MP fluxes as the number of particles flowing per year in the Seine River. We assumed that the MF and MP distributions were the same over the water column. For both MF and MP fluxes, we observed an increasing gradient from Upstream to Downstream 2 (Table 3).

The MF flux ranges from 6.6x10 12 to 9.1x10 13 items/year, increasing from Upstream to Downstream 2 (Table 3). [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF] previously estimated an anthropogenic MF flux in the Seine River between 2.8 x 10 10 and 6.1x10 11 particles/year. With the hypothesis that 65% of the MFs are synthetic, they approximated a flux between 1.8 x 10 10 and 4.0 x 10 11 of synthetic MFs per year. Owing to a lack of data, [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF] considered only fibers and not the fragments. We estimated much higher fluxes for anthropogenic MF fluxes. This difference may be linked to methodological differences between our studies. Samples from [START_REF] Dris | Sources and Fate of Microplastics in Urban Areas: A Focus on Paris Megacity[END_REF] were collected with an 80 µm net plunged into the Seine River, while we pre-filtered raw water with an 80 µm net. This sampling difference may affect the concentrations observed in samples, as reported by [START_REF] Zheng | Comparative study of three sampling methods for microplastics analysis in seawater[END_REF], who found a difference in concentration of two orders of magnitude between the pre-filtration method and trawl net for the same sampling site.

For MPs, we calculated a flux between 4.9 x 10 13 and 6.2 x 10 14 items/year, increasing from Upstream to Downstream 2. µFTIR analyses coupled with the analysis software siMPle gave an order of magnitude for MP mass fluxes transported at each sampling site (Table 3). MP mass fluxes ranged between 58 and 1675 tonnes/year and increased from Upstream to Downstream 2. The MP mass fluxes at Downstream 2 are extremely high. The highest MP concentrations (Figure 3, Table 2 and Table S6) and highest flowrates were reported at this site, which explains the reported mass fluxes. As reported for the number of particles, Downstream 2 mass fluxes may be significant due to the different WWTP effluents (Figure 1). These significant mass fluxes may indicate high MP loads derived from urban water from the Paris megacity. Thus, MP mass fluxes are impacted by urbanisation. The January-February 2018 flood event corresponded to 14.5% of the year (in time) but contributed 40% of the microplastic and microfiber annual loads, indicating the important role of flood events as microplastic inputs in the Seine River. This is consistent with the data collected by [START_REF] Wagner | Relationship between Discharge and River Plastic Concentrations in a Rural and an Urban Catchment[END_REF], who found that 90% of the plastic load in freshwater could be transported in 20% of the year. According to our results, we observed a significant increase in MP mass fluxes from upstream to downstream sites, mainly caused by the increase in flow rates and not by a significant concentration increase. For this reason, high water levels may significantly increase the plastic load in freshwater. (2018), but are one or two orders of magnitude higher than other estimations [START_REF] Haberstroh | Effects of hydrodynamics on the cross-sectional distribution and transport of plastic in an urban coastal river[END_REF][START_REF] Kataoka | Assessment of the sources and inflow processes of microplastics in the river environments of Japan[END_REF]. These estimations may indicate significant plastic inputs from the Greater Paris region. However, our estimation does not correspond to MP mass discharge from land to sea, but only reflects the MP mass flux at certain sampling points.

More data should be collected on plastic mass fluxes, particularly in urban rivers, to confirm the significant microplastic loads we observed.

Conclusion

We evaluated the MF and MP concentrations at three different upstream to downstream sampling sites during both low-flow conditions and a flood event. The results of this study show that the concentrations are of the same order of magnitude regardless of the hydrological conditions. The urbanisation gradient did not significantly influence these concentrations. Similarly, the flood and urbanisation gradient did not significantly affect the size and polymer distributions at the different sampling sites. PP, PE, and PES correspond to more than 60% of all polymers found. However, MP mass fluxes are strongly impacted by the urbanisation gradient, as we observed very high mass fluxes at the most downstream sampling site (924-1675 tonnes/year at Downstream 2). The January-February 2018 flood event, which corresponds to 14.5% of the year (in terms of time), contributed 40% of the MF and MP loads in the Seine River. In the future, greater attention should be paid to flood events, as they constitute major pathways for microlitter contamination. A better understanding of MF and MP dynamics in freshwater environments is needed to evaluate the impact of transitory events such as floods and significant rainfall events.

Acknowledgements

We would like to thank the Urban Pollutants Observatory (OPUR) project for its support and the OSU-Efluve for access to the µFTIR. We would also like to thank Mathilde Ropiquet and Léa Parent for their contributions to the sampling campaigns and microfiber counts during their internships.

  major potential sources of microplastics are: (i) Combined Sewer Overflows (CSO) of Greater Paris, (ii) Waste Water Treatment Plants (treatment capacity > 75 000 m 3 per day), (iii) untreated stormwater, and (iv) densely populated areas with intense industrial activities near the different sampling sites.

Figure 1 :

 1 Figure 1: Location of the sampling sites, most significant Wastewater Treatment Plants (WWTPs, treatment capacity > 75 000 m 3 per day) and densely populated areas (the hydrographic network is from Geoportail France).

Figure 2 :

 2 Figure 2: Daily flowrates (black lines) and monthly mean flowrate (blue bars) of the different sampling sites for 2018. Date of sampling is represented by the red arrows (data from

Table 1 :

 1 Variation in concentrations between minimum and maximum values for each sampling site, for samples collected in low flow conditions and during the flood %Variation between min-max values for MFs are combined, we obtain MF and MP median concentrations of 2.6 and 15.5 items/L and interquartile ranges of 1.6 and 4.9 items/L, respectively (n = 10). Other studies in freshwater environments generally have found concentrations below 1 items/L (de

Figure 3 :

 3 Figure 3: Microfiber and microplastic concentrations in the Seine river, relative to the hydrograph of each site (y-axis are different depending on the sampling site)

  Microfiber and microplastic size distribution Boxplots of the MF and MP sizes relative to river discharge are shown in Figure 4. The size distribution of these particles under low-flow conditions and during the flood event is presented in Figure 5. During the flood event, the median MF sizes of Upstream, Downstream 1, and Downstream 2 samples ranged from 1960 to 5410 µm, whereas the median MP sizes ranged from 115 to 205 µm (Figure

Figure 4 :

 4 Figure 4: Boxplots of microfiber and microplastic length relative to the hydrographs of each sampling site (y-axis may be different depending on the sampling site); mean values are displayed as crosses; %R: resuspension percentage; N: number of particles

Figure 6 :

 6 Figure 6: Percentage of polymers in each sample relative to river discharge at each site. N: number of microplastics (MP) particles found for a given resuspension volume; %R:

3. 4 .

 4 Figure2) and the MF and MP concentrations (first and third quartiles, see supplementary

  For macroplastic fluxes,[START_REF] Van Emmerik | Seine Plastic Debris Transport Tenfolded During Increased River Discharge[END_REF] observed an increase of one order of magnitude during high water levels in the Seine River. According toTramoy et al. (2020a), flood events may effectively flush plastic debris from upstream to downstream regions owing to their high flow rates. Tramoy et al. (2021, under review) estimated that the macroplastic mass fluxes from the Seine River estuary to the ocean range between 100 and 200 metric tons per year. The high value found in Downstream 2 is most likely linked to the significant mass concentrations and high flowrates for this sampling point. Although MP mass concentrations are rarely assessed in freshwater systems, our results are consistent with the estimations from Rodrigues et al.

Table 2 :

 2 Several studies have reported lower mass concentrations. In surface water samples, Haberstroh et al. (2021) found a mean mass concentration of 5.4 µg/L in the Estimation of MP mass concentrations in Seine River water based on siMPle software analysis.

	Hillsborough River, USA. Kataoka et al. (2019) observed variable MP mass concentrations
	between 0 and 3.2 µg/L.

mass concentrations between 5 and 51.7 µg/L in Antuã River, Portugal. These values were comparable to our estimations.

Table 3 :

 3 Estimations of MF and MP fluxes for each sampling point

		MF Fluxes in	MPs Fluxes in	MPs Fluxes in
		items/year	items/year	tonnes/year
	Upstream	6.6-7.1x10 12	4.9-6.0x10 13	58-74
	Downstream 1	4.4-4.8x10 13	1.8-2.2x10 14	56-146
	Downstream 2	4.9-9.1x10 13	3.6-6.0x10 14	924-1675

Table S4 :

 S4 Details of the category "Other" from Figure6569

	567
	Microplastics	N	Mean (µm)	Standard deviation (µm)	Median (µm)	Interquartile range (µm)
	Upstream	45	133		116	96	90
	Downstream 1	27	124		91	96	56
	Downstream 2	75	386		409	249	390
	568
	Polymers from the category "Other" Abbreviation
	Acrylonitrile butadiene styrene	ABS
	Cellulose Acetate				CA
	Polyacrylonitrile				PAN
	Polyamide				PA
	Polyurethane				PU
	Polyvinyl Acetate				PVAC
	Styrene butadiene rubber		SBR
	570

Table S5 :

 S5 Details of the polymers found in the different samples 571

		Number of polymer types found	Details
	260118_Upstream	7	CA, PAN, PE, PES, PP, PS, PVC
	260118_Downstream 1	5	ABS, PE, PP, PS, SBR
	260118_Downstream 2	4	PE, PES, PP, PS
	050218_Upstream	3	PE, PES, PP
	050218_Downstream 1	5	PA, PE, PES, PP, PVAC
	050218_Downstream 2	5	PA, PE, PES, PP, PU
	210218_Upstream	6	PAN, PE, PES, PP, PS, PVAC
	170718_Upstream	3	PE, PES, PP
	170718_Downstream 1	5	PA, PE, PP, PS, PVC
	170718_Downstream 2	5	ABS, PE, PP, PS, PVC
	572
	573

Table S6 :

 S6 MF and MP concentrations (first and third quartile) for each sampling site 574

		First and third quartile	First and third quartile	First and third quartile
		(concentration in	(concentration in	(concentration in µg of
		microfibers per liter)	microplastics per liter)	microplastics per liter)
	Upstream	1.9-2.0	14.3-17.4	16.8-21.3
	Downstream 1	3.0-3.4	12.3-15.6	3.9-10.3
	Downstream 2	2.5-4.6	18.5-30.4	47.0-85.1
	575

Supplementary data


H Garcia Mayén

J Kergomard

C Vergez

P Guillemain

M Jousserand

M Pachebat

P Sanchez

Characterization of open woodwind toneholes by the tube reversed method

Woodwind tonehole's linear behavior is characterized by two complex quantities: the series and shunt acoustic impedances. A method to determine experimentally these two quantities is presented for the case of open toneholes. It is based on two input impedance measurements. The method can be applied to clarinet-like instruments, and can be used for undercut toneholes as well as toneholes with pads above their output, under the condition that a symmetry axis exists. The robustness of the method proposed is explored numerically through the simulation of the experiment when considering geometrical and measurement uncertainties. Experimental results confirm the relevance of the method proposed to estimate the shunt impedance. Even the effect of small changes in the hole's geometry, such as those induced by undercutting, are characterized experimentally. The main effect of undercutting is shown to be a decrease of the tonehole's acoustic mass, in agreement with theoretical considerations based on the shape of the tonehole. Investigation on the effects of pads will be studied in a further work. Experimental results also reveal that losses in toneholes are significantly higher than those predicted by the theory. Therefore the method is suitable for the experimental determination of the shunt impedance, but it is not convenient for the characterization of the series impedance.

I. INTRODUCTION

For woodwind instruments, the effect of toneholes on the intonation and the ease of playing is essential. The present paper focuses on linear behaviour of open toneholes, which is especially important for the playing frequencies.

The characterization of holes can be independent of the geometry of the resonator (either cylindrical or conical, see e.g. [START_REF] Petersen | On the tonehole lattice cutoff frequency of conical resonators: applications to the saxophone[END_REF] ).

The first theory was given by Keefe 2 , and completed by [START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF][START_REF] Nederveen | Corrections for woodwind tone-hole calculations[END_REF] . It is based on matching plane waves within the resonator and the tonehole. The tonehole is characterized by a transfer matrix of order 2. Because of reciprocity, only three elements of the matrix are necessary. Furthermore, in the present paper, the tonehole is assumed to be symmetrical, and two elements (i.e., two complex impedances) are sufficient (see [START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF] ) for symmetrical toneholes. This can approximately happen for undercut toneholes. For toneholes with pads above their output, the radiation of the tonehole is modified, but it can be assumed that a symmetry axis exists, and two elements are also sufficient. The theory, based upon modal expansion, assumes the tonehole to be cylindrical, and this leads to a difficulty of the geometric matching between two a kergomard@lma.cnrs-mrs.fr cylinders. However, the number and nature of the matrix elements does not depend on the shape of the toneholes, and they can be determined either by experiment or numerical discretization (see e.g. [START_REF] Dickens | Flute acoustics, Measurement, modelling and design[END_REF][START_REF] Lefebvre | Characterization of woodwind instrument toneholes with the finite element method[END_REF][START_REF] Dalmont | Experimental determination of the equivalent circuit of an open side hole: linear and non linear behaviour[END_REF] ). The Finite Element Method can be used, but the geometric and acoustic modeling of boundary layers (see [START_REF] Lefebvre | Characterization of woodwind instrument toneholes with the finite element method[END_REF] ) and nonlinear behaviour is not straightforward. Acoustic experiment can be also used for the computation of the input impedance of an instrument by using the transfer matrix method: the measurement of the two acoustic impedances make unnecessary the knowledge of the precise geometry. For the computation of the input impedance of an instrument, the acoustic characterization of the open toneholes is sufficient. We notice that the measured elements correspond to the pair tonehole-tube, because they depend on the tube diameter, and are useful for predicting (and maybe for optimizing) the input or transfer impedances. Moreover, the presence of pads located above the output of the open hole modifies their radiation, and therefore the shunt impedance. This paper is limited to open holes without pads, but the present method can be used for holes with pads.

Considering the equivalent circuit of an open tonehole, the elements are essentially acoustic masses. One is in series, modifying the acoustic pressure, and the other is in parallel, modifying the acoustic flow rate. They can be regarded as length corrections to the main tube and to the tonehole, respectively. Nevertheless, for high (i.e., long) toneholes, compressibility (and propagation) effects can appear. Moreover, for both the impedances in series and in parallel, losses (i.e., resistances) exist. Losses added to the series mass are generally ignored, and no theoretical determination exists, while experimental evidence was found by Dalmont et al 10 in a nonlinear regime. At low frequencies, the two masses are almost independent of frequency, but they increase when approaching the first cutoff of the main tube. This variation has been theoretically studied only for the 2D, rectangular case(see [START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF] ), but it is general [START_REF] Marcuwitz | Waveguide Handbook[END_REF] . Other shunt acoustic masses intervene, in particular that of the plane mode in the hole, and a resonance of the total shunt mass can occur at high frequency: this is detailed in Section II.

Previous articles [START_REF] Coltman | Acoustical analysis of the Boehm flute[END_REF][START_REF] Dalmont | Experimental determination of the equivalent circuit of an open side hole: linear and non linear behaviour[END_REF][START_REF] Keefe | Experiments on the single woodwind tone hole[END_REF][START_REF] Dalmont | Acoustic measurement, part II: a new calibration method[END_REF] used experiment devices for the measurement of the series and shunt impedances for open or/and closed toneholes, including the possibility of hole undercutting and pad existence [START_REF] Coltman | Acoustical analysis of the Boehm flute[END_REF][START_REF] Benade | Measured end-correction for woodwind tonehole[END_REF][START_REF] Benade | Fundamentals of Musical Acoustics[END_REF][START_REF] Keefe | Acoustic streaming, dimensional analysis, of nonlinearities, and tone hole mutual interactions in woodwinds[END_REF][START_REF] Keefe | Experiments on the single woodwind tone hole[END_REF] . They took advantage of the tonehole symmetry to limit the experiment to simultaneous measurement of two quantities, the input impedance of a tube with one tonehole at its middle, and a transfer impedance. This allows avoiding dismantling the apparatus during the measurement. The present paper aims at exploring another method. It limits the measurement to two input impedances, by reversing the cylindrical tube (see Fig. 1), the extremity being open. Thus the termination impedance is unchanged when turning the tube. The drawback is the need of dismantling the set up. In Sect. II, the calculation is performed by using the theoretical, known model of a cylindrical tonehole on a cylindrical tube. From the theoretical values of the two characteristics, the calculation determines the two input impedances of the tube in the two situations, the second being the reversed situation of the first. In Sect. III, the inverse problem (often called the crime inverse problem) is computed. It necessitates the determination of the two tonehole characteristics from the two input impedances of the tube in two different situations. In other words two input impedances become the starting point from which the two characteristics are derived. Therefore the tube reversed method consists in reversing the tube. If the calculations are correct, the two tonehole characteristics obtained by solving the inverse problem are identical to the initial values calculated from the model. In practice there is a very small error because of the numerical computation (direct and inverse). If some data of the inverse problem are slightly wrong, the two characteristics obtained slightly differ from the initial values. The data of the inverse problem are either geometric data or measured input impedances. Modifying these data allows assessing the sensitivity of the method to uncertainties on these data. This is the purpose of Sect. IV, which discusses some parameter choices of the experiment, such as the main tube length and the location of the tonehole.

Sect. V describes the experiment including the measurement method of the input impedance and results for cylindrical toneholes, with dimensions similar to those of a clarinet. Sect. VI presents experimental results for examples of undercut toneholes. Sect. VII discusses the validity and interest of the method.

II. DIRECT PROBLEM: MODEL OF A TUBE WITH AN OPEN TONEHOLE

The radii of the main tube and the hole are denoted a and b, respectively. The wavenumber in free space is denoted k = ω/c; ω is the angular frequency, and c is the sound speed in free space. The wavenumber involving viscous-thermal losses in the main tube is given by a standard expression 3 (p. 242):

k a = k 1 + 1.044 -2j/r v -1.08j/r 2 v (1)
where r v = a ωρ/µ for the main tube. ρ is the air density, and µ the air viscosity. The same formula holds for the tonehole, with the notations k b and b. The characteristic impedances are Z c = ρc/πa 2 and Z ch = ρc/πb 2 . The quantities at the left (resp. right) of the tonehole are denoted with subscript 1 (resp. 2). The lengths of the main tube on the two sides of the tonehole are L 1 and L 2 . The height of the tonehole is t. The schematic of the tonehole geometry and the acoustic variables are shown in Fig. 1. In both the main tube and the tonehole, only the plane mode propagates, i.e., higher order modes are evanescent, i.e., the frequency is low enough (k < 1.84/a). The plane mode can be matched on the two sides of the tonehole symmetry axis by a second order transfer matrix 2 . The effect of the tonehole is described by the following equation:

P 1 U 1 = M h P 2 U 2 , (2)
where acoustic pressure and volume velocity are denoted P and U , respectively. For the volume velocity, the axis is oriented to the right. M h is a symmetrical matrix with unity determinant [START_REF] Debut | Analysis and optimisation of the tuning of the tweflthes for a clarinet resonator[END_REF] . It corresponds to the T-circuit (see [START_REF] Chaigne | Acoustics of musical instrumens[END_REF][START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF] ) shown in Fig. 2. It is written as follows:

M h = 1 1 -Y s Z a /4 1 + Y s Z a /4 Z a Y s 1 + Y s Z a /4 (3)
The series impedance Z a and the shunt impedance Z s = 1/Y s are the impedances corresponding to the antisymmetric and symmetric parts of the velocity at the input of the tonehole 2,3 , respectively. For an open tonehole, they are given by the following equations [START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF] :

Z a = jkZ c t a (4)
Z s = jZ ch (kt i + tan [k b t + k(t m + t r )]). ( 5
)
In the equivalent circuit and the transfer matrix the effective shunt impedance Z h appears. It is defined by:

Z h = Z s -Z a /4. (6)

FIG. 2. Equivalent circuit for the tonehole

The lengths included in the above expressions are given hereafter. If δ = b/a, the series length correction t a is given by 4 :

t a = -bδ 2 / 1.78tanh(1.84t/b) + 0.94 + 0.540δ + 0.285δ 2 .
(7) This quantity is very small (a typical value is 0.5 mm). For this reason several authors neglect the corresponding term in Eq. 6. However, in the matrix M h it is not consistent to ignore a quantity in one element while keeping it in the other elements. This remark can be related to the dual role of pressure and volume velocity in Eq. ( 3). An important remark is that the corresponding acoustic mass is negative 2 . No failure of causality is done, because causality is ensured by the complete matrix Eq. (3).

At low frequencies, the length t i , due to evanescent modes, is independent of frequency and can be regarded as an internal length correction for the tonehole height. It can be written as (see [START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF] , and 10 for a correction):

t i = b(0.82 -0.193δ -1.09δ 2 + 1.27δ 3 -0.71δ 4 ). (8)
The length t m is related to the matching volume between the tonehole and the main tube, and cannot be exactly computed with the modal matching method, except when the main tube is rectangular (in which case it vanishes). Its value is given by 7 :

t m = bδ(1 + 0.207δ 3 )/8. ( 9
)
The length t rh is the (complex) radiation length given by t rh = Z rh /(jkZ ch ), where rh is the subscript for the hole end, and Z rh the radiation impedance of the tonehole. Different expressions exist in the literature. For the sake of simplicity, we assume that it is equal to the radiation of a tube without flange (see e.g. 17 ). At low frequencies, the order of magnitude of the uncertainty concerning the real length correction t rh = Re(t r ) is 0.2b, which is the difference between the two extreme cases (without flange and with infinite flange, respectively). If losses near the walls are ignored, the total equivalent height of the tonehole is defined as:

t s = Im(Z s /(kZ ch )). ( 10
)
At low frequencies, it is equal to:

t s = t i + t + t m + t r . ( 11
)
The geometric values chosen in this paper are the tonehole radius b = 4 mm (the main tube radius is a = 7.3 mm), and height t = 8.5 mm; the matching length correction is t m = 0.3 mm. The length correction for radiation is t r = 2.5 mm (with a significant uncertainty of 0.2b = 0.8 mm) and the internal length correction is t i = 2.1 mm. The total equivalent height is therefore t s = 13.4 mm. This quantity is of major interest for the computation of the input impedance of an instrument.

Using the standard transmission line theory, the effect of a tonehole height difference by 1 mm can be computed: it implies a typical shift of the first impedance peak of a typical clarinet by 0.5% to 1% (i.e., 9 to 17 cents). Therefore the cumulative shift for several toneholes can be rather high.

It remains to derive the input impedance Z in . in is the subscript of the tube input, and r that of the termination. The basic equation is:

P in U in = M 1 M h M 2 P r U r . (12)
M 1 and M 2 are the transfer matrices of the cylindrical sections of the tube (i = 1, 2):

M i = A i B i C i A i = cos k a L i jZ c sin k a L i jZ -1 c sin k a L i cos k a L i . ( 13
)
The terminal impedance Z r is projected back to the right of the tonehole, as follows:

Z 2 = A 2 Z r + B 2 C 2 Z r + A 2 . ( 14
)
Similarly, the impedance Z 1 at the left of the tonehole is projected from Z 2 by using the matrix M h and Eq. ( 2).

Finally the input impedance Z in is projected from Z 1 by using the matrix M 1 . A second choice of the lengths L 1 and L 2 lead to another value of the input impedance.

III. INVERSE PROBLEM

The aim of the inverse problem is to derive the two tonehole characteristics from the two input impedances Z in and Z ′ in . The apostrophe indicates the reverse situation. The two different situations are L 1 < L 2 , and L ′ 1 < L ′ 2 , when in the second case the tube is reversed such that L ′ 1 = L 2 , and L ′ 2 = L 1 . The tonehole is not located at the middle of the tube, in order to obtain two different input impedances when the tube is reversed. For the present method, the main tube is open: Z r is the radiation impedance. It is assumed to be equal to its theoretical value without flange [START_REF] Silva | Approximation formulae of the acoustic radiation impedance of a cylindrical pipe[END_REF] . It was checked that the results are not very sensitive to the precise value of the radiation impedance. Using of the measured value of the radiation impedance does not change significantly the results. The important condition is that the radiation impedance is the same for the two situations. Now the input impedance is assumed to be known, and is projected back to the left of the tonehole, using the inverse matrix of M 1 as:

P 1 U 1 = A 1 -B 1 -C 1 A 1 P in U in (15)
⇒ Z 1 = A 1 Z in -B 1 -C 1 Z in + A 1 . (16)
Following Fig. 2, the equations for the 3 elements of the electrical equivalent circuit can be written: Defining

P = Z h (U 1 -U 2 ); P 1 = Z 1 U 1 = P + Z a /2U 1 ; and P 2 = Z 2 U 2 = P -Z a /2U 2 ,
the following equation is obtained:

1 Z h = 1 Z 1 -Z a /2 - 1 Z 2 + Z a /2 . ( 17
)
A similar equation holds for the second situation (reversed tube), replacing Z 1 and Z 2 by Z ′ 1 and Z ′ 2 , respectively.

1

Z h = 1 Z ′ 1 -Z a /2 - 1 Z ′ 2 + Z a /2 . ( 18
)
The following quadratic equation is obtained by eliminating Z h :

AZ 2 a /4 + BZ a /2 + C = 0, (19)
A = (Z ′ 1 -Z 1 ) -(Z ′ 2 -Z 2 ); B = 2(Z ′ 1 Z ′ 2 -Z 1 Z 2 ); C = Z ′ 2 Z 2 (Z ′ 1 -Z 1 ) -Z ′ 1 Z 1 (Z ′ 2 -Z 2 ) (20)
Eq. ( 19) can be solved for Z a , then Z h is derived from Eq. (17) or Eq. (18). However a simpler solution is obtained by expressing Z h with respect to Z a from Eq (17. A term Z 2 a appears. Using the latter expression and Eq. 19), and eliminating Z 2 a , it can be written:

Z a = - B A -2Z h . (21)
Then, introducing this result in the quadratic equation (19), the following result is obtained:

Z 2 h = B 2 4A 2 - C A . (22)
Two solutions exist for this equation. The solution with a negative real part can be eliminated because the physical system is passive. Z s can be deduced from Eq. ( 6):

Z s = Z h + Z a /4. (23)
Throughout this paper, the results are focussed on 3 quantities: the total equivalent height of the tonehole t s , given by Eqs. (10, 22, 23); the real part of the effective shunt impedance Z h and the imaginary part of Z a , from Eq. ( 21).

The results of the inverse problem were checked by using computed input impedances, and the order of magnitude of the numerical error is smaller than 10 -14 . Fig. 3 shows the comparison between the direct and the inverse computations for the equivalent height of the tonehole t s (see Eq.( 10)). For Z a the numerical error is smaller than 10 -12 . For other choices of termination such as an infinite impedance or the characteristic impedance, the entire computation remains valid. When the frequency tends to zero, the small increase is due to the visco-thermal dispersion, which diminishes the sound speed, and increases the equivalent length. Furthermore, the strong variation at higher frequencies is due to the propagation of the planar mode in the tonehole (see the function tan(x) in Eq. ( 5)). The resonance near 7540 Hz corresponds to the minimum of the input impedance of the tonehole.

IV. SIMULATION OF THE EXPERIMENT

In order to simulate the experiment, errors are introduced on the data of the inverse problem. The input impedance is first computed by using the model, and the values are treated as experimental data.

A. Effect of uncertainty on the main tube length

For the second case, an error of 0.2 mm is added to the length L 1 . It includes the uncertainty of the measurement, and the uncertainty on the tube manufacture. For the second case, an error of 0.2 mm on the length L 1 is considered together with an opposite error on the length L 2 (the later case corresponds to an error on the location of the tonehole, without change in the total length

L 1 + L 2 ).
For the equivalent height of the hole t s , Fig. 4 shows the comparison between results for the two cases simulated and the theoretical result (without errors introduced). Between 1550 Hz and 1650 Hz, the error on the result is very large. Because this also happens at other higher frequencies, the figure is limited to 2000 Hz. The frequency ranges with large error are close to the input impedance minima of the main tube (1560 Hz for Z in and 1610 Hz for Z ′ in ). A simple qualitative interpretation is the following: suppose that the radiation impedance of the tube is 0 (whatever the frequency), and that the input impedance vanishes at a given frequency, therefore the eigenfrequencies of the tube in the two positions are equal, and the problem becomes ill-posed (one equation for two unknowns): the solutions tend to infinity. This reasoning is not exact, because the radiation impedance is small, but not 0. The variations of t s are very small up to 1400 Hz, as well as the discrepancies with the theoretical values. Concerning the real part of the shunt impedance Z h , it can be seen in Fig. 5 that the accuracy of the simulated results is satisfactory up to 1400 Hz. However, concerning the imaginary part of the series impedance Z a , even a very small error on the lengths causes large errors on the result (see Fig. 6). Even the sign of the quantity is not determined. This result suggests that it is extremely difficult to expect a precise measurement of the series impedance. From this perspective, the method is less robust than the method of 10 , even if the later is not very precise (the uncertainty is almost 35%). The present method is probably not suitable for measuring this element through experimentation.

B. Effect of the data uncertainty on the measured input impedance

A second attempt to simulate the experiment is based on the introduction of a random error on the modulus of the input impedance (for the two configurations of the main tube Z in and Z ′ in )). The input impedance is modified as follows:

Z in = Z in {1 + 0.005[rand(N ) -0.5]}. ( 24
)
The number N is the size of the input impedance vector. rand is a Matlab function that generates uniform pseudo-random numbers in the interval [0, 1]. The value 0.005 is determined by the measurement of many input impedances. It means that the error modelled ranges from -0.25% to 0.25% of Z in . The three figures 7 to 9 show a confirmation of the previous observations: the measurement can be accurate up to 1600 Hz for the shunt impedance, but the measurement of the series impedance is not possible (see Figs. 7 to 9). The relative error on the equivalent height is less than 7%. 24)). Yellow line: no random error.

C. Practical considerations for the dimensions of the main tube

A conclusion of the simulation study implies that the main tube has to be chosen to be as short as possible. In order to avoid the coupling of evanescent modes between the tonehole and the radiating termination, the distance L 1 between the tonehole and the termination can be chosen between 2 and 3 times the main tube diameter. Furthermore the value of the first minimum frequency implies a small total length L 1 + L 2 . However it is essential that the two lengths are sufficiently different, in order to avoid the quadratic equation to become degenerate. A convenient choice is L 2 between 1/3 and 1/2 times the total length L 1 + L 2 . We note that other terminations for he the tube lead to correct results, but, for instance, when the tube is closed, the first anti-resonance is rather low and this limits the frequency range of the measurement.

V. EXPERIMENTAL RESULTS FOR CYLINDRICAL TONE-HOLES A. Input impedance measurement

The previous analysis encourages us to study an experiment based upon the method presented in the present paper. The method is tested experimentally by using wood pieces, and the CTTM sensor [START_REF] Macaluso | Trumpet with near-perfect harmonicity: Design and acoustic results[END_REF] for the impedance measurement. A piezoelectric buzzer is used as a source. The pressure in the back cavity of the buzzer is measured by a microphone, which gives an estimation of the volume velocity. The measured pipe is connected to the front of the buzzer via a small open cavity in which a second microphone measures the pressure. The input impedance of the pipe is at first order proportional to the transfer function between the two microphones. The comparison with theoretical results for cylindrical tubes (without toneholes) is satisfactory: the discrepancy for a closed tube is 4 cents for the resonance frequencies and 1 dB for the peak heights, except at very low frequencies. For this reason, measurements are done above 200 Hz.

B. Preliminary results concerning the repeatability of the measurement

We first study the repeatability for a tube and a tonehole with dimensions equal to those previously considered. For the frequency range 200 to 1400 Hz, the equivalent height t s of the tonehole is found to be between 14.4 mm and 15.5 mm, while the theoretical value (from Eq. 10 is 13.4 mm. For 4 measurements after disassembly and assembly, the uncertainty is found to be about 1 to 2% (see Fig. 10). Furthermore Fig. 11 shows the comparison between the measurements of 4 tubes built with the same tools. The material of the tubes is a composite material built by Buffet-Crampon for the Greenline clarinet, and the holes were deburred. The results are distributed on both sides of the theoretical one. This is an effect of the manufacturing tolerance, which is of the same order of magnitude as the measurement uncertainty, or higher. For all experimental results, the Matlab function smooth has been used. We remark measurements are not necessarily taken on the same day and at the same temperature, but the computation took it into account.

C. Comparison between two tubes of different lengths

Two tubes with the same length L 2 = 44 mm abd with a length L 1 = 74 mm and 118 mm are compared. The value of L 2 is chosen to be 3 times the tube diameter. The dimensions of the tonehole are identical for the two tube lengths (b = 4 mm; t = 8.5 mm). Fig. 12 shows a small increase when the frequency approaches the eigenfrequency of the tubes. As explained above, the short tube yields better results on a wider frequency range.

The discrepancy between the results of the two tubes is less than 3 Concerning the real part of the shunt impedance, it appears that the two tubes yield very similar values, except in the vicinity of the eigenfrequency. Fig. 13 shows that they are higher than the theoretical values. Remember that for a linear functioning, radiation losses are proportional to ω 2 , while visco-thermal losses increase as √ ω. We refer to [START_REF] Dalmont | Experimental determination of the equivalent circuit of an open side hole: linear and non linear behaviour[END_REF] for a discussion about the theoretical aspects. Finally, the experiment confirms that the se- ries impedance cannot be measured by the tube reversed method, as shown in Fig. 14.

VI. EXPERIMENTAL RESULTS FOR UNDERCUT TONE-HOLES

Undercutting toneholes was studied in 10 for high excitation level and in [START_REF] Macdonald | A Study of the Undercutting of Woodwind Toneholes Using Particle Image Velocimetry[END_REF] (see also [START_REF] Temiz | Nonlinear behavior in tone holes in musical instruments: an experimetal study[END_REF] ) for rectangular geometry. Eight short tubes of length 118 mm have holes drilled at L 1 = 44 mm that have three different geome-tries: three are straight (but the hole is deburred), three are undercut with a cylinder length of 6.7 mm (tubes denoted UC1) and two are undercut with a cylinder length of 5.7mm (tubes denoted UC2). Figs. 15 and16 show the effect of undercutting the toneholes. The quantity shown by Fig. 15 is slightly different from that shown previously (see e.g. Fig. 13), because considering the length correction in Eq. ( 10) implies a division by the cross-section area S h , but for the case of undercut toneholes, the area is not constant. For this reason, we choose the acoustic mass (per unit density) m s :

m s = Z h /(jωρ). ( 25
)
The figures represent the average quantities for each geometry. The effect of undercutting is a decrease of 10m -1 to 20m -1 for the acoustic mass when the undercutting becomes wider. The jump below 400 Hz in Fig. 15 remains unexplained. Two causes for this mass increase can be analysed. The widening implies a decrease of the acoustic mass of the plane mode, and also of the internal length correction due to the discontinuity between the main tube and the tonehole. The first of these causes can be modelled. Considering the acoustic mass for the cylindrical tonehole case, calculating the average value, we obtain 280 m -1 . For the cases of undercutting, we obtain 270 m -1 and 264 m -1 . An elementary model can be made in order to interpret these results. The shape of the most undercut tonehole (UC2) is close to a cylinder extended in a truncated cone joining the internal wall of the main tube. For the cases studied, the lengths of the cylinder ℓ and of the cone ℓ ′ are approximately equal to 5.5 and 5 mm, respectively. The radius of the cylinder is b = 4 mm, the small radius of the cone is R 1 = b and its large radius is R 2 = 5.4 mm. The calculation of the mass of a tube with variable cross section is done by integrating the inverse of the area along the axis. For a cone, the result is published in 3 , p. 325. It is that of a cylinder with a cross section equal to the geometric average of the radius: S = πR 1 R 2 . The difference between the cylindrical tonehole and the undercutting one is:

δ m = ℓ ′ πb 2 1 - b R 2 . ( 26
)
The result of this formula is 26m -1 . This result, based on approximate geometric and acoustic models, is consistent with the experimental data. This is encouraging for the use of an accurate measurement method for the computation of the input impedance of an instrument. Furthermore, Fig. 16 shows that the effect of undercutting on the real part of the shunt impedance is small, but significant: it causes a decrease in resistance by approximately 10 % as the undercut is increased from 0 to that of tubes UC2. It is difficult to interpret the differences between the three geometries and their variation with frequency, and the influence of nonlinear effects cannot be ignored. However, a linear reasoning can be applied here: undercutting a tonehole broadens the effective radius, and visco-thermal effects diminish.

VII. CONCLUSION

The method presented in this paper allows an evaluation of the effect of the complex shunt impedance of an open tonehole. We recall that the aim is to insert the experimental value in the computation of the input impedance of an instrument. The effect of a hole modification on the input impedance of an instrument is significant: a difference of 1 mm for the equivalent height may imply a shift of the first impedance peak. The cumula-tive shift for several toneholes can be rather high (see e.g. an article on the clarinet tuning [START_REF] Debut | Analysis and optimisation of the tuning of the tweflthes for a clarinet resonator[END_REF] ).

It is important to use a short tube for this method, due to anti-resonances associated to the total tube length. We remark that a similar problem concerning the "forbidden" frequency ranges is encountered in other methods. Moreover the distance of the hole to the tube end needs to be short.

Concerning the real part of the shunt impedance, the results appear to be robust, and suggest further studies on the theoretical aspects, even for cylindrical toneholes in the linear regime.

Concerning the equivalent height of the tonehole (related to the imaginary part of the shunt impedance), the primary quantity studied here, the results seem to be very sensitive to small geometric differences. The relative variation of the equivalent height with frequency is small, and the absolute variation remains small. For a cylindrical tonehole, at approximately 500 Hz, the discrepancy between experiment and theory is very small for the equivalent height (0.5 mm), and is of the same order of magnitude as the result obtained in [START_REF] Dalmont | Experimental determination of the equivalent circuit of an open side hole: linear and non linear behaviour[END_REF] . The paper is limited to the frequency range [200 Hz, 1400 Hz] for the measurements. It is concluded that the variation with frequency is mainly due to the measurement method. Assuming that the true value of the tonehole equivalent height is independent of frequency, the choice of an average of the values between 400 and 600 Hz as appropriate can be extended to any hole geometry. This result of the different cases examined in the present work can be used for including the acoustic characteristics of undercut toneholes in a computation of input impedances of an instrument.

The method is not convenient for measuring the series impedance. Actually this quantity is very small, but for this quantity the methods proposed in previous publications seem to be better. Concerning undercut toneholes, which are generally not symmetrical, in certain cases it could be useful to search for a circuit with 3 unknowns (see [START_REF] Dubos | Theory of sound propagation in a duct with a branched tube using modal decomposition[END_REF] ). The aim of the present paper is not to improve a model, but it is useful in that it highlights some of the complications inherent in existing open tonehole models. The main improvement to existing models could be done on the radiation impedance of a tonehole, including the influence of the pads. and manufacturing the wood pieces used in this article. Erik Petersen provided a careful reading of the English of the paper and gave useful comments, and Fabrice Silva helped for the experiment: they deserve the thanks of the authors.

FIG. 1 .

 1 FIG. 1. Scheme of the tonehole geometry and acoustic variables. For the second situation, an apostrophe is added to the geometrical and acoustic quantities, and L ′ 1 = L2, and L ′ 2 = L1

FIG. 3 .

 3 FIG. 3. (Color online) Equivalent height ts of the tonehole (in m). Solid, red line: model; blue, dotted line: inverse problem (from Eq. (22)). Dimensions a = 7.3 mm, b = 4 mm, t = 8.5 mm, L1 = 44 mm, L2 = 74 mm.

FIG. 4 .

 4 FIG. 4. (Color online) Equivalent height ts (in m). Red, solid thin line: theory without length errors. Blue, thick, solid line: inverse problem (Eq. (22)) with 0.2 mm error on L1. Black, dashed line: inverse problem with 0.2 mm error on L1 and -0.2 mm error on L2.

FIG. 5 .FIG. 6 .

 56 FIG. 5. (Color online) Real part of the reduced shunt impedance Re(Z h /Zc) (dimensionless). See line definitions in the caption of Fig. 4.

FIG. 7 .FIG. 8 .

 78 FIG. 7. (Color online) Tonehole equivalent height ts (in m).Black lines: result of a simulation with a random error on the input impedance of the tube (Eq. 24). Yellow line: no random error.

FIG. 9 .

 9 FIG.9. (Color online) Imaginary part of the reduced series impedance Im(Za/Zc) (dimensionless). Black lines: result of a simulation with a random error on the input impedance of the tube (Eq. (24)). Yellow line: no random error.

FIG. 10 .

 10 FIG. 10. (Color online) Tonehole equivalent height (in m) measured 4 times after disassembly. Blue, dashed lines: measurements. Red, solid line: theory. Dimensions a = 7.3 mm, b = 4 mm, t = 8.5 mm, L1 = 44 mm, L2 = 74 mm.

FIG. 11 .

 11 FIG. 11. (Color online) Tonehole equivalent height ts (in m) for 4 tubes built with the same tool. Blue, dashed lines: measurements. Solid, red line: theory.

FIG. 13

 13 FIG. 13. (Color online) Measured value of the real part of the reduced shunt impedance Re(Z h /Zc) (dimensionless). See the line definitions in the caption of Fig. 12.

FIG. 14 .

 14 FIG. 14. (Color online) Measured value of the imaginary part of the reduced series impedance Im(Za/Zc) (dimensionless). See the line definitions in the caption of Fig. 12.

FIG. 15 .FIG. 16 .

 1516 FIG. 15. (Color online) Measured value of the acoustic mass per unit density ms of the hole. Red, solid line: theory of a cylindrical tonehole in m -1 . From top to bottom, 3 geometries of the tonehole: Blue, dashed line: no undercutting; Green, dash-dot line: undercut tubes UC1, Magenta, dotted line: undercut tubes UC2.

J. Acoust. Soc. Am. / 13 October 2021 JASA/ Tube reversed method

J. Acoust. Soc. Am. / 13 October 2021 JASA/ Tube reversed method

J. Acoust. Soc. Am. / 13 October 2021 JASA/ Tube reversed method

J. Acoust. Soc. Am. / 13 October 2021 JASA/ Tube reversed method

ACKNOWLEDGEMENTS

The authors gratefully thank the French Association Nationale de la Recherche et la Technologie for the PhD grant of Hector Garcia (CONVENTION CIFRE N°2 017 1600), as well as the french Agence Nationale de la Recherche, through the joint laboratory"Liamfi" between the Laboratoire de Mécanique et d'Acoustique and Buffet Crampon (ANR LCV2-16-007-01). Furthermore the authors thank the Consejo Nacional de Ciencia y Tecnología Políticas de Privacidad Acceso (Conacyt) for the International Scholarship 707987. The authors thank Thierry Mialet (Buffet Crampon company) for designing